Modelling a racing driver
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Modelling a racing driver. Robin Sharp Visiting Professor University of Surrey. Partners. Dr Simos Evangelou (Imperial College) Mark Thommyppillai (Imperial College) Robin Gearing (Williams F1). Published work.

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Modelling a racing driver

Modelling a racing driver

Robin Sharp

Visiting Professor

University of Surrey


Partners

Partners

  • Dr Simos Evangelou (Imperial College)

  • Mark Thommyppillai (Imperial College)

  • Robin Gearing (Williams F1)


Published work

Published work

  • R. S. Sharp and V. Valtetsiotis, Optimal preview car steering control, ICTAM Selected Papers from 20th Int. Cong. (P. Lugner and K. Hedrick eds), supplement to VSD 35, 2001, 101-117.

  • R. S. Sharp, Driver steering control and a new perspective on car handling qualities, Journal of Mechanical Engineering Science, Proc. I. Mech. E., 219(C8), 2005, 1041-1051.

  • R. S. Sharp, Optimal linear time-invariant preview steering control for motorcycles, The Dynamics of Vehicles on Roads and on Tracks (S. Bruni and G. Mastinu eds), supplement to VSD 44, Taylor and Francis (London), 2006, 329-340.

  • R. S. Sharp, Motorcycle steering control by road preview, Trans. ASME, Journal of Dynamic Systems, Measurement and Control, 129(4), 2007, 373-381.

  • R. S. Sharp, Optimal preview speed-tracking control for motorcycles, Multibody System Dynamics, 18(3), 397-411, 2007.

  • R. S. Sharp, Application of optimal preview control to speed tracking of road vehicles, Journal of Mechanical Engineering Science, Proc. I. Mech. E., Part C, 221(12), 2007, 1571-1578.

  • M. Thommyppillai, S. Evangelou and R. S. Sharp, Car driving at the limit by adaptive linear optimal preview control, Vehicle System Dynamics, in press, 2009.


Objectives

Objectives

  • Enable manoeuvre-based simulations

  • Understand man-machine interactions

  • Perfect virtual driver

    • able to fully exploit a virtual racecar

    • real-time performance

  • Find best performance

  • Find what limits performance

  • Understand matching of car to circuit


Strategy

Strategy

  • Specify racing line and speed – (x, y, t) (x, y) gives the racing line, t the speed

  • Track the demand with a high-quality tracking controller

  • Continuously identify the vehicle

  • Modify the t-array and iterate to find limit


Optimal tracking

Linear Quadratic Regulator (LQR) control with preview

linear constant coefficient plant

discrete-time car model

road model by shift register (delay line)

join vehicle and road through cost function

specify weights for performance and control

apply LQR software

Optimal tracking


Modelling a racing driver

Close-up of car and road with sampling

uT

x

O

y

yr4

yr3

yr2

yr1

road

yr0

car

current road angle = (yr1-yr0)/(uT)

speed, u; time step, T


Modelling a racing driver

Optimal controls from Preview LQR

path yr1

K21

shift register state feedback

path yr2

K22

steerangle

command

path yrq

K2q

K11

car states

K12

car state feedback

K13

K14


Discrete time control scheme

+

+

-

-

Discrete-time control scheme

shift register; n = 14

car linearised for operation near to a trim state

xdem

xc

ydem

yc

c

K2

throttle

K1

steer

car states

to cost function

to cost function


Minimal car model

Minimal car model

x

Mass M; Inertia Iz

inertial system

0

b

a

Fylr

Fylf

y

2w

u, constant

v

Fyrr

Fyrf


Modelling a racing driver

K2 (preview) gains for saloon and sports cars

Buick

Ferrari


Modelling a racing driver

The rally car (1)


Modelling a racing driver

Tyre-force saturation

  • Saturating nonlinearity of real car

  • Optimal race car control idea

  • Trim states and linearisation for small perturbations

  • Storage and retrieval of gain sets

  • Adaptive control by gain scheduling


Car model tyre forces

car model tyre forces

,


Equilibrium states of front heavy car

Equilibrium states of front-heavy car

decreasing turn radius for fixed speed

Axle lateral force / axle weight

unique rear slip for given front slip


Modelling a racing driver

Optimal preview gain sequences as functions of front axle sideslip ratio

Gain value

Front tyre side slip angle (Rad)

Preview length (s)


Frequency responses

Frequency responses

input

x

IC

datum line

previous input stored in shift register

Perfect tracking requires:

unity gain

phase lag equal to transport lag

For cornering, trim involves circular datum


Controlled car frequency responses

Controlled car frequency responses


Small perturbations from trim

Small perturbations from trim

path tangent for cornering trim state

IC

reference line for straight-running trim state

ydem2

ydem1

ydem3

ydem4

ydem3 from curved reference line

reference line for cornering trim state

ydem4 from curved reference line

road path


Modelling a racing driver

Tracking runs of simple car at 30m/s(Fixed gain vs. Gain scheduled)

1

1

1

2

3

4

2

2

3

3

4

4

Fixed gain Gain scheduled


Conclusions

Conclusions

  • Optimal preview controls found for cornering trim states

  • Gain scheduling applied to nonlinear tracking problem

  • Effectiveness demonstrated in simple application

  • Rear-heavy car studied similarly

  • Identification and learning work under way


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