Self-tuned robust fractional order fuzzy PD controller for uncertain and nonlinear active suspension system

Abstract

In this paper, a self-tuned robust fractional order fuzzy proportional derivative (FO-FPD) controller is proposed for nonlinear active suspension system of a quarter car. Quarter car is a highly uncertain system as the number of riders or payload may vary. The control objective is to improve the level of ride comfort by minimizing the root mean square of vertical vibration acceleration (RMSVVA) of car body and maintaining hard constraints such as tracking force, ratio of tyre dynamic and static loads and suspension travel. The used FO-FPD controller is a nonlinear fuzzy logic controller having self-tuning capability, i.e. it changes its gains at runtime. The FO-FPD controller is realized using non-integer differentiator operator in FPD controller. The gains of FO-FPD and FPD controllers are tuned using Genetic Algorithm optimization method for a sinusoidal road surface. To evaluate the performances, extensive simulation studies were carried out and FO-FPD and FPD controllers were compared for different roads profiles such as sinusoidal, random and bump. It has been observed that FO-FPD and FPD controllers outperform passive suspension system in terms of RMSVVA and offer much better comfort ride while keeping all the hard constraint in the specified limits. Furthermore, FO-FPD controller demonstrated an excellent comfort ride, especially in uncertain environment, wherein it offered very robust behaviour as compared to FPD controller. Also, bonded-input and bounded-output stability conditions are established for overall closed loop control system by using small gain theorem.