Simplicial Dirac structures as finite analogues of the canonical Stokes Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related b...
详细信息
Simplicial Dirac structures as finite analogues of the canonical Stokes Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input output finite-dimensional port-Hamiltonian systems that emulate the behavior of distributed-parameter port-Hamiltonian systems. This paper elaborates on the matrix representations of simplicial Dirac structures and the resulting port-Hamiltonian systems on simplicial manifolds. Employing these representations, we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port-Hamiltonian systems on simplicial manifolds. (C) 2013 Elsevier Ltd. All rights reserved.
This contribution considers the backstepping design of robust state feedback regulators for second order hyperbolic partial integro-differential equations (PIDEs). To this end, the internal model principle is applied,...
详细信息
This contribution considers the backstepping design of robust state feedback regulators for second order hyperbolic partial integro-differential equations (PIDEs). To this end, the internal model principle is applied, which amounts to designing a stabilizing backstepping controller for a PIDE-ODE system. By transforming this system into a PDE-ODE cascade a systematic design procedure is presented. Then, robust output regulation is verified for non-destabilizing model uncertainties by means of the extended regulator equations. The results of the article are applied for the robust output regulation of a shear beam with a destabilizing boundary condition. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
The computation of an optimal steady-state operating point in an experimental annealing furnace is considered. In particular, the optimum spatial distribution of electric power supplied to IR-lamps is computed to ensu...
详细信息
The computation of an optimal steady-state operating point in an experimental annealing furnace is considered. In particular, the optimum spatial distribution of electric power supplied to IR-lamps is computed to ensure the temperature uniformity in the specimen fillet. A control-oriented reduced-order model of the steady-state 2D temperature distribution is derived and compared with the full-order model. Saturation functions are used to consider input constraints in a tailored optimization problem. The evaluation of the optimal control input is carried out with the full-order model. Uniqueness of the solution of the optimization problem is investigated numerically. The temperature field in the specimen fillet deviates less than 0.4% of the setpoint value if sufficient heating power is available. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on ...
详细信息
This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the state, the backstepping approach is not directly applicable to obtaining an observer gain that stabilizes the error dynamics. Therefore, we attempt to convert the error system into another system to which backstepping is applicable. The conversion is successfully achieved for a class of weighting functions, and the resultant observer realizes exponential convergence of the estimation error with an arbitrary decay rate in terms of the L-2 norm. In addition, an explicit expression of the observer gain is available in a special case. The effectiveness of the proposed observer is also confirmed by numerical simulations. (C) 2014 Elsevier Ltd. All rights reserved.
In this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach. Thereby, the outputs to be controlled are no...
详细信息
In this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach. Thereby, the outputs to be controlled are not required to be measurable and can be pointwise, distributed or boundary quantities, whereas the measurement is located at the boundary. By solving the state feedback regulator problem in the backstepping coordinates regulator equations with a simple structure result, so that their analysis and solution is facilitated. The output feedback regulator design is completed by determining a finite-dimensional reference observer and an infinite-dimensional disturbance observer. For the latter a backstepping approach is presented that consists of a triangular decoupling in the backstepping coordinates. This allows a systematic design and the explicit derivation of directly verifiable existence conditions for the disturbance observer. It is shown that for the resulting compensator the separation principle holds implying output regulation for the exponentially stable closed-loop system with a prescribed stability margin. The output regulation results of the article are illustrated by means of a parabolic system with an in-domain pointwise controlled output. (C) 2015 Elsevier Ltd. All rights reserved.
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...
详细信息
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 he 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 nonminimilm-phase systems. The example of the shallow water equations serves to illustrate the design steps and to present simulation results. (C) 2015, ILAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
The use of beams and similar structural elements is finding increasing application in many areas, including micro and nanotechnology devices For the purpose of buckling analysis and control, it is essential to account...
详细信息
The use of beams and similar structural elements is finding increasing application in many areas, including micro and nanotechnology devices For the purpose of buckling analysis and control, it is essential to account for nonlinear let in the strains while modeling these flexible structures. Further, in modeling of micro and nanotechnology devices, the micro length scale parameter effects can be accounted by the use of a 2 dimensional stress-strain relationship. This paper studies the buckling effect, for a slender, vertical beam with a tip mass at one end and fixed on a movable platform at the other. For the purpose of illustration, the movable platform is assumed to be a cart. Accounting for a 2 dimensional stress-strain relationship, nonlinear expressions for strains, and incorporating an inextensibility constraint of the beam, the Hamiltonian equations of motion are obtained. The equations of motion are then cast in a port-Hamiltonian form with appropriately defined flows and efforts. We then carry out a preliminary modal analysis of the system to describe candidate post-buckling configurations and study the stability properties of these equilibria. The vertical configuration of the beam under the action of gravity is without loss of generality, since the objective is to model a potential field that determines the equilibria. (C) 2015, ILAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
This paper addresses state estimation for spatially distributedsystems governed by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatia...
详细信息
ISBN:
(纸本)9783952426937
This paper addresses state estimation for spatially distributedsystems governed by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A decentralised and scalable approach is undertaken by decomposing the domain into overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional Kalman filter which exploits the finite element approach for spatial discretisation and the parallel Schwarz method to iteratively enforce consensus on the estimates and covariances over the boundaries of adjacent subdomains. The effectiveness of the proposed distributed consensus-based finite element Kalman filter is demonstrated via simulation experiments concerning a temperature estimation problem modelled by the bi-dimensional heat equation.
This paper aims at developing a Brayton-Moser analogue of an infinite-dimensional system in the port-Hamiltonian framework, defined with respect to a Stokes-Dirac structure. It is shown that such a formulation leads t...
详细信息
This paper aims at developing a Brayton-Moser analogue of an infinite-dimensional system in the port-Hamiltonian framework, defined with respect to a Stokes-Dirac structure. It is shown that such a formulation leads to defining alternative passive maps, which differ from those in the port-Hamiltonian framework via a "power-like" function called the mixed-potential function. This mixed-potential function can also be used for stability analysis. We present our results for a general port-Hamiltonian system, with Maxwell's equations and the transmission line, with nonzero boundary conditions, as examples. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
The use of beams and similar structural elements is finding increasing application inmany areas, including micro and nanotechnology devices. For the purpose of buckling analysis and control, it is essential to account...
详细信息
The use of beams and similar structural elements is finding increasing application in
many areas, including micro and nanotechnology devices. For the purpose of buckling analysis and control, it is essential to account for nonlinear terms in the strains while modeling these exible structures. Further, in modeling of micro and nanotechnology devices, the micro length scale parameter effects can be accounted by the use of a 2 dimensional stress-strain relationship. This paper studies the buckling effect for a slender, vertical beam with a tip-mass at one end and fixed on a movable platform at the other. For the purpose of illustration, the movable platform is assumed to be a cart. Accounting for a 2 dimensional stress-strain relationship, nonlinear expressions for strains, and incorporating an inextensibility constraint of the beam, the Hamiltonian equations of motion are obtained. The equations of motion are then cast in a port-Hamiltonian form with appropriately defined flows and efforts. We then carry out a preliminary modal analysis of the system to describe candidate post-buckling configurations and study the stability properties of these equilibria. The vertical configuration of the beam under the action of gravity is without loss of generality, since the objective is to model a potential field that determines the equilibria.
暂无评论