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Backstepping Approach to the Adaptive Regulator Design for a One-Dimensional Wave Equation with General Input Harmonic Disturbance

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Journal of systems Science & Complexity 2017年第2期30卷 253-279页

作者： GUO Wei SHAO Zhi-Chao Department of Applied Mathematics School of StatisticsUniversity of International Business and EconomicsBeijing 100029China

This paper considers the parameter estimation and stabilization of an unstable one-dimen- sional wave equation with matched general harmonic disturbance at the controlled end. The back- stepping method for infinite-dimensional system is adopted in the design of the adaptive regulator. 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 unes tn ~n^nitv

关键词： Backstepping method distributed parameter system disturbance rejection stability.

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Nonlinear disturbance observer-based direct joint control for manipulation of a flexible payload with output constraints

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INTERNATIONAL JOURNAL OF CONTROL 2023年第5期96卷 1377-1388页

作者： Liu, Shuyang Liu, Zhijie Li, Yuanchun He, Wei Changchun Univ Technol Sch Elect & Elect Engn Changchun Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Inst Artificial Intelligence Xueyuan Rd 30 Beijing 100083 Peoples R China

This paper discusses a nonlinear direct joint control scheme for manipulation of a flexible payload by a single-arm system with disturbances, parametric uncertainty and output constraints. The flexible payload can be considered as an Euler-Bernoulli beam. The equations of the coupled rigid-flexible motion are established on the basis of the ordinary differential equations (ODEs) and partial differential equation (PDE), which can avoid system spillover instability. A novel nonlinear disturbance observer-based control approach is proposed to enhance its disturbance attenuation ability. To handle the system parametric uncertainty, we apply adaptive direct joint control to approximate the unknown parameter, which does not require endpoint boundary control. Then a Barrier Lyapunov Function (BLF) is adopted to eliminate the impact of output restriction. The asymptotic stability of the closed-loop system is rigorously proven by semi-group theory and LaSalle's Invariance Principle extended to an infinite-dimensional system. Finally, the performance of the direct joint control is validated via numerical simulations.

关键词： Nonlinear disturbance observer adaptive control output constraints direct joint control distributed parameter system

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Pointwise exponential stabilization of a linear parabolic PDE system using non-collocated pointwise observation

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AUTOMATICA 2018年 93卷 197-210页

作者： Wang, Jun-Wei Liu, Ya-Qiang Sun, Chang-Yin Univ Sci & Technol Beijing Minist Educ Sch Automat & Elect Engn Key Lab Knowledge Automat Ind Proc Beijing 100083 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Jiangsu Peoples R China

This paper deals with the problem of exponential stabilization for a linear distributed parameter system (DPS) using pointwise control and non-collocated pointwise observation, where the system is modeled by a parabolic partial differential equation (PDE). The main objective of this paper is to construct an output feedback controller for pointwise exponential stabilization of the linear parabolic PDE system using the non-collocated pointwise observation. The observer-based output feedback control technique is utilized to overcome the design difficulty caused by the non-collocation pointwise observation. We construct a Luenberger-type PDE state observer to exponentially track the state of the PDE system. A collocated pointwise feedback controller is proposed based on the estimated state. A variation of Poincare - Wirtinger inequality is derived and the spatial domain is decomposed into multiple sub-domains according to the number of the actuators and sensors. By using Lyapunov's direct method, integration by parts, and the variation of Poincare - Wirtinger inequality at each sub-domain, sufficient conditions for the existence of the observer-based out feedback controller are developed such that the resulting closed loop system is exponentially stable, and presented in terms of standard linear matrix inequalities (LMIs). Furthermore, the closed-loop well-posedness analysis is also provided by the C-0-semigroup approach. Extensive numerical simulation results are presented to show the performance of the proposed output feedback controller. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Non-collocation Pointwise stabilization Co-semigroup Observer-based output feedback control distributed parameter system

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Adaptive Boundary Vibration Control and Angle Tracking Consensus of Networked Flexible Timoshenko Manipulator systems

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IEEE TRANSACTIONS ON systemS MAN CYBERNETICS-systemS 2023年第5期53卷 2949-2960页

作者： Yao, Xiangqian Liu, Yu Zhao, Wei South China Univ Technol Sch Automation Sci & Engn Guangzhou 510640 Peoples R China Guangzhou Inst Modern Ind Technol Res & Dev Ctr Precis Elect Mfg Technol Guangzhou 511458 Peoples R China

The adaptive boundary vibration control and leader-follower angle tracking consensus problem of networked flexible Timoshenko manipulator systems in the case of parametric uncertainties and external disturbances are investigated. To mitigate the impacts of external disturbances and parameter uncertainties, we employ the adaptive tuning techniques to design some suitable adaptive terms. Then with network topology is connected, we propose some novel distributed adaptive continuous-time boundary control algorithms. Based on a novel combination of Lyapunov-based control and Barbalat's lemma, the asymptotic control performances can be achieved. Besides, some novel distributed adaptive event-triggered boundary control algorithms are also proposed for the undisturbed Timoshenko manipulators. The advantage of the considered event-triggered algorithms is that they can avoid continuous updates of the controller and thereby can effectively save control resources. Moreover, Zeno behaviors are excluded for all agents to ensure the practicality of digital sampling. Finally, we illustrate the feasibility of the proposed control algorithms through numerical simulation examples.

关键词： Angle tracking consensus distributed parameter system event-based control Timoshenko manipulator vibration control

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VALIDATION OF FINITE-DIMENSIONAL APPROXIMATE SOLUTIONS FOR DYNAMICS OF distributed-parameter systemS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1995年第1期18卷 87-95页

作者： JUNKINS, JL LEE, SC Texas A&M University College Station Texas 77843

An inverse dynamics method is introduced for constructing exact special-case solutions for hybrid coordinate ordinary/partial systems of differential equations (hybrid ODE/PDE systems). The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special-case solutions can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. The exact solution is constructed such that it is a differentiable, continuous-function neighbor of the given approximate numerical solution. This continuous solution is then substituted into the governing system of ODEs/PDEs and a full complement of distributed and boundary forces is determined algebraically to exactly satisfy the differential equations, This process has been automated by computer symbol manipulation. Since the exact special-case algebraic solutions can be evaluated anywhere in space and time, this approach is ideally suited to providing a true exact motion and the corresponding forces for studying the convergence errors in a family of approximate solutions. This methodology makes it possible for one to rigorously determine exact solution errors for a significant class of ODE/PDE systems for which the initial-value problem is not, in general, exactly solvable. We explore the utility of this method in validating numerical solution methods.

关键词： distributed parameter system Finite Element Approximation Second Order Differential Equations Flexible Structures Numerical Simulation Solution Algorithm Runge Kutta Methods Shear Deformation Feedback Control Riccati Equations

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INFINITE-DIMENSIONAL VOLTERRA-STIELTJES EVOLUTION-EQUATIONS AND RELATED OPTIMAL-CONTROL PROBLEMS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1993年第3期31卷 539-568页

作者： YONG, JM Fudan Univ Shanghai China

Due to impulse control problems, a controlled Volterra-Stieltjes system in some Banach space is studied. In the system, the vector measure appearing in the Stieltjes-type integral (called Young integral here) is taken as a part of control action. In this paper, a general theory for infinite-dimensional Volterra-Stieltjes evolution equations is presented, and, for an optimal control problem governed by such type controlled system with a general endpoint constraint, a Pontryagin-type maximum principle is proved.

关键词： YOUNG INTEGRAL VOLTERRA-STIELTJES INTEGRAL EQUATION distributed parameter system MEASURE CONTROL MAXIMUM PRINCIPLE OPTIMAL CONTROL

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Boundary Antidisturbance Control of a Spatially Nonlinear Flexible String system

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2020年第6期67卷 4846-4856页

作者： Zhao, Zhijia Ahn, Choon Ki Li, Han-Xiong Guangzhou Univ Sch Mech & Elect Engn Guangzhou 510006 Peoples R China Korea Univ Sch Elect Engn Seoul 136701 South Korea City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China

The aim of this article is to establish a novel boundary antidisturbance control to dampen the oscillation of a spatially nonlinear flexible string system influenced by unknown disturbances. To realize this, new disturbance rejection controllers are constructed to effectively suppress the external disturbances for vibration reduction with the help of a newly designed disturbance observer. Adopting Lyapunov direct method, we ensure that the derived control system is uniformly bounded stable. Simulations are also performed to demonstrate the feasibility and validity of the suggested strategy.

关键词： Vibrations Estimation error Control systems Three-dimensional displays Oscillators Disturbance observers Antidisturbance control boundary control disturbance observer (DO) distributed parameter system vibration control

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Luenberger boundary observer synthesis for Sturm-Liouville systems

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INTERNATIONAL JOURNAL OF CONTROL 2010年第7期83卷 1504-1514页

作者： Vries, D. Keesman, K. J. Zwart, H. Wageningen Univ Syst & Control Grp NL-6700 AA Wageningen Netherlands KWR Watercycle Res Inst Water Technol Grp NL-3433 PE Nieuwegein Netherlands Univ Twente Fac EEMCS Dept Appl Math NL-7500 AE Enschede Netherlands

A static Luenberger observer of a system with Sturm-Liouville operator is synthesised with the aid of a boundary control formulation. To this aim, approximate observability, detectability and stability of the system i... 详细信息

关键词： boundary control system observer synthesis Luenberger observer distributed parameter system Sturm-Liouville system

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distributed PIEZOELECTRIC POLYMER ACTIVE VIBRATION CONTROL OF A CANTILEVER BEAM

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1985年第5期8卷 605-611页

作者： BAILEY, T HUBBARD, JE Massachusetts Institute of Technology Cambridge Massachusetts

An active vibration damper for a cantilever beam was designed using a distributed-parameter actuator and distributed-parameter control theory. The distributed-parameter actuator was a piezoelectric polymer, poly(vinylidene fluoride). Lyapuov's second method for distributed-parameter systems was used to design a control algorithm for the damper. If the angular velocity of the tip of the beam is known, all modes of the beam can be controlled simultaneously. Preliminary testing of the damper was performed on the first mode of the cantilever beam. A linear constant-gain controller and a nonlinear constant-amplitude controller were compared. The constant-gain controller provided more than a factor of two increase in the modal damping with a feedback voltage limit of 200 V rms. With the same voltage limit, the constant-amplitude controller achieved the same damping, but increased the modal loss factor by more than an order of magnitude to at least 0.040 for small vibration levels.

关键词： Cantilever Beam Piezoelectric Polymer Active Vibration Control distributed parameter system Actuators Control Algorithm Accelerometer Bernoulli Euler Beams Transverse Vibrations Angular Motion Oscilloscope

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A Lyapunov-based design of dynamic feedback compensator for linear parabolic MIMO PDEs

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2020年第2期37卷 455-474页

作者： Liu, Ya-Qiang Wang, Jun-Wei Sun, Chang-Yin Univ Sci & Technol Beijing Sch Automat & Elect Engn Minist Educ Key Lab Knowledge Automat Ind Proc Beijing 100083 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Peoples R China

This paper discusses dynamic feedback compensator design for a linear parabolic partial differential equation (PDE) with multiple inputs and multiple outputs. Actuating control inputs are provided by actuators distributed over partial areas (or active at specified positions) of the spatial domain, and observation outputs are taken from the non-collocated sensors distributed over partial areas of the spatial domain. An observer-based dynamic feedback compensator is constructed via the observer-based feedback control technique to exponentially stabilize the multi-input-multi-output PDE in the spatial L-2 norm. By constructing an appropriate Lyapunov function candidate and using two variants of Poincare-Wirtinger inequality, sufficient conditions on the existence of such observer-based dynamic feedback compensator are developed and presented in terms of linear matrix inequalities. The well posedness of the closed-loop coupled PDEs is also analyzed within the framework of C-0 semigroup theory. Finally, numerical simulation results are given to show the effectiveness of the proposed method.

关键词： dynamic feedback compensator MIMO Poincare-Wirtinger inequality linear matrix inequality distributed parameter system

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