Brake-Based Wheel Speed Control Design of a Rear Wheel Open Differential Vehicle by Eli Jeon

AN ABSTRACT OF THE THESIS OF Eli Jeon for the degree of Master of Science in Mechanical Engineering presented on June 14, 2006 Title: Brake-Based Wheel Speed Control Design of a Rear Wheel Open Defferential Vehicle Abstract approved: John Schmitt A brake-based wheel speed control system for a rear-wheel drive vehicle is developed and simulated in this thesis The OSU mini-Baja vehicle team will use this study in the development and implementation of a similar system for upcoming competitions Vehicle submittals must differ to a specified degree from previous year’s designs, according to the Society of Automotive Engineers (SAE) competition guidelines The OSU team intends to satisfy this requirement by implementing an electronic traction control system, hereafter referred to as the Smart Brake System (SBS) The SBS design will not only enable OSU to satisfy SAE guidelines, but will reduce undesired drive torque distribution to the wheels The development of SBS is based on a rear-wheel drive, open-differential vehicle and turning dynamics data gathered by the 2004 OSU Baja team The vehicle model and the control system are designed and simulated using MatLab Brake-Based Wheel Speed Control Design of a Rear Wheel Open Differential Vehicle by Eli Jeon A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Presented June 14, 2006 Commencement June 2007 Master of Science thesis of Eli Jeon presented on June 14, 2006 APPROVED: Major Professor, representing Mechanical Engineering Head of the Department of Mechanical Engineering Dean of the Graduate School I understand that my thesis will become part of the permanent collection of Oregon State University libraries My signature below authorizes release of my thesis to any reader upon request Eli Jeon, Author ACKNOWLEDGEMENTS The author would like to thank the persons who provided support and encouragement throughout the pursuit of this project In particular: Dr Belinda Batten and Dr John Schmitt for guiding my efforts to code it into simulation, for providing inspiration by being excellent academic role models and for providing a helping hand; my officemates, roommates, and other friends for listening to me think outloud, for asking questions about the project, for keeping me informed about other areas of study and for making my time at OSU an enjoyable experience Thanks also to my family who provided this opportunity Thank you for standing by me through my educational career TABLE OF CONTENTS Page Introduction……………………………………………………….………………… 2 Background of SBS………………………………………………………………… Available Traction Control Systems………………………………………… Automobile Differentials…………………………………………………… Development of SBS………………………………………… …………………… 3.1 SBS platform…………………………………………………………… 3.2 Longitudinal vehicle motion……………………….…………………… 3.3 SBS test environment…………………………………………………… 12 3.4 Controllability……………………………………… ………………… 13 3.5 Desired wheel speeds……………………………………… ………… 14 3.6 Model following control method……………………….……………… 22 3.7 Simulation of SBS in a linear vehicle model…………………………… 25 Simulation Results ……………………………………………………………… … 26 Discussion ……………………………………………………………………… … 53 Conclusion and Future Work….………………………………………………… … 59 References ………………………………………………………………………… 60 Appendices ………………………………………………………….……………… 61 - Appendix A: Smart Brake System simulation code……………… …62 LIST OF FIGURES Figure Page Fig.1 Vehicle turning geometry……………………………………….….6 Fig.2 Free-body diagram of the vehicle………………….……………….8 Fig.3 Quarter model of the vehicle wheels……………………………… Fig.4 Simplified Pacejka model………………………………………….11 Fig.5 DWSR as a function of steering wheel position………………… 17 Fig.6 Buffered DWSR as a function of steering wheel position…………18 Fig.7 Control loops of SBS………………………………………………22 Fig.10a Wheel Speeds for simulation #1.1………………………………27 Fig.10b Braking response for simulation#1.1……………………………28 10 Fig.10c DWSR v AWSR for simulation #1.1………………………… 28 11 Fig.10d Wheel speeds for simulation #1.2 …………………………… 29 12 Fig.10e Braking response for simulation #1.2………………………… 29 13 Fig.10f DWSR v AWSR for simulation #1.2 ………………………… 30 14 Fig.10g Wheel speeds for simulation #1.3 ………………………………31 15 Fig.10h Braking response for simulation #1.3………………………….32 16 Fig.10i DWSR v AWSR for simulation #1.3………………………… 32 17 Fig.10j Wheel speeds for simulation #1.4 ………………………………33 18 Fig.10k Braking response for simulation #1.4………………………….34 19 Fig.10l DWSR v AWSR for simulation #1.4………………………… 34 20 Fig 11a Wheel speeds for simulation #2.1 ……………………………36 LIST OF FIGURES (Continued) Figure Page 21 Fig 11b Wheel speeds for simulation #2.2…………………….……….37 22 Fig 11c DWSR v AWSR for simulation #2.2…………………………38 23 Fig 11d Wheel speeds for simulation #2.3 …………………………….39 24 Fig 11e Braking response for simulation #2.3…………………………40 25 Fig 11f DWSR v AWSR for simulation #2.3 ……………………… 40 26 Fig.12a Steering Wheel position for simulation #3.1………………… 42 27 Fig.12b Wheel speeds for simulation #3.1………………………………43 28 Fig.12c DWSR v AWSR for simulation #3.1………………….……….44 29 Fig.12d Wheel speeds for simulation #3.2…………… ………………45 30 Fig.12e Braking response for simulation #3.2………………………… 45 31 Fig.12f DWSR v AWSR for simulation #3.2……………….….….… 46 32 Fig.13a SW for simulation #4.1………………………………… … 48 33 Fig.13b Wheel speeds for simulation #4.1……………………… ……49 34 Fig.13c DWSR v AWSR for simulation #4.1…………………… … 49 35 Fig.13d Wheel speeds for simulation #4.2………………………… …50 36 Fig.13e Braking response for simulation #4.2…………………………51 37 Fig.13f DWSR v AWSR for simulation #4.2………………………….51 38 Drive torque distribution during no slip……………………… ………53 39 Traction coefficients during no slip…………………………… ….… 54 40 Uncontrolled drive torque distribution during slip……………… ……55 LIST OF FIGURES (Continued) Figure Page 41 Traction coefficients during uncontrolled slip …………………… … 56 42 Drive torque distribution with SBS control during slip………… …….57 43 Traction coefficients during SBS controlled slip……………….… … 58 LIST OF TABLES Table Page I: Turning radius with respect to steering wheel positions……………… … ……….16 II: DWSR with respect to vehicle geometry …………………………… ….………….16 III: DWSR with user-defined points …………………………………….………………17 IV: Desired wheel speed calculations …………………………………….….………….21 V: Vehicle specifications used in simulations …………………………………………26 LIST OF SYMBOLS English Symbols Fv aerodynamic and viscous forces on vehicle, [N ] FT, i longitudinal traction force between ground and the i-th wheel (the wheel under consideration), [N ] Fz, i a quarter of the normal force from the ground to the vehicle, [N ] N Td, i driving torque applied to the i-th wheel, ⎡⎢ ⎤⎥ ⎣m⎦ N Tb, i braking torque applied to the i-th wheel, ⎡⎢ ⎤⎥ ⎣m⎦ Tb, o braking torque applied to the o-th wheel (the wheel “opposite”, with ⎡N⎤ respect to the differential, of the wheel in consideration, ⎢ ⎥ ⎣m⎦ C v is the aerodynamic drag coefficient m mass of the vehicle, [kg] t track width of the vehicle [m] r effective rolling wheel radius, [m] V ⎡m⎤ longitudinal vehicle velocity, ⎢ ⎥ ⎢⎣ s ⎥⎦ g ⎡m⎤ acceleration of gravity, ⎢ ⎥ ⎢⎣ s ⎥⎦ 63 x(3) = x3val(i); if(x(2)==0 & x(3)==0) u(1)=0; u(2)=0; z1 = 0; z2 = 0; end % % Left hand turn or straight path cases if ( SW 0 & x(3)>0) AWSR = x(2)/x(3); end if(round(AWSR*100) == round(DWSR*100)), u(1)=0; u(2)=0; end if(round(AWSR*100) > round(DWSR*100)), DELTA = (x(2) - DWSR*x(3) ) / (1 + DWSR); z1 = x(2) - abs(DELTA); %Left wheel is slipping 64 z2 = x(3) + abs(DELTA); if(round(z1*100) < round(x(2)*100)), u(1) = Kx(1,1)*x(2) + Kx(1,2)*x(3) + Kz(1,1)*z1 + Kz(1,2)*z2; % u(2)= Kx(2,1)*x(2) + Kx(2,2)*x(3) + Kz(2,1)*z1 + Kz(2,2)*z2; u(2) = 0; if(u(1)>=600), u(1)=600; end if(u(1)=600), u(2)=600; end if(u(2)0 & x(3)>0) AWSR = x(3)/x(2); end if(round(AWSR*100)==round(DWSR*100)), u(1)=0; u(2)=0; end if(round(AWSR*100) < round(DWSR*100)), % Left is slipping DELTA = (-x(3) + DWSR*x(2) ) / (1 + DWSR); z1 = x(2) - abs(DELTA); z2 = x(3) + abs(DELTA); 66 if(round(z1*100) < round(x(2)*100)), u(1) = Kx(1,1)*x(2) + Kx(1,2)*x(3) + Kz(1,1)*z1 + Kz(1,2)*z2; u(2)=0; if(u(1)>=600), u(1)=600; end if(u(1) round(DWSR*100)), % Right is slipping DELTA = (x(3) - DWSR*x(2) ) / (1 + DWSR); z1 = x(2) + abs(DELTA); z2 = x(3) - abs(DELTA); if(round(z2*100) < round(x(3)*100)), u(1)=0; u(2)= Kx(2,1)*x(2)+ Kx(2,2)*x(3) + Kz(2,1)*z1 + Kz(2,2)*z2; if(u(2)>=600), u(2)=600; end if(u(1)0) AWSR = x(3)/x(2); end if(round(AWSR*100)==round(DWSR*100)), u(1)=0; u(2)=0; end if(round(AWSR*100) < round(DWSR*100)), % Left is slipping DELTA = (-x(3) + DWSR*x(2) ) / (1 + DWSR); z1 = x(2) - abs(DELTA); z2 = x(3) + abs(DELTA); if(round(z1*100) < round(x(2)*100)), u(1) = Kx(1,1)*x(2) + Kx(1,2)*x(3) + Kz(1,1)*z1 + Kz(1,2)*z2; u(2)=0; if(u(1)>=600), u(1)=600; end if(u(1) round(DWSR*100)), % Right is slipping DELTA = (x(3) - DWSR*x(2) ) / (1 + DWSR); z1 = x(2) + abs(DELTA); z2 = x(3) - abs(DELTA); if(round(z2*100) < round(x(3)*100)), u(1)=0; u(2)= Kx(2,1)*x(2)+ Kx(2,2)*x(3) + Kz(2,1)*z1 + Kz(2,2)*z2; if(u(2)>=600), u(2)=600; end if(u(1)