We consider infinite-dimensional port-Hamiltonian systems with respect to control issues. In contrast to the well-established representation relying on Stokes-Dirac structures that are based on skew-adjoint differenti...
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We consider infinite-dimensional port-Hamiltonian systems with respect to control issues. In contrast to the well-established representation relying on Stokes-Dirac structures that are based on skew-adjoint differential operators and the use of energy variables, we employ a different port-Hamiltonian framework. Based on this system representation conditions for Casimir functionals will be derived where in this context the variational derivative plays an extraordinary role. Furthermore the coupling of finite-and infinite-dimensional systems will be analyzed in the spirit of the control by interconnection problem.
In this article, the finite-dimensional control of distributed-parameter systems with boundary control and unbounded observation is considered. This problem is solved by extending the concept of dual observer-based co...
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In this article, the finite-dimensional control of distributed-parameter systems with boundary control and unbounded observation is considered. This problem is solved by extending the concept of dual observer-based compensators to infinite dimensions. These compensators have the advantage that, on the one hand, the separation principle can be used to directly determine a finite-dimensional compensator and, on the other hand they can be directly applied to boundary control systems with a time-derivative of the input. In order to achieve a low controller order as well as a desired control performance, a parametric approach is proposed to parameterise the degrees of freedom contained in the controller. Consequently, desired design specifications can be achieved by using a parameter optimisation. The proposed design of finite-dimensional dual observer-based compensators is demonstrated by means of a heat-conducting system with Neumann boundary control and boundary measurements.
Proper modelling of a dynamic system can benefit analysis, simulation, design, evaluation and control of the system. The linear-graph (LG) approach is suitable for modelling lumped-parameter dynamic systems. By using ...
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Proper modelling of a dynamic system can benefit analysis, simulation, design, evaluation and control of the system. The linear-graph (LG) approach is suitable for modelling lumped-parameter dynamic systems. By using the concepts of graph trees, it provides a graphical representation of the system, with a direct correspondence to the physical component topology. This paper systematically extends the application of LGs to multi-domain (mixed-domain or multi-physics) dynamic systems by presenting a unified way to represent different domains - mechanical, electrical, thermal and fluid. Preservation of the structural correspondence across domains is a particular advantage of LGs when modelling mixed-domain systems. The generalisation of Thevenin and Norton equivalent circuits to mixed-domain systems, using LGs, is presented. The structure of an LG model may follow a specific pattern. Vector LGs are introduced to take advantage of such patterns, giving a general LG representation for them. Through these vector LGs, the model representation becomes simpler and rather compact, both topologically and parametrically. A new single LG element is defined to facilitate the modelling of distributed-parameter (DP) systems. Examples are presented using multi-domain systems (a motion-control system and a flow-controlled pump), a multi-body mechanical system (robot manipulator) and DP systems (structural rods) to illustrate the application and advantages of the methodologies developed in the paper.
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.
The solution of transport equations results in functional differential equations with time-delays. This papers deals with the control of linear systems with lumped and distributed delays that represent a coupled syste...
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The solution of transport equations results in functional differential equations with time-delays. This papers deals with the control of linear systems with lumped and distributed delays that represent a coupled system of transport processes and ordinary differential equations. These time-delay systems can be viewed as modules over a ring of entire functions. It is shown that spectral controllability and freeness of the module over an associated ring are necessary and sufficient for the module to be free. Using a module basis, a flatness-based tracking controller is derived that is infinite-dimensional, in general, due to the distributed delays. However, no (explicit) predictions are required to assign a finite spectrum to the delay system. Two examples illustrate the results, one of which being a neutral type system.
The trajectory planning problem is considered for coupled linear diffusion-convection-reaction equations using a semi-numerical approach. For this, spatial discretization is applied to determine approximate solutions ...
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The trajectory planning problem is considered for coupled linear diffusion-convection-reaction equations using a semi-numerical approach. For this, spatial discretization is applied to determine approximate solutions to the eigenvalue problem, which are processed in a spectral approach for flatness-based trajectory planning and feedforward control. The assignment of suitable desired trajectories for the flat output is considered to realize finite time transitions between operating points as well as transient output trajectories. Simulation results for an example with cross-diffusion document the applicability of the proposed method.
This article presents the automation of set point changes of an industrial glass feeder in container glass production. A model is proposed consisting of multiple first order partial differential equations (PDEs). Base...
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This article presents the automation of set point changes of an industrial glass feeder in container glass production. A model is proposed consisting of multiple first order partial differential equations (PDEs). Based on the derived model a feedforward control approach is presented. The approach allows for the calculation of control inputs out of reference trajectories of the system outputs and is used to perform automated set point changes with short transition time. Finally, the approach is implemented at an industrial glass feeder. Measurement results from the Thuringer Behalterglas GmbH (Schleusingen, Germany) are included. (C) 2011 Elsevier Ltd. All rights reserved.
Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of...
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Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems with a nonzero boundary energy flow. Simplicial triangulation of the underlaying manifold leads to the so-called simplicial Dirac structures, discrete analogues of Stokes-Dirac structures, and thus provides a natural framework for deriving finite-dimensional port-Hamiltonian systems that emulate their infinite-dimensional counterparts. The port-Hamiltonian systems defined with respect to Stokes-Dirac and simplicial Dirac structures exhibit gauge and a discrete gauge symmetry, respectively. In this paper, employing Poisson reduction we offer a unified technique for the symmetry reduction of a generalized canonical infinite-dimensional Dirac structure to the Poisson structure associated with Stokes-Dirac structures and of a fine-dimensional Dirac structure to simplicial Dirac structures. We demonstrate this Poisson scheme on a physical example of the vibrating string.
Abstract This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal...
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Abstract This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal and dual cochains related by the coboundary operators. This finite-dimensional Dirac structure, as discrete analogue of the canonical Stokes-Dirac structure, allows for the formulation of finite-dimensional port-Hamiltonian systems that emulate the behaviour of the open distributed-parameter systems with Hamiltonian dynamics.
Linear systems with lumped and distributed delays can be represented by modules over the ring of entire functions in Ĉ( s )[e – τs ]. While in the case of commensurate delays spectral controllability is sufficient f...
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Linear systems with lumped and distributed delays can be represented by modules over the ring of entire functions in Ĉ( s )[e – τs ]. While in the case of commensurate delays spectral controllability is sufficient for the existence of a basis of this module, in the incommensurate case addressed here additional conditions are required. Exploiting the relations between the (known) delay amplitudes a new module with favorable freeness properties can be defined. Based on that, necessary and sufficient conditions for the freeness of this module are presented. If these conditions are satisfied a basis can be used to derive a flatness-based tracking control without any explicit predictions. The approach is illustrated on a neutral system and on a system with distributed delays.
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