Mismatched Disturbance Rejection Control for Second-Order Discrete-Time Systems

TL;DR

This paper introduces a novel disturbance rejection control method for second-order discrete-time systems that does not require coordinate transformations and effectively handles both known and unknown disturbances.

Contribution

It proposes a new disturbance compensation gain design based on controllability, eliminating the need for coordinate transformations, and incorporates an extended state observer for unknown disturbances.

Findings

Effective disturbance rejection for known disturbances demonstrated through simulations.

Proposed method successfully rejects unknown disturbances in a permanent-magnet DC motor example.

Controller shows excellent performance in numerical simulations.

Abstract

This paper is concerned with mismatched disturbance rejection control for the second-order discrete-time systems.Different from previous work, the controllability of the system is applied to design the disturbance compensation gain, which does not require any coordinate transformations. Via this new idea, it is shown that disturbance in the regulated output is immediately and directly compensated in the case that the disturbance is known. When the disturbance is unknown, an extra generalized extended state observer is applied to design the controller. Two examples are given to show the effectiveness of the proposed methods. Numerical simulation shows that the designed controller has excellent disturbance rejection effect when the disturbance is known. The example with respect to the permanent-magnet direct current motor illustrates that the proposed control method for unknown disturbance rejection is effective.