IMC controller design for multivariable systems

Abstract

A systematic internal model control (IMC) controller design methodology has been developed for various types of multivariable processes. When we try to apply IMC to various systems several implementation problems are encounted. These are the followings: (1) An exact determination of zeros of the process model can be difficult due to numerical errors. For this reason, a factorization of the "unstable zeros" of the process model is difficult. (2) An IMC controller designed by inverting the invertible part of the system``s transfer matrix has numerical difficulties. (3) In the case of n×n systems(n≥3) and 2×2 systems whose elements are high order transfer functions, a general inverse formula of the invertible part of the system``s transfer matrix is very complicated. (4) Handling of the constraints of various processes. (5) Location of poles as we stabilize the unstable process by pole placement. In this work, these problems are resolved and a systematic IMC controller design methodology is suggested. IMC shows very good performance and is easy to tune for opne-loop stable systems. For unstable systems we apply IMC after stabilizing the systems using the pole placement technique. A combination of quadratic programming and IMC can handle constraints on manipulated and controlled variables.