Applications of a Compact Controller Architecture

A compact formulation of the well-known controller architecture based on the Youla–Jabr–Bongiorno–Kucera (YJBK) parameterization is considered in this paper. The architecture includes an internal feedback loop known from observer-based controllers. It is shown in this paper how this compact formulation of the YJBK controller architecture is related to several other architectures in feedback control.

First, the relation between the architecture and the double Bezout equation is described. The controller architecture is based on the Bezout matrices. Next, the connection with a full-order observer-based feedback controller is described. Using a coprime factorization of a full-order observer-based feedback controller, it is easy to show that this controller can be implemented in the compact controller architecture.

The concept of Loop Transfer Recovery (LTR) design of observer-based controllers is strongly related to the compact YJBK controller architecture. It is shown that the LTR design is equivalent to minimizing the internal feedback loop in the compact controller architecture. Input saturation is another important issue in connection with closed-loop systems.

It is shown that anti-windup with respect to input saturation can easily be included in the compact controller architecture by moving the internal feedback loop in the controller from the input size to the output size of the saturation block.