Optimal fuzzy adaptive robust PID control for an active suspension system

This work proposes an optimal fuzzy adaptive robust proportional-integral-derivative (PID) controller for a quarter-car model with an active suspension system. To this end, at first, the errors of the relative displacement and acceleration of the chassis and their integrals and derivatives are implemented to design a PID controller. Integral sliding surfaces defined based on the errors and their integrals are utilised to design the adaptation rules via the gradient descent method and the chain derivative rule. Afterwards, a fuzzy system consisted of the singleton fuzzifier, centre average defuzzifier and the product inference engine is applied to regulate the control parameters. Finally, the particle swarm optimisation (PSO) algorithm is utilised to ascertain the optimum gains of the designed controller. The body acceleration and the relative displacement between tire and sprung mass are considered as two objective functions for minimisation by the algorithm. Results show the dominance of the proposed active suspension system over previous published research works.