Structures of Multivariable Processes

Abstract

Part E considers some design methods for linear discrete-time multivariable processes. As shown in Figure 18.1 the inputs u _i and outputs y_j of multivariable processes influence each other, resulting in mutual interactions of the direct signal paths U ₁ — y ₁ , u ₂ — y ₂, etc. The internal structure of multivariable processes has a significant effect on the design of multivariable control systems. This structure can be obtained by theoretical modelling if there is sufficient knowledge of the process. The structures of technical processes are very different such that they cannot be described in terms of only a few standardized structures. However, the real structure can often be transformed into a canonical model structure using similarity transformations or simply block diagram conversion rules. The following sections consider special structures of multivariable processes based on the transfer function representation, matrix polynomial representation and state representation. These structures are the basis for the designs of multivariable controllers presented in the following chapters.