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Boundary control of dual Timoshenko arms for grasping and orientation control

INTERNATIONAL JOURNAL OF CONTROL 2020年第7期93卷 1510-1520页

作者： Endo, Takahiro Wu, Dongming Matsuno, Fumitoshi Kyoto Univ Dept Mech Engn & Sci Kyoto Japan

This paper discusses grasping and orientation control of an object by dual one-link Timoshenko arms. The control objective is to control the grasping force and the orientation of the object, and to suppress the vibration of the arms at the same time. For this objective, we derive a boundary controller based on the total energy of the system described by a hybrid PDE-ODE model, and asymptotic stability of the closed-loop system is proven by the LaSalle's invariance principle. In addition, numerical simulations are conducted and the results indicate that the derived controller can realise the grasping and orientation control of an object by dual one-link Timoshenko arms.

关键词： Flexible arms grasping and manipulation asymptotic stability distributed parameter systems

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Delay compensated control of the Stefan problem and robustness to delay mismatch

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2020年第6期30卷 2304-2334页

作者： Koga, Shumon Bresch-Pietri, Delphine Krstic, Miroslav Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA PSL Res Univ CAS MINES ParisTech Paris France

This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first-order hyperbolic partial differential equation (PDE), resulting in a cascaded transport-diffusion PDE system defined on a time-varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the Script capital H1 norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.

关键词： backstepping distributed parameter systems nonlinear stabilization Stefan problem time delay systems

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Network-based control of a semilinear damped beam equation under point and pointlike measurements

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systems & CONTROL LETTERS 2020年第0期136卷 104617-000页

作者： Terushkin, Maria Fridman, Emilia Tel Aviv Univ Dept Elect Engn & Syst IL-69978 Tel Aviv Israel

We consider distributed static output-feedback stabilization of a damped semilinear beam equation. distributed in space measurements are either point or pointlike, where a pointlike measurement is the state value averaged on a small subdomain. Network-based implementation of the control law which enters the PDE through shape functions is studied, where variable sampling intervals and transmission delays are taken into account. Our main objective is to derive and compare the results under both types of measurements in terms of the upper bound on the delays and sampling intervals that preserve the stability for the same (as small as possible) number of sensors/actuators. For locally Lipschitz nonlinearities, regional stabilization is achieved. Numerical results show that the pointlike measurements lead to larger delays and samplings, provided the subdomains, where these measurements are averaged, are not too small. (C) 2019 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Sampled-data control Delay Point measurements Lyapunov-Krasovskii method

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Spatial domain decomposition approach to dynamic compensator design for linear space-varying parabolic MIMO PDEs

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IET CONTROL THEORY AND APPLICATIONS 2020年第1期14卷 39-51页

作者： Wang, Jun-Wei Univ Sci & Technol Beijing Sch Automat & Elect Engn Key Lab Knowledge Automat Ind Proc Minist Educ Beijing 100083 Peoples R China

This study addresses the problem of dynamic compensator design for exponential stabilisation of linear space-varying parabolic multiple-input-multiple-output (MIMO) partial differential equations (PDEs) subject to periodic boundary conditions. With the aid of the observer-based feedback control technique, an observer-based dynamic feedback compensator, whose implementation requires only a few actuators and sensors active over partial areas of the spatial domain, is constructed such that the resulting closed-loop coupled PDEs is exponentially stable. The spatial domain is divided into multiple subdomains according to the minimum of the actuators' number and the sensors' one. By Lyapunov direct method and two general variants of Poincare-Wirtinger inequality at each subdomain, sufficient conditions for the existence of such feedback compensator are developed and presented in terms of algebraic linear matrix inequalities (LMIs) in space. Based on the extreme value theorem, LMI-based sufficient and necessary conditions are presented for the feasibility of algebraic LMIs in space. Finally, numerical simulation results are presented to support the proposed design method.

关键词： actuators feedback closed loop systems Lyapunov methods compensation control system synthesis distributed parameter systems nonlinear control systems linear matrix inequalities asymptotic stability partial differential equations observers spatial domain decomposition approach dynamic compensator design linear space-varying parabolic MIMO exponential stabilisation periodic boundary conditions observer-based feedback control technique observer-based dynamic feedback compensator partial areas actuators subdomain conditions sufficient conditions algebraic linear matrix inequalities LMI-based conditions closed-loop coupled PDEs multiple-input-multiple-output partial differential equations

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On the Lyapunov-based second-order SMC design for some classes of distributed parameter systems

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2012年第4期29卷 437-457页

作者： Orlov, Yury Pisano, Alessandro Scodina, Stefano Usai, Elio Univ Cagliari Dept Elect & Elect Engn Cagliari Italy CICESE Res Ctr Ensenada Baja California Mexico

This paper addresses the Lyapunov-based design of second-order sliding mode controllers in the domain of distributed parameter systems (DPSs). To the best of our knowledge, the recent authors' publications (Orlov et al., 2010, Continuous state-feedback tracking of an uncertain heat diffusion process. Syst. Control Lett., 59, 754-759;Orlov et al., 2011, Exponential stabilization of the uncertain wave equation via distributed dynamic input extension. IEEE Trans. Autom. Control, 56, 212-217;Pisano et al., 2011, Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J. Control Optim., 49, 363-382) represent the seminal applications of second-order sliding mode control techniques to DPSs. A Lyapunov-based framework of analysis was found to be appropriate in the above publications. While reviewing the main existing results in this new field of investigation, the paper provides the novelty as well and gives several hints and perspectives for the generalization, listing some open problems.

关键词： distributed parameter systems heat equation wave equation second-order sliding mode control Lyapunov analysis

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DNN-state identification of 2D distributed parameter systems

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INTERNATIONAL JOURNAL OF systems SCIENCE 2012年第2期43卷 296-307页

作者： Chairez, I. Fuentes, R. Poznyak, A. Poznyak, T. Escudero, M. Viana, L. IPN UPIBI Dept Bioelect Mexico City 07738 DF Mexico IPN CINVESTAV Dept Automat Control Mexico City 07738 DF Mexico IPN ESIQIE SEPI Mexico City 07738 DF Mexico

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs is proposed. The adaptive laws for weights ensure the 'practical stability' of the DNN-trajectories to the parabolic 2D-PDE states. To verify the qualitative behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.

关键词： neural networks adaptive identification distributed parameter systems partial differential equations practical stability

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An LMI Approach to Stability Analysis of Coupled Parabolic systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第1期65卷 404-411页

作者： Wakaiki, Masashi Kobe Univ Grad Sch Syst Informat Kobe Hyogo 6578501 Japan

We analyze the exponential stability of a class of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis. Using a quadratic Lyapunov function, we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities.

关键词： Stability analysis Control theory Lyapunov methods distributed parameter systems Approximation error Linear matrix inequalities Exponential stability linear matrix inequalities (LMIs) lyapunov functional partial differential equations (PDE)

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Twenty years of distributed port-Hamiltonian systems: a literature review

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2020年第4期37卷 1400-1422页

作者： Rashad, Ramy Califano, Federico van der Schaft, Arjan J. Stramigioli, Stefano Univ Twente Robot & Mechatron Grp Enschede Netherlands Univ Groningen Bernoulli Inst Math Comp Sci & AI Groningen Netherlands ITMO Univ St Petersburg Russia

The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups.

关键词： port-Hamiltonian theory distributed parameter systems multi-physical systems energy-based control spatial discretization

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Laser Sintering Control for Metal Additive Manufacturing by PDE Backstepping

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IEEE TRANSACTIONS ON CONTROL systems TECHNOLOGY 2020年第5期28卷 1928-1939页

作者： Koga, Shumon Krstic, Miroslav Beaman, Joseph Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA Univ Texas Austin Dept Mech Engn Austin TX 78705 USA

Metal additive manufacturing (AM) has been intensively advanced due to numerous industrial applications, such as automobiles, aerospace, consumer electronics, and medical devices. The dynamics of the melt pool via laser sintering for metal AM has been studied by means of the thermodynamic phase change model known as the "Stefan problem". In this article, we develop a control design for the laser power to drive the depth of the melt pool to the desired set point. The governing equation is described by a partial differential equation (PDE) defined on a time-varying spatial domain, which is dependent on the PDE state, and the optical penetration of the laser energy affects the PDE dynamics in the domain as well as at the surface boundary. First, we design the full-state feedback control law utilizing the entire spatial profile of the temperature in the melt pool and the moving interface position. The closed-loop system is proven to satisfy some conditions to validate the physical model, and its origin is shown to be exponentially stable. Next, we propose an observer-based output feedback control law by reconstructing the temperature profile with the availability of only the measured interface position and prove the analogous properties of the closed-loop system. Numerical simulation for a controller designed on a single-phase Stefan model is conducted on a more complex and realistic two-phase Stefan model, which incorporates the cooling effect from the solid phase. In addition, a bias in the interface location measurement is considered. The numerical results illustrate the robustness of the proposed feedback. By lowering the initial temperature in the solid and by increasing the interface sensor bias to more extreme levels, which leads to the controller's failure (where the failure is exhibited through the entire metal freezing and the melt pool disappearing), we explore the limits of how much uncertainty our control law can handle.

关键词： Metals Power lasers Solid modeling Laser modes Temperature control Laser feedback Laser sintering Backstepping distributed parameter systems Laser sintering nonlinear stabilization Stefan problem

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Stabilization and tracking control of a time-variant linear hyperbolic PIDE using backstepping

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AUTOMATICA 2020年 116卷 108929-000页

作者： Anfinsen, Henrik Aamo, Ole Morten Norwegian Univ Sci & Technol NTNU Dept Engn Cybernet N-7491 Trondheim Norway

We extend previous results regarding infinite-dimensional backstepping-based controller design for linear hyperbolic partial (integro-)differential equations (P(I)DEs), and derive a state-feedback controller for a PIDE system with time-varying system parameters. The system state converges to zero in the -norm, in a finite time corresponding to the propagation time between the boundaries. Secondly, the controller is slightly modified to solve an output tracking problem. The derived controllers are demonstrated in simulations. The derived state-feedback controllers can also be combined with state observers into output-feedback controllers. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Hyperbolic systems Linear systems Boundary control

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