ABSTRACT
This chapter provides an introduction of multi-input multi-output systems, coupling, and decoupling matrices in the forward and the feedback path. It analyzes feedback systems in only the linear state of operation, that is, for small-amplitude signals, with saturation links equivalently replaced by unity links. The command feedforward scheme is equivalent to using a prefilter, or using a feedback path with a specified transfer function. All of these methods enable one to obtain the desired input–output closed-loop transfer function with any arbitrary compensator transfer function. Major practical types of multi-loop systems are studied: local and common loops, nested loops, crossed loops, and the main/vernier loop configuration. In accordance with Bode’s definition of physical multi-loop systems, only the loops that comprise nonlinear saturation-type elements are counted. The command is given to the vernier loop summer, and the vernier actuator tries to reduce the error rapidly.
