From fc628bd021b81499e14bd41d92b3c47fafd2a10d Mon Sep 17 00:00:00 2001 From: Markus Koschi Date: Wed, 24 Apr 2019 17:01:05 +0200 Subject: [PATCH] added Release 2017a --- MATLAB/init_KS.m | 69 ++++ MATLAB/init_MB.m | 134 +++++++ MATLAB/init_ST.m | 72 ++++ MATLAB/parameters_vehicle1.m | 128 ++++++ MATLAB/parameters_vehicle2.m | 128 ++++++ MATLAB/parameters_vehicle3.m | 128 ++++++ MATLAB/readme.txt | 19 + MATLAB/testVehicle.m | 224 +++++++++++ MATLAB/unitConversions/ft2_IN_m2.m | 7 + MATLAB/unitConversions/ft_IN_m.m | 7 + MATLAB/unitConversions/ft_lb_IN_m_N.m | 8 + MATLAB/unitConversions/ft_lb_rad_IN_N_m_rad.m | 8 + MATLAB/unitConversions/lb_ft_sec2_IN_kg_m2.m | 10 + MATLAB/unitConversions/lb_sec2_ft_IN_kg.m | 8 + MATLAB/unitConversions/lb_sec_ft_IN_N_s_m.m | 8 + MATLAB/unitConversions/lbs_ft_IN_N_m.m | 9 + MATLAB/unitConversions/rad_ft_IN_rad_m.m | 7 + .../rad_ft_lb_IN_rad_sec2_kg_m2.m | 9 + MATLAB/vehicleDynamics_KS.m | 50 +++ MATLAB/vehicleDynamics_MB.m | 373 ++++++++++++++++++ MATLAB/vehicleDynamics_ST.m | 70 ++++ Python/init_KS.py | 67 ++++ Python/init_MB.py | 132 +++++++ Python/init_ST.py | 70 ++++ Python/parameters_vehicle1.py | 135 +++++++ Python/parameters_vehicle2.py | 131 ++++++ Python/parameters_vehicle3.py | 135 +++++++ Python/readme.txt | 19 + Python/testVehicle.py | 190 +++++++++ Python/tireModel.py | 106 +++++ Python/tireParameters.py | 38 ++ Python/unitConversions/__init__.py | 0 Python/unitConversions/unitConversion.py | 95 +++++ Python/vehicleDynamics_KS.py | 54 +++ Python/vehicleDynamics_MB.py | 287 ++++++++++++++ Python/vehicleDynamics_ST.py | 73 ++++ Python/vehicleParameters.py | 65 +++ README.md | 10 +- vehicleModels_commonRoad.pdf | Bin 0 -> 360690 bytes 39 files changed, 3082 insertions(+), 1 deletion(-) create mode 100644 MATLAB/init_KS.m create mode 100644 MATLAB/init_MB.m create mode 100644 MATLAB/init_ST.m create mode 100644 MATLAB/parameters_vehicle1.m create mode 100644 MATLAB/parameters_vehicle2.m create mode 100644 MATLAB/parameters_vehicle3.m create mode 100644 MATLAB/readme.txt create mode 100644 MATLAB/testVehicle.m create mode 100644 MATLAB/unitConversions/ft2_IN_m2.m create mode 100644 MATLAB/unitConversions/ft_IN_m.m create mode 100644 MATLAB/unitConversions/ft_lb_IN_m_N.m create mode 100644 MATLAB/unitConversions/ft_lb_rad_IN_N_m_rad.m create mode 100644 MATLAB/unitConversions/lb_ft_sec2_IN_kg_m2.m create mode 100644 MATLAB/unitConversions/lb_sec2_ft_IN_kg.m create mode 100644 MATLAB/unitConversions/lb_sec_ft_IN_N_s_m.m create mode 100644 MATLAB/unitConversions/lbs_ft_IN_N_m.m create mode 100644 MATLAB/unitConversions/rad_ft_IN_rad_m.m create mode 100644 MATLAB/unitConversions/rad_ft_lb_IN_rad_sec2_kg_m2.m create mode 100644 MATLAB/vehicleDynamics_KS.m create mode 100644 MATLAB/vehicleDynamics_MB.m create mode 100644 MATLAB/vehicleDynamics_ST.m create mode 100644 Python/init_KS.py create mode 100644 Python/init_MB.py create mode 100644 Python/init_ST.py create mode 100644 Python/parameters_vehicle1.py create mode 100644 Python/parameters_vehicle2.py create mode 100644 Python/parameters_vehicle3.py create mode 100644 Python/readme.txt create mode 100644 Python/testVehicle.py create mode 100644 Python/tireModel.py create mode 100644 Python/tireParameters.py create mode 100644 Python/unitConversions/__init__.py create mode 100644 Python/unitConversions/unitConversion.py create mode 100644 Python/vehicleDynamics_KS.py create mode 100644 Python/vehicleDynamics_MB.py create mode 100644 Python/vehicleDynamics_ST.py create mode 100644 Python/vehicleParameters.py create mode 100644 vehicleModels_commonRoad.pdf diff --git a/MATLAB/init_KS.m b/MATLAB/init_KS.m new file mode 100644 index 0000000..b15fd78 --- /dev/null +++ b/MATLAB/init_KS.m @@ -0,0 +1,69 @@ +function x0 = init_KS(initState, p) +% init_KS - generates the initial state vector for the kinematic +% single-track model +% +% Syntax: +% x0 = init_KS(initState, p) +% +% Inputs: +% initState - core initial states +% p - parameter vector +% +% Outputs: +% x0 - initial state vector +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 11-January-2017 +% Last update: --- +% Last revision:--- + +%------------- BEGIN CODE -------------- + +%states +%x1 = s_x x-position in a global coordinate system +%x2 = s_y y-position in a global coordinate system +%x3 = δ steering angle of front wheels +%x4 = u velocity in x-direction +%x5 = Ψ yaw angle + +%u1 = v_delta steering angle velocity of front wheels +%u2 = ax longitudinal acceleration + + +%obtain initial states from vector +sx0 = initState(1); +sy0 = initState(2); +vel0 = initState(3); +Psi0 = initState(4); +dotPsi0 = initState(5); +beta0 = initState(6); + + +%create equivalent bicycle parameters +g = 9.81; %[m/s^2] +mu = p.tire.p_dy1; +C_Sf = -p.tire.p_ky1/p.tire.p_dy1; +C_Sr = -p.tire.p_ky1/p.tire.p_dy1; +lf = p.a; +lr = p.b; + +%initial steering angle from steady state of slip angle +delta0 = vel0*(lf + lr)/(C_Sf*g*lr*mu)*dotPsi0 ... + + 1/(C_Sf*lr)*((C_Sr*lf + C_Sf*lr)*beta0 - (C_Sr - C_Sf)*lr*lf*dotPsi0/vel0); + +%sprung mass states +x0(1) = sx0; % s_x x-position in a global coordinate system +x0(2) = sy0; % s_y y-position in a global coordinate system +x0(3) = delta0; % steering angle of front wheels +x0(4) = vel0; % velocity +x0(5) = Psi0; % Ψ yaw angle + +%------------- END OF CODE -------------- \ No newline at end of file diff --git a/MATLAB/init_MB.m b/MATLAB/init_MB.m new file mode 100644 index 0000000..4feff05 --- /dev/null +++ b/MATLAB/init_MB.m @@ -0,0 +1,134 @@ +function x0 = init_MB(initState, p) +% init_MB - generates the initial state vector for the multi-body model +% +% Syntax: +% x0 = init_MB(initState, p) +% +% Inputs: +% initState - core initial states +% p - parameter vector +% +% Outputs: +% x0 - initial state vector +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 11-January-2017 +% Last update: --- +% Last revision:--- + +%------------- BEGIN CODE -------------- + +%states +%x1 = s_x x-position in a global coordinate system +%x2 = s_y y-position in a global coordinate system +%x3 = δ steering angle of front wheels +%x4 = u velocity in x-direction +%x5 = Ψ yaw angle +%x6 = Ψ yaw rate + +%x7 = ΦS roll angle +%x8 = ΦS roll rate +%x9 = ΘS pitch angle +%x10 = ΘS pitch rate +%x11 = v velocity in y-direction +%x12 = zS z-position +%x13 = w velocity in z-direction + +%x14 = ΦUF roll angle front +%x15 = ΦUF roll rate front +%x16 = vUF velocity in y-direction front +%x17 = zUF z-position front +%x18 = wUF velocity in z-direction front + +%x19 = ΦUR roll angle rear +%x20 = ΦUR roll rate rear +%x21 = vUR velocity in y-direction rear +%x22 = zUR z-position rear +%x23 = wUR velocity in z-direction rear + +%x24 = ωLF left front wheel angular speed +%x25 = ωRF right front wheel angular speed +%x26 = ωLR left rear wheel angular speed +%x27 = ωRR right rear wheel angular speed + +%x28 = delta_y_f +%x29 = delta_y_r + +%u1 = v_delta steering angle velocity of front wheels +%u2 = acceleration + + +%obtain initial states from vector +sx0 = initState(1); +sy0 = initState(2); +vel0 = initState(3); +Psi0 = initState(4); +dotPsi0 = initState(5); +beta0 = initState(6); + + +%create equivalent bicycle parameters +g = 9.81; %[m/s^2] +mu = p.tire.p_dy1; +C_Sf = -p.tire.p_ky1/p.tire.p_dy1; +C_Sr = -p.tire.p_ky1/p.tire.p_dy1; +lf = p.a; +lr = p.b; + +%initial steering angle from steady state of slip angle +delta0 = vel0*(lf + lr)/(C_Sf*g*lr*mu)*dotPsi0 ... + + 1/(C_Sf*lr)*((C_Sr*lf + C_Sf*lr)*beta0 - (C_Sr - C_Sf)*lr*lf*dotPsi0/vel0); + +%auxiliary initial states +F0_z_f = p.m_s*g*p.b/((p.a + p.b)) + p.m_uf*g; +F0_z_r = p.m_s*g*p.a/((p.a + p.b)) + p.m_ur*g; + +%sprung mass states +x0(1) = sx0; % s_x x-position in a global coordinate system +x0(2) = sy0; % s_y y-position in a global coordinate system +x0(3) = delta0; % steering angle of front wheels +x0(4) = cos(beta0)*vel0; % u velocity in x-direction +x0(5) = Psi0; % Ψ yaw angle +x0(6) = dotPsi0; % Ψ yaw rate +x0(7) = 0; % ΦS roll angle +x0(8) = 0; % ΦS roll rate +x0(9) = 0; % ΘS pitch angle +x0(10) = 0; % ΘS pitch rate +x0(11) = sin(beta0)*vel0; % v velocity in y-direction +x0(12) = 0; % zS z-position (zero height corresponds to steady state solution) +x0(13) = 0; % w velocity in z-direction + +%unsprung mass states (front) +x0(14) = 0; % ΦUF roll angle front +x0(15) = 0; % ΦUF roll rate front +x0(16) = sin(beta0)*vel0 + p.a*dotPsi0; % vUF velocity in y-direction front +x0(17) = (F0_z_f)/(2*p.K_zt); % zUF z-position front +x0(18) = 0; % wUF velocity in z-direction front + +%unsprung mass states (rear) +x0(19) = 0; % ΦUR roll angle rear +x0(20) = 0; % ΦUR roll rate rear +x0(21) = sin(beta0)*vel0 - p.b*dotPsi0; % vUR velocity in y-direction rear +x0(22) = (F0_z_r)/(2*p.K_zt); % zUR z-position rear +x0(23) = 0; % wUR velocity in z-direction rear + +%wheel states +x0(24) = x0(4)/(p.R_w); % ωLF left front wheel angular speed +x0(25) = x0(4)/(p.R_w); % ωRF right front wheel angular speed +x0(26) = x0(4)/(p.R_w); % ωLR left rear wheel angular speed +x0(27) = x0(4)/(p.R_w); % ωRR right rear wheel angular speed + +x0(28) = 0; % delta_y_f +x0(29) = 0; % delta_y_r + + + +%------------- END OF CODE -------------- \ No newline at end of file diff --git a/MATLAB/init_ST.m b/MATLAB/init_ST.m new file mode 100644 index 0000000..ff2f462 --- /dev/null +++ b/MATLAB/init_ST.m @@ -0,0 +1,72 @@ +function x0 = init_ST(initState, p) +% init_MB - generates the initial state vector for the single-track model +% +% Syntax: +% x0 = init_ST(initState, p) +% +% Inputs: +% initState - core initial states +% p - parameter vector +% +% Outputs: +% x0 - initial state vector +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 11-January-2017 +% Last update: --- +% Last revision:--- + +%------------- BEGIN CODE -------------- + +%states +%x1 = s_x x-position in a global coordinate system +%x2 = s_y y-position in a global coordinate system +%x3 = δ steering angle of front wheels +%x4 = u velocity in x-direction +%x5 = Ψ yaw angle +%x6 = Ψ yaw rate +%x7 = β slip angle at vehicle center + +%u1 = v_delta steering angle velocity of front wheels +%u2 = ax longitudinal acceleration + + +%obtain initial states from vector +sx0 = initState(1); +sy0 = initState(2); +vel0 = initState(3); +Psi0 = initState(4); +dotPsi0 = initState(5); +beta0 = initState(6); + + +%create equivalent bicycle parameters +g = 9.81; %[m/s^2] +mu = p.tire.p_dy1; +C_Sf = -p.tire.p_ky1/p.tire.p_dy1; +C_Sr = -p.tire.p_ky1/p.tire.p_dy1; +lf = p.a; +lr = p.b; + +%initial steering angle from steady state of slip angle +delta0 = vel0*(lf + lr)/(C_Sf*g*lr*mu)*dotPsi0 ... + + 1/(C_Sf*lr)*((C_Sr*lf + C_Sf*lr)*beta0 - (C_Sr - C_Sf)*lr*lf*dotPsi0/vel0); + +%sprung mass states +x0(1) = sx0; % s_x x-position in a global coordinate system +x0(2) = sy0; % s_y y-position in a global coordinate system +x0(3) = delta0; % steering angle of front wheels +x0(4) = vel0; % velocity +x0(5) = Psi0; % Ψ yaw angle +x0(6) = dotPsi0; % Ψ yaw rate +x0(7) = beta0; % β slip angle at vehicle center + +%------------- END OF CODE -------------- \ No newline at end of file diff --git a/MATLAB/parameters_vehicle1.m b/MATLAB/parameters_vehicle1.m new file mode 100644 index 0000000..b7bedd9 --- /dev/null +++ b/MATLAB/parameters_vehicle1.m @@ -0,0 +1,128 @@ +function p = parameters_vehicle1() +% parameters_vehicle1 - parameter set of the multi-body vehicle dynamics +% based on the DOT (department of transportation) vehicle dynamics; +% values are taken from a Ford Escort +% +% Syntax: +% p = parameters_vehicle1() +% +% Inputs: +% --- +% +% Outputs: +% p - parameter vector +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 15-January-2017 +% Last update: 05-July-2017 +% Last revision:--- + +%------------- BEGIN CODE -------------- + +%vehicle body dimensions +p.l = 4.298; %vehicle length [m] +p.w = 1.674; %vehicle width [m] + +%masses +p.m = lb_sec2_ft_IN_kg(84); %vehicle mass [kg]; MASS +p.m_s = lb_sec2_ft_IN_kg(75); %sprung mass [kg]; SMASS +p.m_uf = lb_sec2_ft_IN_kg(4.5); %unsprung mass front [kg]; UMASSF +p.m_ur = lb_sec2_ft_IN_kg(4.5); %unsprung mass rear [kg]; UMASSR + +%axes distances +p.a = ft_IN_m(2.9); %distance from spring mass center of gravity to front axle [m]; LENA +p.b = ft_IN_m(4.95); %distance from spring mass center of gravity to rear axle [m]; LENB + +%moments of inertia of sprung mass +p.I_Phi_s = lb_ft_sec2_IN_kg_m2(180); %moment of inertia for sprung mass in roll [kg m^2]; IXS +p.I_y_s = lb_ft_sec2_IN_kg_m2(990); %moment of inertia for sprung mass in pitch [kg m^2]; IYS +p.I_z = lb_ft_sec2_IN_kg_m2(1135); %moment of inertia for sprung mass in yaw [kg m^2]; IZZ +p.I_xz_s = lb_ft_sec2_IN_kg_m2(0); %moment of inertia cross product [kg m^2]; IXZ + +%suspension parameters +p.K_sf = lbs_ft_IN_N_m(1500); %suspension spring rate (front) [N/m]; KSF +p.K_sdf = lb_sec_ft_IN_N_s_m(100); %suspension damping rate (front) [N s/m]; KSDF +p.K_sr = lbs_ft_IN_N_m(1500); %suspension spring rate (rear) [N/m]; KSR +p.K_sdr = lb_sec_ft_IN_N_s_m(100); %suspension damping rate (rear) [N s/m]; KSDR + +%geometric parameters +p.T_f = ft_IN_m(4.56); %track width front [m]; TRWF +p.T_r = ft_IN_m(4.67); %track width rear [m]; TRWB +p.K_ras = lbs_ft_IN_N_m(12000); %lateral spring rate at compliant compliant pin joint between M_s and M_u [N/m]; KRAS + +p.K_tsf = ft_lb_rad_IN_N_m_rad(-9500); %auxiliary torsion roll stiffness per axle (normally negative) (front) [N m/rad]; KTSF +p.K_tsr = ft_lb_rad_IN_N_m_rad(0); %auxiliary torsion roll stiffness per axle (normally negative) (rear) [N m/rad]; KTSR +p.K_rad = lb_sec_ft_IN_N_s_m(700); % damping rate at compliant compliant pin joint between M_s and M_u [N s/m]; KRADP +p.K_zt = lbs_ft_IN_N_m(13000); % vertical spring rate of tire [N/m]; TSPRINGR + +p.h_cg = ft_IN_m(1.83); %center of gravity height of total mass [m]; HCG (mainly required for conversion to other vehicle models) +p.h_raf = ft_IN_m(0); %height of roll axis above ground (front) [m]; HRAF +p.h_rar = ft_IN_m(0); %height of roll axis above ground (rear) [m]; HRAR + +p.h_s = ft_IN_m(1.95); %M_s center of gravity above ground [m]; HS + +p.I_uf = lb_ft_sec2_IN_kg_m2(24); %moment of inertia for unsprung mass about x-axis (front) [kg m^2]; IXUF +p.I_ur = lb_ft_sec2_IN_kg_m2(24); %moment of inertia for unsprung mass about x-axis (rear) [kg m^2]; IXUR +p.I_y_w = 1.7; %wheel inertia, from internet forum for 235/65 R 17 [kg m^2] + +p.K_lt = ft_lb_IN_m_N(0.00015); %lateral compliance rate of tire, wheel, and suspension, per tire [m/N]; KLT +p.R_w = 0.344; %effective wheel/tire radius; chosen as tire rolling radius RR; taken from ADAMS documentation [m] + +%split of brake and engine torque +p.T_sb = 0.76; +p.T_se = 1; + +%suspension parameters +p.D_f = rad_ft_IN_rad_m(-0.19); %[rad/m]; DF +p.D_r = rad_ft_IN_rad_m(-0.064); %[rad/m]; DR +p.E_f = 0; %[needs conversion if nonzero]; EF +p.E_r = 0; %[needs conversion if nonzero]; ER + + +%tire parameters from ADAMS handbook +%longitudinal coefficients +p.tire.p_cx1 = 1.6411; %Shape factor Cfx for longitudinal force +p.tire.p_dx1 = 1.1739; %Longitudinal friction Mux at Fznom +p.tire.p_dx3 = 0; %Variation of friction Mux with camber +p.tire.p_ex1 = 0.46403; %Longitudinal curvature Efx at Fznom +p.tire.p_kx1 = 22.303; %Longitudinal slip stiffness Kfx/Fz at Fznom +p.tire.p_hx1 = 0.0012297; %Horizontal shift Shx at Fznom +p.tire.p_vx1 = -8.8098e-006; %Vertical shift Svx/Fz at Fznom +p.tire.r_bx1 = 13.276; %Slope factor for combined slip Fx reduction +p.tire.r_bx2 = -13.778; %Variation of slope Fx reduction with kappa +p.tire.r_cx1 = 1.2568; %Shape factor for combined slip Fx reduction +p.tire.r_ex1 = 0.65225; %Curvature factor of combined Fx +p.tire.r_hx1 = 0.0050722; %Shift factor for combined slip Fx reduction + +%lateral coefficients +p.tire.p_cy1 = 1.3507; %Shape factor Cfy for lateral forces +p.tire.p_dy1 = 1.0489; %Lateral friction Muy +p.tire.p_dy3 = -2.8821; %Variation of friction Muy with squared camber +p.tire.p_ey1 = -0.0074722; %Lateral curvature Efy at Fznom +p.tire.p_ky1 = -21.92; %Maximum value of stiffness Kfy/Fznom +p.tire.p_hy1 = 0.0026747; %Horizontal shift Shy at Fznom +p.tire.p_hy3 = 0.031415; %Variation of shift Shy with camber +p.tire.p_vy1 = 0.037318; %Vertical shift in Svy/Fz at Fznom +p.tire.p_vy3 = -0.32931; %Variation of shift Svy/Fz with camber +p.tire.r_by1 = 7.1433; %Slope factor for combined Fy reduction +p.tire.r_by2 = 9.1916; %Variation of slope Fy reduction with alpha +p.tire.r_by3 = -0.027856; %Shift term for alpha in slope Fy reduction +p.tire.r_cy1 = 1.0719; %Shape factor for combined Fy reduction +p.tire.r_ey1 = -0.27572; %Curvature factor of combined Fy +p.tire.r_hy1 = 5.7448e-006; %Shift factor for combined Fy reduction +p.tire.r_vy1 = -0.027825; %Kappa induced side force Svyk/Muy*Fz at Fznom +p.tire.r_vy3 = -0.27568; %Variation of Svyk/Muy*Fz with camber +p.tire.r_vy4 = 12.12; %Variation of Svyk/Muy*Fz with alpha +p.tire.r_vy5 = 1.9; %Variation of Svyk/Muy*Fz with kappa +p.tire.r_vy6 = -10.704; %Variation of Svyk/Muy*Fz with atan(kappa) + + +%------------- END OF CODE -------------- diff --git a/MATLAB/parameters_vehicle2.m b/MATLAB/parameters_vehicle2.m new file mode 100644 index 0000000..59a275b --- /dev/null +++ b/MATLAB/parameters_vehicle2.m @@ -0,0 +1,128 @@ +function p = parameters_vehicle2() +% parameters_vehicle2 - parameter set of the multi-body vehicle dynamics +% based on the DOT (department of transportation) vehicle dynamics; +% values are taken from a BMW 320i +% +% Syntax: +% p = parameters_vehicle2() +% +% Inputs: +% --- +% +% Outputs: +% p - parameter vector +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 15-January-2017 +% Last update: 05-July-2017 +% Last revision:--- + +%------------- BEGIN CODE -------------- + +%vehicle body dimensions +p.l = 4.508; %vehicle length [m] (with US bumpers) +p.w = 1.610; %vehicle width [m] + +%masses +p.m = lb_sec2_ft_IN_kg(74.91452); %vehicle mass [kg]; MASS +p.m_s = lb_sec2_ft_IN_kg(66.17221); %sprung mass [kg]; SMASS +p.m_uf = lb_sec2_ft_IN_kg(4.371153); %unsprung mass front [kg]; UMASSF +p.m_ur = lb_sec2_ft_IN_kg(4.371153); %unsprung mass rear [kg]; UMASSR + +%axes distances +p.a = ft_IN_m(3.793293); %distance from spring mass center of gravity to front axle [m]; LENA +p.b = ft_IN_m(4.667707); %distance from spring mass center of gravity to rear axle [m]; LENB + +%moments of inertia of sprung mass +p.I_Phi_s = lb_ft_sec2_IN_kg_m2(152.871); %moment of inertia for sprung mass in roll [kg m^2]; IXS +p.I_y_s = lb_ft_sec2_IN_kg_m2(1154.888); %moment of inertia for sprung mass in pitch [kg m^2]; IYS +p.I_z = lb_ft_sec2_IN_kg_m2(1321.416); %moment of inertia for sprung mass in yaw [kg m^2]; IZZ +p.I_xz_s = lb_ft_sec2_IN_kg_m2(0); %moment of inertia cross product [kg m^2]; IXZ + +%suspension parameters +p.K_sf = lbs_ft_IN_N_m(1675); %suspension spring rate (front) [N/m]; KSF +p.K_sdf = lb_sec_ft_IN_N_s_m(122.3966); %suspension damping rate (front) [N s/m]; KSDF +p.K_sr = lbs_ft_IN_N_m(1345); %suspension spring rate (rear) [N/m]; KSR +p.K_sdr = lb_sec_ft_IN_N_s_m(112.9981); %suspension damping rate (rear) [N s/m]; KSDR + +%geometric parameters +p.T_f = ft_IN_m(4.55); %track width front [m]; TRWF +p.T_r = ft_IN_m(4.475); %track width rear [m]; TRWB +p.K_ras = lbs_ft_IN_N_m(12000); %lateral spring rate at compliant compliant pin joint between M_s and M_u [N/m]; KRAS + +p.K_tsf = ft_lb_rad_IN_N_m_rad(-5100.155); %auxiliary torsion roll stiffness per axle (normally negative) (front) [N m/rad]; KTSF +p.K_tsr = ft_lb_rad_IN_N_m_rad(-1949.82); %auxiliary torsion roll stiffness per axle (normally negative) (rear) [N m/rad]; KTSR +p.K_rad = lb_sec_ft_IN_N_s_m(700); % damping rate at compliant compliant pin joint between M_s and M_u [N s/m]; KRADP +p.K_zt = lbs_ft_IN_N_m(10842.89); % vertical spring rate of tire [N/m]; TSPRINGR + +p.h_cg = ft_IN_m(1.886053); %center of gravity height of total mass [m]; HCG (mainly required for conversion to other vehicle models) +p.h_raf = ft_IN_m(0); %height of roll axis above ground (front) [m]; HRAF +p.h_rar = ft_IN_m(0); %height of roll axis above ground (rear) [m]; HRAR + +p.h_s = ft_IN_m(2.01355); %M_s center of gravity above ground [m]; HS + +p.I_uf = lb_ft_sec2_IN_kg_m2(22.62345); %moment of inertia for unsprung mass about x-axis (front) [kg m^2]; IXUF +p.I_ur = lb_ft_sec2_IN_kg_m2(21.88377); %moment of inertia for unsprung mass about x-axis (rear) [kg m^2]; IXUR +p.I_y_w = 1.7; %wheel inertia, from internet forum for 235/65 R 17 [kg m^2] + +p.K_lt = ft_lb_IN_m_N(2.397884e-4); %lateral compliance rate of tire, wheel, and suspension, per tire [m/N]; KLT +p.R_w = 0.344; %effective wheel/tire radius; chosen as tire rolling radius RR; taken from ADAMS documentation [m] + +%split of brake and engine torque +p.T_sb = 0.66; +p.T_se = 0; + +%suspension parameters +p.D_f = rad_ft_IN_rad_m(-0.12); %[rad/m]; DF +p.D_r = rad_ft_IN_rad_m(-0.276); %[rad/m]; DR +p.E_f = 0; %[needs conversion if nonzero]; EF +p.E_r = 0; %[needs conversion if nonzero]; ER + + +%tire parameters from ADAMS handbook +%longitudinal coefficients +p.tire.p_cx1 = 1.6411; %Shape factor Cfx for longitudinal force +p.tire.p_dx1 = 1.1739; %Longitudinal friction Mux at Fznom +p.tire.p_dx3 = 0; %Variation of friction Mux with camber +p.tire.p_ex1 = 0.46403; %Longitudinal curvature Efx at Fznom +p.tire.p_kx1 = 22.303; %Longitudinal slip stiffness Kfx/Fz at Fznom +p.tire.p_hx1 = 0.0012297; %Horizontal shift Shx at Fznom +p.tire.p_vx1 = -8.8098e-006; %Vertical shift Svx/Fz at Fznom +p.tire.r_bx1 = 13.276; %Slope factor for combined slip Fx reduction +p.tire.r_bx2 = -13.778; %Variation of slope Fx reduction with kappa +p.tire.r_cx1 = 1.2568; %Shape factor for combined slip Fx reduction +p.tire.r_ex1 = 0.65225; %Curvature factor of combined Fx +p.tire.r_hx1 = 0.0050722; %Shift factor for combined slip Fx reduction + +%lateral coefficients +p.tire.p_cy1 = 1.3507; %Shape factor Cfy for lateral forces +p.tire.p_dy1 = 1.0489; %Lateral friction Muy +p.tire.p_dy3 = -2.8821; %Variation of friction Muy with squared camber +p.tire.p_ey1 = -0.0074722; %Lateral curvature Efy at Fznom +p.tire.p_ky1 = -21.92; %Maximum value of stiffness Kfy/Fznom +p.tire.p_hy1 = 0.0026747; %Horizontal shift Shy at Fznom +p.tire.p_hy3 = 0.031415; %Variation of shift Shy with camber +p.tire.p_vy1 = 0.037318; %Vertical shift in Svy/Fz at Fznom +p.tire.p_vy3 = -0.32931; %Variation of shift Svy/Fz with camber +p.tire.r_by1 = 7.1433; %Slope factor for combined Fy reduction +p.tire.r_by2 = 9.1916; %Variation of slope Fy reduction with alpha +p.tire.r_by3 = -0.027856; %Shift term for alpha in slope Fy reduction +p.tire.r_cy1 = 1.0719; %Shape factor for combined Fy reduction +p.tire.r_ey1 = -0.27572; %Curvature factor of combined Fy +p.tire.r_hy1 = 5.7448e-006; %Shift factor for combined Fy reduction +p.tire.r_vy1 = -0.027825; %Kappa induced side force Svyk/Muy*Fz at Fznom +p.tire.r_vy3 = -0.27568; %Variation of Svyk/Muy*Fz with camber +p.tire.r_vy4 = 12.12; %Variation of Svyk/Muy*Fz with alpha +p.tire.r_vy5 = 1.9; %Variation of Svyk/Muy*Fz with kappa +p.tire.r_vy6 = -10.704; %Variation of Svyk/Muy*Fz with atan(kappa) + + +%------------- END OF CODE -------------- diff --git a/MATLAB/parameters_vehicle3.m b/MATLAB/parameters_vehicle3.m new file mode 100644 index 0000000..bfe2d92 --- /dev/null +++ b/MATLAB/parameters_vehicle3.m @@ -0,0 +1,128 @@ +function p = parameters_vehicle3() +% parameters_vehicle3 - parameter set of the multi-body vehicle dynamics +% based on the DOT (department of transportation) vehicle dynamics; +% values are taken from a VW Vanagon +% +% Syntax: +% p = parameters_vehicle3() +% +% Inputs: +% --- +% +% Outputs: +% p - parameter vector +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 15-January-2017 +% Last update: 05-July-2017 +% Last revision:--- + +%------------- BEGIN CODE -------------- + +%vehicle body dimensions +p.l = 4.569; %vehicle length [m] +p.w = 1.844; %vehicle width [m] + +%masses +p.m = lb_sec2_ft_IN_kg(101.3367); %vehicle mass [kg]; MASS +p.m_s = lb_sec2_ft_IN_kg(90.21635); %sprung mass [kg]; SMASS +p.m_uf = lb_sec2_ft_IN_kg(5.56015); %unsprung mass front [kg]; UMASSF +p.m_ur = lb_sec2_ft_IN_kg(5.56015); %unsprung mass rear [kg]; UMASSR + +%axes distances +p.a = ft_IN_m(3.775563); %distance from spring mass center of gravity to front axle [m]; LENA +p.b = ft_IN_m(4.334437); %distance from spring mass center of gravity to rear axle [m]; LENB + +%moments of inertia of sprung mass +p.I_Phi_s = lb_ft_sec2_IN_kg_m2(353.9445); %moment of inertia for sprung mass in roll [kg m^2]; IXS +p.I_y_s = lb_ft_sec2_IN_kg_m2(1625.825); %moment of inertia for sprung mass in pitch [kg m^2]; IYS +p.I_z = lb_ft_sec2_IN_kg_m2(1824.078); %moment of inertia for sprung mass in yaw [kg m^2]; IZZ +p.I_xz_s = lb_ft_sec2_IN_kg_m2(0); %moment of inertia cross product [kg m^2]; IXZ + +%suspension parameters +p.K_sf = lbs_ft_IN_N_m(2300); %suspension spring rate (front) [N/m]; KSF +p.K_sdf = lb_sec_ft_IN_N_s_m(164.8335); %suspension damping rate (front) [N s/m]; KSDF +p.K_sr = lbs_ft_IN_N_m(2680); %suspension spring rate (rear) [N/m]; KSR +p.K_sdr = lb_sec_ft_IN_N_s_m(189.7866); %suspension damping rate (rear) [N s/m]; KSDR + +%geometric parameters +p.T_f = ft_IN_m(5.165); %track width front [m]; TRWF +p.T_r = ft_IN_m(5.065); %track width rear [m]; TRWB +p.K_ras = lbs_ft_IN_N_m(12000); %lateral spring rate at compliant compliant pin joint between M_s and M_u [N/m]; KRAS + +p.K_tsf = ft_lb_rad_IN_N_m_rad(-25038.92); %auxiliary torsion roll stiffness per axle (normally negative) (front) [N m/rad]; KTSF +p.K_tsr = ft_lb_rad_IN_N_m_rad(-5702.369); %auxiliary torsion roll stiffness per axle (normally negative) (rear) [N m/rad]; KTSR +p.K_rad = lb_sec_ft_IN_N_s_m(700); % damping rate at compliant compliant pin joint between M_s and M_u [N s/m]; KRADP +p.K_zt = lbs_ft_IN_N_m(14565.6); % vertical spring rate of tire [N/m]; TSPRINGR + +p.h_cg = ft_IN_m(2.453467); %center of gravity height of total mass [m]; HCG (mainly required for conversion to other vehicle models) +p.h_raf = ft_IN_m(0); %height of roll axis above ground (front) [m]; HRAF +p.h_rar = ft_IN_m(0); %height of roll axis above ground (rear) [m]; HRAR + +p.h_s = ft_IN_m(2.639405); %M_s center of gravity above ground [m]; HS + +p.I_uf = lb_ft_sec2_IN_kg_m2(37.08234); %moment of inertia for unsprung mass about x-axis (front) [kg m^2]; IXUF +p.I_ur = lb_ft_sec2_IN_kg_m2(35.66033); %moment of inertia for unsprung mass about x-axis (rear) [kg m^2]; IXUR +p.I_y_w = 1.7; %wheel inertia, from internet forum for 235/65 R 17 [kg m^2] + +p.K_lt = ft_lb_IN_m_N(1.7850283e-04); %lateral compliance rate of tire, wheel, and suspension, per tire [m/N]; KLT +p.R_w = 0.344; %effective wheel/tire radius; chosen as tire rolling radius RR; taken from ADAMS documentation [m] + +%split of brake and engine torque +p.T_sb = 0.64; +p.T_se = 0; + +%suspension parameters +p.D_f = rad_ft_IN_rad_m(-0.1); %[rad/m]; DF; modified from orig. paper due to stability issues when damping is ignored +p.D_r = rad_ft_IN_rad_m(-0.1); %[rad/m]; DR; modified from orig. paper due to stability issues when damping is ignored +p.E_f = 0; %[needs conversion if nonzero]; EF +p.E_r = 0; %[needs conversion if nonzero]; ER + + +%tire parameters from ADAMS handbook +%longitudinal coefficients +p.tire.p_cx1 = 1.6411; %Shape factor Cfx for longitudinal force +p.tire.p_dx1 = 1.1739; %Longitudinal friction Mux at Fznom +p.tire.p_dx3 = 0; %Variation of friction Mux with camber +p.tire.p_ex1 = 0.46403; %Longitudinal curvature Efx at Fznom +p.tire.p_kx1 = 22.303; %Longitudinal slip stiffness Kfx/Fz at Fznom +p.tire.p_hx1 = 0.0012297; %Horizontal shift Shx at Fznom +p.tire.p_vx1 = -8.8098e-006; %Vertical shift Svx/Fz at Fznom +p.tire.r_bx1 = 13.276; %Slope factor for combined slip Fx reduction +p.tire.r_bx2 = -13.778; %Variation of slope Fx reduction with kappa +p.tire.r_cx1 = 1.2568; %Shape factor for combined slip Fx reduction +p.tire.r_ex1 = 0.65225; %Curvature factor of combined Fx +p.tire.r_hx1 = 0.0050722; %Shift factor for combined slip Fx reduction + +%lateral coefficients +p.tire.p_cy1 = 1.3507; %Shape factor Cfy for lateral forces +p.tire.p_dy1 = 1.0489; %Lateral friction Muy +p.tire.p_dy3 = -2.8821; %Variation of friction Muy with squared camber +p.tire.p_ey1 = -0.0074722; %Lateral curvature Efy at Fznom +p.tire.p_ky1 = -21.92; %Maximum value of stiffness Kfy/Fznom +p.tire.p_hy1 = 0.0026747; %Horizontal shift Shy at Fznom +p.tire.p_hy3 = 0.031415; %Variation of shift Shy with camber +p.tire.p_vy1 = 0.037318; %Vertical shift in Svy/Fz at Fznom +p.tire.p_vy3 = -0.32931; %Variation of shift Svy/Fz with camber +p.tire.r_by1 = 7.1433; %Slope factor for combined Fy reduction +p.tire.r_by2 = 9.1916; %Variation of slope Fy reduction with alpha +p.tire.r_by3 = -0.027856; %Shift term for alpha in slope Fy reduction +p.tire.r_cy1 = 1.0719; %Shape factor for combined Fy reduction +p.tire.r_ey1 = -0.27572; %Curvature factor of combined Fy +p.tire.r_hy1 = 5.7448e-006; %Shift factor for combined Fy reduction +p.tire.r_vy1 = -0.027825; %Kappa induced side force Svyk/Muy*Fz at Fznom +p.tire.r_vy3 = -0.27568; %Variation of Svyk/Muy*Fz with camber +p.tire.r_vy4 = 12.12; %Variation of Svyk/Muy*Fz with alpha +p.tire.r_vy5 = 1.9; %Variation of Svyk/Muy*Fz with kappa +p.tire.r_vy6 = -10.704; %Variation of Svyk/Muy*Fz with atan(kappa) + + +%------------- END OF CODE -------------- diff --git a/MATLAB/readme.txt b/MATLAB/readme.txt new file mode 100644 index 0000000..5d95fc7 --- /dev/null +++ b/MATLAB/readme.txt @@ -0,0 +1,19 @@ +To execute a test function, which produces the plots of the vehicle models documentation, run 'testVehicle.m'. + +Initialization of models------------------------------------------ +kinematic single-track model: init_KS.m +single-track model: init_ST.m +multi-body model: init_MB.m +------------------------------------------------------------------ + +Parameter sets---------------------------------------------------- +Ford Escort: parameters_vehicle1.m +BMW 320i: parameters_vehicle2.m +VW Vanagon: parameters_vehicle3.m +------------------------------------------------------------------ + +Vehicle models---------------------------------------------------- +kinematic single-track model: vehicleDynamics_KS.m +single-track model: vehicleDynamics_ST.m +multi-body model: vehicleDynamics_MB.m +------------------------------------------------------------------ diff --git a/MATLAB/testVehicle.m b/MATLAB/testVehicle.m new file mode 100644 index 0000000..9bd784b --- /dev/null +++ b/MATLAB/testVehicle.m @@ -0,0 +1,224 @@ +function testVehicle() +% testVehicle - tests vehicle dynamics +% +% Syntax: +% testVehicle() +% +% Inputs: +% --- +% +% Outputs: +% --- +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 11-January-2017 +% Last update: --- +% Last revision:--- + +%------------- BEGIN CODE -------------- + +%load parameters +p = parameters_vehicle2; +g = 9.81; %[m/s^2] + +%set options -------------------------------------------------------------- +tStart = 0; %start time +tFinal = 1; %start time + +% vel0 = 15; +% Psi0 = 0.1; +% dotPsi0 = -0.1; +% beta0 = 0.05; +% sy0 = 1; +vel0 = 15; +Psi0 = 0; +dotPsi0 = 0; +beta0 = 0; +sy0 = 0; +initialState = [0,sy0,vel0,Psi0,dotPsi0,beta0]; %initial state for simulation +x0_KS = init_KS(initialState, p); %initial state for kinematic single-track model +x0_ST = init_ST(initialState, p); %initial state for single-track model +x0_MB = init_MB(initialState, p); %initial state for multi-body model +%-------------------------------------------------------------------------- + +% %specify continuous dynamics----------------------------------------------- +% carDyn = vehicleSys('vehicleDynamics',28,2,@vehicleDynamics_MB,[]); %initialize car +% carDyn_bicycle = vehicleSys('vehicleDynamics_bicycle',6,2,@DOTBicycleDynamics,[]); %initialize car +% %-------------------------------------------------------------------------- + +% %generate ode options +% stepsizeOptions = odeset('MaxStep',options.tStart-options.tFinal); +% opt = odeset(stepsizeOptions); + +%set input: rolling car (velocity should stay constant) +u = [0 0]; +%simulate car +[t_roll,x_roll] = ode45(getfcn(@vehicleDynamics_MB,u,p),[tStart, tFinal],x0_MB); +figure +plot(t_roll,x_roll(:,4)); +plot(x_roll(:,1),x_roll(:,2)); + +%set input: braking car (wheel spin and velocity should decrease; similar wheel spin) +v_delta = 0.15; +acc = -0.7*g; +u = [v_delta acc]; +%simulate car +[t_brake,x_brake] = ode45(getfcn(@vehicleDynamics_MB,u,p),[tStart, tFinal],x0_MB); +figure %position +hold on +plot(x_brake(:,1),x_brake(:,2)) +figure % velocity +plot(t_brake,x_brake(:,4)); +figure % wheel spin +hold on +plot(t_brake,x_brake(:,24)); +plot(t_brake,x_brake(:,25)); +plot(t_brake,x_brake(:,26)); +plot(t_brake,x_brake(:,27)); +figure % pitch +plot(t_brake,x_brake(:,9)); + +%set input: accelerating car (wheel spin and velocity should increase; more wheel spin at rear) +v_delta = 0.15; +acc = 0.63*g; +u = [v_delta acc]; +%simulate car +[t_acc,x_acc] = ode45(getfcn(@vehicleDynamics_MB,u,p),[tStart, tFinal],x0_MB); +figure %position +hold on +plot(x_acc(:,1),x_acc(:,2)) +figure % velocity +plot(t_acc,x_acc(:,4)); +figure % wheel spin +hold on +plot(t_acc,x_acc(:,24)); +plot(t_acc,x_acc(:,25)); +plot(t_acc,x_acc(:,26)); +plot(t_acc,x_acc(:,27)); +figure % pitch +plot(t_acc,x_acc(:,9)); +figure %orientation +hold on +plot(t_acc,x_acc(:,5)) + + +%steering to left +v_delta = 0.15; +u = [v_delta 0]; + +%simulate full car +[t_left,x_left] = ode45(getfcn(@vehicleDynamics_MB,u,p),[tStart, tFinal],x0_MB); + +%simulate single-track model +[t_left_st,x_left_st] = ode45(getfcn(@vehicleDynamics_ST,u,p),[tStart, tFinal],x0_ST); + +%simulate kinematic single-track model +[t_left_ks,x_left_ks] = ode45(getfcn(@vehicleDynamics_KS,u,p),[tStart, tFinal],x0_KS); + +figure %position +hold on +plot(x_left(:,1),x_left(:,2)) +plot(x_left_st(:,1),x_left_st(:,2)) +plot(x_left_ks(:,1),x_left_ks(:,2)) +figure %orientation +hold on +plot(t_left,x_left(:,5)) +plot(t_left_st,x_left_st(:,5),'r') +plot(t_left_ks,x_left_ks(:,5),'g') +figure %steering +hold on +plot(t_left,x_left(:,3)) +plot(t_left_st,x_left_st(:,3),'r') +plot(t_left_ks,x_left_ks(:,3),'g') +figure %yaw rate +hold on +plot(t_left,x_left(:,6)) +plot(t_left_st,x_left_st(:,6),'r') +figure %slip angle +hold on +plot(t_left,atan(x_left(:,11)./x_left(:,4))) +plot(t_left_st,x_left_st(:,7)) +% figure % wheel spin +% hold on +% plot(t_acc,x_acc(:,24)); +% plot(t_acc,x_acc(:,25)); +% plot(t_acc,x_acc(:,26)); +% plot(t_acc,x_acc(:,27)); + + +%compare position for braking/normal +figure %position +hold on +plot(x_left(:,1),x_left(:,2)) +plot(x_brake(:,1),x_brake(:,2)) +plot(x_acc(:,1),x_acc(:,2)) +for i=1:10 + t_next = tFinal/10*i; + ind = find(t_left kg.m^2 + +post_val = 4.4482216152605*0.3048*prev_val; \ No newline at end of file diff --git a/MATLAB/unitConversions/lb_sec2_ft_IN_kg.m b/MATLAB/unitConversions/lb_sec2_ft_IN_kg.m new file mode 100644 index 0000000..7e89cda --- /dev/null +++ b/MATLAB/unitConversions/lb_sec2_ft_IN_kg.m @@ -0,0 +1,8 @@ +function post_val = lb_sec2_ft_IN_kg(prev_val) + +% 1lb is 4.4482216152605 N +% 1ft is 0.3048 m + +% lb.sec^2/ft --> kg + +post_val = 4.4482216152605/0.3048*prev_val; \ No newline at end of file diff --git a/MATLAB/unitConversions/lb_sec_ft_IN_N_s_m.m b/MATLAB/unitConversions/lb_sec_ft_IN_N_s_m.m new file mode 100644 index 0000000..e981adb --- /dev/null +++ b/MATLAB/unitConversions/lb_sec_ft_IN_N_s_m.m @@ -0,0 +1,8 @@ +function post_val = lb_sec_ft_IN_N_s_m(prev_val) +% original: [lb sec/ft] +% new: [N sec/m] + +% 1lb is 4.4482216152605 N +% 1ft is 0.3048 m + +post_val = 4.4482216152605/0.3048*prev_val; \ No newline at end of file diff --git a/MATLAB/unitConversions/lbs_ft_IN_N_m.m b/MATLAB/unitConversions/lbs_ft_IN_N_m.m new file mode 100644 index 0000000..7fb1b24 --- /dev/null +++ b/MATLAB/unitConversions/lbs_ft_IN_N_m.m @@ -0,0 +1,9 @@ +function post_val = lbs_ft_IN_N_m(prev_val) +% original: [lbs/ft] +% new: [N/m] + +% 1lbs is 0.45359237 kg +% 1kg is around 9.81 N assuming being close to sea level +% 1ft is 0.3048 m + +post_val = 0.45359237*9.81/0.3048*prev_val; \ No newline at end of file diff --git a/MATLAB/unitConversions/rad_ft_IN_rad_m.m b/MATLAB/unitConversions/rad_ft_IN_rad_m.m new file mode 100644 index 0000000..dc54d6c --- /dev/null +++ b/MATLAB/unitConversions/rad_ft_IN_rad_m.m @@ -0,0 +1,7 @@ +function post_val = rad_ft_IN_rad_m(prev_val) +%original: [rad/ft] +%new: [rad/m] + +% 1ft is 0.3048 m + +post_val = 1/0.3048*prev_val; \ No newline at end of file diff --git a/MATLAB/unitConversions/rad_ft_lb_IN_rad_sec2_kg_m2.m b/MATLAB/unitConversions/rad_ft_lb_IN_rad_sec2_kg_m2.m new file mode 100644 index 0000000..0b63b0c --- /dev/null +++ b/MATLAB/unitConversions/rad_ft_lb_IN_rad_sec2_kg_m2.m @@ -0,0 +1,9 @@ +function post_val = rad_ft_lb_IN_rad_sec2_kg_m2(prev_val) + +%original: [rad/(ft lb)] +%new: [rad/(N m)] = [rad s^2/(kg m^2)] + +% 1lb is 4.4482216152605 N +% 1ft is 0.3048 m + +post_val = 1/(4.4482216152605*0.3048)*prev_val; \ No newline at end of file diff --git a/MATLAB/vehicleDynamics_KS.m b/MATLAB/vehicleDynamics_KS.m new file mode 100644 index 0000000..e9b9a3c --- /dev/null +++ b/MATLAB/vehicleDynamics_KS.m @@ -0,0 +1,50 @@ +function f = vehicleDynamics_KS(x,u,p) +% vehicleDynamics_KS - kinematic single-track vehicle dynamics +% +% Syntax: +% f = vehicleDynamics_KS(x,u,p) +% +% Inputs: +% x - vehicle state vector +% u - vehicle input vector +% p - vehicle parameter vector +% +% Outputs: +% f - right-hand side of differential equations +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 12-January-2017 +% Last update: --- +% Last revision:--- + +%------------- BEGIN CODE -------------- + +%create equivalent kinematic single-track parameters +l = p.a + p.b; + +%states +%x1 = s_x x-position in a global coordinate system +%x2 = s_y y-position in a global coordinate system +%x3 = δ steering angle of front wheels +%x4 = u velocity in x-direction +%x5 = Ψ yaw angle + +%u1 = v_delta steering angle velocity of front wheels +%u2 = ax longitudinal acceleration + +%system dynamics +f(1,1) = x(4)*cos(x(5)); +f(2,1) = x(4)*sin(x(5)); +f(3,1) = u(1); +f(4,1) = u(2); +f(5,1) = x(4)/l*tan(x(3)); + +%------------- END OF CODE -------------- diff --git a/MATLAB/vehicleDynamics_MB.m b/MATLAB/vehicleDynamics_MB.m new file mode 100644 index 0000000..4168fc3 --- /dev/null +++ b/MATLAB/vehicleDynamics_MB.m @@ -0,0 +1,373 @@ +function f = vehicleDynamics_MB(x,u,p) +% vehicleDynamics_MB - multi-body vehicle dynamics based on the DOT +% (department of transportation) vehicle dynamics +% +% Syntax: +% f = vehicleDynamics_MB(t,x,u,p) +% +% Inputs: +% x - vehicle state vector +% u - vehicle input vector +% p - vehicle parameter vector +% +% Outputs: +% f - right-hand side of differential equations +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 05-January-2017 +% Last update: --- +% Last revision:--- + +%------------- BEGIN CODE -------------- + +% set gravity constant +g = 9.81; %[m/s^2] + +%states +%x1 = s_x x-position in a global coordinate system +%x2 = s_y y-position in a global coordinate system +%x3 = δ steering angle of front wheels +%x4 = u velocity in x-direction +%x5 = Ψ yaw angle +%x6 = Ψ yaw rate + +%x7 = ΦS roll angle +%x8 = ΦS roll rate +%x9 = ΘS pitch angle +%x10 = ΘS pitch rate +%x11 = v velocity in y-direction +%x12 = zS z-position +%x13 = w velocity in z-direction + +%x14 = ΦUF roll angle front +%x15 = ΦUF roll rate front +%x16 = vUF velocity in y-direction front +%x17 = zUF z-position front +%x18 = wUF velocity in z-direction front + +%x19 = ΦUR roll angle rear +%x20 = ΦUR roll rate rear +%x21 = vUR velocity in y-direction rear +%x22 = zUR z-position rear +%x23 = wUR velocity in z-direction rear + +%x24 = ωLF left front wheel angular speed +%x25 = ωRF right front wheel angular speed +%x26 = ωLR left rear wheel angular speed +%x27 = ωRR right rear wheel angular speed + +%x28 = delta_y_f +%x29 = delta_y_r + +%u1 = v_delta steering angle velocity of front wheels +%u2 = acceleration + + +%compute slip angle at cg +beta = atan(x(11)/x(4)); +vel = sqrt(x(4)^2 + x(11)^2); + +%vertical tire forces +F_z_LF = (x(17) + p.R_w*(cos(x(14)) - 1) - 0.5*p.T_f*sin(x(14)))*p.K_zt; +F_z_RF = (x(17) + p.R_w*(cos(x(14)) - 1) + 0.5*p.T_f*sin(x(14)))*p.K_zt; +F_z_LR = (x(22) + p.R_w*(cos(x(19)) - 1) - 0.5*p.T_r*sin(x(19)))*p.K_zt; +F_z_RR = (x(22) + p.R_w*(cos(x(19)) - 1) + 0.5*p.T_r*sin(x(19)))*p.K_zt; + +%obtain individual tire speeds +u_w_lf = (x(4) + 0.5*p.T_f*x(6))*cos(x(3)) + (x(11) + p.a*x(6))*sin(x(3)); +u_w_rf = (x(4) - 0.5*p.T_f*x(6))*cos(x(3)) + (x(11) + p.a*x(6))*sin(x(3)); +u_w_lr = x(4) + 0.5*p.T_r*x(6); +u_w_rr = x(4) - 0.5*p.T_r*x(6); + +%compute longitudinal slip +s_lf = 1 - p.R_w*x(24)/u_w_lf; +s_rf = 1 - p.R_w*x(25)/u_w_rf; +s_lr = 1 - p.R_w*x(26)/u_w_lr; +s_rr = 1 - p.R_w*x(27)/u_w_rr; + +%lateral slip angles +alpha_LF = atan((x(11) + p.a*x(6) - x(15)*(p.R_w - x(17)))/(x(4) + 0.5*p.T_f*x(6))) - x(3); +alpha_RF = atan((x(11) + p.a*x(6) - x(15)*(p.R_w - x(17)))/(x(4) - 0.5*p.T_f*x(6))) - x(3); +alpha_LR = atan((x(11) - p.b*x(6) - x(20)*(p.R_w - x(22)))/(x(4) + 0.5*p.T_r*x(6))); +alpha_RR = atan((x(11) - p.b*x(6) - x(20)*(p.R_w - x(22)))/(x(4) - 0.5*p.T_r*x(6))); + +%auxiliary suspension movement +z_SLF = (p.h_s - p.R_w + x(17) - x(12))/cos(x(7)) - p.h_s + p.R_w + p.a*x(9) + 0.5*(x(7) - x(14))*p.T_f; +z_SRF = (p.h_s - p.R_w + x(17) - x(12))/cos(x(7)) - p.h_s + p.R_w + p.a*x(9) - 0.5*(x(7) - x(14))*p.T_f; +z_SLR = (p.h_s - p.R_w + x(22) - x(12))/cos(x(7)) - p.h_s + p.R_w - p.b*x(9) + 0.5*(x(7) - x(19))*p.T_r; +z_SRR = (p.h_s - p.R_w + x(22) - x(12))/cos(x(7)) - p.h_s + p.R_w - p.b*x(9) - 0.5*(x(7) - x(19))*p.T_r; + +dz_SLF = x(18) - x(13) + p.a*x(10) + 0.5*(x(8) - x(15))*p.T_f; +dz_SRF = x(18) - x(13) + p.a*x(10) - 0.5*(x(8) - x(15))*p.T_f; +dz_SLR = x(23) - x(13) - p.b*x(10) + 0.5*(x(8) - x(20))*p.T_r; +dz_SRR = x(23) - x(13) - p.b*x(10) - 0.5*(x(8) - x(20))*p.T_r; + +%camber angles +gamma_LF = x(7) + p.D_f*z_SLF + p.E_f*(z_SLF)^2; +gamma_RF = x(7) - p.D_f*z_SRF - p.E_f*(z_SRF)^2; +gamma_LR = x(7) + p.D_r*z_SLR + p.E_r*(z_SLR)^2; +gamma_RR = x(7) - p.D_r*z_SRR - p.E_r*(z_SRR)^2; + +%compute longitudinal tire forces using the magic formula for pure slip +F0_x_LF = mFormulaLongitudinal(s_lf, gamma_LF, F_z_LF, p.tire); +F0_x_RF = mFormulaLongitudinal(s_rf, gamma_RF, F_z_RF, p.tire); +F0_x_LR = mFormulaLongitudinal(s_lr, gamma_LR, F_z_LR, p.tire); +F0_x_RR = mFormulaLongitudinal(s_rr, gamma_RR, F_z_RR, p.tire); + +%compute lateral tire forces using the magic formula for pure slip +[F0_y_LF, mu_y_LF] = mFormulaLateral(alpha_LF, gamma_LF, F_z_LF, p.tire); +[F0_y_RF, mu_y_RF] = mFormulaLateral(alpha_RF, gamma_RF, F_z_RF, p.tire); +[F0_y_LR, mu_y_LR] = mFormulaLateral(alpha_LR, gamma_LR, F_z_LR, p.tire); +[F0_y_RR, mu_y_RR] = mFormulaLateral(alpha_RR, gamma_RR, F_z_RR, p.tire); + +%compute longitudinal tire forces using the magic formula for combined slip +F_x_LF = mFormulaLongitudinalComb(s_lf, alpha_LF, F0_x_LF, p.tire); +F_x_RF = mFormulaLongitudinalComb(s_rf, alpha_RF, F0_x_RF, p.tire); +F_x_LR = mFormulaLongitudinalComb(s_lr, alpha_LR, F0_x_LR, p.tire); +F_x_RR = mFormulaLongitudinalComb(s_rr, alpha_RR, F0_x_RR, p.tire); + +%compute lateral tire forces using the magic formula for combined slip +F_y_LF = mFormulaLateralComb(s_lf, alpha_LF, gamma_LF, mu_y_LF, F_z_LF, F0_y_LF, p.tire); +F_y_RF = mFormulaLateralComb(s_rf, alpha_RF, gamma_RF, mu_y_RF, F_z_RF, F0_y_RF, p.tire); +F_y_LR = mFormulaLateralComb(s_lr, alpha_LR, gamma_LR, mu_y_LR, F_z_LR, F0_y_LR, p.tire); +F_y_RR = mFormulaLateralComb(s_rr, alpha_RR, gamma_RR, mu_y_RR, F_z_RR, F0_y_RR, p.tire); + +%auxiliary movements for compliant joint equations +delta_z_f = p.h_s - p.R_w + x(17) - x(12); +delta_z_r = p.h_s - p.R_w + x(22) - x(12); + +delta_phi_f = x(7) - x(14); +delta_phi_r = x(7) - x(19); + +dot_delta_phi_f = x(8) - x(15); +dot_delta_phi_r = x(8) - x(20); + +dot_delta_z_f = x(18) - x(13); +dot_delta_z_r = x(23) - x(13); + +dot_delta_y_f = x(11) + p.a*x(6) - x(16); +dot_delta_y_r = x(11) - p.b*x(6) - x(21); + +delta_f = delta_z_f*sin(x(7)) - x(28)*cos(x(7)) - (p.h_raf - p.R_w)*sin(delta_phi_f); +delta_r = delta_z_r*sin(x(7)) - x(29)*cos(x(7)) - (p.h_rar - p.R_w)*sin(delta_phi_r); + +dot_delta_f = (delta_z_f*cos(x(7)) + x(28)*sin(x(7)))*x(8)... + + dot_delta_z_f*sin(x(7)) - dot_delta_y_f*cos(x(7)) - (p.h_raf - p.R_w)*cos(delta_phi_f)*dot_delta_phi_f; +dot_delta_r = (delta_z_r*cos(x(7)) + x(29)*sin(x(7)))*x(8)... + + dot_delta_z_r*sin(x(7)) - dot_delta_y_r*cos(x(7)) - (p.h_rar - p.R_w)*cos(delta_phi_r)*dot_delta_phi_r; + +%compliant joint forces +F_RAF = delta_f*p.K_ras + dot_delta_f*p.K_rad; +F_RAR = delta_r*p.K_ras + dot_delta_r*p.K_rad; + +%auxiliary suspension forces (bump stop neglected; squat/lift forces neglected) +F_SLF = p.m_s*g*p.b/(2*(p.a+p.b)) - z_SLF*p.K_sf - dz_SLF*p.K_sdf + (x(7) - x(14))*p.K_tsf/p.T_f; + +F_SRF = p.m_s*g*p.b/(2*(p.a+p.b)) - z_SRF*p.K_sf - dz_SRF*p.K_sdf - (x(7) - x(14))*p.K_tsf/p.T_f; + +F_SLR = p.m_s*g*p.a/(2*(p.a+p.b)) - z_SLR*p.K_sr - dz_SLR*p.K_sdr + (x(7) - x(19))*p.K_tsr/p.T_r; + +F_SRR = p.m_s*g*p.a/(2*(p.a+p.b)) - z_SRR*p.K_sr - dz_SRR*p.K_sdr - (x(7) - x(19))*p.K_tsr/p.T_r; + + +%auxiliary variables sprung mass +sumX = F_x_LR + F_x_RR + (F_x_LF + F_x_RF)*cos(x(3)) - (F_y_LF + F_y_RF)*sin(x(3)); + +sumN = (F_y_LF + F_y_RF)*p.a*cos(x(3)) + (F_x_LF + F_x_RF)*p.a*sin(x(3))... + + (F_y_RF - F_y_LF)*0.5*p.T_f*sin(x(3)) + (F_x_LF - F_x_RF)*0.5*p.T_f*cos(x(3))... + + (F_x_LR - F_x_RR)*0.5*p.T_r - (F_y_LR + F_y_RR)*p.b; + +sumY_s = (F_RAF + F_RAR)*cos(x(7)) + (F_SLF + F_SLR + F_SRF + F_SRR)*sin(x(7)); + +sumL = 0.5*F_SLF*p.T_f + 0.5*F_SLR*p.T_r - 0.5*F_SRF*p.T_f - 0.5*F_SRR*p.T_r... + - F_RAF/cos(x(7))*(p.h_s - x(12) - p.R_w + x(17) - (p.h_raf - p.R_w)*cos(x(14)))... + - F_RAR/cos(x(7))*(p.h_s - x(12) - p.R_w + x(22) - (p.h_rar - p.R_w)*cos(x(19))); + +sumZ_s = (F_SLF + F_SLR + F_SRF + F_SRR)*cos(x(7)) - (F_RAF + F_RAR)*sin(x(7)); + +sumM_s = p.a*(F_SLF + F_SRF) - p.b*(F_SLR + F_SRR) + ((F_x_LF + F_x_RF)*cos(x(3))... + - (F_y_LF + F_y_RF)*sin(x(3)) + F_x_LR + F_x_RR)*(p.h_s - x(12)); + +%auxiliary variables unsprung mass +sumL_uf = 0.5*F_SRF*p.T_f - 0.5*F_SLF*p.T_f - F_RAF*(p.h_raf - p.R_w)... + + F_z_LF*(p.R_w*sin(x(14)) + 0.5*p.T_f*cos(x(14)) - p.K_lt*F_y_LF)... + - F_z_RF*(-p.R_w*sin(x(14)) + 0.5*p.T_f*cos(x(14)) + p.K_lt*F_y_RF)... + - ((F_y_LF + F_y_RF)*cos(x(3)) + (F_x_LF + F_x_RF)*sin(x(3)))*(p.R_w - x(17)); + +sumL_ur = 0.5*F_SRR*p.T_r - 0.5*F_SLR*p.T_r - F_RAR*(p.h_rar - p.R_w)... + + F_z_LR*(p.R_w*sin(x(19)) + 0.5*p.T_r*cos(x(19)) - p.K_lt*F_y_LR)... + - F_z_RR*(-p.R_w*sin(x(19)) + 0.5*p.T_r*cos(x(19)) + p.K_lt*F_y_RR)... + - (F_y_LR + F_y_RR)*(p.R_w - x(22)); + +sumZ_uf = F_z_LF + F_z_RF + F_RAF*sin(x(7)) - (F_SLF + F_SRF)*cos(x(7)); + +sumZ_ur = F_z_LR + F_z_RR + F_RAR*sin(x(7)) - (F_SLR + F_SRR)*cos(x(7)); + +sumY_uf = (F_y_LF + F_y_RF)*cos(x(3)) + (F_x_LF + F_x_RF)*sin(x(3))... + - F_RAF*cos(x(7)) - (F_SLF + F_SRF)*sin(x(7)); + +sumY_ur = (F_y_LR + F_y_RR)... + - F_RAR*cos(x(7)) - (F_SLR + F_SRR)*sin(x(7)); + + +%dynamics common with single-track model +f(1,1) = cos(beta + x(5))*vel; +f(2,1) = sin(beta + x(5))*vel; +f(3,1) = u(1); +f(4,1) = 1/p.m*sumX + x(6)*x(11); +f(5,1) = x(6); +f(6,1) = 1/(p.I_z - (p.I_xz_s)^2/p.I_Phi_s)*(sumN + p.I_xz_s/p.I_Phi_s*sumL); + + +% remaining sprung mass dynamics +f(7,1) = x(8); +f(8,1) = 1/(p.I_Phi_s - (p.I_xz_s)^2/p.I_z)*(p.I_xz_s/p.I_z*sumN + sumL); +f(9,1) = x(10); +f(10,1) = 1/p.I_y_s*sumM_s; +f(11,1) = 1/p.m_s*sumY_s - x(6)*x(4); +f(12,1) = x(13); +f(13,1) = g - 1/p.m_s*sumZ_s; + +%unsprung mass dynamics (front) +f(14,1) = x(15); +f(15,1) = 1/p.I_uf*sumL_uf; +f(16,1) = 1/p.m_uf*sumY_uf - x(6)*x(4); +f(17,1) = x(18); +f(18,1) = g - 1/p.m_uf*sumZ_uf; + +%unsprung mass dynamics (rear) +f(19,1) = x(20); +f(20,1) = 1/p.I_ur*sumL_ur; +f(21,1) = 1/p.m_ur*sumY_ur - x(6)*x(4); +f(22,1) = x(23); +f(23,1) = g - 1/p.m_ur*sumZ_ur; + +%convert acceleration input to brake and engine torque +if u(2)>0 + T_B = 0; + T_E = p.m*p.R_w*u(2); +else + T_B = p.m*p.R_w*u(2); + T_E = 0; +end + +%wheel dynamics (p.T; new parameter for torque splitting) +f(24,1) = 1/p.I_y_w*(-p.R_w*F_x_LF + 0.5*p.T_sb*T_B + 0.5*p.T_se*T_E); +f(25,1) = 1/p.I_y_w*(-p.R_w*F_x_RF + 0.5*p.T_sb*T_B + 0.5*p.T_se*T_E); +f(26,1) = 1/p.I_y_w*(-p.R_w*F_x_LR + 0.5*(1-p.T_sb)*T_B + 0.5*(1-p.T_se)*T_E); +f(27,1) = 1/p.I_y_w*(-p.R_w*F_x_RR + 0.5*(1-p.T_sb)*T_B + 0.5*(1-p.T_se)*T_E); + +%negative wheel spin forbidden +for iState = 24:27 + if x(iState)<0 + x(iState) = 0; + f(iState,1) = 0; + end +end + +%compliant joint equations +f(28,1) = dot_delta_y_f; +f(29,1) = dot_delta_y_r; + + +%longitudinal tire forces +function F_x = mFormulaLongitudinal(kappa, gamma, F_z, p) + +%turn slip is neglected, so xi_i=1; +%all scaling factors lambda = 1; + +%coordinate system transformation +kappa = -kappa; + +S_hx = p.p_hx1; +S_vx = F_z*p.p_vx1; + +kappa_x = kappa + S_hx; +mu_x = p.p_dx1*(1-p.p_dx3*gamma^2); + +C_x = p.p_cx1; +D_x = mu_x*F_z; +E_x = p.p_ex1; +K_x = F_z*p.p_kx1; +B_x = K_x/(C_x*D_x); + +%magic tire formula +F_x = D_x*sin(C_x*atan(B_x*kappa_x - E_x*(B_x*kappa_x - atan(B_x*kappa_x))) + S_vx); + + +%lateral tire forces +function [F_y, mu_y] = mFormulaLateral(alpha, gamma, F_z, p) + +%turn slip is neglected, so xi_i=1; +%all scaling factors lambda = 1; + +%coordinate system transformation +%alpha = -alpha; + +S_hy = sign(gamma)*(p.p_hy1 + p.p_hy3*abs(gamma)); +S_vy = sign(gamma)*F_z*(p.p_vy1 + p.p_vy3*abs(gamma)); + +alpha_y = alpha + S_hy; +mu_y = p.p_dy1*(1-p.p_dy3*gamma^2); + +C_y = p.p_cy1; +D_y = mu_y*F_z; +E_y = p.p_ey1; +K_y = F_z*p.p_ky1; %simplify K_y0 to p.p_ky1*F_z +B_y = K_y/(C_y*D_y); + +%magic tire formula +F_y = D_y*sin(C_y*atan(B_y*alpha_y - E_y*(B_y*alpha_y - atan(B_y*alpha_y)))) + S_vy; + + +%longitudinal tire forces for combined slip +function F_x = mFormulaLongitudinalComb(kappa, alpha, F0_x, p) + +%turn slip is neglected, so xi_i=1; +%all scaling factors lambda = 1; + +S_hxalpha = p.r_hx1; + +alpha_s = alpha + S_hxalpha; + +B_xalpha = p.r_bx1*cos(atan(p.r_bx2*kappa)); +C_xalpha = p.r_cx1; +E_xalpha = p.r_ex1; +D_xalpha = F0_x/(cos(C_xalpha*atan(B_xalpha*S_hxalpha - E_xalpha*(B_xalpha*S_hxalpha - atan(B_xalpha*S_hxalpha))))); + +%magic tire formula +F_x = D_xalpha*cos(C_xalpha*atan(B_xalpha*alpha_s - E_xalpha*(B_xalpha*alpha_s - atan(B_xalpha*alpha_s)))); + + + +%longitudinal tire forces for combined slip +function F_y = mFormulaLateralComb(kappa, alpha, gamma, mu_y, F_z, F0_y, p) + +%turn slip is neglected, so xi_i=1; +%all scaling factors lambda = 1; + +S_hykappa = p.r_hy1; + +kappa_s = kappa + S_hykappa; + +B_ykappa = p.r_by1*cos(atan(p.r_by2*(alpha-p.r_by3))); +C_ykappa = p.r_cy1; +E_ykappa = p.r_ey1; +D_ykappa = F0_y/(cos(C_ykappa*atan(B_ykappa*S_hykappa - E_ykappa*(B_ykappa*S_hykappa - atan(B_ykappa*S_hykappa))))); + +D_vykappa = mu_y*F_z*(p.r_vy1 + p.r_vy3*gamma) * cos(atan(p.r_vy4*alpha)); +S_vykappa = D_vykappa*sin(p.r_vy5*atan(p.r_vy6*kappa)); + +%magic tire formula +F_y = D_ykappa*cos(C_ykappa*atan(B_ykappa*kappa_s - E_ykappa*(B_ykappa*kappa_s - atan(B_ykappa*kappa_s)))) + S_vykappa; + + +%------------- END OF CODE -------------- \ No newline at end of file diff --git a/MATLAB/vehicleDynamics_ST.m b/MATLAB/vehicleDynamics_ST.m new file mode 100644 index 0000000..3d6b589 --- /dev/null +++ b/MATLAB/vehicleDynamics_ST.m @@ -0,0 +1,70 @@ +function f = vehicleDynamics_ST(x,u,p) +% vehicleDynamics_ST - single-track vehicle dynamics +% +% Syntax: +% f = vehicleDynamics_ST(x,u,p) +% +% Inputs: +% x - vehicle state vector +% u - vehicle input vector +% p - vehicle parameter vector +% +% Outputs: +% f - right-hand side of differential equations +% +% Example: +% +% Other m-files required: none +% Subfunctions: none +% MAT-files required: none +% +% See also: --- + +% Author: Matthias Althoff +% Written: 12-January-2017 +% Last update: --- +% Last revision:--- + +%------------- BEGIN CODE -------------- + +% set gravity constant +g = 9.81; %[m/s^2] + +%create equivalent bicycle parameters +mu = p.tire.p_dy1; +C_Sf = -p.tire.p_ky1/p.tire.p_dy1; +C_Sr = -p.tire.p_ky1/p.tire.p_dy1; +lf = p.a; +lr = p.b; +h = p.h_s; +m = p.m; +I = p.I_z; + +%states +%x1 = s_x x-position in a global coordinate system +%x2 = s_y y-position in a global coordinate system +%x3 = δ steering angle of front wheels +%x4 = u velocity in x-direction +%x5 = Ψ yaw angle +%x6 = Ψ yaw rate +%x7 = β slip angle at vehicle center + +%u1 = v_delta steering angle velocity of front wheels +%u2 = ax longitudinal acceleration + + +%system dynamics +f(1,1) = x(4)*cos(x(7) + x(5)); +f(2,1) = x(4)*sin(x(7) + x(5)); +f(3,1) = u(1); +f(4,1) = u(2); +f(5,1) = x(6); +f(6,1) = -mu*m/(x(4)*I*(lr+lf))*(lf^2*C_Sf*(g*lr-u(2)*h) + lr^2*C_Sr*(g*lf + u(2)*h))*x(6) ... + +mu*m/(I*(lr+lf))*(lr*C_Sr*(g*lf + u(2)*h) - lf*C_Sf*(g*lr - u(2)*h))*x(7) ... + +mu*m/(I*(lr+lf))*lf*C_Sf*(g*lr - u(2)*h)*x(3); +f(7,1) = (mu/(x(4)^2*(lr+lf))*(C_Sr*(g*lf + u(2)*h)*lr - C_Sf*(g*lr - u(2)*h)*lf)-1)*x(6) ... + -mu/(x(4)*(lr+lf))*(C_Sr*(g*lf + u(2)*h) + C_Sf*(g*lr-u(2)*h))*x(7) ... + +mu/(x(4)*(lr+lf))*(C_Sf*(g*lr-u(2)*h))*x(3); + + +%------------- END OF CODE -------------- \ No newline at end of file diff --git a/Python/init_KS.py b/Python/init_KS.py new file mode 100644 index 0000000..7188577 --- /dev/null +++ b/Python/init_KS.py @@ -0,0 +1,67 @@ +def init_KS(initState, p): + # init_KS - generates the initial state vector for the kinematic single-track model + + # Syntax: + # x0 = init_KS(initState, p) + # + # Inputs: + # initState - core initial states + # p - parameter vector + # + # Outputs: + # x0 - initial state vector + # + # Example: + # + # See also: --- + + # Author: Matthias Althoff + # Written: 11-January-2017 + # Last update: --- + # Last revision:--- + + + #------------- BEGIN CODE -------------- + + #states + #x1 = x-position in a global coordinate system + #x2 = y-position in a global coordinate system + #x3 = steering angle of front wheels + #x4 = velocity in x-direction + #x5 = yaw angle + + #u1 = steering angle velocity of front wheels + #u2 = ongitudinal acceleration + + + #obtain initial states from vector + sx0 = initState[0] + sy0 = initState[1] + vel0 = initState[2] + Psi0 = initState[3] + dotPsi0 = initState[4] + beta0 = initState[5] + + + #create equivalent bicycle parameters + g = 9.81 #[m/s^2] + mu = p.tire.p_dy1 + C_Sf = -p.tire.p_ky1/p.tire.p_dy1 + C_Sr = -p.tire.p_ky1/p.tire.p_dy1 + lf = p.a + lr = p.b + + #initial steering angle from steady state of slip angle + delta0 = vel0*(lf + lr)/(C_Sf*g*lr*mu)*dotPsi0 + 1/(C_Sf*lr)*((C_Sr*lf + C_Sf*lr)*beta0 - (C_Sr - C_Sf)*lr*lf*dotPsi0/vel0) + + #sprung mass states + x0 = [] # init initial state vector + x0.append(sx0) # x-position in a global coordinate system + x0.append(sy0) # y-position in a global coordinate system + x0.append(delta0) # steering angle of front wheels + x0.append(vel0) # velocity + x0.append(Psi0) # yaw angle + + return x0 + + #------------- END OF CODE -------------- diff --git a/Python/init_MB.py b/Python/init_MB.py new file mode 100644 index 0000000..a78bcc5 --- /dev/null +++ b/Python/init_MB.py @@ -0,0 +1,132 @@ +import math + +def init_MB(initState, p): + # init_MB - generates the initial state vector for the multi-body model + # + # Syntax: + # x0 = init_MB(initState, p) + # + # Inputs: + # initState - core initial states + # p - parameter vector + # + # Outputs: + # x0 - initial state vector + # + # Example: + # + # See also: --- + + # Author: Matthias Althoff + # Written: 11-January-2017 + # Last update: --- + # Last revision:--- + + #------------- BEGIN CODE -------------- + + #states + #x1 = x-position in a global coordinate system + #x2 = y-position in a global coordinate system + #x3 = steering angle of front wheels + #x4 = velocity in x-direction + #x5 = yaw angle + #x6 = yaw rate + + #x7 = roll angle + #x8 = roll rate + #x9 = pitch angle + #x10 = pitch rate + #x11 = velocity in y-direction + #x12 = z-position + #x13 = velocity in z-direction + + #x14 = roll angle front + #x15 = roll rate front + #x16 = velocity in y-direction front + #x17 = z-position front + #x18 = velocity in z-direction front + + #x19 = roll angle rear + #x20 = roll rate rear + #x21 = velocity in y-direction rear + #x22 = z-position rear + #x23 = velocity in z-direction rear + + #x24 = left front wheel angular speed + #x25 = right front wheel angular speed + #x26 = left rear wheel angular speed + #x27 = right rear wheel angular speed + + #x28 = delta_y_f + #x29 = delta_y_r + + #u1 = steering angle velocity of front wheels + #u2 = acceleration + + + #obtain initial states from vector + sx0 = initState[0] + sy0 = initState[1] + vel0 = initState[2] + Psi0 = initState[3] + dotPsi0 = initState[4] + beta0 = initState[5] + + + #create equivalent bicycle parameters + g = 9.81 #[m/s^2] + mu = p.tire.p_dy1 + C_Sf = -p.tire.p_ky1/p.tire.p_dy1 + C_Sr = -p.tire.p_ky1/p.tire.p_dy1 + lf = p.a + lr = p.b + + #initial steering angle from steady state of slip angle + delta0 = vel0*(lf + lr)/(C_Sf*g*lr*mu)*dotPsi0 + 1/(C_Sf*lr)*((C_Sr*lf + C_Sf*lr)*beta0 - (C_Sr - C_Sf)*lr*lf*dotPsi0/vel0) + + #auxiliary initial states + F0_z_f = p.m_s*g*p.b/((p.a + p.b)) + p.m_uf*g + F0_z_r = p.m_s*g*p.a/((p.a + p.b)) + p.m_ur*g + + #sprung mass states + x0 = [] # init initial state vector + x0.append(sx0) # x-position in a global coordinate system + x0.append(sy0) # y-position in a global coordinate system + x0.append(delta0) # steering angle of front wheels + x0.append(math.cos(beta0)*vel0) # velocity in x-direction + x0.append(Psi0) # yaw angle + x0.append(dotPsi0) # yaw rate + x0.append(0) # roll angle + x0.append(0) # roll rate + x0.append(0) # pitch angle + x0.append(0) # pitch rate + x0.append(math.sin(beta0)*vel0) # velocity in y-direction + x0.append(0) # z-position (zero height corresponds to steady state solution) + x0.append(0) # velocity in z-direction + + #unsprung mass states (front) + x0.append(0) # roll angle front + x0.append(0) # roll rate front + x0.append(math.sin(beta0)*vel0 + p.a*dotPsi0) # velocity in y-direction front + x0.append((F0_z_f)/(2*p.K_zt)) # z-position front + x0.append(0) # velocity in z-direction front + + #unsprung mass states (rear) + x0.append(0) # roll angle rear + x0.append(0) # roll rate rear + x0.append(math.sin(beta0)*vel0 - p.b*dotPsi0) # velocity in y-direction rear + x0.append((F0_z_r)/(2*p.K_zt)) # z-position rear + x0.append(0) # velocity in z-direction rear + + #wheel states + x0.append(x0[3]/(p.R_w)) # left front wheel angular speed + x0.append(x0[3]/(p.R_w)) # right front wheel angular speed + x0.append(x0[3]/(p.R_w)) # left rear wheel angular speed + x0.append(x0[3]/(p.R_w)) # right rear wheel angular speed + + x0.append(0) # delta_y_f + x0.append(0) # delta_y_r + + return x0 + + #------------- END OF CODE -------------- diff --git a/Python/init_ST.py b/Python/init_ST.py new file mode 100644 index 0000000..8f32b93 --- /dev/null +++ b/Python/init_ST.py @@ -0,0 +1,70 @@ +def init_ST(initState, p): + # init_MB - generates the initial state vector for the single-track model + # + # Syntax: + # x0 = init_ST(initState, p) + # + # Inputs: + # initState - core initial states + # p - parameter vector + # + # Outputs: + # x0 - initial state vector + # + # Example: + # + # See also: --- + + # Author: Matthias Althoff + # Written: 11-January-2017 + # Last update: --- + # Last revision:--- + + #------------- BEGIN CODE -------------- + + #states + #x1 = x-position in a global coordinate system + #x2 = y-position in a global coordinate system + #x3 = steering angle of front wheels + #x4 = velocity in x-direction + #x5 = yaw angle + #x6 = yaw rate + #x7 = slip angle at vehicle center + + #u1 = steering angle velocity of front wheels + #u2 = longitudinal acceleration + + + #obtain initial states from vector + sx0 = initState[0] + sy0 = initState[1] + vel0 = initState[2] + Psi0 = initState[3] + dotPsi0 = initState[4] + beta0 = initState[5] + + + #create equivalent bicycle parameters + g = 9.81 #[m/s^2] + mu = p.tire.p_dy1 + C_Sf = -p.tire.p_ky1/p.tire.p_dy1 + C_Sr = -p.tire.p_ky1/p.tire.p_dy1 + lf = p.a + lr = p.b + + #initial steering angle from steady state of slip angle + delta0 = vel0*(lf + lr)/(C_Sf*g*lr*mu)*dotPsi0 + 1/(C_Sf*lr)*((C_Sr*lf + C_Sf*lr)*beta0 - (C_Sr - C_Sf)*lr*lf*dotPsi0/vel0) + + #sprung mass states + x0 = [] # init initial state vector + x0.append(sx0) # x-position in a global coordinate system + x0.append(sy0) # y-position in a global coordinate system + x0.append(delta0) # steering angle of front wheels + x0.append(vel0) # velocity + x0.append(Psi0) # yaw angle + x0.append(dotPsi0) # yaw rate + x0.append(beta0) # slip angle at vehicle center + + return x0 + +#------------- END OF CODE -------------- diff --git a/Python/parameters_vehicle1.py b/Python/parameters_vehicle1.py new file mode 100644 index 0000000..ba4c22e --- /dev/null +++ b/Python/parameters_vehicle1.py @@ -0,0 +1,135 @@ +#from unitConversions.unitConversion import ft_IN_m +from unitConversions import unitConversion +from vehicleParameters import VehicleParameters + +def parameters_vehicle1(): + # parameters_vehicle1 - parameter set of the multi-body vehicle dynamics + # based on the DOT (department of transportation) vehicle dynamics + # values are taken from a Ford Escort + # + # Syntax: + # p = parameters_vehicle1() + # + # Inputs: + # --- + # + # Outputs: + # p - parameter vector + # + # Example: + # + # Subfunctions: none + # + # See also: --- + + # Author: Matthias Althoff + # Written: 15-January-2017 + # Last update: 05-July-2017 + # Last revision:--- + + #------------- BEGIN CODE -------------- + + #init vehicle parameters + p = VehicleParameters() + + #vehicle body dimensions + p.l = 4.298 #vehicle length [m] + p.w = 1.674 #vehicle width [m] + + #masses + p.m = unitConversion.lb_sec2_ft_IN_kg(84) #vehicle mass [kg] MASS + p.m_s = unitConversion.lb_sec2_ft_IN_kg(75) #sprung mass [kg] SMASS + p.m_uf = unitConversion.lb_sec2_ft_IN_kg(4.5) #unsprung mass front [kg] UMASSF + p.m_ur = unitConversion.lb_sec2_ft_IN_kg(4.5) #unsprung mass rear [kg] UMASSR + + #axes distances + p.a = unitConversion.ft_IN_m(2.9) #distance from spring mass center of gravity to front axle [m] LENA + p.b = unitConversion.ft_IN_m(4.95) #distance from spring mass center of gravity to rear axle [m] LENB + + #moments of inertia of sprung mass + p.I_Phi_s = unitConversion.lb_ft_sec2_IN_kg_m2(180) #moment of inertia for sprung mass in roll [kg m^2] IXS + p.I_y_s = unitConversion.lb_ft_sec2_IN_kg_m2(990) #moment of inertia for sprung mass in pitch [kg m^2] IYS + p.I_z = unitConversion.lb_ft_sec2_IN_kg_m2(1135) #moment of inertia for sprung mass in yaw [kg m^2] IZZ + p.I_xz_s = unitConversion.lb_ft_sec2_IN_kg_m2(0) #moment of inertia cross product [kg m^2] IXZ + + #suspension parameters + p.K_sf = unitConversion.lbs_ft_IN_N_m(1500) #suspension spring rate (front) [N/m] KSF + p.K_sdf = unitConversion.lb_sec_ft_IN_N_s_m(100) #suspension damping rate (front) [N s/m] KSDF + p.K_sr = unitConversion.lbs_ft_IN_N_m(1500) #suspension spring rate (rear) [N/m] KSR + p.K_sdr = unitConversion.lb_sec_ft_IN_N_s_m(100) #suspension damping rate (rear) [N s/m] KSDR + + #geometric parameters + p.T_f = unitConversion.ft_IN_m(4.56) #track width front [m] TRWF + p.T_r = unitConversion.ft_IN_m(4.67) #track width rear [m] TRWB + p.K_ras = unitConversion.lbs_ft_IN_N_m(12000) #lateral spring rate at compliant compliant pin joint between M_s and M_u [N/m] KRAS + + p.K_tsf = unitConversion.ft_lb_rad_IN_N_m_rad(-9500) #auxiliary torsion roll stiffness per axle (normally negative) (front) [N m/rad] KTSF + p.K_tsr = unitConversion.ft_lb_rad_IN_N_m_rad(0) #auxiliary torsion roll stiffness per axle (normally negative) (rear) [N m/rad] KTSR + p.K_rad = unitConversion.lb_sec_ft_IN_N_s_m(700) # damping rate at compliant compliant pin joint between M_s and M_u [N s/m] KRADP + p.K_zt = unitConversion.lbs_ft_IN_N_m(13000) # vertical spring rate of tire [N/m] TSPRINGR + + p.h_cg = unitConversion.ft_IN_m(1.83) #center of gravity height of total mass [m] HCG (mainly required for conversion to other vehicle models) + p.h_raf = unitConversion.ft_IN_m(0) #height of roll axis above ground (front) [m] HRAF + p.h_rar = unitConversion.ft_IN_m(0) #height of roll axis above ground (rear) [m] HRAR + + p.h_s = unitConversion.ft_IN_m(1.95) #M_s center of gravity above ground [m] HS + + p.I_uf = unitConversion.lb_ft_sec2_IN_kg_m2(24) #moment of inertia for unsprung mass about x-axis (front) [kg m^2] IXUF + p.I_ur = unitConversion.lb_ft_sec2_IN_kg_m2(24) #moment of inertia for unsprung mass about x-axis (rear) [kg m^2] IXUR + p.I_y_w = 1.7 #wheel inertia, from internet forum for 235/65 R 17 [kg m^2] + + p.K_lt = unitConversion.ft_lb_IN_m_N(0.00015) #lateral compliance rate of tire, wheel, and suspension, per tire [m/N] KLT + p.R_w = 0.344 #effective wheel/tire radius chosen as tire rolling radius RR taken from ADAMS documentation [m] + + #split of brake and engine torque + p.T_sb = 0.76 + p.T_se = 1 + + #suspension parameters + p.D_f = unitConversion.rad_ft_IN_rad_m(-0.19) #[rad/m] DF + p.D_r = unitConversion.rad_ft_IN_rad_m(-0.064) #[rad/m] DR + p.E_f = 0 #[needs conversion if nonzero] EF + p.E_r = 0 #[needs conversion if nonzero] ER + + + #tire parameters from ADAMS handbook + #longitudinal coefficients + p.tire.p_cx1 = 1.6411 #Shape factor Cfx for longitudinal force + p.tire.p_dx1 = 1.1739 #Longitudinal friction Mux at Fznom + p.tire.p_dx3 = 0 #Variation of friction Mux with camber + p.tire.p_ex1 = 0.46403 #Longitudinal curvature Efx at Fznom + p.tire.p_kx1 = 22.303 #Longitudinal slip stiffness Kfx/Fz at Fznom + p.tire.p_hx1 = 0.0012297 #Horizontal shift Shx at Fznom + p.tire.p_vx1 = -8.8098e-006 #Vertical shift Svx/Fz at Fznom + p.tire.r_bx1 = 13.276 #Slope factor for combined slip Fx reduction + p.tire.r_bx2 = -13.778 #Variation of slope Fx reduction with kappa + p.tire.r_cx1 = 1.2568 #Shape factor for combined slip Fx reduction + p.tire.r_ex1 = 0.65225 #Curvature factor of combined Fx + p.tire.r_hx1 = 0.0050722 #Shift factor for combined slip Fx reduction + + #lateral coefficients + p.tire.p_cy1 = 1.3507 #Shape factor Cfy for lateral forces + p.tire.p_dy1 = 1.0489 #Lateral friction Muy + p.tire.p_dy3 = -2.8821 #Variation of friction Muy with squared camber + p.tire.p_ey1 = -0.0074722 #Lateral curvature Efy at Fznom + p.tire.p_ky1 = -21.92 #Maximum value of stiffness Kfy/Fznom + p.tire.p_hy1 = 0.0026747 #Horizontal shift Shy at Fznom + p.tire.p_hy3 = 0.031415 #Variation of shift Shy with camber + p.tire.p_vy1 = 0.037318 #Vertical shift in Svy/Fz at Fznom + p.tire.p_vy3 = -0.32931 #Variation of shift Svy/Fz with camber + p.tire.r_by1 = 7.1433 #Slope factor for combined Fy reduction + p.tire.r_by2 = 9.1916 #Variation of slope Fy reduction with alpha + p.tire.r_by3 = -0.027856 #Shift term for alpha in slope Fy reduction + p.tire.r_cy1 = 1.0719 #Shape factor for combined Fy reduction + p.tire.r_ey1 = -0.27572 #Curvature factor of combined Fy + p.tire.r_hy1 = 5.7448e-006 #Shift factor for combined Fy reduction + p.tire.r_vy1 = -0.027825 #Kappa induced side force Svyk/Muy*Fz at Fznom + p.tire.r_vy3 = -0.27568 #Variation of Svyk/Muy*Fz with camber + p.tire.r_vy4 = 12.12 #Variation of Svyk/Muy*Fz with alpha + p.tire.r_vy5 = 1.9 #Variation of Svyk/Muy*Fz with kappa + p.tire.r_vy6 = -10.704 #Variation of Svyk/Muy*Fz with atan(kappa) + + return p + + + #------------- END OF CODE -------------- diff --git a/Python/parameters_vehicle2.py b/Python/parameters_vehicle2.py new file mode 100644 index 0000000..696b9a2 --- /dev/null +++ b/Python/parameters_vehicle2.py @@ -0,0 +1,131 @@ +from unitConversions import unitConversion +from vehicleParameters import VehicleParameters + +def parameters_vehicle2(): + # parameters_vehicle2 - parameter set of the multi-body vehicle dynamics + # based on the DOT (department of transportation) vehicle dynamics + # values are taken from a BMW 320i + # + # Syntax: + # p = parameters_vehicle2() + # + # Inputs: + # --- + # + # Outputs: + # p - parameter vector + # + # Example: + # + # See also: --- + + # Author: Matthias Althoff + # Written: 15-January-2017 + # Last update: 05-July-2017 + # Last revision:--- + + #------------- BEGIN CODE -------------- + + #init vehicle parameters + p = VehicleParameters() + + #vehicle body dimensions + p.l = 4.508 #vehicle length [m] (with US bumpers) + p.w = 1.610 #vehicle width [m] + + #masses + p.m = unitConversion.lb_sec2_ft_IN_kg(74.91452) #vehicle mass [kg] MASS + p.m_s = unitConversion.lb_sec2_ft_IN_kg(66.17221) #sprung mass [kg] SMASS + p.m_uf = unitConversion.lb_sec2_ft_IN_kg(4.371153) #unsprung mass front [kg] UMASSF + p.m_ur = unitConversion.lb_sec2_ft_IN_kg(4.371153) #unsprung mass rear [kg] UMASSR + + #axes distances + p.a = unitConversion.ft_IN_m(3.793293) #distance from spring mass center of gravity to front axle [m] LENA + p.b = unitConversion.ft_IN_m(4.667707) #distance from spring mass center of gravity to rear axle [m] LENB + + #moments of inertia of sprung mass + p.I_Phi_s = unitConversion.lb_ft_sec2_IN_kg_m2(152.871) #moment of inertia for sprung mass in roll [kg m^2] IXS + p.I_y_s = unitConversion.lb_ft_sec2_IN_kg_m2(1154.888) #moment of inertia for sprung mass in pitch [kg m^2] IYS + p.I_z = unitConversion.lb_ft_sec2_IN_kg_m2(1321.416) #moment of inertia for sprung mass in yaw [kg m^2] IZZ + p.I_xz_s = unitConversion.lb_ft_sec2_IN_kg_m2(0) #moment of inertia cross product [kg m^2] IXZ + + #suspension parameters + p.K_sf = unitConversion.lbs_ft_IN_N_m(1675) #suspension spring rate (front) [N/m] KSF + p.K_sdf = unitConversion.lb_sec_ft_IN_N_s_m(122.3966) #suspension damping rate (front) [N s/m] KSDF + p.K_sr = unitConversion.lbs_ft_IN_N_m(1345) #suspension spring rate (rear) [N/m] KSR + p.K_sdr = unitConversion.lb_sec_ft_IN_N_s_m(112.9981) #suspension damping rate (rear) [N s/m] KSDR + + #geometric parameters + p.T_f = unitConversion.ft_IN_m(4.55) #track width front [m] TRWF + p.T_r = unitConversion.ft_IN_m(4.475) #track width rear [m] TRWB + p.K_ras = unitConversion.lbs_ft_IN_N_m(12000) #lateral spring rate at compliant compliant pin joint between M_s and M_u [N/m] KRAS + + p.K_tsf = unitConversion.ft_lb_rad_IN_N_m_rad(-5100.155) #auxiliary torsion roll stiffness per axle (normally negative) (front) [N m/rad] KTSF + p.K_tsr = unitConversion.ft_lb_rad_IN_N_m_rad(-1949.82) #auxiliary torsion roll stiffness per axle (normally negative) (rear) [N m/rad] KTSR + p.K_rad = unitConversion.lb_sec_ft_IN_N_s_m(700) # damping rate at compliant compliant pin joint between M_s and M_u [N s/m] KRADP + p.K_zt = unitConversion.lbs_ft_IN_N_m(10842.89) # vertical spring rate of tire [N/m] TSPRINGR + + p.h_cg = unitConversion.ft_IN_m(1.886053) #center of gravity height of total mass [m] HCG (mainly required for conversion to other vehicle models) + p.h_raf = unitConversion.ft_IN_m(0) #height of roll axis above ground (front) [m] HRAF + p.h_rar = unitConversion.ft_IN_m(0) #height of roll axis above ground (rear) [m] HRAR + + p.h_s = unitConversion.ft_IN_m(2.01355) #M_s center of gravity above ground [m] HS + + p.I_uf = unitConversion.lb_ft_sec2_IN_kg_m2(22.62345) #moment of inertia for unsprung mass about x-axis (front) [kg m^2] IXUF + p.I_ur = unitConversion.lb_ft_sec2_IN_kg_m2(21.88377) #moment of inertia for unsprung mass about x-axis (rear) [kg m^2] IXUR + p.I_y_w = 1.7 #wheel inertia, from internet forum for 235/65 R 17 [kg m^2] + + p.K_lt = unitConversion.ft_lb_IN_m_N(2.397884e-4) #lateral compliance rate of tire, wheel, and suspension, per tire [m/N] KLT + p.R_w = 0.344 #effective wheel/tire radius chosen as tire rolling radius RR taken from ADAMS documentation [m] + + #split of brake and engine torque + p.T_sb = 0.66 + p.T_se = 0 + + #suspension parameters + p.D_f = unitConversion.rad_ft_IN_rad_m(-0.12) #[rad/m] DF + p.D_r = unitConversion.rad_ft_IN_rad_m(-0.276) #[rad/m] DR + p.E_f = 0 #[needs conversion if nonzero] EF + p.E_r = 0 #[needs conversion if nonzero] ER + + + #tire parameters from ADAMS handbook + #longitudinal coefficients + p.tire.p_cx1 = 1.6411 #Shape factor Cfx for longitudinal force + p.tire.p_dx1 = 1.1739 #Longitudinal friction Mux at Fznom + p.tire.p_dx3 = 0 #Variation of friction Mux with camber + p.tire.p_ex1 = 0.46403 #Longitudinal curvature Efx at Fznom + p.tire.p_kx1 = 22.303 #Longitudinal slip stiffness Kfx/Fz at Fznom + p.tire.p_hx1 = 0.0012297 #Horizontal shift Shx at Fznom + p.tire.p_vx1 = -8.8098e-006 #Vertical shift Svx/Fz at Fznom + p.tire.r_bx1 = 13.276 #Slope factor for combined slip Fx reduction + p.tire.r_bx2 = -13.778 #Variation of slope Fx reduction with kappa + p.tire.r_cx1 = 1.2568 #Shape factor for combined slip Fx reduction + p.tire.r_ex1 = 0.65225 #Curvature factor of combined Fx + p.tire.r_hx1 = 0.0050722 #Shift factor for combined slip Fx reduction + + #lateral coefficients + p.tire.p_cy1 = 1.3507 #Shape factor Cfy for lateral forces + p.tire.p_dy1 = 1.0489 #Lateral friction Muy + p.tire.p_dy3 = -2.8821 #Variation of friction Muy with squared camber + p.tire.p_ey1 = -0.0074722 #Lateral curvature Efy at Fznom + p.tire.p_ky1 = -21.92 #Maximum value of stiffness Kfy/Fznom + p.tire.p_hy1 = 0.0026747 #Horizontal shift Shy at Fznom + p.tire.p_hy3 = 0.031415 #Variation of shift Shy with camber + p.tire.p_vy1 = 0.037318 #Vertical shift in Svy/Fz at Fznom + p.tire.p_vy3 = -0.32931 #Variation of shift Svy/Fz with camber + p.tire.r_by1 = 7.1433 #Slope factor for combined Fy reduction + p.tire.r_by2 = 9.1916 #Variation of slope Fy reduction with alpha + p.tire.r_by3 = -0.027856 #Shift term for alpha in slope Fy reduction + p.tire.r_cy1 = 1.0719 #Shape factor for combined Fy reduction + p.tire.r_ey1 = -0.27572 #Curvature factor of combined Fy + p.tire.r_hy1 = 5.7448e-006 #Shift factor for combined Fy reduction + p.tire.r_vy1 = -0.027825 #Kappa induced side force Svyk/Muy*Fz at Fznom + p.tire.r_vy3 = -0.27568 #Variation of Svyk/Muy*Fz with camber + p.tire.r_vy4 = 12.12 #Variation of Svyk/Muy*Fz with alpha + p.tire.r_vy5 = 1.9 #Variation of Svyk/Muy*Fz with kappa + p.tire.r_vy6 = -10.704 #Variation of Svyk/Muy*Fz with atan(kappa) + + return p + + #------------- END OF CODE -------------- diff --git a/Python/parameters_vehicle3.py b/Python/parameters_vehicle3.py new file mode 100644 index 0000000..c28a1e8 --- /dev/null +++ b/Python/parameters_vehicle3.py @@ -0,0 +1,135 @@ +from unitConversions import unitConversion +from vehicleParameters import VehicleParameters + +def parameters_vehicle3(): + # parameters_vehicle3 - parameter set of the multi-body vehicle dynamics + # based on the DOT (department of transportation) vehicle dynamics + # values are taken from a VW Vanagon + # + # Syntax: + # p = parameters_vehicle3() + # + # Inputs: + # --- + # + # Outputs: + # p - parameter vector + # + # Example: + # + # Other m-files required: none + # Subfunctions: none + # MAT-files required: none + # + # See also: --- + + # Author: Matthias Althoff + # Written: 15-January-2017 + # Last update: 05-July-2017 + # Last revision:--- + + #------------- BEGIN CODE -------------- + + #init vehicle parameters + p = VehicleParameters() + + #vehicle body dimensions + p.l = 4.569 #vehicle length [m] + p.w = 1.844 #vehicle width [m] + + #masses + p.m = unitConversion.lb_sec2_ft_IN_kg(101.3367) #vehicle mass [kg] MASS + p.m_s = unitConversion.lb_sec2_ft_IN_kg(90.21635) #sprung mass [kg] SMASS + p.m_uf = unitConversion.lb_sec2_ft_IN_kg(5.56015) #unsprung mass front [kg] UMASSF + p.m_ur = unitConversion.lb_sec2_ft_IN_kg(5.56015) #unsprung mass rear [kg] UMASSR + + #axes distances + p.a = unitConversion.ft_IN_m(3.775563) #distance from spring mass center of gravity to front axle [m] LENA + p.b = unitConversion.ft_IN_m(4.334437) #distance from spring mass center of gravity to rear axle [m] LENB + + #moments of inertia of sprung mass + p.I_Phi_s = unitConversion.lb_ft_sec2_IN_kg_m2(353.9445) #moment of inertia for sprung mass in roll [kg m^2] IXS + p.I_y_s = unitConversion.lb_ft_sec2_IN_kg_m2(1625.825) #moment of inertia for sprung mass in pitch [kg m^2] IYS + p.I_z = unitConversion.lb_ft_sec2_IN_kg_m2(1824.078) #moment of inertia for sprung mass in yaw [kg m^2] IZZ + p.I_xz_s = unitConversion.lb_ft_sec2_IN_kg_m2(0) #moment of inertia cross product [kg m^2] IXZ + + #suspension parameters + p.K_sf = unitConversion.lbs_ft_IN_N_m(2300) #suspension spring rate (front) [N/m] KSF + p.K_sdf = unitConversion.lb_sec_ft_IN_N_s_m(164.8335) #suspension damping rate (front) [N s/m] KSDF + p.K_sr = unitConversion.lbs_ft_IN_N_m(2680) #suspension spring rate (rear) [N/m] KSR + p.K_sdr = unitConversion.lb_sec_ft_IN_N_s_m(189.7866) #suspension damping rate (rear) [N s/m] KSDR + + #geometric parameters + p.T_f = unitConversion.ft_IN_m(5.165) #track width front [m] TRWF + p.T_r = unitConversion.ft_IN_m(5.065) #track width rear [m] TRWB + p.K_ras = unitConversion.lbs_ft_IN_N_m(12000) #lateral spring rate at compliant compliant pin joint between M_s and M_u [N/m] KRAS + + p.K_tsf = unitConversion.ft_lb_rad_IN_N_m_rad(-25038.92) #auxiliary torsion roll stiffness per axle (normally negative) (front) [N m/rad] KTSF + p.K_tsr = unitConversion.ft_lb_rad_IN_N_m_rad(-5702.369) #auxiliary torsion roll stiffness per axle (normally negative) (rear) [N m/rad] KTSR + p.K_rad = unitConversion.lb_sec_ft_IN_N_s_m(700) # damping rate at compliant compliant pin joint between M_s and M_u [N s/m] KRADP + p.K_zt = unitConversion.lbs_ft_IN_N_m(14565.6) # vertical spring rate of tire [N/m] TSPRINGR + + p.h_cg = unitConversion.ft_IN_m(2.453467) #center of gravity height of total mass [m] HCG (mainly required for conversion to other vehicle models) + p.h_raf = unitConversion.ft_IN_m(0) #height of roll axis above ground (front) [m] HRAF + p.h_rar = unitConversion.ft_IN_m(0) #height of roll axis above ground (rear) [m] HRAR + + p.h_s = unitConversion.ft_IN_m(2.639405) #M_s center of gravity above ground [m] HS + + p.I_uf = unitConversion.lb_ft_sec2_IN_kg_m2(37.08234) #moment of inertia for unsprung mass about x-axis (front) [kg m^2] IXUF + p.I_ur = unitConversion.lb_ft_sec2_IN_kg_m2(35.66033) #moment of inertia for unsprung mass about x-axis (rear) [kg m^2] IXUR + p.I_y_w = 1.7 #wheel inertia, from internet forum for 235/65 R 17 [kg m^2] + + p.K_lt = unitConversion.ft_lb_IN_m_N(1.7850283e-04) #lateral compliance rate of tire, wheel, and suspension, per tire [m/N] KLT + p.R_w = 0.344 #effective wheel/tire radius chosen as tire rolling radius RR taken from ADAMS documentation [m] + + #split of brake and engine torque + p.T_sb = 0.64 + p.T_se = 0 + + #suspension parameters + p.D_f = unitConversion.rad_ft_IN_rad_m(-0.1) #[rad/m] DF; modified from orig. paper due to stability issues when damping is ignored + p.D_r = unitConversion.rad_ft_IN_rad_m(-0.1) #[rad/m] DR; modified from orig. paper due to stability issues when damping is ignored + p.E_f = 0 #[needs conversion if nonzero] EF + p.E_r = 0 #[needs conversion if nonzero] ER + + + #tire parameters from ADAMS handbook + #longitudinal coefficients + p.tire.p_cx1 = 1.6411 #Shape factor Cfx for longitudinal force + p.tire.p_dx1 = 1.1739 #Longitudinal friction Mux at Fznom + p.tire.p_dx3 = 0 #Variation of friction Mux with camber + p.tire.p_ex1 = 0.46403 #Longitudinal curvature Efx at Fznom + p.tire.p_kx1 = 22.303 #Longitudinal slip stiffness Kfx/Fz at Fznom + p.tire.p_hx1 = 0.0012297 #Horizontal shift Shx at Fznom + p.tire.p_vx1 = -8.8098e-006 #Vertical shift Svx/Fz at Fznom + p.tire.r_bx1 = 13.276 #Slope factor for combined slip Fx reduction + p.tire.r_bx2 = -13.778 #Variation of slope Fx reduction with kappa + p.tire.r_cx1 = 1.2568 #Shape factor for combined slip Fx reduction + p.tire.r_ex1 = 0.65225 #Curvature factor of combined Fx + p.tire.r_hx1 = 0.0050722 #Shift factor for combined slip Fx reduction + + #lateral coefficients + p.tire.p_cy1 = 1.3507 #Shape factor Cfy for lateral forces + p.tire.p_dy1 = 1.0489 #Lateral friction Muy + p.tire.p_dy3 = -2.8821 #Variation of friction Muy with squared camber + p.tire.p_ey1 = -0.0074722 #Lateral curvature Efy at Fznom + p.tire.p_ky1 = -21.92 #Maximum value of stiffness Kfy/Fznom + p.tire.p_hy1 = 0.0026747 #Horizontal shift Shy at Fznom + p.tire.p_hy3 = 0.031415 #Variation of shift Shy with camber + p.tire.p_vy1 = 0.037318 #Vertical shift in Svy/Fz at Fznom + p.tire.p_vy3 = -0.32931 #Variation of shift Svy/Fz with camber + p.tire.r_by1 = 7.1433 #Slope factor for combined Fy reduction + p.tire.r_by2 = 9.1916 #Variation of slope Fy reduction with alpha + p.tire.r_by3 = -0.027856 #Shift term for alpha in slope Fy reduction + p.tire.r_cy1 = 1.0719 #Shape factor for combined Fy reduction + p.tire.r_ey1 = -0.27572 #Curvature factor of combined Fy + p.tire.r_hy1 = 5.7448e-006 #Shift factor for combined Fy reduction + p.tire.r_vy1 = -0.027825 #Kappa induced side force Svyk/Muy*Fz at Fznom + p.tire.r_vy3 = -0.27568 #Variation of Svyk/Muy*Fz with camber + p.tire.r_vy4 = 12.12 #Variation of Svyk/Muy*Fz with alpha + p.tire.r_vy5 = 1.9 #Variation of Svyk/Muy*Fz with kappa + p.tire.r_vy6 = -10.704 #Variation of Svyk/Muy*Fz with atan(kappa) + + return p + +#------------- END OF CODE -------------- diff --git a/Python/readme.txt b/Python/readme.txt new file mode 100644 index 0000000..8ea5ee8 --- /dev/null +++ b/Python/readme.txt @@ -0,0 +1,19 @@ +To execute a test function, which produces the plots of the vehicle models documentation, run 'testVehicle.py'. + +Initialization of models------------------------------------------ +kinematic single-track model: init_KS.py +single-track model: init_ST.py +multi-body model: init_MB.py +------------------------------------------------------------------ + +Parameter sets---------------------------------------------------- +Ford Escort: parameters_vehicle1.py +BMW 320i: parameters_vehicle2.py +VW Vanagon: parameters_vehicle3.py +------------------------------------------------------------------ + +Vehicle models---------------------------------------------------- +kinematic single-track model: vehicleDynamics_KS.py +single-track model: vehicleDynamics_ST.py +multi-body model: vehicleDynamics_MB.py +------------------------------------------------------------------ diff --git a/Python/testVehicle.py b/Python/testVehicle.py new file mode 100644 index 0000000..bcc7fa9 --- /dev/null +++ b/Python/testVehicle.py @@ -0,0 +1,190 @@ +from parameters_vehicle1 import parameters_vehicle1 +from init_KS import init_KS +from init_ST import init_ST +from init_MB import init_MB +from vehicleDynamics_KS import vehicleDynamics_KS +from vehicleDynamics_ST import vehicleDynamics_ST +from vehicleDynamics_MB import vehicleDynamics_MB +from scipy.integrate import odeint +import numpy +import matplotlib.pyplot as plt + + +def func_KS(x, t, u, p): + f = vehicleDynamics_KS(x, u, p) + return f + + +def func_ST(x, t, u, p): + f = vehicleDynamics_ST(x, u, p) + return f + + +def func_MB(x, t, u, p): + f = vehicleDynamics_MB(x, u, p) + return f + + +#load parameters +p = parameters_vehicle1() +g = 9.81 #[m/s^2] + +#set options -------------------------------------------------------------- +tStart = 0 #start time +tFinal = 1 #start time + +# vel0 = 15 +# Psi0 = 0.1 +# dotPsi0 = -0.1 +# beta0 = 0.05 +# sy0 = 1 +vel0 = 15 +Psi0 = 0 +dotPsi0 = 0 +beta0 = 0 +sy0 = 0 +initialState = [0,sy0,vel0,Psi0,dotPsi0,beta0] #initial state for simulation +x0_KS = init_KS(initialState, p) #initial state for kinematic single-track model +x0_ST = init_ST(initialState, p) #initial state for single-track model +x0_MB = init_MB(initialState, p) #initial state for multi-body model +#-------------------------------------------------------------------------- +# + +t = numpy.arange(0,tFinal, 0.01) +u = [0, 0] +x = odeint(func_KS, x0_KS, t, args=(u, p)) + +print(x) + +t = numpy.arange(0,tFinal, 0.01) +u = [0, 5] +x = odeint(func_KS, x0_KS, t, args=(u, p)) + +print(x) + +#set input: rolling car (velocity should stay constant) +t = numpy.arange(0,tFinal, 0.01) +u = [0, 0] +print(x0_MB) +#simulate car +x = odeint(func_MB, x0_MB, t, args=(u, p)) +#plot velocity +plt.plot(t, [tmp[3] for tmp in x]) +plt.show() + +#set input: braking car (wheel spin and velocity should decrease similar wheel spin) +v_delta = 0.15 +acc = -0.7*g +u = [v_delta, acc] +#simulate car +x_brake = odeint(func_MB, x0_MB, t, args=(u, p)) +#position +plt.plot([tmp[0] for tmp in x_brake], [tmp[1] for tmp in x_brake]) +plt.show() +# velocity +plt.plot(t, [tmp[3] for tmp in x_brake]) +plt.show() +# wheel spin +plt.plot(t, [tmp[23] for tmp in x_brake]) +plt.plot(t, [tmp[24] for tmp in x_brake]) +plt.plot(t, [tmp[25] for tmp in x_brake]) +plt.plot(t, [tmp[26] for tmp in x_brake]) +plt.show() +# pitch +plt.plot(t, [tmp[8] for tmp in x_brake]) +plt.show() + +#set input: accelerating car (wheel spin and velocity should increase more wheel spin at rear) +v_delta = 0.15 +acc = 0.63*g +u = [v_delta, acc] +#simulate car +x_acc = odeint(func_MB, x0_MB, t, args=(u, p)) +#position +plt.plot([tmp[0] for tmp in x_acc], [tmp[1] for tmp in x_acc]) +plt.show() +# velocity +plt.plot(t, [tmp[3] for tmp in x_acc]) +plt.show() +# wheel spin +plt.plot(t, [tmp[23] for tmp in x_acc]) +plt.plot(t, [tmp[24] for tmp in x_acc]) +plt.plot(t, [tmp[25] for tmp in x_acc]) +plt.plot(t, [tmp[26] for tmp in x_acc]) +plt.show() +# pitch +plt.plot(t, [tmp[8] for tmp in x_acc]) +plt.show() +#orientation +plt.plot(t, [tmp[4] for tmp in x_acc]) +plt.show() + + +#steering to left +v_delta = 0.15 +u = [v_delta, 0] + +#simulate full car +x_left = odeint(func_MB, x0_MB, t, args=(u, p)) + +#simulate single-track model +x_left_st = odeint(func_ST, x0_ST, t, args=(u, p)) + +#simulate kinematic single-track model +x_left_ks = odeint(func_KS, x0_KS, t, args=(u, p)) + +#position +plt.plot([tmp[0] for tmp in x_left], [tmp[1] for tmp in x_left]) +plt.plot([tmp[0] for tmp in x_left_st], [tmp[1] for tmp in x_left_st]) +plt.plot([tmp[0] for tmp in x_left_ks], [tmp[1] for tmp in x_left_ks]) +plt.show() +#orientation +plt.plot(t, [tmp[4] for tmp in x_left]) +plt.plot(t, [tmp[4] for tmp in x_left_st]) +plt.plot(t, [tmp[4] for tmp in x_left_ks]) +plt.show() +#steering +plt.plot(t, [tmp[2] for tmp in x_left]) +plt.plot(t, [tmp[2] for tmp in x_left_st]) +plt.plot(t, [tmp[2] for tmp in x_left_ks]) +plt.show() +#yaw rate +plt.plot(t, [tmp[5] for tmp in x_left]) +plt.plot(t, [tmp[5] for tmp in x_left_st]) +plt.show() +#slip angle +plt.plot(t, [tmp[10]/tmp[3] for tmp in x_left]) +plt.plot(t, [tmp[6] for tmp in x_left_st]) +plt.show() + +# figure # wheel spin +# hold on +# plot(t_acc,x_acc(:,24)) +# plot(t_acc,x_acc(:,25)) +# plot(t_acc,x_acc(:,26)) +# plot(t_acc,x_acc(:,27)) + + +#compare position for braking/normal +#position +plt.plot([tmp[0] for tmp in x_left], [tmp[1] for tmp in x_left]) +plt.plot([tmp[0] for tmp in x_brake], [tmp[1] for tmp in x_brake]) +plt.plot([tmp[0] for tmp in x_acc], [tmp[1] for tmp in x_acc]) +plt.show() +#compare slip angles +plt.plot(t, [tmp[10]/tmp[3] for tmp in x_left]) +plt.plot(t, [tmp[10]/tmp[3] for tmp in x_brake]) +plt.plot(t, [tmp[10]/tmp[3] for tmp in x_acc]) +plt.show() +#orientation +plt.plot(t, [tmp[4] for tmp in x_left]) +plt.plot(t, [tmp[4] for tmp in x_brake]) +plt.plot(t, [tmp[4] for tmp in x_acc]) +plt.show() +#pitch +plt.plot(t, [tmp[8] for tmp in x_left]) +plt.plot(t, [tmp[8] for tmp in x_brake]) +plt.plot(t, [tmp[8] for tmp in x_acc]) +plt.show() + +#------------- END OF CODE -------------- diff --git a/Python/tireModel.py b/Python/tireModel.py new file mode 100644 index 0000000..29912ee --- /dev/null +++ b/Python/tireModel.py @@ -0,0 +1,106 @@ +import math + +#sign function +def sign(x): + if x > 0: + return 1 + elif x < 0: + return -1 + else: + return 0 + +#longitudinal tire forces +def mFormulaLongitudinal(kappa, gamma, F_z, p): + + #turn slip is neglected, so xi_i=1 + #all scaling factors lambda = 1 + + #coordinate system transformation + kappa = -kappa + + S_hx = p.p_hx1 + S_vx = F_z*p.p_vx1 + + kappa_x = kappa + S_hx + mu_x = p.p_dx1*(1-p.p_dx3*gamma**2) + + C_x = p.p_cx1 + D_x = mu_x*F_z + E_x = p.p_ex1 + K_x = F_z*p.p_kx1 + B_x = K_x/(C_x*D_x) + + #magic tire formula + return D_x*math.sin(C_x*math.atan(B_x*kappa_x - E_x*(B_x*kappa_x - math.atan(B_x*kappa_x))) + S_vx) + + +#lateral tire forces +def mFormulaLateral(alpha, gamma, F_z, p): + + #turn slip is neglected, so xi_i=1 + #all scaling factors lambda = 1 + + #coordinate system transformation + #alpha = -alpha + + S_hy = sign(gamma)*(p.p_hy1 + p.p_hy3*math.fabs(gamma)) + S_vy = sign(gamma)*F_z*(p.p_vy1 + p.p_vy3*math.fabs(gamma)) + + alpha_y = alpha + S_hy + mu_y = p.p_dy1*(1-p.p_dy3*gamma**2) + + C_y = p.p_cy1 + D_y = mu_y*F_z + E_y = p.p_ey1 + K_y = F_z*p.p_ky1 #simplify K_y0 to p.p_ky1*F_z + B_y = K_y/(C_y*D_y) + + #magic tire formula + F_y = D_y*math.sin(C_y*math.atan(B_y*alpha_y - E_y*(B_y*alpha_y - math.atan(B_y*alpha_y)))) + S_vy + + res = [] + res.append(F_y) + res.append(mu_y) + return res + + +#longitudinal tire forces for combined slip +def mFormulaLongitudinalComb(kappa, alpha, F0_x, p): + + #turn slip is neglected, so xi_i=1 + #all scaling factors lambda = 1 + + S_hxalpha = p.r_hx1 + + alpha_s = alpha + S_hxalpha + + B_xalpha = p.r_bx1*math.cos(math.atan(p.r_bx2*kappa)) + C_xalpha = p.r_cx1 + E_xalpha = p.r_ex1 + D_xalpha = F0_x/(math.cos(C_xalpha*math.atan(B_xalpha*S_hxalpha - E_xalpha*(B_xalpha*S_hxalpha - math.atan(B_xalpha*S_hxalpha))))) + + #magic tire formula + return D_xalpha*math.cos(C_xalpha*math.atan(B_xalpha*alpha_s - E_xalpha*(B_xalpha*alpha_s - math.atan(B_xalpha*alpha_s)))) + + + +#longitudinal tire forces for combined slip +def mFormulaLateralComb(kappa, alpha, gamma, mu_y, F_z, F0_y, p): + + #turn slip is neglected, so xi_i=1 + #all scaling factors lambda = 1 + + S_hykappa = p.r_hy1 + + kappa_s = kappa + S_hykappa + + B_ykappa = p.r_by1*math.cos(math.atan(p.r_by2*(alpha-p.r_by3))) + C_ykappa = p.r_cy1 + E_ykappa = p.r_ey1 + D_ykappa = F0_y/(math.cos(C_ykappa*math.atan(B_ykappa*S_hykappa - E_ykappa*(B_ykappa*S_hykappa - math.atan(B_ykappa*S_hykappa))))) + + D_vykappa = mu_y*F_z*(p.r_vy1 + p.r_vy3*gamma) * math.cos(math.atan(p.r_vy4*alpha)) + S_vykappa = D_vykappa*math.sin(p.r_vy5*math.atan(p.r_vy6*kappa)) + + #magic tire formula + return D_ykappa*math.cos(C_ykappa*math.atan(B_ykappa*kappa_s - E_ykappa*(B_ykappa*kappa_s - math.atan(B_ykappa*kappa_s)))) + S_vykappa diff --git a/Python/tireParameters.py b/Python/tireParameters.py new file mode 100644 index 0000000..e5c8d0a --- /dev/null +++ b/Python/tireParameters.py @@ -0,0 +1,38 @@ +class TireParameters(): + def __init__(self): + #tire parameters from ADAMS handbook + #longitudinal coefficients + self.p_cx1 = [] #Shape factor Cfx for longitudinal force + self.p_dx1 = [] #Longitudinal friction Mux at Fznom + self.p_dx3 = [] #Variation of friction Mux with camber + self.p_ex1 = [] #Longitudinal curvature Efx at Fznom + self.p_kx1 = [] #Longitudinal slip stiffness Kfx/Fz at Fznom + self.p_hx1 = [] #Horizontal shift Shx at Fznom + self.p_vx1 = [] #Vertical shift Svx/Fz at Fznom + self.r_bx1 = [] #Slope factor for combined slip Fx reduction + self.r_bx2 = [] #Variation of slope Fx reduction with kappa + self.r_cx1 = [] #Shape factor for combined slip Fx reduction + self.r_ex1 = [] #Curvature factor of combined Fx + self.r_hx1 = [] #Shift factor for combined slip Fx reduction + + #lateral coefficients + self.p_cy1 = [] #Shape factor Cfy for lateral forces + self.p_dy1 = [] #Lateral friction Muy + self.p_dy3 = [] #Variation of friction Muy with squared camber + self.p_ey1 = [] #Lateral curvature Efy at Fznom + self.p_ky1 = [] #Maximum value of stiffness Kfy/Fznom + self.p_hy1 = [] #Horizontal shift Shy at Fznom + self.p_hy3 = [] #Variation of shift Shy with camber + self.p_vy1 = [] #Vertical shift in Svy/Fz at Fznom + self.p_vy3 = [] #Variation of shift Svy/Fz with camber + self.r_by1 = [] #Slope factor for combined Fy reduction + self.r_by2 = [] #Variation of slope Fy reduction with alpha + self.r_by3 = [] #Shift term for alpha in slope Fy reduction + self.r_cy1 = [] #Shape factor for combined Fy reduction + self.r_ey1 = [] #Curvature factor of combined Fy + self.r_hy1 = [] #Shift factor for combined Fy reduction + self.r_vy1 = [] #Kappa induced side force Svyk/Muy*Fz at Fznom + self.r_vy3 = [] #Variation of Svyk/Muy*Fz with camber + self.r_vy4 = [] #Variation of Svyk/Muy*Fz with alpha + self.r_vy5 = [] #Variation of Svyk/Muy*Fz with kappa + self.r_vy6 = [] #Variation of Svyk/Muy*Fz with atan(kappa) diff --git a/Python/unitConversions/__init__.py b/Python/unitConversions/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/Python/unitConversions/unitConversion.py b/Python/unitConversions/unitConversion.py new file mode 100644 index 0000000..92d625e --- /dev/null +++ b/Python/unitConversions/unitConversion.py @@ -0,0 +1,95 @@ +def lb_sec2_ft_IN_kg(prev_val): + +# 1lb is 4.4482216152605 N +# 1ft is 0.3048 m + + return 4.4482216152605/0.3048*prev_val + + +def ft_IN_m(prev_val): +#original: [ft] +#new: [m] + +# 1ft is 0.3048 m + + return 0.3048*prev_val + + +def lb_ft_sec2_IN_kg_m2(prev_val): + +#[kg m^2] = [N m sec^2] + +# 1lb is 4.4482216152605 N +# 1ft is 0.3048 m + + return 4.4482216152605*0.3048*prev_val + + +def rad_ft_lb_IN_rad_sec2_kg_m2(prev_val): + +#original: [rad/(ft lb)] +#new: [rad/(N m)] = [rad s^2/(kg m^2)] + +# 1lb is 4.4482216152605 N +# 1ft is 0.3048 m + + return 1/(4.4482216152605*0.3048)*prev_val + + +def ft2_IN_m2(prev_val): +#original: [ft^2] +#new: [m^2] + +# 1ft is 0.3048 m + + return pow(0.3048, 2)*prev_val + + +def lbs_ft_IN_N_m(prev_val): +#original: [lbs/ft] +#new: [N/m] + +# 1lbs is 0.45359237 kg +# 1kg is around 9.81 N assuming being close to sea level +# 1ft is 0.3048 m + + return 0.45359237*9.81/0.3048*prev_val + + +def lb_sec_ft_IN_N_s_m(prev_val): +#original: [lb sec/ft] +#new: [N sec/m] + +# 1lb is 4.4482216152605 N +# 1ft is 0.3048 m + + return 4.4482216152605/0.3048*prev_val + + +def ft_lb_rad_IN_N_m_rad(prev_val): +#original: [lb ft/rad] +#new: [N m/rad] + +# 1lb is 4.4482216152605 N +# 1ft is 0.3048 m + + return 4.4482216152605*0.3048*prev_val + + +def ft_lb_IN_m_N(prev_val): +#original: [ft/lb] +#new: [m/N] + +# 1lb is 4.4482216152605 N +# 1ft is 0.3048 m + + return 0.3048/4.4482216152605*prev_val + + +def rad_ft_IN_rad_m(prev_val): +#original: [rad/ft] +#new: [rad/m] + +# 1ft is 0.3048 m + + return 1/0.3048*prev_val diff --git a/Python/vehicleDynamics_KS.py b/Python/vehicleDynamics_KS.py new file mode 100644 index 0000000..eedc8ed --- /dev/null +++ b/Python/vehicleDynamics_KS.py @@ -0,0 +1,54 @@ +import math + +def vehicleDynamics_KS(x,u,p): + # vehicleDynamics_KS - kinematic single-track vehicle dynamics + # + # Syntax: + # f = vehicleDynamics_KS(x,u,p) + # + # Inputs: + # x - vehicle state vector + # u - vehicle input vector + # p - vehicle parameter vector + # + # Outputs: + # f - right-hand side of differential equations + # + # Example: + # + # Other m-files required: none + # Subfunctions: none + # MAT-files required: none + # + # See also: --- + + # Author: Matthias Althoff + # Written: 12-January-2017 + # Last update: --- + # Last revision:--- + + #------------- BEGIN CODE -------------- + + #create equivalent kinematic single-track parameters + l = p.a + p.b + + #states + #x1 = x-position in a global coordinate system + #x2 = y-position in a global coordinate system + #x3 = steering angle of front wheels + #x4 = velocity in x-direction + #x5 = yaw angle + + #u1 = steering angle velocity of front wheels + #u2 = longitudinal acceleration + + #system dynamics + f = [x[3]*math.cos(x[4]), + x[3]*math.sin(x[4]), + u[0], + u[1], + x[3]/l*math.tan(x[2])] + + return f + + #------------- END OF CODE -------------- diff --git a/Python/vehicleDynamics_MB.py b/Python/vehicleDynamics_MB.py new file mode 100644 index 0000000..504d7bb --- /dev/null +++ b/Python/vehicleDynamics_MB.py @@ -0,0 +1,287 @@ +import tireModel +import math + +def vehicleDynamics_MB(x,u,p): + # vehicleDynamics_MB - multi-body vehicle dynamics based on the DOT + # (department of transportation) vehicle dynamics + # + # Syntax: + # f = vehicleDynamics_MB(t,x,u,p) + # + # Inputs: + # x - vehicle state vector + # u - vehicle input vector + # p - vehicle parameter vector + # + # Outputs: + # f - right-hand side of differential equations + # + # Example: + # + # See also: --- + + # Author: Matthias Althoff + # Written: 05-January-2017 + # Last update: --- + # Last revision:--- + + #------------- BEGIN CODE -------------- + + # set gravity constant + g = 9.81 #[m/s^2] + + #states + #x1 = x-position in a global coordinate system + #x2 = y-position in a global coordinate system + #x3 = steering angle of front wheels + #x4 = velocity in x-direction + #x5 = yaw angle + #x6 = yaw rate + + #x7 = roll angle + #x8 = roll rate + #x9 = pitch angle + #x10 = pitch rate + #x11 = velocity in y-direction + #x12 = z-position + #x13 = velocity in z-direction + + #x14 = roll angle front + #x15 = roll rate front + #x16 = velocity in y-direction front + #x17 = z-position front + #x18 = velocity in z-direction front + + #x19 = roll angle rear + #x20 = roll rate rear + #x21 = velocity in y-direction rear + #x22 = z-position rear + #x23 = velocity in z-direction rear + + #x24 = left front wheel angular speed + #x25 = right front wheel angular speed + #x26 = left rear wheel angular speed + #x27 = right rear wheel angular speed + + #x28 = delta_y_f + #x29 = delta_y_r + + #u1 = steering angle velocity of front wheels + #u2 = acceleration + + + #compute slip angle at cg + beta = math.atan(x[10]/x[3]) + vel = math.sqrt(x[3]**2 + x[10]**2) + + #vertical tire forces + F_z_LF = (x[16] + p.R_w*(math.cos(x[13]) - 1) - 0.5*p.T_f*math.sin(x[13]))*p.K_zt + F_z_RF = (x[16] + p.R_w*(math.cos(x[13]) - 1) + 0.5*p.T_f*math.sin(x[13]))*p.K_zt + F_z_LR = (x[21] + p.R_w*(math.cos(x[18]) - 1) - 0.5*p.T_r*math.sin(x[18]))*p.K_zt + F_z_RR = (x[21] + p.R_w*(math.cos(x[18]) - 1) + 0.5*p.T_r*math.sin(x[18]))*p.K_zt + + #obtain individual tire speeds + u_w_lf = (x[3] + 0.5*p.T_f*x[5])*math.cos(x[2]) + (x[10] + p.a*x[5])*math.sin(x[2]) + u_w_rf = (x[3] - 0.5*p.T_f*x[5])*math.cos(x[2]) + (x[10] + p.a*x[5])*math.sin(x[2]) + u_w_lr = x[3] + 0.5*p.T_r*x[5] + u_w_rr = x[3] - 0.5*p.T_r*x[5] + + #compute longitudinal slip + s_lf = 1 - p.R_w*x[23]/u_w_lf + s_rf = 1 - p.R_w*x[24]/u_w_rf + s_lr = 1 - p.R_w*x[25]/u_w_lr + s_rr = 1 - p.R_w*x[26]/u_w_rr + + #lateral slip angles + alpha_LF = math.atan((x[10] + p.a*x[5] - x[14]*(p.R_w - x[16]))/(x[3] + 0.5*p.T_f*x[5])) - x[2] + alpha_RF = math.atan((x[10] + p.a*x[5] - x[14]*(p.R_w - x[16]))/(x[3] - 0.5*p.T_f*x[5])) - x[2] + alpha_LR = math.atan((x[10] - p.b*x[5] - x[19]*(p.R_w - x[21]))/(x[3] + 0.5*p.T_r*x[5])) + alpha_RR = math.atan((x[10] - p.b*x[5] - x[19]*(p.R_w - x[21]))/(x[3] - 0.5*p.T_r*x[5])) + + #auxiliary suspension movement + z_SLF = (p.h_s - p.R_w + x[16] - x[11])/math.cos(x[6]) - p.h_s + p.R_w + p.a*x[8] + 0.5*(x[6] - x[13])*p.T_f + z_SRF = (p.h_s - p.R_w + x[16] - x[11])/math.cos(x[6]) - p.h_s + p.R_w + p.a*x[8] - 0.5*(x[6] - x[13])*p.T_f + z_SLR = (p.h_s - p.R_w + x[21] - x[11])/math.cos(x[6]) - p.h_s + p.R_w - p.b*x[8] + 0.5*(x[6] - x[18])*p.T_r + z_SRR = (p.h_s - p.R_w + x[21] - x[11])/math.cos(x[6]) - p.h_s + p.R_w - p.b*x[8] - 0.5*(x[6] - x[18])*p.T_r + + dz_SLF = x[17] - x[12] + p.a*x[9] + 0.5*(x[7] - x[14])*p.T_f + dz_SRF = x[17] - x[12] + p.a*x[9] - 0.5*(x[7] - x[14])*p.T_f + dz_SLR = x[22] - x[12] - p.b*x[9] + 0.5*(x[7] - x[19])*p.T_r + dz_SRR = x[22] - x[12] - p.b*x[9] - 0.5*(x[7] - x[19])*p.T_r + + #camber angles + gamma_LF = x[6] + p.D_f*z_SLF + p.E_f*(z_SLF)**2 + gamma_RF = x[6] - p.D_f*z_SRF - p.E_f*(z_SRF)**2 + gamma_LR = x[6] + p.D_r*z_SLR + p.E_r*(z_SLR)**2 + gamma_RR = x[6] - p.D_r*z_SRR - p.E_r*(z_SRR)**2 + + #compute longitudinal tire forces using the magic formula for pure slip + F0_x_LF = tireModel.mFormulaLongitudinal(s_lf, gamma_LF, F_z_LF, p.tire) + F0_x_RF = tireModel.mFormulaLongitudinal(s_rf, gamma_RF, F_z_RF, p.tire) + F0_x_LR = tireModel.mFormulaLongitudinal(s_lr, gamma_LR, F_z_LR, p.tire) + F0_x_RR = tireModel.mFormulaLongitudinal(s_rr, gamma_RR, F_z_RR, p.tire) + + #compute lateral tire forces using the magic formula for pure slip + res = tireModel.mFormulaLateral(alpha_LF, gamma_LF, F_z_LF, p.tire) + F0_y_LF = res[0] + mu_y_LF = res[1] + res = tireModel.mFormulaLateral(alpha_RF, gamma_RF, F_z_RF, p.tire) + F0_y_RF = res[0] + mu_y_RF = res[1] + res = tireModel.mFormulaLateral(alpha_LR, gamma_LR, F_z_LR, p.tire) + F0_y_LR = res[0] + mu_y_LR = res[1] + res = tireModel.mFormulaLateral(alpha_RR, gamma_RR, F_z_RR, p.tire) + F0_y_RR = res[0] + mu_y_RR = res[1] + + #compute longitudinal tire forces using the magic formula for combined slip + F_x_LF = tireModel.mFormulaLongitudinalComb(s_lf, alpha_LF, F0_x_LF, p.tire) + F_x_RF = tireModel.mFormulaLongitudinalComb(s_rf, alpha_RF, F0_x_RF, p.tire) + F_x_LR = tireModel.mFormulaLongitudinalComb(s_lr, alpha_LR, F0_x_LR, p.tire) + F_x_RR = tireModel.mFormulaLongitudinalComb(s_rr, alpha_RR, F0_x_RR, p.tire) + + #compute lateral tire forces using the magic formula for combined slip + F_y_LF = tireModel.mFormulaLateralComb(s_lf, alpha_LF, gamma_LF, mu_y_LF, F_z_LF, F0_y_LF, p.tire) + F_y_RF = tireModel.mFormulaLateralComb(s_rf, alpha_RF, gamma_RF, mu_y_RF, F_z_RF, F0_y_RF, p.tire) + F_y_LR = tireModel.mFormulaLateralComb(s_lr, alpha_LR, gamma_LR, mu_y_LR, F_z_LR, F0_y_LR, p.tire) + F_y_RR = tireModel.mFormulaLateralComb(s_rr, alpha_RR, gamma_RR, mu_y_RR, F_z_RR, F0_y_RR, p.tire) + + #auxiliary movements for compliant joint equations + delta_z_f = p.h_s - p.R_w + x[16] - x[11] + delta_z_r = p.h_s - p.R_w + x[21] - x[11] + + delta_phi_f = x[6] - x[13] + delta_phi_r = x[6] - x[18] + + dot_delta_phi_f = x[7] - x[14] + dot_delta_phi_r = x[7] - x[19] + + dot_delta_z_f = x[17] - x[12] + dot_delta_z_r = x[22] - x[12] + + dot_delta_y_f = x[10] + p.a*x[5] - x[15] + dot_delta_y_r = x[10] - p.b*x[5] - x[20] + + delta_f = delta_z_f*math.sin(x[6]) - x[27]*math.cos(x[6]) - (p.h_raf - p.R_w)*math.sin(delta_phi_f) + delta_r = delta_z_r*math.sin(x[6]) - x[28]*math.cos(x[6]) - (p.h_rar - p.R_w)*math.sin(delta_phi_r) + + dot_delta_f = (delta_z_f*math.cos(x[6]) + x[27]*math.sin(x[6]))*x[7] + dot_delta_z_f*math.sin(x[6]) - dot_delta_y_f*math.cos(x[6]) - (p.h_raf - p.R_w)*math.cos(delta_phi_f)*dot_delta_phi_f + dot_delta_r = (delta_z_r*math.cos(x[6]) + x[28]*math.sin(x[6]))*x[7] + dot_delta_z_r*math.sin(x[6]) - dot_delta_y_r*math.cos(x[6]) - (p.h_rar - p.R_w)*math.cos(delta_phi_r)*dot_delta_phi_r + + #compliant joint forces + F_RAF = delta_f*p.K_ras + dot_delta_f*p.K_rad + F_RAR = delta_r*p.K_ras + dot_delta_r*p.K_rad + + #auxiliary suspension forces (bump stop neglected squat/lift forces neglected) + F_SLF = p.m_s*g*p.b/(2*(p.a+p.b)) - z_SLF*p.K_sf - dz_SLF*p.K_sdf + (x[6] - x[13])*p.K_tsf/p.T_f + + F_SRF = p.m_s*g*p.b/(2*(p.a+p.b)) - z_SRF*p.K_sf - dz_SRF*p.K_sdf - (x[6] - x[13])*p.K_tsf/p.T_f + + F_SLR = p.m_s*g*p.a/(2*(p.a+p.b)) - z_SLR*p.K_sr - dz_SLR*p.K_sdr + (x[6] - x[18])*p.K_tsr/p.T_r + + F_SRR = p.m_s*g*p.a/(2*(p.a+p.b)) - z_SRR*p.K_sr - dz_SRR*p.K_sdr - (x[6] - x[18])*p.K_tsr/p.T_r + + + #auxiliary variables sprung mass + sumX = F_x_LR + F_x_RR + (F_x_LF + F_x_RF)*math.cos(x[2]) - (F_y_LF + F_y_RF)*math.sin(x[2]) + + sumN = (F_y_LF + F_y_RF)*p.a*math.cos(x[2]) + (F_x_LF + F_x_RF)*p.a*math.sin(x[2]) \ + + (F_y_RF - F_y_LF)*0.5*p.T_f*math.sin(x[2]) + (F_x_LF - F_x_RF)*0.5*p.T_f*math.cos(x[2]) \ + + (F_x_LR - F_x_RR)*0.5*p.T_r - (F_y_LR + F_y_RR)*p.b + + sumY_s = (F_RAF + F_RAR)*math.cos(x[6]) + (F_SLF + F_SLR + F_SRF + F_SRR)*math.sin(x[6]) + + sumL = 0.5*F_SLF*p.T_f + 0.5*F_SLR*p.T_r - 0.5*F_SRF*p.T_f - 0.5*F_SRR*p.T_r \ + - F_RAF/math.cos(x[6])*(p.h_s - x[11] - p.R_w + x[16] - (p.h_raf - p.R_w)*math.cos(x[13])) \ + - F_RAR/math.cos(x[6])*(p.h_s - x[11] - p.R_w + x[21] - (p.h_rar - p.R_w)*math.cos(x[18])) + + sumZ_s = (F_SLF + F_SLR + F_SRF + F_SRR)*math.cos(x[6]) - (F_RAF + F_RAR)*math.sin(x[6]) + + sumM_s = p.a*(F_SLF + F_SRF) - p.b*(F_SLR + F_SRR) + ((F_x_LF + F_x_RF)*math.cos(x[2]) \ + - (F_y_LF + F_y_RF)*math.sin(x[2]) + F_x_LR + F_x_RR)*(p.h_s - x[11]) + + #auxiliary variables unsprung mass + sumL_uf = 0.5*F_SRF*p.T_f - 0.5*F_SLF*p.T_f - F_RAF*(p.h_raf - p.R_w) \ + + F_z_LF*(p.R_w*math.sin(x[13]) + 0.5*p.T_f*math.cos(x[13]) - p.K_lt*F_y_LF) \ + - F_z_RF*(-p.R_w*math.sin(x[13]) + 0.5*p.T_f*math.cos(x[13]) + p.K_lt*F_y_RF) \ + - ((F_y_LF + F_y_RF)*math.cos(x[2]) + (F_x_LF + F_x_RF)*math.sin(x[2]))*(p.R_w - x[16]) + + sumL_ur = 0.5*F_SRR*p.T_r - 0.5*F_SLR*p.T_r - F_RAR*(p.h_rar - p.R_w) \ + + F_z_LR*(p.R_w*math.sin(x[18]) + 0.5*p.T_r*math.cos(x[18]) - p.K_lt*F_y_LR) \ + - F_z_RR*(-p.R_w*math.sin(x[18]) + 0.5*p.T_r*math.cos(x[18]) + p.K_lt*F_y_RR) \ + - (F_y_LR + F_y_RR)*(p.R_w - x[21]) + + sumZ_uf = F_z_LF + F_z_RF + F_RAF*math.sin(x[6]) - (F_SLF + F_SRF)*math.cos(x[6]) + + sumZ_ur = F_z_LR + F_z_RR + F_RAR*math.sin(x[6]) - (F_SLR + F_SRR)*math.cos(x[6]) + + sumY_uf = (F_y_LF + F_y_RF)*math.cos(x[2]) + (F_x_LF + F_x_RF)*math.sin(x[2]) \ + - F_RAF*math.cos(x[6]) - (F_SLF + F_SRF)*math.sin(x[6]) + + sumY_ur = (F_y_LR + F_y_RR) \ + - F_RAR*math.cos(x[6]) - (F_SLR + F_SRR)*math.sin(x[6]) + + + #dynamics common with single-track model + f = [] # init 'right hand side' + f.append(math.cos(beta + x[4])*vel) + f.append(math.sin(beta + x[4])*vel) + f.append(u[0]) + f.append(1/p.m*sumX + x[5]*x[10]) + f.append(x[5]) + f.append(1/(p.I_z - (p.I_xz_s)**2/p.I_Phi_s)*(sumN + p.I_xz_s/p.I_Phi_s*sumL)) + + + # remaining sprung mass dynamics + f.append(x[7]) + f.append(1/(p.I_Phi_s - (p.I_xz_s)**2/p.I_z)*(p.I_xz_s/p.I_z*sumN + sumL)) + f.append(x[9]) + f.append(1/p.I_y_s*sumM_s) + f.append(1/p.m_s*sumY_s - x[5]*x[3]) + f.append(x[12]) + f.append(g - 1/p.m_s*sumZ_s) + + #unsprung mass dynamics (front) + f.append(x[14]) + f.append(1/p.I_uf*sumL_uf) + f.append(1/p.m_uf*sumY_uf - x[5]*x[3]) + f.append(x[17]) + f.append(g - 1/p.m_uf*sumZ_uf) + + #unsprung mass dynamics (rear) + f.append(x[19]) + f.append(1/p.I_ur*sumL_ur) + f.append(1/p.m_ur*sumY_ur - x[5]*x[3]) + f.append(x[22]) + f.append(g - 1/p.m_ur*sumZ_ur) + + #convert acceleration input to brake and engine torque + if u[1]>0: + T_B = 0 + T_E = p.m*p.R_w*u[1] + else: + T_B = p.m*p.R_w*u[1] + T_E = 0 + + #wheel dynamics (p.T new parameter for torque splitting) + f.append(1/p.I_y_w*(-p.R_w*F_x_LF + 0.5*p.T_sb*T_B + 0.5*p.T_se*T_E)) + f.append(1/p.I_y_w*(-p.R_w*F_x_RF + 0.5*p.T_sb*T_B + 0.5*p.T_se*T_E)) + f.append(1/p.I_y_w*(-p.R_w*F_x_LR + 0.5*(1-p.T_sb)*T_B + 0.5*(1-p.T_se)*T_E)) + f.append(1/p.I_y_w*(-p.R_w*F_x_RR + 0.5*(1-p.T_sb)*T_B + 0.5*(1-p.T_se)*T_E)) + + #negative wheel spin forbidden + for iState in range(23, 26): + if x[iState]<0: + x[iState] = 0 + f[iState] = 0 + + #compliant joint equations + f.append(dot_delta_y_f) + f.append(dot_delta_y_r) + + + return f + + + #------------- END OF CODE -------------- diff --git a/Python/vehicleDynamics_ST.py b/Python/vehicleDynamics_ST.py new file mode 100644 index 0000000..1619dff --- /dev/null +++ b/Python/vehicleDynamics_ST.py @@ -0,0 +1,73 @@ +import math + +def vehicleDynamics_ST(x,u,p): + # vehicleDynamics_ST - single-track vehicle dynamics + # + # Syntax: + # f = vehicleDynamics_ST(x,u,p) + # + # Inputs: + # x - vehicle state vector + # u - vehicle input vector + # p - vehicle parameter vector + # + # Outputs: + # f - right-hand side of differential equations + # + # Example: + # + # Other m-files required: none + # Subfunctions: none + # MAT-files required: none + # + # See also: --- + + # Author: Matthias Althoff + # Written: 12-January-2017 + # Last update: --- + # Last revision:--- + + #------------- BEGIN CODE -------------- + + # set gravity constant + g = 9.81 #[m/s^2] + + #create equivalent bicycle parameters + mu = p.tire.p_dy1 + C_Sf = -p.tire.p_ky1/p.tire.p_dy1 + C_Sr = -p.tire.p_ky1/p.tire.p_dy1 + lf = p.a + lr = p.b + h = p.h_s + m = p.m + I = p.I_z + + #states + #x1 = x-position in a global coordinate system + #x2 = y-position in a global coordinate system + #x3 = steering angle of front wheels + #x4 = velocity in x-direction + #x5 = yaw angle + #x6 = yaw rate + #x7 = slip angle at vehicle center + + #u1 = steering angle velocity of front wheels + #u2 = longitudinal acceleration + + + #system dynamics + f = [x[3]*math.cos(x[6] + x[4]), + x[3]*math.sin(x[6] + x[4]), + u[0], + u[1], + x[5], + -mu*m/(x[3]*I*(lr+lf))*(lf**2*C_Sf*(g*lr-u[1]*h) + lr**2*C_Sr*(g*lf + u[1]*h))*x[5] \ + +mu*m/(I*(lr+lf))*(lr*C_Sr*(g*lf + u[1]*h) - lf*C_Sf*(g*lr - u[1]*h))*x[6] \ + +mu*m/(I*(lr+lf))*lf*C_Sf*(g*lr - u[1]*h)*x[2], + (mu/(x[3]**2*(lr+lf))*(C_Sr*(g*lf + u[1]*h)*lr - C_Sf*(g*lr - u[1]*h)*lf)-1)*x[5] \ + -mu/(x[3]*(lr+lf))*(C_Sr*(g*lf + u[1]*h) + C_Sf*(g*lr-u[1]*h))*x[6] \ + +mu/(x[3]*(lr+lf))*(C_Sf*(g*lr-u[1]*h))*x[2]] + + return f + + #------------- END OF CODE -------------- diff --git a/Python/vehicleParameters.py b/Python/vehicleParameters.py new file mode 100644 index 0000000..30a24ae --- /dev/null +++ b/Python/vehicleParameters.py @@ -0,0 +1,65 @@ +from tireParameters import TireParameters + +class VehicleParameters(): + def __init__(self): + #vehicle body dimensions + self.l = [] + self.w = [] + + #masses + self.m = [] + self.m_s = [] + self.m_uf = [] + self.m_ur = [] + + #axes distances + self.a = [] #distance from spring mass center of gravity to front axle [m] LENA + self.b = [] #distance from spring mass center of gravity to rear axle [m] LENB + + #moments of inertia of sprung mass + self.I_Phi_s = [] #moment of inertia for sprung mass in roll [kg m^2] IXS + self.I_y_s = [] #moment of inertia for sprung mass in pitch [kg m^2] IYS + self.I_z = [] #moment of inertia for sprung mass in yaw [kg m^2] IZZ + self.I_xz_s = [] #moment of inertia cross product [kg m^2] IXZ + + #suspension parameters + self.K_sf = [] #suspension spring rate (front) [N/m] KSF + self.K_sdf = [] #suspension damping rate (front) [N s/m] KSDF + self.K_sr = [] #suspension spring rate (rear) [N/m] KSR + self.K_sdr = [] #suspension damping rate (rear) [N s/m] KSDR + + #geometric parameters + self.T_f = [] #track width front [m] TRWF + self.T_r = [] #track width rear [m] TRWB + self.K_ras = [] #lateral spring rate at compliant compliant pin joint between M_s and M_u [N/m] KRAS + + self.K_tsf = [] #auxiliary torsion roll stiffness per axle (normally negative) (front) [N m/rad] KTSF + self.K_tsr = [] #auxiliary torsion roll stiffness per axle (normally negative) (rear) [N m/rad] KTSR + self.K_rad = [] # damping rate at compliant compliant pin joint between M_s and M_u [N s/m] KRADP + self.K_zt = [] # vertical spring rate of tire [N/m] TSPRINGR + + self.h_cg = [] #center of gravity height of total mass [m] HCG (mainly required for conversion to other vehicle models) + self.h_raf = [] #height of roll axis above ground (front) [m] HRAF + self.h_rar = [] #height of roll axis above ground (rear) [m] HRAR + + self.h_s = [] #M_s center of gravity above ground [m] HS + + self.I_uf = [] #moment of inertia for unsprung mass about x-axis (front) [kg m^2] IXUF + self.I_ur = [] #moment of inertia for unsprung mass about x-axis (rear) [kg m^2] IXUR + self.I_y_w = [] #wheel inertia, from internet forum for 235/65 R 17 [kg m^2] + + self.K_lt = [] #lateral compliance rate of tire, wheel, and suspension, per tire [m/N] KLT + self.R_w = [] #effective wheel/tire radius chosen as tire rolling radius RR taken from ADAMS documentation [m] + + #split of brake and engine torque + self.T_sb = [] + self.T_se = [] + + #suspension parameters + self.D_f = [] #[rad/m] DF + self.D_r = [] #[rad/m] DR + self.E_f = [] #[needs conversion if nonzero] EF + self.E_r = [] #[needs conversion if nonzero] ER + + #tire parameters + self.tire = TireParameters() diff --git a/README.md b/README.md index d89110c..d7c0a9e 100644 --- a/README.md +++ b/README.md @@ -2,4 +2,12 @@ This repository contains all vehicle models of the [CommonRoad benchmarks](https://commonroad.in.tum.de/). -We provide implementation examples in MATLAB and Python, routines to convert initial states and parameters, simulation examples to demonstrate the advantages of more complicated models, and a detailed documentation. \ No newline at end of file +We provide implementation examples in MATLAB and Python, routines to convert initial states and parameters, simulation examples to demonstrate the advantages of more complicated models, and a detailed documentation. + +## Contribute + +If you want to contribute new vehicle models, you can create a merge request or contact us per [e-mail](mailto:commonroad-i06@in.tum.de). + +## References + +If you use CommonRoad, please cite *[M. Althoff, M. Koschi, and S. Manzinger, ''CommonRoad: Composable Benchmarks for Motion Planning on Roads,'' in Proc. of the IEEE Intelligent Vehicles Symposium, 2017, pp. 719-726](http://mediatum.ub.tum.de/doc/1379638/776321.pdf)*. \ No newline at end of file diff --git a/vehicleModels_commonRoad.pdf b/vehicleModels_commonRoad.pdf new file mode 100644 index 0000000000000000000000000000000000000000..762ef77642db239170d60869c910017ea83b6c2e GIT binary patch literal 360690 zcma&tLy#~)nJGNyLsE*1pr|4EeS#Vl=HOq~em#cT{+OhrtM?M+Pi z_@JC!oJnmsW{aFL;+2ox$NCw)GcnycpN(~T0O1^-g};`8Wleel!d_30OPN_Boa zJvtIj@QYeBcX06zSmoG{+aWkJ4fsFN`r_wDEZKzqfa;)XToWf9~#jF5%7( z{rZ${^!cBu*&zr;-`57%qrbqT@6hPeN3GJibTbJH_BbHEQDgCR2srQfG`2nO9X?K1 zwvtD3^V6Ih&+4E1y5esS>cREt{~Fr=3_f=BE?V`dnBVuw4~0VnF=NQ?EmHL0v^eX# zn)P7ByefU(aF8)fU>fyAhw$?kO%Y~0Z@=_}kaxpAwXjxMFxE3_I6cDvQ~&YJg%lN|AzxuqBP7rkj+|%n;`f7*$@{i}O;J$Uvt1 zzXl*Kod49S5oF$?T0L@8_EjaC14mPx<4jP1J5d+~VyRJiH>czpw}N!1p3PzuJ7=4} z!mmFa_rz$OAEY5mHL5M>q~Hc1Qq7X*v(26wz?XAc(ms`h=Vz;KVJB=-Sd;XVbctZB 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