15 th USER CONFERENCE ROM, 15. - 16. November Vehicle Dynamics Control for a 4 Wheel Steering Prototype Car INSTITUT FÜR KRAFTFAHRWESEN AACHEN Dipl.-Ing. Alfred Pruckner Dipl.-Ing. Sven Fischer Overview - Control Strategy - Development Method - Observation - Control - Outlook
4 Wheel Steering Control Strategy Vehicle β Steady State Cornering 3 1-1 - dry road β -3 icy road -4 1 3 4 5 6 7 8 9 4 Wheel Steering Control Strategy Smaller Wheel Base at low velocity
4 Wheel Steering Control Strategy Larger Wheel Base at high velocity 4 Wheel Steering Control Strategy Minimize the vehicle side slip angle β β estimation control
Overview - Control Strategy - Development Method - Observation - Control - Outlook Virtual Prototyping Measurement Control information
Virtual Prototyping Interface und MATRIXx Full Vehicle Model MATRIXx Control algorithm Subroutine Template FORTRAN-files TIRSUB VARSUB C-Code Control algorithm discrete time interval Overview - Control Strategy - Development Method - Observation - Control - Outlook
Observation Linear l F - linear tire characteristics - small angles - centre of gravity on the street l R F R ψ. a y F F δ v v c sv + c sh β = m * v ψ lh * c sh lv * c Jz sv lv * c sv lh * c 1+ m * v lv * c sv lh * c sh Jz * v sh c sv β * + m * v ψ lv * c sv Jz c sh m * v lh * c J z sh δ * δ v h β BM. ψ BM = A + B u Observation Linear u y steering angle B yaw velocity lateral acceleration = A + B u A yaw velocity side slip angle
.5 1.5 1.5 -.5-1 Observation -1.5-4 5 6 7 8 9 1 11 1 3 yaw velocity [ /s] 1-1 - -3-4 4 5 6 7 8 9 1 11 1 1-1 - -3-4 4 5 6 7 8 9 1 11 1 8 Observation yaw velocity [ /s] 6 4 - -4-6 -8 4 5 6 7 8 9 1 11 1
Observation Linear Observer u y x = Ax+ Bu = A + B u+ L ( y ŷ) B A C ŷ + - ~ x = x = A x+ B u [ A + B u+ L( y ŷ) ] L ( ( ) n det I A LC ) = ( 1 ) ~ x = ( A LC)x ~ i= 1 λ i Observation Non-Linear Observer u y f x ( x,u) x = f(,u ) + (,u ) ( x ) x = f f x~ = x = x (,u ) ( x ) L(,u ) ( y ŷ) ( ) ( )( ) = f,u L,u y ŷ L C ŷ - + β F(,u ) = β ψ β β ψ l ψ l ψ 11 1 l l 1 ay β 1 a λ1 y = ψ λ
yaw velocity [ /s] 1-1 - -3 Luenberger Observer -4 4 5 6 7 8 9 1 11 1 Luenberger Observer 8 6 4 - -4-6 -8 4 5 6 7 8 9 1 11 1 Observation Luenberger Observer 1.5 1.5 -.5-1 -1.5 Luenberger Observer Observation - -.5 4 5 6 7 8 9 1 11 1 Wet Road Luenberger Observer 15 1 5-5 -1-15 4 5 6 7 8 9 1 11 1 Wet Road Luenberger Observer
3 Steady State Cornering 1-1 - -3 Luenberger Observer -4 1 3 4 5 6 7 8 9 Steady State Cornering Luenberger Observer 3 1-1 - -3-4 1 3 4 5 6 7 8 9 Observation Luenberger Observer Overview - Control Strategy - Development Method - Observation - Control - Outlook
Control Controller = A + B u u u k β y k δ H β = = kβ _ stat δv 1+ i ω T 1+ i ω T Static Transfer Function D 1 B.4 Steering Ratio r / f.. -. -.4 -.6 characteristic velocity larger wheel base at high velocity A -.8-1. smaller wheel base at low velocity 1 3 4 5 6 7 8 9 Control State Space Controller x = f( x,u) u y f f x = x + u = A x + B u x u Ricatti Equation ( ) ( )( ) = f,u K L,u y ŷ L + - wanted C ŷ - + T ( k + 1) = A ( k) P ( k) A( k) + Q * P K P T { + R} 1 * T * ( k + 1) = P ( k + 1) B( k) B ( k) P ( k + 1) B( k) * T T * ( k + 1) = P ( k + 1) K ( k + 1) B ( k) P ( k 1) +
Steady State Cornering 3.. side slip angle [ ] 1.. -1. -. -3. -4. 6. without 4WS State Space Controller 1 3 4 5 6 7 8 Steady State Cornering Control Without 4WS rear steering angle [ ] 5. 4. without 4WS 3.. State Space Controller 1.. -1. -. -3. 1 3 4 5 6 7 8 Controller State Space Controller Steady State Cornering 3.. side slip angle [ ] 1.. -1. -. without 4WS -3. State Space Controller -4. 1 3 4 5 6 7 8 Control 6. Steady State Cornering Without 4WS rear steering angle [ ] 5. 4. without 4WS 3.. State Space Controller 1.. -1. -. -3. 1 3 4 5 6 7 8 Controller State Space Controller
6 4 dry road, icy road icy road, state space model icy road, bicycle model icy road, without 4WS dry road y-path [m] - -4-6 1 3 4 5 6 7 8 9 1 x-path [m] Control dry road, icy road Without 4WS side slip angle [ ] icy road, state space model icy road, bicycle model 15 icy road, without 4WS dry road 1 5-5 -1 1 3 4 5 6 7 8 9 1 x-path [m] Controller State Space Controller Overview - Control Strategy - Development Method - Observation - Control - Outlook
Outlook Virtual Prototyping Software Rapid Prototyping Measurement Control information C - Code 15 th USER CONFERENCE ROM, 15. - 16. November Vehicle Dynamics Control for a 4 Wheel Steering Prototype Car INSTITUT FÜR KRAFTFAHRWESEN AACHEN Dipl.-Ing. Alfred Pruckner Dipl.-Ing. Sven Fischer