Infinite Dimensional Disturbance Observer Research Articles

Synchronization controller design for a network of boundary-controlled anti-stable wave equation with time-varying perturbations

In this paper, a output feedback controller based on an infinite dimensional disturbance observer and a state feedback controller based on backstepping method are proposed to solve the synchronous control problem of network anti-stable wave equation with time-varying disturbance at the boundary. One agent in the network wave equation as the virtual leader, and all remaining agents need to track the status of the virtual leader incrementally. Here, the design of synchronous controller is divided into three parts. Firstly, backstepping method is used to design a set of controllers that makes all the systems stable. Secondly, infinite dimensional disturbance observers based on the idea of the active disturbance rejection control (ADRC) technology are used to estimate the disturbance. Finally, the synchronization controllers are designed, and the error between the following system and the virtual leader system converges to 0 in the appropriate sense. The applicability of the closed-loop system is analyzed and proved. The simulation results show the effectiveness of the controller design.

Modeling and Observer-Based Vibration Control of a Flexible Spacecraft With External Disturbances

This paper outlines the vibration reduction of a spacecraft with flexible appendage subject to external disturbances. The hybrid dynamic model of the spacecraft is described by both partial differential equations and ordinary differential equations. A vibration control scheme consisting of two boundary control laws and a distributed control law is developed to restrain the spacecraft's vibration and track the desired attitude. An infinite-dimensional disturbance observer is introduced as a feedforward compensator to handle unknown external disturbances. Based on the semigroup theory, the extended LaSalle's invariance principle and Lyapunov analysis, the well-posedness and stabilities of the designed control system are both discussed. Simulation results are given for validating the effectiveness of the developed vibration control scheme.

Periodic output regulation for general linear heterodirectional hyperbolic systems

This paper presents a backstepping solution of the periodic output regulation problem for general linear heterodirectional hyperbolic systems. By utilizing a time-varying signal model, regulators are determined for a general class of periodic reference inputs and disturbances. A systematic design procedure is developed for the state feedback regulator by solving the periodic regulator equations. In order to obtain an output feedback regulator, a time-varying finite-dimensional reference observer and a time-varying infinite-dimensional disturbance observer are determined. For this, a systematic backstepping approach is provided. The results of the paper are illustrated for a 4 × 4 hyperbolic system with periodic triangle reference inputs and sinusoidal disturbances subject to time-varying frequencies.

Disturbance Rejection Control for a Vibrating String System

AbstractThis paper is concerned with disturbance rejection control for a vibrating flexible string system in the presence of unknown disturbances. First, the boundary disturbance observer is proposed to deal with the boundary disturbance and the infinite dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. Subsequently, the boundary control and distributed control are developed to suppress the vibration and globally stabilize the string system at its equilibrium position. Under the control proposed, the uniformly bounded stability of the controlled system is testified employing rigorous analysis without resorting to discretization of the partial differential equation dynamics depending on the time and space. Finally, the simulation and comparison results verify the performance of the derived control.

Observer-based backstepping boundary control for a flexible riser system

Abstract In order to achieve the disturbance rejection and vibration abatement of a flexible marine riser system, this article discusses the design of disturbance observers and controller. The riser system subjected to external disturbances is a distributed parameter system in essence and represented by infinite-dimensional equation coupled with finite-dimensional equations. In addition to designing a basic boundary disturbance observer to deal with the time-varying boundary disturbance in this paper, an innovative infinite dimensional disturbance observer is also designed to compensate for the spatially distributed disturbance. Applying these two observers as feedforward compensators, an observer-based boundary controller is formulated by means of combining backstepping technique with boundary control method. Moreover, the well-posedness of the closed-loop riser system is discussed, and simulations are presented to display the effectiveness of formulated control approach.

Infinite-dimensional disturbance-observer-based control for an axially moving non-uniform system with input constraint

In this paper, the vibration control and input saturation constraint problem of an axially moving non-uniform system subject to unknown disturbances is investigated. The key control objectives are to control the vibration of the system and eliminate the effects of the input saturation constraint. To that end, a boundary control with an auxiliary system is designed by utilizing Lyapunov’s direct method. Additionally, a boundary disturbance observer is proposed to deal with the boundary disturbance, and an infinite-dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. With the designed boundary control, uniformly bounded stability of the controlled system is achieved through rigorous Lyapunov analysis without any model reduction. Finally, simulation results are given to show the effectiveness of the designed control scheme.

Disturbance observer design and vibration control for a flexible aircraft wing

This study focuses on the disturbance observer design and vibration control problems for a flexible aircraft wing system. The flexible aircraft wing is modeled as a coupled twist-bending infinite dimensional distributed parameter system. The dynamic equations and boundary conditions are described by partial differential equations and ordinary differential equations, respectively. In this paper, an infinite dimensional disturbance observer is proposed to estimate both the boundary disturbances and the distributed spatiotemporally varying disturbances. Considering the coupling between the bending deformation and the twist deformation, a boundary controller is proposed to suppress the vibration and inhibit the adverse effects of external disturbances. By using the proposed disturbance observer and controller, the uniform boundednesss of the closed-loop system is validated through theoretical analysis. Finally, simulation results are carried out to illustrate the effectiveness of the proposed infinite dimensional disturbance observer and boundary controller.

Solving the regulator problem for a 1-D Schrödinger equation via backstepping * *This work was partially supported by grant no. 800/14 of the Israel Science Foundation.

Abstract We solve the output regulator problem for a system described by a Neumann boundary controlled anti-stable one-dimensional Schrodinger equation by the backstepping approach. The output to be controlled is not required to be measured and its observation operator is assumed to be admissible for a certain Co-semigroup that is related to the original system, while the measurements used for control are located at the boundary First we show that the open-loop system is well-posed. Then we find a state feedback control law to solve the output regulator problem by the backstepping method. We design a finite-dimensional reference observer and an infinite-dimensional disturbance observer. Based on this observer, we propose an output feedback controller to achieve output regulation.

Boundary and Distributed Control for a Nonlinear Three‐Dimensional Euler‐Bernoulli Beam Based On Infinite Dimensional Disturbance Observer

AbstractControl problems in spatially distributed systems are challenging because the disturbance is of infinite dimensions. To this end, this paper discusses an infinite dimensional disturbance observer design, which is illustrated based on a partial differential equation (PDE) model of a nonlinear three‐dimensional Euler‐Bernoulli beam. The basic idea of the observer design is to modify the estimations based on the difference between the estimated output and actual output. Moreover, an auxiliary parameter system is established to help with the analysis. Then a Lyapunov function candidate consisting of the energy of the system, the observer error and an auxiliary term is given. After a series of analyses of the function, distributed controllers and boundary controllers based on the proposed observer are given to restrain vibration. Finally, by numerical simulations, the convergence of the observer is demonstrated, and the efficacy of control performance is also shown.

A backstepping approach to the output regulation of boundary controlled parabolic PDEs

In this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach. Thereby, the outputs to be controlled are not required to be measurable and can be pointwise, distributed or boundary quantities, whereas the measurement is located at the boundary. By solving the state feedback regulator problem in the backstepping coordinates regulator equations with a simple structure result, so that their analysis and solution is facilitated. The output feedback regulator design is completed by determining a finite-dimensional reference observer and an infinite-dimensional disturbance observer. For the latter a backstepping approach is presented that consists of a triangular decoupling in the backstepping coordinates. This allows a systematic design and the explicit derivation of directly verifiable existence conditions for the disturbance observer. It is shown that for the resulting compensator the separation principle holds implying output regulation for the exponentially stable closed-loop system with a prescribed stability margin. The output regulation results of the article are illustrated by means of a parabolic system with an in-domain pointwise controlled output.

Boundary control for a flexible manipulator based on infinite dimensional disturbance observer

This paper focuses on disturbance observer and boundary control design for the flexible manipulator in presence of both boundary disturbance and spatially distributed disturbance. Taking the infinite-dimensionality of the flexural dynamics into account, this study proposes a partial differential equation (PDE) model. Since the spatially distributed disturbance is infinite dimensional, it cannot be compensated by the typical disturbance observer, which is designed by finite dimensional approach. To estimate the spatially distributed disturbance, we propose a novel infinite dimensional disturbance observer (IDDO). Applying the IDDO as a feedforward compensator, a boundary control scheme is designed to regulate the joint position and eliminate the elastic vibration simultaneously. Theoretical analysis validates the stability of both the proposed disturbance observer and the boundary controller. The performance of the closed-loop system is demonstrated by numerical simulations.