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Unified iterative learning control for flexible structures with input constraints

AUTOMATICA 2018年 96卷 326-336页

作者： He, Wei Meng, Tingting He, Xiuyu Ge, Shuzhi Sam Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Univ Sci & Technol Beijing Key Lab Knowledge Automat Ind Proc Minist Educ Beijing 100083 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China Natl Univ Singapore Dept Elect & Comp Engn Singapore 117576 Singapore

This paper proposes a unified framework of iterative learning control for typical flexible structures under spatiotemporally varying disturbances. Input constraints and the external disturbances are smoothly tackled through hyperbolic tangent functions. Boundary iterative learning control (BILC) laws are proposed to guarantee the learning convergence. The closed-loop systems can converge to zero along the iteration axis on the basis of time-weighted Lyapunov-Krasovskii-like composite energy functions (CEF). Simulations are implemented to illustrate the effectiveness of the proposed BILC schemes. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Flexible structure distributed parameter system Boundary iterative learning control Disturbance rejection Input constraint

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A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes

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APPLIED SOFT COMPUTING 2014年第1期25卷 309-321页

作者： Qi, Chenkun Li, Han-Xiong Li, Shaoyuan Zhao, Xianchao Gao, Feng Shanghai Jiao Tong Univ Sch Mech Engn State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China Cent South Univ State Key Lab High Performance Complex Mfg Changsha Hunan Peoples R China Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China

Many industrial processes belong to nonlinear distributed parameter systems (DPS) with significant spatio-temporal dynamics. They often work at multiple operating points due to different production and working conditions. To obtain a global model, the direct modeling and experiments in a large operating range are often very difficult. Motivated by the multi-modeling, a fuzzy-based spatio-temporal multi-modeling approach is proposed for nonlinear DPS. To obtain a reasonable operating space division, a priori information and the fuzzy clustering are used to decompose the operating space from coarse scale to fine scale gradually. To reduce the dimension in the local spatio-temporal modeling, the Karhunen-Loeve method is used for the space/time separation. Both multi-modeling and space/time separation can reduce the modeling complexity. Finally, to get a smooth global model, a three-domain (3D) fuzzy integration method is proposed. Using the proposed method, the model accuracy will be improved and the experiments become easier. The effectiveness is verified by simulations. (C) 2014 Elsevier B.V. All rights reserved.

关键词： distributed parameter system Spatio-temporal modeling Multi modeling Kernel model Space/time separation Fuzzy clustering

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Model reference adaptive control of a cantilevered flexible beam

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JSME INTERNATIONAL JOURNAL SERIES C-MECHANICAL systemS MACHINE ELEMENTS AND MANUFACTURING 2003年第2期46卷 640-651页

作者： Yang, KJ Hong, KS Yoo, WS Matsuno, U Pusan Natl Univ Sch Mech Engn Pusan 609735 South Korea Tokyo Inst Technol Midori Ku Yokohama Kanagawa 2268502 Japan

In this paper, model reference adaptive control of a cantilevered flexible beam with Kelvin-Voigt damping and unknown spatially varying coefficients is investigated. Any mechanically flexible robots/structures are inherently distributed parameter systems whose dynamics are described by partial, rather than ordinary, differential equations. Adaptation laws are derived by the Lyapunov redesign method on an infinite dimensional Hilbert space. To show the well-posedness of a coupled nonlinear system, combined state error and parameter estimation error equations are constructed as an initial value problem of an infinite dimensional evolution equation in weak form. It is then shown through the Lyapunov redesign approach that the state error actually converges asymptotically to zero. With an additional persistence of excitation assumption, the parameter estimation errors are shown to converge to zero as well.

关键词： model reference adaptive control cantilevered flexible beam stability persistence of excitation distributed parameter system

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NUMERICAL APPROXIMATION FOR THE INFINITE-DIMENSIONAL DISCRETE-TIME OPTIMAL LINEAR-QUADRATIC REGULATOR PROBLEM

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1988年第2期26卷 428-451页

作者： GIBSON, JS ROSEN, IG NASA LANGLEY RES CTRINST COMP APPLICAT SCI & ENGNHAMPTONVA 23665 UNIV SO CALIF DEPT MATHLOS ANGELESCA 90089

An abstract approximation framework is developed for the finite and infinite horizon discrete-time linear-quadratic regulator problems for systems whose state dynamics are described by a linear semigroup of operators on an infinite-dimensional Hilbert space. The schemes included in the framework yield finite-dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

关键词： 93C25 93C55 65J10 linear-quadratic regulator discrete-time distributed parameter system

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DEPLOYMENT RETRIEVAL CONTROL OF TETHERED SUBSATELLITE THROUGH AN OPTIMAL PATH

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1994年第6期17卷 1292-1298页

作者： FUJII, HA ANAZAWA, S Tokyo Metropolitan Institute of Technology Hino Tokyo 191 Japan

Development of a feedback control law to follow an optimal path is presented concerning the deployment/retrieval phase of a subsatellite connected to the Shuttle through a tether. The optimal path to be tracked is obtained numerically by solving a two-point boundary-value problem with inequality constraints on tether tension that is the control force, with fixed boundary conditions, and with an unspecified terminal time. The feedback control algorithm is designed using a Lyapunov function to asymptotically reduce the deviation of the actual trajectory from the optimal path. The Lyapunov function is defined to be positive definite and to be zero when the trajectory coincides simultaneously with the optimal path. The present method of control is simulated numerically, and the results show excellent controlled response of the tethered subsatellite system. A comparison of the present approach with the neighboring optimum feedback control is also presented and shows the superior performance of the tracking-type control using the Lyapunov function for large initial variations from the optimal path.

关键词： Feedback Control Control Algorithm Boundary Value Problems Optimal Control Numerical Simulation distributed parameter system Conjugate Gradient Method Numerical Analysis Tethered Satellite system Artificial Gravity

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SLIDING MODE CONTROL FOR AN INHOMOGENEOUS HEAT EQUATION WITH GLOBAL CONSTRAINT

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ASIAN JOURNAL OF CONTROL 2017年第6期19卷 2116-2126页

作者： Zhang, Shuang Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Peoples R China

In this paper, an inhomogeneous heat equation with distributed load is controlled, on the basis of an infinite dimensional generalization of sliding-mode control method. The control law is designed so that: (i) the temperature can track a desired reference signal, and (ii) the temperature can remain in a constrained region. We show that, with the designed control, the tracking error is bounded stable without violation of the constraint. The stability is proved under the designed control law. Numerical simulations are given to illustrate the effectiveness of the designed control law.

关键词： distributed parameter system sliding-mode control heat equation infinite dimensional system global constraint

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INVARIANCE OF THE APPROXIMATELY REACHABLE SET UNDER NONLINEAR PERTURBATIONS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1991年第3期29卷 731-750页

作者： NAITO, K SEIDMAN, TI UNIV MARYLAND BALTIMORE CTY DEPT MATH & STAT BALTIMORE MD 21228 USA

This paper considers nonlinear perturbations of control systems with linear dynamics and seeks to analyze whether the approximately reachable set may be left unchanged by this pertubation. Under suitable conditions it is shown that this analysis may be reduced to the presumably simpler analysis of such invariance for a family of affine perturbations. Interest centers on the context of infinite-dimensional state spaces so the system may, for example, correspond to a hyperbolic or parabolic partial differential equation.

关键词： APPROXIMATE REACHABILITY CONTROL distributed parameter system NONLINEAR PERTURBATION INVARIANCE

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WIDE-BAND CONTROL OF GYRO ACCELEROMETER MULTISENSORS IN A STRAPDOWN GUIDANCE-system

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1992年第4期15卷 855-860页

作者： CONSTANCIS, P SORINE, M INST NATL RECH INFORMAT & AUTOMAT F-78153 LE CHESNAYFRANCE UNIV PARIS 09 F-75016 PARISFRANCE

This paper describes an inertial measurement unit based on three dry tuned gyroscopes, two of which are unbalanced. This configuration, without the three usual accelerometers, leads to savings in space, weight, and cost that are necessary in guidance systems for agile missiles. Design objectives are wideband estimation of angular rate and linear acceleration applied to the inertial measurement unit together with high stiffness of caging loops. The contribution of this paper is to show how to address the coupled high-frequency dynamics of the six measurement outputs of the system, by applying the so-called linear quadratic Gaussian technique. First the linearized model of the rotor motion of each dry-tuned gyroscope is derived from a mechanical analysis. Then the design of the controller/estimator is described. Performances are illustrated with test data.

关键词： Accelerometer Guidance system Gyroscopes IMU Linear Quadratic Gaussian Agile Missiles distributed parameter system Gaussian White Noise Riccati Equations Damping Coefficient

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Robust output regulation and the preservation of polynomial closed-loop stability

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2014年第18期24卷 3409-3436页

作者： Paunonen, Lassi Pohjolainen, S. Tampere Univ Technol Dept Math FIN-33101 Tampere Finland

In this paper, we study the robust output regulation problem for distributed parameter systems with infinite-dimensional exosystems. The main purpose of this paper is to demonstrate the several advantages of using a controller that achieves polynomial closed-loop stability, instead of a one stabilizing the closed-loop system strongly. In particular, the most serious unresolved issue related to strongly stabilizing controllers is that they do not possess any known robustness properties. In this paper, we apply recent results on the robustness of polynomial stability of semigroups to show that, on the other hand, many controllers achieving polynomial closed-loop stability are robust with respect to large and easily identifiable classes of perturbations to the parameters of the plant. We construct an observer based feedback controller that stabilizes the closed-loop system polynomially and solves the robust output regulation problem. Subsequently, we derive concrete conditions for finite rank perturbations of the plant's parameters to preserve the closed-loop stability and the output regulation property. The theoretical results are illustrated with an example where we consider the problem of robust output tracking for a one-dimensional heat *** (c) 2013 John Wiley & Sons, Ltd.

关键词： robust output regulation distributed parameter system polynomial stability internal model principle

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A robust observer design for a flexible manipulator based on a PDE model

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JOURNAL OF VIBRATION AND CONTROL 2017年第6期23卷 871-882页

作者： Jiang, Tingting Liu, Jinkun He, Wei Beijing Univ Aeronaut & Astronaut Sch Automat Sci & Elect Engn Beihang Univ Beijing 100191 Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Peoples R China

This paper proposes a robust observer for a flexible single-link manipulator based on the partial differential equation (PDE) dynamic model. Unlike observers for the PDE model introduced by previous researchers, this observer is designed to estimate the distributed spatiotemporally varying states with unknown boundary disturbance and spatially distributed disturbance. The asymptotic stability of the proposed observer is proved by theoretical analysis and demonstrated by simulation results.

关键词： distributed parameter system flexible manipulator PDE model robust observer

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