Multi-objective dynamic state and output feedback controllers for MIMO system using evolutionary algorithm and eigenstructure assignment

Abstract

Most of the complex industrial plants are generally interacting multi-input multi-output (MIMO) systems. Controller design for such complex plants is a challenging task. In this paper, design of eigenstructure assignment (EA)-based multi-objective dynamic state and output feedback controllers for linear discrete MIMO system are considered. The significance of parametric eigenstructure assignment technique is that it provides more design degrees of freedom to obtain multi-objective functions. Based on parametric eigenstructure assignment, control problem is formulated to achieve conflicting multi-objective functions such as robust stability to parameter perturbation and smaller control gain to improve the transient response of the closed loop system. It is difficult to solve the conflicting objective functions using conventional optimisation techniques. In this paper, fast and elitist multi-objective evolutionary algorithm (MOEA) known as non-dominated sorting genetic algorithm-II (NSGA-II) is successfully applied for solving multi-objective problem. The robust stability and transient response are ensured by minimum condition number of eigenvector and minimum norm of controller gain. The proposed controllers use complex valued chromosomes to represent complex parametric vector. The effectiveness of the proposed controllers is validated by implementing the same in an interacting three-tank benchmark system.