Observer Feedback Compensator and Cascade PD Compensator Design Based on Loop Transfer Recovery

The recent development on general observer design enables systematic minimization of the observer gain to system input by observer pole selection. Because this minimization is the necessary and sufficient condition of loop transfer recovery (LTR), an entirely new approach to achieve LTR is therefore initiated. This minimization only requires all observer poles to be clustered around any set of system zeros, while other approximate observer pole selection solutions may also exist. With this new and explicit understanding of the importance of system zeros, a zero assignment problem can thus be initiated. The open loop system zero assignment can be achieved by a cascade PD compensator. As a result, the explicit formulation of PD compensator design for zero assignment, and the explicit overall PD compensator and state/observer feedback compensator design procedure, are presented in this paper. The dual version of this new LTR approach is also presented.