Abstract
Application of the partial LTR (Loop Transfer Recovery) technique to design integral controllers for discrete-time non-minimum phase plants is discussed. We focus our attention to the feedback property at the plant input side assuming that unit step computation delay exists in a controller. First, based on the all-pass/minimum phase decomposition of the plant transfer function matrix, we construct the minimum phase state feedback (MSF) integral controller which feeds back the minimum phase state of a plant. For the output feedback case, we construct the minimum phase estimate feedback (MEF) integral controller by replacing the minimum phase state in the MSF integral controller by its estimate generated by the prediction type Kalman filter. We show that the feedback property achieved by the MEF integral controller approaches that of the MSF integral controller as the intensity of a fictitious disturbance inserted between the minimum phase and the all-pass parts tends to infinity. For the performance index consisting of the quadratic forms of the plant output and input, the feedback property achieved by enforcing the conventional LTR technique coincides with that achieved by the partial LTR technique. This fact clarifies the system theoretic significance of the enforcement of the conventional LTR technique. It should be noted that this fact does not make the partial LTR technique obsolete because it provides more design freedom than the conventional technique. A numerical example making use of the freedom is presented.
