Multiobjective PID controller design for active suspension system: scalarization approach

Abstract

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