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Results for “distributed parameter system”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

New Directions in Asymptotically Stable Finite-dimensional Adaptive Control of Linear Distributed Parameter Systems

Distributed Parameter Systems (DPS), such as systems described by partial differential equations, require infinite-dimensional state space descriptions to correctly model their dynamical behavior. However, any adaptive control algorithm must be finite-dimensional in order to be implemented via on-line digital computers. Finite-dimensional adaptive control of linear DPS requires stability analysis of nonlinear, time-varying, infinite-dimensional systems. The structure of nonadaptive finite-dimensional control of linear DPS is summarized as it relates to the existence of limiting systems for adaptive control. Two candidate schemes for finite-dimensional adaptive control of DPS are described and critical issues in infinite-dimensional stability analysis are discussed, in particular, the invariance principle, center manifold theory, and relationships between input-output and internal stability.

Balas, M. J.↗
NASA NTRS1988

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Bernstein, Dennis S.↗
NASA NTRS1985

Finite Control in Underdamped Distributed Parameter Systems

Specifically, a class of distributed parameter systems is defined using Hilbert space methods based on a partial differential equation model of a structure. In this space a simple, easy to check definition of underdamping is constructed based on the well known single degree of freedom concept of critical damping. It is then shown that if a given distributed parameter system satisfies this definition, each mode of the modal expansion of the solution is in fact an underdamped function of time. It is noted that a distributed parameter system which is underdamped is also uniformly exponentially stable. By appealing to the work of Gibson, a finite dimensional model of the system will yield satisfactory control laws. Furthermore, it is shown that the assumption of the underdamping also allows straightforward computation of rough bounds on the magnitude of the unmodeled or residual modes for a modal truncation scheme. Hence, underdamped systems are precisely that class of distributed parameter systems which are not likely to have spillover problems and which will yield convergence of finite dimensional control laws to control laws which are optimal for the full distributed parameter model of the system.

Inman, D. J.↗
NASA NTRS1982

A domain segmentation approach to modeling distributed parameter systems

Existing modeling methods in distributed parameter systems are directed to field problems for which a single equation gives an adequate representation. As a result, the techniques are severely taxed when coefficients of the governing partial differential equation (PDE) have relatively complex functional forms. The field is postulated to consist of contiguous regions that are easily modeled. During the modeling process itself, the regional boundaries are identified using a method based on pattern recognition (PR) techniques. The method was tested on computer simulations of a water quality resource system. Quantitative measures are developed and used to demonstrate the feasibility of applying the methodology to realistic distributed parameter systems (DPS's).

Apenyo, K.↗
NASA NTRS1988

Variational modal identification of gyroscopic distributed-parameter systems

Variational modal identification of gyroscopic distribution parameter systems is discussed. Topics covered include: equation of motion for gyroscopic distributed-parameter systems; a variational formulation for the eigenvalue problem; a variational formulation for the modal identification of gyroscopic distributed-parameter systems; discretization; and numerical example.

Silverberg, Larry M.↗
NASA NTRS1968

Controllability of distributed-parameter systems

Controllability of distributed-parameter control systems is mathematically studied. A general theory for control systems includes those that cannot be described by ordinary differential equations.

Herget, C. J.↗
NASA NTRS1986

Computational methods for the control of distributed parameter systems

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.

Burns, J. A.↗