Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Factorization and the synthesis of optimal feedback gains for distributed parameter systems

An approach based on Volterra factorization leads to a new methodology for the analysis and synthesis of the optimal feedback gain in the finite-time linear quadratic control problem for distributed parameter systems. The approach circumvents the need for solving and analyzing Riccati equations and provides a more transparent connection between the system dynamics and the optimal gain. The general results are further extended and specialized for the case where the underlying state is characterized by autonomous differential-delay dynamics. Numerical examples are given to illustrate the second-order convergence rate that is derived for an approximation scheme for the optimal feedback gain in the differential-delay problem.

Milman, Mark H.↗
NASA NTRS1987

Suboptimal shape control for quasi-static distributed-parameter systems

An on-line control approach which will adjust the steady-state shape of a large antenna arbitrarily close to any achievable desired profile is approached. The method makes use of distributed-parameter system theory and allows refocusing using a limited number of control actuators and sensors. The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. The controller gain calculation is computationally simpler than that previously proposed. The Galerkin (finite element) approximation method is used for model reduction. It is proved that both gain and state convergence can be achieved by using the proposed approximation scheme.

Balas, M. J.↗
NASA NTRS1987

Convergence properties of modal costs for certain distributed parameter systems

A complete modal cost analysis is presented for the vibration of various kinds of simple continua with different boundary conditions. Explicit formulas for the norm of the response (called the 'cost') are derived for these distributed parameter systems. The convergence theorems developed are useful in the model reduction of the equivalent continuum models of large space structures as well as in the selection of finite-element code for control design.

Hu, A.↗
NASA NTRS1979

State and model error estimation for distributed parameter systems

In-flight estimation of large structure model errors in order to detect inevitable deficiencies in large structure controller/estimator models is discussed. Such an estimation process is particularly applicable in the area of shape control system design required to maintain a prescribed static structural shape and, in addition, suppress dynamic disturbances due to the vehicle vibrational modes. The paper outlines a solution to the problem of static shape estimation where the vehicle shape must be reconstructed from a set of measurements discretely located throughout the structure. The estimation process is based on the principle of least-squares that inherently contains the definition and explicit computation of model error estimates that are optimal in some sense. Consequently, a solution is provided for the problem of estimation of static model errors (e.g., external loads). A generalized formulation applicable to distributed parameters systems is first worked out and then applied to a one-dimensional beam-like structural configuration.

Rodriguez, G.↗
NASA NTRS1991

One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

Taasan, Shlomo↗
NASA NTRS1971

Two examples in the time optimal control theory of distributed parameter systems.

The behavior of hyperbolic and parabolic partial differential equations is contrasted by studying the point-to-point time-optimal control problem for the equation of heat conduction and the equation of motion of a vibrating string. A maximal principle is obtained for the time-optimal control of the one-dimensional heat equation, and it is proven that time optimal controls are weakly bang-bang. The bang-bang principle is proven to be invalid for hyperbolic equations because of the finite speed of wave propagation. In the case of boundary value control of the vibrating spring, the latter is demonstrated by deriving an explicit formula for the time optimal control.

Quinn, J. P.↗
NASA NTRS1981

The reduced order model problem in distributed parameter systems adaptive identification and control

The basic assumption that a large space structure can be decoupled preceding the application of reduced order active control was considered and alternative solutions to the control of such structures (in contrast to the strict modal control) were investigated. The transfer function matrix from the actuators to the sensors was deemed to be a reasonable candidate. More refined models from multivariable systems theory were studied and recent results in the multivariable control field were compared with respect to theoretical deficiencies and likely problems in application to large space structures.

Johnson, C. R., Jr.↗
NASA NTRS1982

Estimation of distributed parameter systems

The estimation and control of large flexible space structures pose significant new control technology problems. One major problem area is the closed-loop stability of a structure that has been modeled with truncated modal dynamics. Stability problems arise due to the control design process beginning with a deficient model. This work provides the necessary conditions for the optimal estimation of infinite dimensional (partial-differential equation) systems. This approach can be particularly useful for initial control studies and for gaining considerable insight into what the optimal estimator for a truly infinite dimensional system should be. A detailed example of the estimation of the continuous shape of a string in tension is presented.

Schaechter, D. B.↗
NASA NTRS1986

On compactness of admissible parameter sets: Convergence and stability in inverse problems for distributed parameter systems

A series of numerical examples is reported and several algorithms compared for estimation of coefficients in differential equation models. Unconstrained, constrained and Tikhonov regularization methods are tested for their behavior with regard to both convergence (of approximation methods for the states and parameters) and stability (continuity of the estimates with respect to perturbations in the data or observed states).

Banks, H. T.↗
NASA NTRS1989

Estimation on nonlinear damping in second order distributed parameter systems

An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.

Banks, H. T.↗
NASA NTRS1990

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter systems

The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed.

Rosen, I. G.↗
NASA NTRS1989

Gradient methods for identification of distributed parameter systems

Parameter-dependence properties are developed in the context of a linear abstract Cauchy problem governed by a parameter-dependent operator. Of particular interest are problems in which the parameter induces an unbounded perturbation of the evolution operator. Conditions are stated under which the derivative of the state with respect to the parameter possesses certain smoothness properties. These properties lead to local convergence results for a gradient-based estimation algorithm based on quasi-linearization. Numerical results concerning a delay-differential equation indicate the effect of a forcing function on parameter sensitivity.

Brewer, Dennis W.↗
NASA NTRS1992

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter system

The convergence of solutions to the discrete- or sampled-time linear quadratic regulator problem and associated Riccati equation for infinite-dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero(infinity) is established. Both the finite-and infinite-time horizon problems are studied. In the finite-time horizon case, strong continuity of the operators that define the control system and performance index, together with a stability and consistency condition on the sampling scheme are required. For the infinite-time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary or delay system, and a flexible beam are presented and discussed.

Rosen, I. G.↗
NASA NTRS1993

Applications of computer algebra to distributed parameter systems

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Storch, Joel A.↗