Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach

Macchelli, Alessandro; Melchiorri, Claudio

doi:10.1137/s0363012903429530

Cited by 177 publications

(152 citation statements)

References 9 publications

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“…More examples of coupled systems of conservation laws may be found of hyperbolic type [17,18,25] but also of parabolic type [14,25]. In this paper we consider a general class of conservation laws with flux variables depending linearly on the state and linear source term:…”

Section: Class Of Pde's and Main Resultsmentioning

confidence: 99%

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Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

et al. 2009

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Abstract.We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.Mathematics Subject Classification. 93C20, 35L40, 35F15, 37Kxx.

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Section: Class Of Pde's and Main Resultsmentioning

confidence: 99%

“…In many models the P 1 only contains ones and zeros, telling how different physical domains are coupled, and all the physical parameters are in L [14,17,18,25]. One may also see P 1 as the matrix obtained by putting all physical constants to one.…”

Section: Class Of Pde's and Main Resultsmentioning

confidence: 99%

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

et al. 2009

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“…While much research work in the area of robotics leads to a good understanding of this approach, its recent successful applications to power systems require new problem formulations and new insights into this approach [14,28]. In recent years, port-controlled Hamiltonian systems [32,31,18] have been well investigated in a series of works [19,7,17,[21][22][23]12,13]. A constructive procedure was proposed in [19] Hamiltonian systems with dissipation to generate a Lyapunov function for non-zero equilibria.…”

Section: Introductionmentioning

confidence: 99%

“…The Hamiltonian function, the sum of potential energy (excluding gravitational potential energy) and kinetic energy in physical systems, is a good candidate of Lyapunov functions for many physical systems, which makes it very easy for stability analysis and control design for the systems. Up to now, the port-controlled Hamiltonian approach has been used in various control problems [17,9,23]. In particular, it has been successfully applied to the control of power systems in a series of works [3,24,14,28].…”

Section: Introductionmentioning

confidence: 99%

Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

Wang

Cheng

2007

Systems & Control Letters

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The key in applying energy-based control approach is to be able to express the system under consideration as a dissipative Hamiltonian system, i.e., to obtain Dissipative Hamiltonian Realization (DHR) for the system. In general, the precise DHR form is hard to obtain for nonlinear dynamic systems. When a precise DHR does not exist for a dynamic system or such a precise realization is difficulty to obtain, it is necessary to consider its approximate realization. This paper investigates approximate DHR and construction of local Lyapunov functions for time-invariant nonlinear systems. It is shown that every nonlinear affine system has an approximate DHR if linearization of the system is controllable. Based on the diagonal normal form of nonlinear dynamic systems, a new algorithm is established for the approximate DHR. Finally, we present the concept of kth degree approximate Lyapunov function, and provide a method to construct such a Lyapunov function. Example studies show that the methodology presented in this paper is very effective.

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“…Moreover, in [9], this StokesDirac structure has been modified in order to model fluid dynamical systems and in [3], [6] to model the Timoshenko beam equation. In any case, it is not completely clear how a general formulation of a multi-variable distributed parameter system within the port Hamiltonian formalism could be obtained.…”

mentioning

confidence: 99%

Port Hamiltonian formulation of infinite dimensional systems I. Modeling

Macchelli

Schaft

Melchiorri

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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Abstract-In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multivariable case. The resulting class of infinite dimensional systems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables.

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Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach

Cited by 177 publications

References 9 publications

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

Port Hamiltonian formulation of infinite dimensional systems I. Modeling

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