A NEW STABLE COMPENSATOR DESIGN FOR EXACT AND APPROXIMATE LOOP TRANSFER RECOVERY

In this paper, a new compensator structure for loop transfer recovery (LTR) is proposed. The proposed compensator (a) is open-loop stable, (b) guarantees closed-loop stability and above all (c) requires much smaller values of gain than the conventional observer-based controller for the same degree of loop-transfer recovery. The fact that the new compensator requires much smaller values of gain than the conventional controller results in several practical advantages, the most important among them being the reduction in controller band-width and freedom from the woes of saturation. The trade-off between the value of gain and the degree of loop transfer recovery as well as the bounds on singular values of sensitivity and complementary sensitivity functions is shown clearly. Both full and reduced order compensators for LTR when the design specifications are reflected either at the input or at the output point of the given plant are considered. Numerical examples illustrate the advantages of the new compensator structure. The new compensator structure is inspired by a careful and clear understanding of how loop transfer recovery occurs when conventional observer based controllers are used. To motivate and deduce our new compensator structure, a unified treatment of observer theory for LTR is presented. In the context of such a unification, some new results are also given.