Abstract
This paper is devoted to investigating the robust control problem for a class of singular systems with model structure uncertainty and external disturbance. Firstly, the uncertainty and disturbance estimator (UDE)-based robust control law is established for uncertain singular systems. Secondly, the two-degree-of-freedom (2DOF) nature of singular systems under the UDE-based robust controller is revealed, which shows that asymptotic reference tracking and disturbance rejection are decoupled. Additionally, on the basis of the small-gain theorem, sufficient conditions are established to ensure robust stability of the closed-loop system and to achieve asymptotic reference tracking and disturbance rejection. Finally, three numerical examples and a practical application to the multi-agent supporting systems are provided to illustrate the validity of the methods proposed.
Highlights
Model uncertainty, external disturbance and parameter perturbation commonly exist in many practical applications, which bring negative effects on the performance of the control system
First of all, an uncertainty and disturbance estimator (UDE)-based control law is presented to ensure that the uncertain singular system (1) is stable, and the state x(t) asymptotically tracks the state xr(t) of reference model
It is shown that 2DOF nature of singular systems under the UDE-based controller is proposed
Summary
External disturbance and parameter perturbation commonly exist in many practical applications, which bring negative effects on the performance of the control system. Since uncertainties are usually unknown and unmeasurable, another class of approaches has been proposed to estimate or compensate for the influence of uncertainties by using the measurable states and known dynamics of systems. This kind of method can be found in [5] for the active disturbance rejection control (ADRC), [6] for the disturbance-observer-based control (DOBC), [7] for the equivalent input disturbance (EID), [8] for the extended state observer (ESO) and [9] for the unknown input observer (UIO). Singular systems consist of differential and algebraic equations, which are different from state-space systems, the solutions of singular systems always contain impulses. Finding regular and impulse-free conditions and designing the controller so that the closed-loop systems are regular, impulse-free and stable are the focus of the study of singular systems, where regularity and impulse-freeness ensure that the singular systems have a unique solution without impulse
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