A class of optimal control problems for hyperbolic systems in two-dimensional space is considered. An approach is proposed to damp the undesirable vibrations in the structures by pointwise moving force actuators exten...
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A class of optimal control problems for hyperbolic systems in two-dimensional space is considered. An approach is proposed to damp the undesirable vibrations in the structures by pointwise moving force actuators extending over the spatial region occupied by the structure. A class of performance indices is introduced that includes functions of the state variable, its first and second-order space derivatives and first-order time derivative evaluated at a preassigned terminal time, and a suitable penalty term involving the control forces. A maximum principle is given for such general scanning control problem that facilitates the determination of the unique optimal control. A solution method is developed for the active vibration control of plates of general shape. The implementation of the method is presented and the effectiveness of a single moving force actuator is investigated and compared to a single fixed force actuator by a specific numerical example. (C) 2009 Elsevier B.V. All rights reserved.
The classical Lagrangian and Hamiltonian formulation of an electrical transmission line is reviewed and extended to allow for varying boundary conditions, The method is based on the definition of an infinite-dimension...
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The classical Lagrangian and Hamiltonian formulation of an electrical transmission line is reviewed and extended to allow for varying boundary conditions, The method is based on the definition of an infinite-dimensional analogue of the affine Lagrangian and Hamiltonian input-output systems formulation. The boundary energy flow is then captured in an interaction Lagrangian. This leaves the associated Hamiltonian equations of motion symplectic in form, while the internal Hamiltonian still coincides with the total stored energy in the transmission line. The framework is, however, limited to a line that is terminated on both ends by independent voltage sources. This stems from the fact that the classical formulation captures only one wave equation for a lossless transmission line in terms of an integrated charge density. Additionally, the inclusion of the usual line resistance and shunt conductance via a Rayleigh dissipation function(al) is nontrivial. To circumvent these problems, a family of alternative Lagrangian functionals is proposed. The method is inspired by a (not so well-known) concept from network theory called 'the traditor'.
This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially ...
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ISBN:
(纸本)9781424445233
This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE) in an appropriate functional space setting. Low dimensional representation of the KSE is used in the synthesis of a finite dimensional linear quadratic regulator (LQR) in the full-state feedback control realization and in a compensator design with a Luenberger-type observer. The proposed control problem formulation and the performance and robustness of the closed-loop system in the full state-feedback, output-feedback and in the output-feedback with the presence of noise controller realization have been evaluated through simulations.
In this work an infinite dimensional system representation of a highly dissipative Kuramoto-Sivashinsky equation (KSE) is been utilized in the model modal predictive control (MMPC) synthesis framework to achieve asymp...
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ISBN:
(纸本)9781424438723
In this work an infinite dimensional system representation of a highly dissipative Kuramoto-Sivashinsky equation (KSE) is been utilized in the model modal predictive control (MMPC) synthesis framework to achieve asymptotic stabilization of an unstable KS equation in the presence of input and point exerted state constraints. The KS equation is initially defined in an appropriate functional space setting and an exact transformation is used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE). An appropriate discrete infinite dimensional representation of the abstract boundary control problem is used for synthesis of low dimensional model modal predictive controller (MMPC) incorporating both the pointwise enforced KSE state constraints and input constraints. The proposed control problem formulation and the performance of the closed-loop system in the full state-feedback controller realization have been evaluated through simulations.
Abstract This paper proposes a control strategy for a Diesel Oxidation Catalyst (DOC) which is grounded on a one-dimensional distributedparameter model. This first principles model for the propagation of the temperat...
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Abstract This paper proposes a control strategy for a Diesel Oxidation Catalyst (DOC) which is grounded on a one-dimensional distributedparameter model. This first principles model for the propagation of the temperature variations accounts for spatially distributed heat generation (due to oxidation of reductants). As is discussed, heat generation can be regarded as equivalent inlet temperature variations. This fact is supported by experimental results. By nature, DOC outlet temperature response includes long and time-varying delays. An approximation of the proposed model allows to derive delays analytically, and can be used to schedule control parameters. As a consequence, it is easy to design several standard controllers for the DOC outlet temperature which account for the effects of the inlet temperature (disturbance) and the reductant (control). In this paper, simulation results are presented for a PI, a PID, and a Smith predictor. Interestingly, the three controllers use solely parameters determined from the previous analysis and do not need any extra tuning parameter. The strategies are tested on a standard NEDC driving cycle in simulation. It appears that, among these standard strategies, the DOC partial derivative equations can be efficiently controlled using the presented Smith predictor.
Growing interest in applications of distributedsystems, such as multi-agent systems, increases demands on identification of distributedsystems from partial information sources collected by local agents. We are conce...
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Growing interest in applications of distributedsystems, such as multi-agent systems, increases demands on identification of distributedsystems from partial information sources collected by local agents. We are concerned with fully distributed scenario where system is identified by multiple agents, which do not estimate state of the whole system but only its local ‘state'. The resulting estimate is obtained by merging of marginal and conditional posterior probability density functions (pdf) on such local states. We investigate the use of recently proposed non-parametric log-normal merging of such ‘fragmental’ pdfs for this task. We derive a projection of the optimal merger to the class of weighted empirical pdfs and mixtures of Gaussian pdfs. We illustrate the use of this technique on distributed identification of a controlled autoregressive model.
The problem under consideration is to determine an activation policy of discrete scanning sensors in such a way as to maximize the power of a simple parametric hypothesis test, which verifies the nominal state of the ...
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The problem under consideration is to determine an activation policy of discrete scanning sensors in such a way as to maximize the power of a simple parametric hypothesis test, which verifies the nominal state of the considered distributed system specified over a given multi-dimensional spatial domain. The optimal locations of sensors are determined based on the D s -optimality criterion defined on the respective Fisher Information Matrix. The proposed approach exploits the notion of directly constrained design measures recently introduced in modern optimum experimental design theory which leads to an extremely fast iterative procedure of exchange type. In this work, a general scheme of such an approach leading to maximization of the fault detection efficiency in distributed-parameter systems is delineated and tested via computer simulations regarding an advection-diffusion problem.
This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially ...
详细信息
ISBN:
(纸本)9781424445233
This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE) in an appropriate functional space setting. Low dimensional representation of the KSE is used in the synthesis of a finite dimensional linear quadratic regulator (LQR) in the full-state feedback control realization and in a compensator design with a Luenberger-type observer. The proposed control problem formulation and the performance and robustness of the closed-loop system in the full state-feedback, output-feedback and in the output-feedback with the presence of noise controller realization have been evaluated through simulations.
In this work an infinite dimensional system representation of a highly dissipative Kuramoto-Sivashinsky equation(KSE) is been utilized in the model modal predictive control(MMPC) synthesis framework to achieve asympto...
详细信息
In this work an infinite dimensional system representation of a highly dissipative Kuramoto-Sivashinsky equation(KSE) is been utilized in the model modal predictive control(MMPC) synthesis framework to achieve asymptotic stabilization of an unstable KS equation in the presence of input and point exerted state *** KS equation is initially defined in an appropriate functional space setting and an exact transformation is used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation(PDE).An appropriate discrete infinite dimensional representation of the abstract boundary control problem is used for synthesis of low dimensional model modal predictive controller(MMPC) incorporating both the pointwise enforced KSE state constraints and input *** proposed control problem formulation and the performance of the closed-loop system in the full statefeedback controller realization have been evaluated through simulations.
This paper considers the stabilization problem of a one-dimensional unstable heat conduction system subject to parametric variations and boundary uncertainties. This system is modeled as a parabolic partial differenti...
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ISBN:
(纸本)9781424445233
This paper considers the stabilization problem of a one-dimensional unstable heat conduction system subject to parametric variations and boundary uncertainties. This system is modeled as a parabolic partial differential equation (PDE) and is only powered from one boundary with a Dirichlet type of actuator. By taking the Volterra integral transformation, we obtain a nominal PDE with asymptotic stability characteristics in the new coordinates when an appropriate boundary control input is applied. The associated Lyapunov function can then be used for designing an infinite-dimensional sliding surface, on which the system exhibits exponential stability, invariant of the bounded matched disturbance, and is robust against certain types of parameter variations. A continuous variable structure boundary control law is employed to attain the sliding mode on the sliding surface. The proposed method can be extended to other parabolic PDE systems such as diffusion-advection system. Simulation results are demonstrated and compared with the other outstanding back-stepping control schemes.
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