In this paper, vibration control of a flexible cantilevered beam with collocated piezoelectric sensors and actuators is studied. A dynamic governing equation of motion for the smart cantilevered beam is derived by app...
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In this paper, vibration control of a flexible cantilevered beam with collocated piezoelectric sensors and actuators is studied. A dynamic governing equation of motion for the smart cantilevered beam is derived by applying Hamilton principle. Linear feedback controls for the smart beam are presented. By using LaSall's invariant principle in infinite dimensional space and linear semigroup theory, it is shown that implementation of these controls result in vibration suppression.
systems of conservation laws can be modeled (including dissipation) in an elegant, physically insightful way within the port-Hamiltonian framework. A structure-preserving discretization renders the partial differentia...
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systems of conservation laws can be modeled (including dissipation) in an elegant, physically insightful way within the port-Hamiltonian framework. A structure-preserving discretization renders the partial differential equations ordinary ones. In this paper, we show how the structure of the lumped-parameter state representation for two conservation laws on a one-dimensional spatial domain can be exploited to easily formulate different (inverse) models. Based thereon, a simple modular procedure for feedforward controller design is developed, using known results from the dynamic inversion of nonminimum-phase systems. The example of the shallow water equations serves to illustrate the design steps and to present simulation results.
The presented contribution concerns the model predictive control (MPC) and moving horizon estimation (MHE) of a catalytic fixed-bed reactor model. Rigorous modeling for these systems leads to systems of (transport) pa...
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The presented contribution concerns the model predictive control (MPC) and moving horizon estimation (MHE) of a catalytic fixed-bed reactor model. Rigorous modeling for these systems leads to systems of (transport) partial differential equations. Following a so-called early lumping approach for the model predictive control and estimation yields high-dimensional systems of ordinary differential equations and therefore the need to solve large-scale dynamic optimization problems online. It is shown how a tailored gradient method and efficient numerical integration can be combined to solve the concerned optimization methods in a time-efficient way.
This paper considers the problem of sensor configuration for parameter and/or state estimation in distributedparametersystems. A practical criterion for assessing the influence of the sensor configuration is present...
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This paper considers the problem of sensor configuration for parameter and/or state estimation in distributedparametersystems. A practical criterion for assessing the influence of the sensor configuration is presented, which is based on a measure of independence of the sensor responses in the case of state estimation, and on a measure of independence of the sensitivity functions in the case of parameter estimation, respectively. The procedure is illustrated with the optimal placement of temperature sensors in a catalytic fixed-bed reactor.
This article proposes an infinite-dimensitional state-space representation and a finite-dimensional approximation for fractional linear filters with transfer function C d ( s ) := C 0 ((1 + s / w b ) / (1 + s / w h ))...
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This article proposes an infinite-dimensitional state-space representation and a finite-dimensional approximation for fractional linear filters with transfer function C d ( s ) := C 0 ((1 + s / w b ) / (1 + s / w h )) d where 0 < w b < w h and d is a real number. This representation is derived from the Taylor expansion in zero of the function (1 - z ) d , and is made up of an infinite number of first-order ordinary differential equations. Finite-dimensional approximations obtained by truncating this representation are shown to converge towards C d in H ∞ . The use of C d in a standard linear feedback loop (CRONE control) is discussed, and closed-loop exponential and input-output stabilities are shown to be equivalent. The example of CRONE car suspension is presented, for which robustness of closed-loop resonance and step response overshoot vis-a-vis a variation in the vehicule mass is achieved. Cet article propose une représentation d'état de dimension infinie et une approximation de dimension finie des filtres linéaires fractionnaires de fonction de transfert C d ( s ) := C 0 ((1 + s / w b ) / (1 + s / w h )) d , où 0 < w b < w h et d est un nombre réel. Cette représentation est dérivée du développement de Taylor en zéro de la fonction (1 - z ) d , et est composée d'une infinité d'équations différentielles ordinaires du premier ordre. Les approximations de dimension finie obtenues par troncature de cette représentation convergent vers C d dans H ∞ . L'utilisation de C d dans une boucle linéaire de rétroaction standard (commande CRONE) est discutée, et on montre que la stabilité de la boucle fermée et la stabilité entrées-sorties sont équivalentes. L'exemple de la suspension automobile CRCNE est présenté, pour lequel on obtient la robustesse à des variations de la masse du véhicule de la résonance en boucle fermée et du dépassement de la réponse à l'échelon.
In this paper we develop new results on control systems design for spatially distributed linear systems using an n -D systems approach. The basic ideas are explained using as an example heat conduction in a rod where ...
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In this paper we develop new results on control systems design for spatially distributed linear systems using an n -D systems approach. The basic ideas are explained using as an example heat conduction in a rod where the measurements and control action applied are based on an array of sensors and heaters. The first part of the analysis given shows how the process dynamics for this case can be approximately described by a 2-D transfer function, i.e. a fraction of two bivariate polynomials. This is followed by stability analysis and tests. Finally, a Youla-Kucera parametrization of all stabilizing controllers is used to develop a simple design procedure for H 2 -optimal control laws.
The issue of optimal time-varying operation for transport-reaction processes is considered, when the cost functional and/or equality constraints necessitate the consideration of phenomena that occur over disparate len...
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The issue of optimal time-varying operation for transport-reaction processes is considered, when the cost functional and/or equality constraints necessitate the consideration of phenomena that occur over disparate length scales. Multiscale process models are initially developed, linking continuum conservation laws with microscopic scale simulators. Subsequently, order reduction techniques for dissipative partial-differential equations are combined with adaptive tabulation methods for microscopic simulators to reduce the computational requirements of the optimization problem, which is then solved using standard search algorithms. The method is demonstrated on a thin film deposition process, where optimal surface temperature profiles and inlet switching times that simultaneously maximize thickness uniformity and minimize surface roughness across the film surface are computed.
In this paper we study the controllability properties of the quantum rotational dynamics of a 3D symmetric molecule, with electric dipole moment not collinear to the symmetry axis of the molecule (that is, an accident...
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In this paper we study the controllability properties of the quantum rotational dynamics of a 3D symmetric molecule, with electric dipole moment not collinear to the symmetry axis of the molecule (that is, an accidentally symmetric-top). We control the dynamics with three orthogonally polarized electric fields. When the dipole has a nonzero component along the symmetry axis, it is known that the dynamics is approximately controllable. We focus here our attention to the case where the dipole moment and the symmetry axis are orthogonal (that is, an orthogonal accidentally symmetric-top), providing a description of the reachable sets.
For many manufacturing processes the determination of an optimal control is stated as a constrained optimization problem involving nonconvex objective functions. In practical industrial situations, nonlinear models an...
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For many manufacturing processes the determination of an optimal control is stated as a constrained optimization problem involving nonconvex objective functions. In practical industrial situations, nonlinear models and nonconvexity lead to hard difficulties in the modelization and the control of the process, since, on the one hand, approximations can lead to unrealistic models and, on the other hand, the classical deterministic optimization methods can be inefficient. In such a framework the emergence of evolutive strategies offers new perspectives which have to be investigated. However, these algorithms are mainly proposed for unconstrained optimisation and appropriated development must he constructed for the case where restrictions must be taken into account. In this paper, we consider evolutionnary algorithms for constrained continuous problem. Convergence results are staled and numerical behaviour of the algorithms is compared.
In this paper we present finite-dimensional modeling of heat conduction systems with frequency and space-dependent error bounds where the eigenstruc-tures of the systems are only partially known. It is shown that stea...
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In this paper we present finite-dimensional modeling of heat conduction systems with frequency and space-dependent error bounds where the eigenstruc-tures of the systems are only partially known. It is shown that steady state analysis for dc input of a system is used effectively in reduced order modeling and bounding errors for the whole spatial distribution of temperature. A class of nominal models is clarified with tight additive error bounds, and the nominal models as well as the uncertainty weights are explicitly described as simple real rational form of transfer functions. The feasibility of the presented scheme is demonstrated by a simple example of heat conduction in copper rod.
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