Multiobjective PID controller design for active suspension system: scalarization approach

Abstract

In this study, the PID tuning method (controller design scheme) is proposed for a linear quarter model of active suspension system installed on the vehicles. The PID tuning scheme is considered as a multiobjective problem which is solved by converting this multiobjective problem into single objective problem with the aid of scalarization approaches. In the study, three different scalarization approaches are used and compared to each other. These approaches are called linear scalarization (weighted sum), epsilon-constraint and Benson’s methods. The objectives of multiobjective optimization are selected from the time-domain properties of the transient response of the system which are overshoot, rise time, peak time and error (in total there are four objectives). The aim of each objective is to minimize the corresponding property of the time response of the system. First, these four objective is applied to the scalarization functions and then single objective problem is obtained. Finally, these single objective problems are solved with the aid of heuristic optimization algorithms. For this purpose, four optimization algorithms are selected, which are called Particle Swarm Optimization, Differential Evolution, Firefly, and Cultural Algorithms. In total,twelve implementations are evaluated with the same number of iterations. In this study, the aim is to compare the scalarization approaches and optimization algorithm on active suspension control problem. The performance of the corresponding cases (implementations) are numerically and graphically demonstrated on transient responses of the system.