Control Of Distributed Parameter Systems Research Articles

Stabilization of hereditary distributed parameter control systems

In this paper, we study the asymptotic stabilization of semilinear distributed parameter control systems with delay. Assuming that the semigroup of operators associated with the uncontrolled and undelayed equation is compact we prove that a well known rank condition, which implies the feedback stabilization for lumped systems, can be extended to this type of systems.

Control of one kind of nonlinear parabolic distributed parameter system with moving boundary

This paper presents the modeling of one kind of nonlinear parabolic distributed parameter control system. By transforming the system to that in the fixed domain, or into the lumped parameter system, this paper provides an insight into the basic features of the control system, as well as the critical conditions for the control variable. The equations for one-dimensional systems of planar, cylindrical and spherical cases are formulated as a unified form, and the dynamic characteristics of the open-loop control system and close-cycle feedback control system have been investigated. Numerical results agree well with theoretical results. The simulation results indicate that the system is well posed, stable, measurable and controllable.

A new approach for solving the Stokes problem

In this paper, a new approach for finding the approximate solution of the Stokes problem is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a distributed parameter control system, the theory of measure is used to approximate the velocity functions by piecewise linear functions. Then, the approximate values of pressure are obtained by a finite difference scheme.

A note on stabilization with saturating feedback

We assume, for a distributed parameter control system, that a linear stabilizing is available. We then seek a stabilizing, necessarily nonlinear, subject to an a priori bound on the control.

A new method for solving nonlinear second order partial differential equations

In this paper, a new method for finding the approximate solution of a second order nonlinear partial differential equation is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a distributed parameter control system, the theory of measure is used for obtaining the approximate solution of the original problem.

An approximate-predictor approach to reduced-order models and controllers for distributed-parameter systems

Two reduced-order digital controllers for distributed parameter systems (DPS) are described. Reduced-order models approximate the optimal finite past predictor and error covariance for the full system to minimize an approximation to the Kullback-Leibler information distance (KLID). An LQG controller based on a reduced-order-system model is described. A reduced-order controller is found to minimize the KLID between the closed-loop system outputs with the full- and reduced-order controllers. Noncollocated control of a flexible beam is simulated.

Existence of solutions for parabolic type evolution differential inclusions and the property of the solution set

In this paper, parabolic type differential inclusions with time dependent are considered and this problem is related to the study of the nonlinear distributed parameter control systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J. P. Aubin et al are generalized and improved.

Control of Distributed Parameter Systems as Lumped Input and Distributed Output Systems

In this paper a new decomposition of distributed parameter systems to lumped and distributed parameter subsystems in a framework of a whole structure of lumped input and distributed output system is presented. This new structure offers large possibilities for distributed parameter systems control - practically equivalent to lumped parameter systems control possibilities.

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part II: Nonlinear system simulation and control

As was stated in Part I, the linear control models of a radically rotating elastic rod in all the analysis and design procedures for lead with closed-loop system compensation is presented. For a given linear system model, if the model is accurate, it will be accurate only over a very limit range of operation of the system. However, all the effort of design comes to be meaningful until it is tested using the nonlinear system model. On the other hand, the response of the nonlinear system model will not be as good as that of the linear model. In fact, some iterations on the design and on improving the design based-model are often needed before there is even a resemblance between the linear model response and the nonlinear system response. The present paper is a continuation of [1] and nonlinear control system simulation and a tuning process are presented. While almost all design procedures for physical system contain some tuning process, the development of an analytic design procedure for models of distributed-parameter control system can be evidently shown through this paper.

Two Ways of Stabilizing Systems with Input Delays

Abstract Systems with input delays are a simple and intriguing example of distributed parameter systems. Studied by many researchers these systems are better analyzed by special methods than by the general theory of distributed parameter control systems. The present paper considers two basic approaches in feedback stabilization of such systems. The first one is the delay approximation. The error introduced by the approximation is considered as an uncertainty that may be treated via a robust synthesis. The second one is based on a Smith predictor version used together with some compensator designed for the delayless system. If the compensator is the result of a robust synthesis, then the implementation error for the predictor system could be also viewed as an uncertainty that the robust compensator solves in a satisfactory way. Some simulation results are given.

Identification and control of distributed parameter systems by means of the singular value decomposition

In this paper the basic properties of the singular value decomposition (SVD) for integral equation models of distributed parameter systems (DPS) are presented in the context of process identification and model-based control. In addition, new methods of analysis and computation are described in which SVD-based techniques are used to provide a practical solution for the DPS identification and control problem. Once developed, these novel procedures are applied to a class of linear DPS which are conventionally described by parabolic partial differential equation (PDE) models. An alternative integral equation representation for these processes is used to provide a general and readily identifiable pseudomodal input/output model for a wide variety of such DPS, including both spatially self-adjoint (diffusive) and non-self-adjoint (convective/diffusive) systems It is demonstrated that this SVD-based internal equation model of DPS is a sound and convenient basis for pseudo-modal feedback control system designs. A later paper will extend these methods to allow for model-predictive controller designs and nonlinear DPS

143 Hierarchical control for distributed-parameter systems — The application of PMCP approximation technique for hierarchical optimization of large-scale systems

143 Hierarchical control for distributed-parameter systems — The application of PMCP approximation technique for hierarchical optimization of large-scale systems

Book Review: Distributed Parameter Control Systems: new trends and applications:

Book Review: Distributed Parameter Control Systems: new trends and applications:

On distributed parameter control systems in the abnormal case and in the case of nonoperator equality constraints

In this paper, a general distributed parameter control problem in Banach spaces with integral cost functional and with given initial and terminal data is considered. An extension of the Dubovitskii-Milyutin method to the case of nonregular operator equality constraints, based on Avakov's generalization of the Lusternik theorem, is presented. This result is applied to obtain an extension of the Extremum Principle for the case of abnormal optimal control problems. Then a version of this problem with nonoperator equality constraints is discussed and the Extremum Principle for this problem is presented.

Rothe approach to the existence of solution of an ablation-transpiration cooling control system

A one dimensional ablation model with transpiration cooling control and nonlinear effect is studied, which is a distributed parameter control system with moving boundary and both governing equation and boundary conditions involving control variable. A solution is given by a Rothe approximation scheme.

Nonlinear finite-dimensional control of a class of nonlinear distributed parameter systems using residual mode filters: A proof of local exponential stability

In any attempt to control an infinite-dimensional distributed parameter system (DPS) with a finite-dimensional controller, some compensation for deleterious controller interaction with unmodeled modes is needed. We introduce the concepts of both a finite-dimensional nonlinear controller based on any reasonable, nonlinear reduced-order model of the DPS and stability compensation by a finite-dimensional, nonlinear residual mode filter. Under appropriate Lipschitz continuity conditions on the nonlinearities, this new pair of interconnected finite-dimensional systems will produce closed-loop (exponentially) stable control of the nonlinear DPS.

Spatial Filtering Concepts in Distributed Parameter Control

A new method of analyzing distributed parameter control systems is presented, based upon their input/output representation in a spatially and temporally transformed frequency space. The classes of distributed systems amenable to the analysis are described in terms of their Green’s functions. The plants’ input/output relations are studied in the transformed space using the singular value decomposition to determine the system’s spatial performance. Performance is quantified in terms of generalized command following, disturbance rejection, noise rejection, controllability, and observability over spatial and temporal bandwidths, with suitable design measures presented. The analysis provides insight into the performance of sensor and actuator distributions in achieving spatial frequency performance specifications, determines spatial regimes where the response is directional, and quantifies sensor and actuator placement with respect to limitations of system and transducer spatial modelling. The analysis is shown to be applicable to discrete as well as distributed sensors and actuators, and utilizes commonly available numerical analysis techniques. An example problem is considered.

Maximum principle for optimal control of distributed-parameter systems with singular mass matrix

A maximum principle for the open-loop optimal control of a vibrating system relative to a given convex index of performance is investigated. Though maximum principles have been studied by many people (see, e.g., Refs. 1–5), the principle derived in this paper is of particular use for control problems involving mechanical structures. The state variable satisfies general initial conditions as well as a self-adjoint system of partial differential equations together with a homogeneous system of boundary conditions. The mass matrix is diagonal, constant, and singular, and the viscous damping matrix is diagonal. The maximum principle relates the optimal control with the solution of the homogeneous adjoint equation in which terminal conditions are prescribed in terms of the terminal values of the optimal state variable. An application of this theory to a structural vibrating system is given in a companion paper (Ref. 6).

Necessary conditions for exponential stabilizability of distributed parameter systems with infinite dimensional unbounded feedback

In this paper we consider distributed parameter control systems of the form x′(t) = Ax(t) + Bu(t), where x(t) is in the state space X, u(t) is in an infinite dimensional control space U, and B is an unbounded input operator which is admissible in a standard sense. We find necessary conditions for there to exist a compact operator K : X → U such that A + BK generates a C 0- semigroup which is of exponential growth type μ. In particular, for every γ > μ, A must have at most finitely many eigenvalues of finite multiplicity in { Re(z) ≥ γ} . Furthermore, the part of A corresponding to the remaining spectrum must generate a semigroup with type at most γ. We apply this to a model for a clamped Euler-Bernoulli plate with Dirichlet control applied to the entire boundary. We show that a compact state feedback cannot exponentially stabilize the plate in the state space of maximum regularity.

Optimality conditions for systems with insufficient data

In this paper we use the Dubovitski–Milyutin formalism to establish necessary and sufficient conditions for optimality in a nonlinear, distributed parameter control system, with convex cost criterion and initial condition not given a priori (that is it is not a known function but instead it belongs to a specified set). Our result extends a recent theorem of Lions. Finally a concrete example is worked out in detail.