Loop transfer recovery for general nonminimum phase discrete time systems - part 2: design

This part focuses on the design of controllers for the recovery of target loop transfer function or sensitivity and complimentary sensitivity functions for general nonminimum phase discrete time systems. For general systems, loop transfer recovery is not completely feasible although there exists considerable amount of freedom to shape the inevitable recovery error. Here the necessary design constraints and the available design freedom are reviewed. In view of the available freedom, possible specifications on the eigenstructure of the observer dynamic matrix are formulated. Three different types of controllers which are respectively based on prediction, current and reduced order estimators, are considered. For each one of such controllers, three different design techniques are developed. The first one is an eigen-structure assignment scheme, and the other two are optimisation based designs. Eigenstructure assignment method yields a controller design which achieves any chosen recovery error matrix among a set of admissible recovery error matrices. On the other hand, one of the optimisation based design methods leads to a controller that achieves a recovery error matrix having the infimum H_∞ norm, while the other does the same except it achieves a recovery error matrix having the infimum H₂ norm. All the developed design methods are implemented in a ´Matlab´ software package.