Vehicle Yaw Motion Control Using Takagi-Sugeno Modeling and Quadratic Boundedness via Dynamic Output Feedback

Sai¨D Mammar,Nicoleta Minoiu-Enache,Dominique Gruyer,Benoit Lusetti,Se´Bastien Glaser,Lydie Nouvelie`Re

doi:10.1115/esda2010-24809

Abstract

This paper presents the design and the simulation test of a Takagi-Sugeno (TS) fuzzy output feedback for yaw motion control. An integrated steering and differential braking controller based on invariant sets, quadratic boundedness theory and a common Lyapunov function has been developed. The TS fuzzy model is able to handle elegantly the nonlinear behavior the vehicle lateral dynamics. The computation of the control law has been achieved using Linear and Bilinear Matrix Inequalities (LMI-BMI) methods. Simulation test shows the controlled car is able to achieve the ISO3888-2 transient maneuver. Some design parameters can be adjusted to handle the tradeoff between safety constraints and comfort specifications.

Highlights

There is no doubt that electronic stability control systems (ESC) have largely contributed to accident and death reduction during this last decade [18]
Recent studies have demonstrated that differential braking may have a better effect on yaw dynamics than independent active wheel braking [21]
The dynamic output feedback formulation considered in this paper presents two main advantages: better flexibility to formulate the stabilization conditions and ability to handle input or state constraints and bounded disturbances

Summary

INTRODUCTION

There is no doubt that electronic stability control systems (ESC) have largely contributed to accident and death reduction during this last decade [18]. The dynamic output feedback formulation considered in this paper presents two main advantages: better flexibility to formulate the stabilization conditions and ability to handle input or state constraints and bounded disturbances This controller uses the property of quadratic boundedness and invariant set [4]. Afterwards, a dynamic control fuzzy output feedback is synthesized [4], [8] It handles both input and state constraints using only measurements of the yaw rate and the steering angle [16]. In order to ensure at nominal speed, the same steady state value for the controlled and the conventional car, the reference model is chosen as a first order transfer function with the same steady state gain as the conventional car The implication wT Qw ≤ xT Px =⇒ (Φzx(t) + Γw(t))T P(Φzx(t) + Γw(t)) ≤ xT Pxis equivalent to:

P1 0 P2

DcC Cc 2DcD u2

CONCLUSIONS AND FUTURE WORKS