Exact, optimal, and partial loop transfer recovery

A novel approach for loop transfer recovery (LTR) is developed. This approach uses a general feedback/feedforward structure for model matching control which includes the observer-based state feedback control as a special case. Under this framework, the problem of LTR is both generalized and simplified. First, the necessary and sufficient condition for the exact LTR is trivially obtained for both minimum phase and nonminimum phase systems and the corresponding controller is simply computed without any asymptotic tuning procedure. Secondly, for the nonminimum phase systems for which the exact LTR may not be possible, the author addresses the optimal LTR problem and shows that it can be formulated as an H_∞ optimization problem and can be solved by using either the Nevanlinna-Pick theory or the Riccati equation approach. In the case where a good rejection for measurement noise is needed, the problem of partial LTR is addressed. The proposed approach applies to both continuous-time and discrete time systems