Performance issues in the individual channel design of 2-input 2-output systems Part 1. Structural issues

Abstract

A new applications-oriented approach—individual channel design (ICD)—to multivariable feedback control—was presented in an earlier paper (O'Reilly and Leithead 1991). This paper is the first part of a three-part investigation into the performance issues raised by ICD for 2-input 2-output multivariable systems. The three-part series of papers also develops an analytic framework for investigating and understanding the potential and limitations of the feedback design of any linear time-invariant controller. The main results of this first paper are threefold. First, the ICD framework advanced by O'Reilly and Leithead (1991) is justified for all multivariable system structures. In particular, it is shown that ICD on the original 2-input 2-output cross-coupled multivariable system is valid irrespective of the degree of cross-coupling. Second, the influence of (individual transfer function, channel, transmission) right half-plane zeros on controller design and closed-loop channel performance is elucidated. Third, a generalization of a result concerning the existence of fixed stabilizing controllers for uncertain systems, equivalent to one due to Kwakernaak (1982), is presented.