Robust feedback synthesis for margins at the plant input

Abstract

In its present form, the Quantitative Feedback Theory (QFT) for uncertain MIMO feedback systems is a tool to design the two degree-of-freedom of a feedback system. It satisfies demands of robustness, performance, and gain and phase margin at the plant input for diagonal controllers. The method is now extended to meet the requirements of gain and phase margin specifications (including as a function of frequency) at the plant input for non-diagonal controllers. The advantages are: (1) elimination of underdamped closed loop transfer function from any plant input into itself and elimination of underdamped closed loop poles in the effective bandwidth of the system. In the most general terms the time response at the plant input owing to disturbances, sensor noise and/or tracking commands is improved and long-duration ‘ringing’ is avoided; (2) the margins fit the conditions of the circle criterion of guarantee stability for memoryless elements at one of the plant inputs; and (3) the design can be tailored to meet disturbance rejection specifications at the plant input for a given disturbance spectrum.