Control and Optimal Design of Distributed Parameter Systems (original) (raw)

Control of Distributed Parameter Systems : a Practical Approach

2009

Control on finite and infinite horizons as well as state and parameter estimation of distributed parameter systems are dealt with in the paper. If the target output is a particular point of the distributed parameter plant, control may be achieved through a discretized lumped parameter model. Several target outputs may be handled through model change, averaging or multivariable control. Once a discretized model is obtained, design methods developed for control of lumped parameter systems may be applied, including methods for adaptive control. State and parameter estimation may be achieved, too, similarly to the lumped parameter case through dynamic optimization on a finite horizon.

Computational methods for the control of distributed parameter systems

Proceedings of the IEEE Conference on Decision and Control

Finite dimensional approximation schemes that work well for distributed parameter systems are often not suitable for the analysis and implementation of feedback control systems. The relationship between approximation schemes for distributed parameter systems and their application to optimal control problems is discussed. A numerical example is given.

Control of Distributed Parameter Systems

Distributed parameter systems (DPS) is an established area of research in control which can trace its roots back to the sixties. While the general aims are the same as for lumped parameter systems, to adequately describe the distributed nature of the system one needs to use partial differential equation (PDE) models. The modelling issue is in itself nontrivial, especially when there is boundary control action and sensing on the boundary. Controllability and observability concepts are subtle and investigating these for a single PDE example leads to a sophisticated mathematical problem. The action of controlling the system introduces feedback into the PDE model which results in a more complicated mathematical model; the resulting closed-loop system may not be well-posed and this issue has only quite recently become well understood. At this stage, the mathematical machinery for formulating the basic control problems is available (although not so well known), and this has led to a wealth of new system theoretic results for DPS.

Optimal Design and Control of Distributed Parameter Systems

1991

Research has been conducted on nonlinear optimization in the areas of (i) dual based methods and decomposition; (ii) regularization and approximation techniques; (iii) nonsmooth optimization and (iv) algorithms development for large-scale optimization. The methods developed are applicable to a wide range of important applications incLuding; optimal shape design, structural optimization, and image reconstruction. 14 SUBJECT TERMS 15. NUMBER OF PAGES 16, PRICE CODE 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19 SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED SAR 'C' "540-0'-2B0 5500 Standard Form 298 (Rev 2-89) P'"' C3p th ANS. 'SI Z39-'S

An Account of Chronological Developments in Control of Distributed Parameter Systems

Control systems arising in many engineering fields are often of distributed parameter type, which are modeled by partial differential equations. Decades of research have lead to a great deal of literature on distributed parameter systems scattered in a wide spectrum. Extensions of popular finite-dimensional techniques to infinite-dimensional systems as well as innovative infinite-dimensional specific control design approaches have been proposed. A comprehensive account of all the developments would probably require several volumes and is perhaps a very difficult task. In this paper, however, an attempt has been made to give a brief yet reasonably representative account of many of these developments in a chronological order. To make it accessible to a wide audience, mathematical descriptions have been completely avoided with the assumption that an interested reader can always find the mathematical details in the relevant references.

Optimal Design Techniques for Distributed Parameter Systems

2013 Proceedings of the Conference on Control and its Applications, 2013

Parameter estimation problems consist in approximating parameter values of a given mathematical model based on measured data. They are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. The problem of collecting data in the "best way" in order to assure a statistically efficient estimate of the parameter is known as Optimal Design. In this work we consider the problem of finding optimal locations for source identification in the 3D unit sphere from data on its boundary. We apply three different optimal design criteria to this 3D problem: the Incremental Generalized Sensitivity Function (IGSF), the classical D-optimal criterion and the SE-criterion recently introduced in [3]. The estimation of the parameters is then obtained by means of the Ordinary Least Square procedure. In order to analyze the performance of each strategy, the data are numerically simulated and the estimated values are compared with the values used for simulation.

Computer Aided Design of the Distributed Parameter Control Systems

Simulation of Control Systems, 1987

The computer aided design (CAD) of the optimal discrete control systems is considered. The CAD system is intended for the automatic synthesis of state and parameter estimation systems and control systems of stochastic distributed parameter systems (DPS) which are described by quasi-linear parabolic-hiperbolic partial differential equations.Applied the state estimation and control algorithms are suboptimal but they considerably reduce computer calculations while realization of such algorithms in comparison with optimal algorithms and assure good convergence.

On an approach to designing control of the distributed-parameter processes

2012

Consideration was given to a class of the problems of optimal control of rod (plate) heating by controlling the furnace temperature. Control relies on the process information feedbacked continuously or discretely only from the individual points on the rod where the temperature sensors are installed. For the continuous and discrete observation, the mathematical model of the controlled process was reduced to the pointwise loaded parabolic equation. The paper established formulas for the functional gradient, proposed schemes of their numerical solution, and presented the results of the numerical experiments.