QFT type design for maximizing tolerable disturbances in structured uncertain systems

Abstract

A QFT type methodology is developed for an SISO system for maximizing the size of a persistent bounded disturbance in the presence of hard time domain constraints on system states, control input, output and the bandwidth. It is assumed that the system dynamics can be represented by a combination of structured uncertainty in the low frequencies and unstructured uncertainty in the high frequencies. The design procedure is based on mapping the time domain constraints into an equivalent set of frequency domain constraints which are then used to determine an allowed design region in the amplitude-phase plane, for the nominal loop transfer function. Once such a region is found, classical loop shaping determines a suitable loop transfer function. The pole-zero structure of the compensator is a natural consequence of loop shaping and is not preconceived. A procedure is also presented for determining the maximum size of the nominal persistent bounded disturbance that can be tolerated by the resulting closed loop system.