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

Abstract

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.

Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain

“…DF replaces nonlinear input-output responses with corresponding linear approximation in nonlinear control systems. It filters out the higher-order harmonics from the nonlinear part and just the sinusoidal wave of the fundamental frequency is obtained in the output (see [27,29,30,32,34]).…”

“…DF approach is a well-known and practical tool in the frequency domain framework to predict the existence of limit cycle [19]. The stability analysis of FCSs has been successfully discussed based on the limit cycles prediction [24][25][26][27][28][29][30][31][32][33][34]. In these studies, integrating the parameter plane, stability equation, and DF methods provides a systematic procedure to analyze the stability of dynamic FCSs [26], uncertain fuzzy vehicle [27], and fuzzy vehicle lateral [30] control systems.…”

“…The stability analysis of FCSs has been successfully discussed based on the limit cycles prediction [24][25][26][27][28][29][30][31][32][33][34]. In these studies, integrating the parameter plane, stability equation, and DF methods provides a systematic procedure to analyze the stability of dynamic FCSs [26], uncertain fuzzy vehicle [27], and fuzzy vehicle lateral [30] control systems. Analysis of stability margins is a major concern for nonlinear control systems to test controller design.…”

Describing Function Approach with PID Controller to Reduce Nonlinear Action

“…The DF is one of the frequency response approximate methods used to o predict jump phenomenon, oscillations characteristics, the limit cycles and, sub-harmonic when the NL system is subjected to sinusoidal, Gaussian noise and level inputs. Stability of a linear system and a static nonlinear using a Nyquist plot developed in [6] through a DF approach. Limit cycle and stability using Fuzzy logic in [7].…”