Analysis and robust control of system with uncertainty and disturbance using equivalent-input-disturbance approach

Abstract

This paper addresses the control problem of an uncertain system suffering from an exogenous disturbance. A new degree of control freedom is developed to handle the problem based on the equivalent-input-disturbance (EID) approach. The effect of the disturbance and uncertainties is equivalent to that of a fictitious disturbance on the control input channel, which is called an EID. A state observer and an improved EID (IEID) estimator are devised to produce an estimate that is used to compensate for the disturbance and uncertainties in a control law. A second-order low-pass filter is employed in the estimator to provide a way to solve a tradeoff between disturbance rejection and noise suppression. The slope of the Bode magnitude curve at high frequencies is two times larger for the IEID estimator than for a conventional one. This makes the IEID estimator less sensitive to measurement noise and more practical. Sufficient analyses reveal the mechanism of disturbance rejection, uncertainty attenuation, and noise suppression of an IEID-based control system. A theorem is derived to guarantee system stability and a procedure is presented for system design. Simulations and experiments of the position control of a magnetic levitation system are carried out to show the validity of the presented method.