Comparision of Multivariable Controllers for Non-Minimum Phase Systems

Abstract

A system with one or more right half plane transmission (RHPT) zero is generally called a non-minimum phase system. In this paper, the authors compare two methods of designing multivariable controllers for systems with RHPT zeros. The methods used are decoupled internal model controller and a simple tuning method. In the decoupled IMC method, controller design procedure is developed with the help of a model reduction theorem. Davison has proposed a simple tuning method, which is based on inverse of the steady-state gain matrix [G(0)]. Previously the method was applied to multivariable minimum phase systems only. In the present work the Davison method is applied to systems with multivariable right half plane zero. The decoupled IMC method involves some complex calculations in designing controllers, whereas the Davison method is simple to apply. Simulation results are given for the following 2 × 2 transfer function matrix of the systems: (1) a four-tank system, a benchmark example of multivariable system; (2) a system with individual and multivariable transmission zero at s = 1; and (3) binary distillation column. The performance comparisons are given by the sum of IAE values based on response and interaction both for servo and regulatory problems. The presented simple tuning method gives an improved performance.