Loop Transfer Recovery for General Nonminimum Phase Non- Strictly Proper Systems, Part 2-design*

This part focuses on the design of full order observer based controllers for the recovery of target loop transfer function or sensitivity and complimentary sensitivity functions for general non-strictly proper, not necessarily left invertible and not necessarily minimum phase 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 time-scale and/or eigenstructure of the observer dynamic matrix are formulated. Then three types of design schemes are developed in detail. The first one is an asymptotic time-scale and eigenstructure assignment (ATEA) scheme, and the other two are optimization based designs; one dealing with the minimization of H 2 norm of a so called 'recovery matrix' while the other dealing with the minimizationof H 00 norm of the same. Relative advantages and disadvantages of both ATEA and optimization based design schemes are discussed. Besides the conventional LTR problem which is concerned with the recovery over the entire control space, another generalized recovery problem where the concern is with the recovery over a specified subspace of the control space is also considered. All the developed design methods are implemented in a "Matlab" software package. A bank of examples illustrate the developed design schemes. Key Words-Loop transfer recovery, robust control, asymptotic time-scale and eigenstructure assignment, H 2or H oo-optimization.