Robust Disturbance-Rejection Design for Systems With Uncertainties, Disturbances, and Noise

This article presents a robust modified equivalent input disturbance (RMEID) design algorithm that effectively attenuates the effects of uncertainties and disturbances on the control output while considering the measurement noise. A robust disturbance-rejection framework is presented including a modified equivalent input disturbance (MEID) estimation and a robust feedback. The MEID approach estimates an equivalent input disturbance (EID) in two steps: Obtaining a prior disturbance estimate and updating the prior disturbance estimate to obtain a posteriori disturbance estimate. Since the MEID compensation for the EID cannot guarantee the stability of a control system, a robust feedback control law is used to stabilize a control system with the MEID-based compensation. The parameters of the RMEID-based control system are obtained by solving linear matrix inequalities, which are derived based on a stability condition and a performance condition. The effectiveness of the approach are demonstrated through a case study involving a mechatronic control system. A comparative analysis with a robust improved equivalent-input-disturbance approach validates the superiority of the RMEID approach.

I. Introduction

Disturbances and uncertainties pose significant challenges to control systems. Various techniques for disturbance/uncertainty estimation and attenuation (DUEA) have been developed to address disturbances [1], such as the disturbance observer (DOB) [2], the proportional-integral observer (PIO) [3], the extended state observer (ESO) [4], the uncertainty-and-disturbance estimator (UDE) [5], the equivalent input disturbance (EID) approach [6]. Among these methods, DOB, ESO, and EID approaches only require the control input and output information. Compared to the DOB, the EID approach does not require the dynamic inverse of the plant [7], which avoids the unstable zero-pole pair cancellation. The main difference with the ESO is that the EID approach requires some practical information to enhance the robustness of the control system [8], whereas with ESO desires to compensate the system into an integral chained system.