Hua-Cheng Zhou

The Active Disturbance Rejection Control to Stabilization for Multi-Dimensional Wave Equation with Boundary Control Matched Disturbance

In this paper, we consider boundary stabilization for a multi-dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables. The active disturbance rejection control (ADRC) approach is adopted in investigation. An extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi-dimensional system by infinitely many test functions. The disturbance is canceled in the feedback loop together with a collocated stabilizing controller. All subsystems in the closed-loop are shown to be asymptotically stable. In particular, the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature. The overall picture of the ADRC in dealing with the disturbance for multi-dimensional partial differential equation is presented through this system. The numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction.

Active Disturbance Rejection Control Approach to Output-Feedback Stabilization of a Class of Uncertain Nonlinear Systems Subject to Stochastic Disturbance

The active disturbance rejection control (ADRC) is now considered as a powerful control strategy in dealing with large uncertainty covering unknown dynamics, external disturbance, and unknown part in coefficient of the control. However, all theoretical works up to present are limited to deterministic uncertainty. In this technical note, we generalize the ADRC to uncertain nonlinear systems subject to external bounded stochastic disturbance described by an uncertain stochastic differential equation driven by white noise. We first design an extended state observer (ESO) that is used to estimate both state, and total disturbance which includes the internal uncertain nonlinear part and the external uncertain stochastic disturbance. It is shown that the resulting closed-loop system is practically stable in the mean-square topology. The numerical experiments are carried out to illustrate effectiveness of the proposed approach.

Parameter estimation and stabilization for one-dimensional Schrödinger equation with boundary output constant disturbance and non-collocated control

Abstract We consider parameter estimation and stabilization for a one-dimensional Schrodinger equation with an unknown constant disturbance suffered from the boundary observation at one end and the non-collocated control at other end. An adaptive observer is designed in terms of measured position with unknown constant by the Lyapunov functional approach. By a backstepping transformation for infinite-dimensional systems, it is shown that the resulting closed-loop system is asymptotically stable. Meanwhile, the estimated parameter is shown to be convergent to the unknown parameter as time goes to infinity. The numerical experiments are carried out to illustrate the proposed approach.

Output feedback stabilisation for a cascaded wave PDE-ODE system subject to boundary control matched disturbance

ABSTRACT In this paper, we consider output feedback stabilisation for a wave PDE-ODE system with Dirichlet boundary interconnection and external disturbance flowing the control end. We first design a variable structure unknown input type state observer which is shown to be exponentially convergent. Then, we estimate the disturbance in terms of the estimated state, an idea from active disturbance rejection control. These enable us to design an observer-based output feedback stabilising control to this uncertain PDE-ODE system.

Output feedback stabilization for multi-dimensional Kirchhoff plate with general corrupted boundary observation ☆

Abstract We consider boundary output feedback stabilization for a multi-dimensional Kirchhoff plate with boundary observation suffered from a general external disturbance. We adopt for the first time the active disturbance rejection control approach to stabilization of multi-dimensional partial differential equations under corrupted output feedback. In terms of this approach, the disturbance is estimated by a relatively independent estimator, based on (possibly) an infinite number of ordinary differential equations reduced from the original PDEs by infinitely many time-dependent test functions. This gives a state observer, an additional result via this approach. The disturbance is compensated in the feedback-loop. As a result, the control law can be designed almost as the same as that for the system without disturbance. We show that with a time varying gain properly designed, the observer driven by the disturbance estimator is convergent; and that all subsystems in the closed-loop are asymptotically stable. We also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying high gain estimator.

Performance output tracking for one-dimensional wave equation subject to unmatched general disturbance and non-collocated control

Abstract In this paper, we consider performance output tracking for a boundary controlled one-dimensional wave equation with possibly unknown internal nonlinear uncertainty and external disturbance. We first show that the open-loop system is well-posed and then propose a disturbance estimator. It is shown that the disturbance estimator can estimate successfully the total disturbance that consists of internal uncertainty and external disturbance. An servomechanism based on the estimated total disturbance is then designed. It is shown that the closed-loop system is well-posed. Three control objectives are achieved: (a) the output is tracking the reference signal; (b) all the internal signals are uniformly bounded; (c) the closed-loop system is internally asymptotically stable if both the reference signal and the disturbance vanish or belong to the space H 2 (0, ∞) and L 2 (0, ∞), respectively. The unmatched performance output tracking control is first time applied to a system described by the partial differential equation for complete general disturbance rejection and reference tracking purpose. Another key feature of this paper is that we do not use the high-gain to estimate total disturbance for unmatched system. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.

Comments on “Stabilization of a class of nonlinear systems with actuator saturation via active disturbance rejection control” [Automatica 63 (2016) 302–310]

Abstract In this comment, we point out that there are four errors leading to question of the validity of Theorem 3 and Proposition 4 of a recent paper Ran, Wang, and Dong (2016a).

The Stabilization of Multi-Dimensional Wave Equation with Boundary Control Matched Disturbance

Abstract We consider boundary stabilization for a multi-dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables. The active disturbance rejection control (ADRC) approach is adopted in investigation. An disturbance estimator is designed to estimate, in real time, the disturbance, and the disturbance is canceled in the feedback loop with its approximation. All subsystems in the closed-loop are shown to be asymptotically stable. The numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction.

Stabilization of multi-dimensional Kirchhoff plate with corrupted boundary observation

The boundary output feedback stabilization for a multi-dimensional Kirchhoff plate with boundary observation suffered from general external disturbance is considered. The active disturbance rejection control approach is adopted in investigation. By using this approach, the disturbance is estimated by a relatively independent estimator. The disturbance is canceled in the feedback-loop. As a result, the control law can be designed almost as same as that for the system without disturbance. We show that with a time varying gain properly designed, the observer driven by the disturbance estimator is convergent; and that all subsystems in the closedloop are asymptotically stable. Some numerical simulations are provided.