14.1 Background

Chapter 13 presented the problem of control-loop interaction, and a method (RGA) to help determine the best input-output pairing to form a set of SISO control loops. The goal of this chapter is severalfold. One is to understand the inherent performance limitations of a multivariable system due to RHP transmission zeros. Also, multivariable systems exhibit a "directional sensitivity" that can be detected by performing a singular value decomposition (SVD). Use of the SVD requires that the gain matrix be properly scaled, so that the scaled inputs and outputs have roughly the same ranges of expected values.

Two forms of multivariable control are presented in this chapter: decoupling and IMC. The more commonly used multivariable technique in practice, model predictive control (MPC), is the topic of Chapter 16.