Showing papers on "Model order reduction published in 1988"

Model Reduction for Robust Control: A Schur Relative-Error Method

Abstract: A numerically robust Relative Error Method (REM) for state-space model order reduction is described. Our algorithm is based on Desai's Balanced Stochastic Truncation (BST) technique for which M. Green has obtained an L? relative-error bound. However, unlike previous methods, our Schur method completely circumvents the numerically delicate initial step of obtaining a minimal balanced stochastic realiztion (BSR) of the the power spectrum matrix G(s)GT(-s).

Model reduction for robust control: A schur relative error method

Abstract: A numerically robust relative error method for state-space model order reduction is described. Our algorithm is based on Desai's balanced stochastic truncation technique for which Green has obtained an L∞ relative error bound. However, unlike previous methods, our Schur method completely circumvents the numerically delicate initial step of obtaining a minimal balanced stochastic realization of the power spectrum matrix G(s)GT(−s).

Differentiation reduction method as a multipoint Pade approximant

Abstract: The differentiation method for model order reduction is shown to be a special case of multipoint Pade approximation. This link also extends to other reduction methods where reduced models are generated successively. An example illustrates the main points.

System Identification And Control Using SVD's On Systolic Arrays

Abstract: A new class of algorithms based upon a generalized singular value decomposition (SVD) is considered for system identification, statistical model order determination, model order reduction, and predictive control. Currently available algorithms for system identification and control are not completely reliable for automatic implementation on microprocessors in real time. In the generalized SVD approach, the algorithms are computationally stable and numerically accurate and can be implemented on systolic array processors using recently developed algorithms resulting in a considerable speedup. The method is based upon a recent generalized canonical variate analysis (CVA) method for determining the optimal state of a restricted order in system identification, reduced order stochastic filtering, and model predictive control. This permits a unified approach to the solution of these problems from the viewpoints of a prediction problem as well as an approximation problem. Algorithms for online computation in identification, filtering, and control of high order linear multivariable systems are developed. Implementing these algorithms on systolic array processors are discussed.

Singular perturbation analysis of the atmospheric orbital plane change problem

Abstract: A three-state model is presented for the aeroassisted orbital plane change problem. A further model order reduction to a single state model is examined using singular perturbation theory. The optimal solution for this single state model compares favorably with the exact numerical solution using a four-state model; however, a separate boundary layer solution is required to satisfy the terminal constraint on altitude. This, in general, involves the solution of a two-point boundary value problem, but for a two-state model. An approximation is introduced to obtain an analytical control solution for lift and bank angle. Included are numerical simulation results of a guidance law derived from this analysis, along with comparison to earlier work by other researchers.

Time domain effects of model order reduction

Abstract: It is suggested that a preliminary and essential step in the design of flight control systems for highly augmented aircraft is obtaining an accurate open-loop dynamics model. Very large-order open-loop state-space models are constructed from analytical and empirical data obtained from knowledge of the vehicle's aerodynamics, propulsion, and structure dynamics. A balancing methodology for reducing a very large-order state-space representation to a more practical size is discussed. The balancing algorithm has a frequency domain error bound that guarantees the the magnitude of the reduced-order model's frequency response will be bounded. It is suggested that implementing techniques to preserve the number of nonminimum-phase zeros while performing model order reduction, and using residualizaton to match the steady-state magnitude, should improve the time history responses. A 140th-order aeroservoelastic model and a fourth-order critically damped system with an oscillator are considered as examples. >

Pole-placement and model-order reduction techniques applied to a hydro-unit—system for dynamic stability improvement

Abstract: A pole-placement method, which is amenable to either a complete or incomplete state (output) feedback, is employed to drastically improve the dynamic stability characteristics of a practical power system (original open-loop system) by designing a suitable controller (i.e. a closed-loop system) with output feedback. Furthermore, an adequate reduced-order model of the original system is obtained by using three distinct pole selection criteria. The pole-placement method is also used to design an appropriate closed-loop system of the attained reduced-order model based on complete state feedback.

Control system design - a case study

Abstract: A modelling technique has been developed for gas distribution networks which includes a model order reduction procedure to facilitate simulation and control system design studies. The model is validated against test result data. The effect of the model reduction procedure is to introduce uncertainties into the model and the implicatian of the uncertainties are investigated in relation to control system design.

Algorithms for Robust Identification and Control of Large Space Structures. Phase 1.

Abstract: : A new method of providing robust attitude control for tracking and slewing maneuvers for large flexible space structures in orbit is developed, and preliminary analyses and performance studies are conducted. The key elements of the method are system identification inreal time, based on canonical variate analysis, and adaptive robust control using Model Predictive Control. The Canonical Variate Analysis method also possesses the built-in capability for performing statistically optimal model order reduction. Computational algorithms are developed using several low order flexible models. The results of this Phase I SBIR feasibility effort demonstrate that the new method is subject to careful design to reduce computer core size problems, but that its overall performance offers encouraging potential for more complete development. Keywords: Mathematical models, Computations. (KR)

A state-space realization for matrix fraction descriptions: applications to model order reduction and circuit synthesis

Abstract: An algebraic algorithm for a block-tridiagonal realization has been utilized to provide a matrix continued fraction of the Stieltjes form from a square right matrix fraction description. The matrix continued fraction form is then applied to the problem of model order reduction for multivariable systems. The same algorithm, performed in reverse, is utilized to synthesize voltage transfer function matrices using RC ladder networks and summers. >

Model order reduction techniques in large space structure applications

Abstract: The reduction of the large order models of complex systems into a sufficiently low dimensional order in such a way that important dynamic characteristics of the real system are preserved, is a nontrivial task. The motivations for such a model order reduction are either to reduce computations for analysis and practical control design or to simplify the control system structure. In the present article, major techniques in model order reduction are briefly discussed. The characteristic similarities and differences are highlighted, their advantages and disadvantages are underlined, and further research requirements and trends are commented upon. Introduction and Perspective One of the central issues in the active control of complex systems such as large flexible space structures (LFSS) is the derivation of a "correct" mathematical model for both the controlled and the uncontrolled dynamical systems. Theoretically, there are infinitely many elastic modes or degrees of freedom (DOF) in the distributed parameter (DP) models of LFSS, usually with very low natural damping. Moreover, the flexible modes contribute to the actual deformation of the structure.' The truly infinite dimensional character of LFSS models has to be approximated by some "high fidelity" finite (but usually very large) dimensional model. The normal approach taken by engineers to achieve this end is via modal models with a large number of modes that provide a reasonable representation of the spacecraft dynamic characteristics. However, a difficult problem still remains to be the development of a model of lowenough dimensional order that it can be utilized by the onboard controller, yet high enough dimensional order that it preserves the dynamic characteristics of the real system represented and controlled. The motivations for such a reduction are either to reduce computations for analysis and practical control design or to simplify the control system structure. Discretization procedures will not be discussed herein and it will be assumed that a large finite dimensional model has been generated somehow and for implementation and other practical considerations, the model needs to be further reduced. *This work was-supported, in part, by the Air Force Wright Aeronautical, Air Force Systems Command, Flight Dynamics Lab, Structures and Dynamics Division, while the author was employed with HR-Textron, Valencia, California. There are various approaches to model order reduction; some are optimal or pseudo-optimal and others are ad-hoc methods based on practical considerations and engineering experience and judgment. These techniques are known by different names such as "reduction," "condensation," "economization," "aggregation," "optimal projection," and other combinations thereof. It has often been pointed out that such techniques generally constitute application of Rayleigh-Ritz/Galerkin optimization, and matrix transformation methods to the eigenvalue/eigenvector formulation for structural dynamic problems. The reduction or the condensation methods are based on transformations of the coordinates in the equations of motion that essentially maintain the invariance of the quadratic forms of the potential and kinetic energies. An important feature of these methods is that the reduced order model often loses the basic characteristics of the original system. Considerable progress was made by Likins, Ohkami, and wong5 in this respect. However, they failed to develop a general enough criterion that could reduce the system model in an optimal sense without significantly affecting the eigenvalues of the original model. The optimization or the mathematical reduction procedure, on the other hand, is based on the reduction of the eigenvalue problem to a smaller size based on some optimality criterion (usually quadratic). In these techniques, the reductions are carried out without actually resorting to approximations, i .e. , without truncatiag any coordinates or states of the original system. "Balanced" model reduction of linear timeinvariant dynamical systems is essentially based on the controllability and observability relations of the states of the system. Subsystem models are obtained by deleting those states that contribute the least to the controllability and observability (or the impulse response) of the original system7 and thus are optimal only in this sense. A more recent approach to model reduction is proposed in Skelton's work,* where each state of the system model is assigned a "cost" relative to a given basis, via a quadratic criterion, and the states with the least cost are deleted in a systematic manner. The resulting reduced model is a function of the state-space basis, and thus there is no guarantee for optimality for all choices. The latest development in model order reduction techniques is the work by Hyland and erns stein.^ Herein first order necessary conditions for reduced order modeling of linear time-invariant systems are derived via a pair of modified Lyapunov equations coupled by a nonorthogonal projection. This approach reveals the possibility of multiple extrema forsome of the abovementioned methods. "Copyright @ 1988 by the American Institute of Aeronautics and Astronautics. Inc. All Rights Reserved."

The implication of model order reduction for control system design-a case study

Abstract: A modeling technique has been developed for gas distribution networks which includes a model-order-reduction procedure to facilitate simulation and control system design studies. The model is validated against test result data. The effect of the model-reduction procedure is to introduce uncertainties into the model, and the implications of the uncertainties are investigated in relation to control system design. The design results in a high-order controller, and a final reduction procedure is applied at this stage to give a control system that can be implemented on a PC. >