Improved Identification and Control of 2-by-2 MIMO System using Relay Feedback

Abstract

Several groups^6-8 have analyzed Multi Input Multi Output (MIMO) system by approximating all the individual transfer functions as First Order plus Dead Time (FOPDT), which may result in degraded closed loop performance. In this work, ideal relay feedback tests are conducted on transfer function models of 2-by-2 MIMO systems, having individual transfer function elements without approximating them as FOPDT. A systematic approach for the identification and control of 2-by-2 MIMO (Wardle and Wood distillation column) system using Relay feedback test is proposed. Generalized expressions are derived based on the observation that a relay feedback test consists of a series of step inputs and a stable limit cycle implies a convergent infinite series. These analytical expressions are used to estimate unknown system parameters. The model parameters are estimated by applying boundary conditions obtained from the limit cycle data on the derived expressions and the interaction is analyzed by using RGA method. The model thus identified is used for the design of controllers to carryout closed loop studies. The advantages of proposed scheme are highlighted.