Robust Stability Analysis of a Fuzzy Vehicle Lateral Control System Using Describing Function Method

In this paper, the robust stability analysis of a fuzzy vehicle lateral system with perturbed parameters is presented. Firstly, the fuzzy controller can be linearized by utilizing the describing function method with experiments. After the describing function is obtained, the stability analysis of the vehicle lateral control system with the variations of velocity and friction is then carried out by the use of parameter plane method. Afterward some limit cycle loci caused by the fuzzy controller can be easily pointed out in the parameter plane. Computer simulation shows the efficiency of this approach.

[1]  Arthur Gelb,et al.  Multiple-Input Describing Functions and Nonlinear System Design , 1968 .

[2]  Dragoslav D. Šiljak,et al.  Nonlinear systems;: The parameter analysis and design , 1968 .

[3]  J. Ackermann,et al.  Actuator rate limits in robust car steering control , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[4]  Francisco Gordillo,et al.  Determining limit cycles in fuzzy control systems , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[5]  Paluri S. V. Nataraj,et al.  Limit cycle computation for describing function approximable nonlinear systems with box‐constrained parametric uncertainties , 2005 .

[6]  Wai-Kai Chen,et al.  Nonlinear Control Systems: Some Practical Methods , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  D. Siljak.  Parameter Space Methods for Robust Control Design: A Guided Tour , 1988, 1988 American Control Conference.

[8]  R. M. Bass,et al.  Analysis of the class AD audio amplifier including hysteresis effects , 2003 .

[9]  Euntai Kim,et al.  Limit-cycle prediction of a fuzzy control system based on describing function method , 2000, IEEE Trans. Fuzzy Syst..

[10]  A. Delgado.  Stability analysis of neurocontrol systems using a describing function , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[11]  R. Miller,et al.  Qualitative analysis of oscillations in nonlinear control systems: A describing function approach , 1986 .

[12]  Péricles R. Barros,et al.  Relay-based gain and phase margins PI controller design , 2003, IEEE Trans. Instrum. Meas..

[13]  G. Siouris,et al.  Nonlinear Control Engineering , 1977, IEEE Transactions on Systems, Man, and Cybernetics.