Grey Wolf Optimization Algorithm Based Weight Selection for Tuning H-Infinity Loop Shaping Controller in Application to A Benchmark Multivariable System with Transmission Zero

Abstract

This paper presents a method based on Grey-Wolf Optimization(GWO) algorithm based algorithm for the H-infinity loop shaping controller(HILSC) design for a multivariable system in non-minimum phase and minimum phase The role of GWO is to determine the weighing function parameters of the HILSC by minimizing the norm (H-infinity) of the CLTF of the multivariable process which is a quadruple tank in this case. The optimal stability margin in an HILSC is taken as objective function of GWO to compute the utmost appropriate weighting parameters. The mathematical equivalent for non-minimum phase and minimum phase of quadruple tank is obtained in state-space form by moving the operating position of the valve and the benchmark HILS procedure is employed to determine the weighting functions of the HILSC. The difficulties usually arise in finding compensators that implement most design decisions. It is revealed that the proposed method subsequently reduces the technical hitches in the designing method of H-infinity controller for a multivariable system(MVS). GWO based optimization provides comparatively better results than PSO based optimization for a quadruple tank, which is evident in the simulation resultants obtained against plant perturbations and disturbances. The integral square error is reduced appreciably with the proposed technique. The necessary computations and the analysis of the behavior of the system are done in MATLAB simulation environment.