Showing papers on "Model order reduction published in 1992"

Convergence improvement for component mode synthesis

Abstract: Model order reduction by component mode synthesis relies on the truncation of high-frequenc y component modes. Such truncations inevitably lead to approximate solutions for the system frequencies and mode shapes. A technique is proposed to improve the accuracy of the computed system modal content. An upper bound is derived for the norm of the residual vector corresponding to each eigenvalue-eigenvector pair. The proposed scheme is aimed at lowering this upper bound, thereby consistently improving the overall accuracy of the system eigen solution. This method is not designed to lead to complete convergence. However, significant improvement is consistently obtained at virtually no cost and by using only practically available information. Numerical examples are included for demonstration purposes.

Minimal Parameter Homotopies for the L2 Optimal Model Order Reduction Problem

Abstract: The problem of finding a reduced order model, optimal in the L2 sense, to a given system model is a fundamental one in control system analysis and design. The problem is very difficult without the global convergence of homotopy methods, and a number of homotopy based approaches have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on several formulations are developed and compared here. The main conclusions are that dimensionality is inversely related to numerical well conditioning and algorithmic efficiency is inversely related to robustness of the algorithm.

Eigenvalue inclusion for model approximations to distributed parameter systems

Abstract: The impact of model order reduction on the dynamics of open-loop and closed-loop processes is studied. The concept of eigenvalue inclusion regions (EIR) is utilized to assess the practicality of finite-order models for distributed parameter systems (DPS) such as tubular reactors. It is demonstrated that the EIRs account for the neglected modes of the process and give indications as to the dominance of the models retained in the finite-order model. A simulation study illustrates the computation of EIRs and investigates the significance and the restrictions of the methodology

Nonlinear control of a double effect evaporator

Abstract: An application of nonlinear feedback theory to the control of a double effect evaporator is presented. Modeling of the evaporator and model order reduction are briefly considered. The nonlinear controller is designed in a two-stage procedure. First, one considers a linearizing control, then a PI control is designed. Some numerical results are illustrated to compare performances of the nonlinear control with a PID control whose design is based on a linear approximation of a nonlinear model. The disturbance decoupling problem is also studied.

Continuum modeling of the Space Shuttle Remote Manipulator System

Abstract: The formulation of structural dynamics models for the Space Shuttle Remote Manipulator System (RMS) is discussed. Continuum models are used instead of finite element models because of the improved accuracy, the reduced number of model parameters, the avoidance of model order reduction, and the ability to represent the structural dynamics and control system dynamics in the same system of equations. Dynamics analysis of both linear and nonlinear versions of the model is performed and compared with finite element model results. A distributed parameter model of the Space Shuttle-RMS payload was generated using the transfer matrix method and the software PDEMOD. The model included an active control system which generated damping at the RMS joints. A stability and control analysis was then performed to detemine the reduction in settling time for RMS operations. >

A Reduced Order Model of Turbo Charged Diesel Engine

Abstract: A turbo charged diesel engine without any governor or controller is normally represented by a fourth order model. When the inlet and outlet manifolds are small, their effect is neglected and the model is then simplified to a second order model and does not reflect the effect of the two manifolds. The present paper uses model order reduction technique by Anderson, by separating the dynamics into fast & slow modes and assuming that the fast modes settle quickly. The model has been validated through simulation using typical data. It has been shown that there is a close resemblance in step response between the fourth order and the reduced order model for all the four states. On the other hand, a simpified model, obtained by neglecting the manifold volumes would give erroneous results.

Homotopy Methods in Control System Design and Analysis

Abstract: Recent technologies have led to stringent control system requirements. This has increased the importance and complexity of the analysis and design of control systems, which often require the solution of systems of nonlinear equations of high order. Some challenging computational problems in control design include model order reduction, high dimensional Riccati equations, fixed-structure optimization, robust analysis and feedback synthesis, sensor/actuator placement, and simultaneous controller/structure design. This paper describes these problems, and the directions in which globally convergent homotopy methods must be extented in order to be applicable to computational problems in control. By way of illustration, a computationally effective probability-one homotopy algorithm is presented for the optimal projection formulation of the reduced order model problem, together with some numerical results.

Approximated models for the analysis of interconnected circuits with transmission lines

Abstract: A new method for the time-domain response computation of an interconnected circuit with transmission lines is proposed. In the first step, a lumped approximated model of each transmission line is computed. In the second step, a model-order reduction of the resulting system is performed by means of balancing approximation techniques. An example is shown to validate the suitability of the proposed strategy. >

Advanced Topics in Model Reduction

Abstract: The approximation of high-order time-invariant systems with low-order models has been considered in the previous chapters. By high-order systems with unknown but bounded parameters we mean the class of linear systems where some parameters, not numerically known but bounded, appear either in the state-space formulation or in the frequency domain representation. For this class of systems, only a few investigations [1] have been performed for model order reduction. By this problem we mean obtaining a low-order model of the original one, but which formally contains the unknown parameters present in the high-order model. Moreover, some structural properties must be saved in the reduced-order model: the stability and the minimal form in the range of given bounded parameters.