Reduced-order Controller Design Research Articles

Structured singular value controller synthesis using constant D-scales without D-K iteration

Structured singular value synthesis allows the design of controllers that are robust with respect to multiple block uncertainty. This type of design process commonly relies on D-K iteration and curve fitting. In particular, the optimal D-scales and the controller are iteratively optimized. Since the D-scales are optimized over frequency, they must be curve fitted with rational transfer functions before the controller is optimized. This curve fitting can be difficult and lead to suboptimal designs. This paper presents a structured singular value process that allows the D-scales to be constrained, to be constant and simultaneously optimizes the D-scales and the controller K. The approach relies on recent results on mixed-norm H/sub 2//H controller synthesis and also enables the direct design of reduced-order controllers.

Nearly nonminimal linear-quadratic-Gaussian compensators for reduced-order control design initialization

Nearly nonminimal linear-quadratic-Gaussian compensators for reduced-order control design initialization

Polynomial interpolation between input samples for continuous-time simulation

sional parameter indicating the degree of usefulness of a fundamental quantity in the design and analysis of many engineering disciplines, namely, the power. This Note demonstrates that a focus on the system control power efficiency does not curtail the designer's ability in monitoring other important quantities of the overall design; on the contrary, it brings in an added, but necessary, dimension to the SCS that is a time-tested proven concept in engineering design. The improvement of efficiency, in the least, simply makes better use of available control power since it results in reduced power interaction with the unmodeled dynamics. Furthermore, this reduction is not merely qualitative but it is quantified via efficiency. More importantly, all efficiency computations only involve the reducedorder control design model while extracting information about the behavior of the truth-model of the system.

Computer-aided analysis and design of control systems using model approximation techniques

One of the objectives of this paper is to describe some of the available techniques and tools which are believed to be particularly useful in practical problems of model approximation. The issues and methods described are grouped under the following headings: (i) order-reduction algorithms, (ii) dominant pole selection, (iii) quality indices, (iv) open- and closed-loop optimization procedures, and (v) model validation. Another objective is to show that model approximation techniques can also be used in quite an effective way in the analysis and synthesis of control systems. It is shown, by way of examples, how the techniques and tools described in the first part of the paper may be used not only to compute reliable simplified models but also to obtain qualitative and quantitative information regarding the original system. In addition, an example is provided which illustrates how some of the tools and methods can be easily used in the design of reduced-order controllers. Examples taken from the models of a power system and a thermal power station are provided to illustrate the main points of the paper.

A new parametrization of H∞ suboptimal controllers

Elementary state-space concepts are used to derive a transparent solution to the H ∞ control problem on an infinite horizon. The main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric Riccati equations with a coupling constraint. Unlike the classical parametrization in terms of linear fractional transformation, this state-space representation has a homogeneous Riccati formulation which should help to make the most of the suboptimal controller diversity. Potential applications include the design of reduced-order controllers and, more generally, the selection of suboptimal controllers to meet or optimize additional constraints.

Reduced order controller design for discrete time systems

Robust discrete control system design techniques and model reduction are discussed. A new linear quadratic guussian/loop transfer recovery procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has the desired loop shape, and then recovered by a realizable linear quadratic gaussian controller. To do this, results that show the effects of the weighting matrices (noise intensities) on linear quadratic regulator (Kalman-Bucy filter) return difference and inverse-return difference arc derived and a procedure to recover the linear quadratic regulator loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed-loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization and the second is P frequency weighting technique where it is possible to vary the approximation accuracy with frequency. The controller design and re...

Adaptive Temperature Control of Industrial Diffusion/LPCVD Reactors

Abstract A mathematical model describing the heat transfer characteristics of a hot-wall batch electric furnace serves as the basis for the design of a temperature controller of LQG type. Because the model is of high order, reduced-order controller design techniques are applied to satisfy constraints on on-line computations imposed by available computing power. In contrast to classical techniques for reduced-order controller design that use system-theoretic considerations, this paper adopts the optimal projection approach, thus yielding an optimal reduced-order controller. An algorithm is presented for solving the associated set of coupled (modified) Riccati and Lyapunov equations. The algorithm utilizes a homotopic continuation method. A sequential prediction error algorithm is added to estimate the parameters, making the control law adaptive. The feedback is calculated by performing a few iterations of a Riccati equation in every sample interval. Some performance results are presented.

Stability condition for flexible structure control with mode residualization

Chun-Liang Lin* and Fei-Bin Hsiaoj National Cheng Kung University, Tainan, Taiwan, Republic of China and Bor-Sen Chen J National Tsing Hua University, Hsinchu, Taiwan, Republic of China accommodated in controller design. One of the methods for obtaining a reduced-order controller is to use the formalism of mode residualization. This is extensively applied in the flutter suppression and structural control' problems. This formulation of the reduced-order model is obtained by assuming that the residual modal states of the system quickly reach steady state values. The reduced-order controller design is then based on this simplified model. Although such a controller usually works well on the reduced-order system, it may not stabilize the actual closed-loop system. This is, of course, the most important evaluation criterion for a control law selection. In this Note, we develop the general idea of mode residualization for a high-order, flexible structure and obtain results for the operation of an observer-based controller, based on the reduced-order model, in closed-loop with the actual system. By applying the perturbation theory, we derive a new stability condition on the basis of the frequency domain representation, which guarantees the stability of the overall closedloop system even when the sensors and actuators are not collocated. In the flutter suppression or other structural control problems, the natural frequency, mode shape, and damping characteristics of modes are all known imprecisely. Thus, parameter uncertainty may cause the system to be unstable. Addressing this issue, we also present a simple robust stability condition, which insures the overall stability so that the controlled system will not be destabilized by parametric perturbations.

Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds

A feedback control-design problem involving structured plant parameter uncertainties is considered. Two robust control-design issues are addressed. The Robust Stability Problem involves deterministic bounded structured parameter variations, while the Robust Performance Problem includes, in addition, a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations. The optimal projection approach to fixed-order, dynamic compensation is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design. The principle result is a sufficient condition for characterizing dynamic controllers of fixed dimension which are guaranteed to provide both robust stability and performance. The sufficient conditions involve a system of modified Riccati and Lyapunov equations coupled by an oblique projection and the uncertainty bounds. The full-order result involves a system of two modified Riccati equations and two modified Lyapunov equations coupled by the uncertainty bounds. The coupling illustrates the breakdown of the separation principle for LQG control with structured plant parameter variations.

Reduced-order controller design using coprime factor model reduction

Two procedures for reduced-order controller design that incorporate coprime factor model reduction techniques and a related robust stabilization problem are proposed. It is shown that robust stability can be achieved with these controllers. The results obtained show how to reduce the controller degree systematically. They clearly indicate how the maximum stability margin influences allowable model reduction error. >

On direct versus indirect methods for reduced-order controller design

Comparisons are obtained between direct (parameter optimization) and indirect (controller reduction) methods in reduced-order controller design. In particular, the authors compare the controller canonical correlation coefficients method of C. De Villemagne and R.E. Skelton (1988) to the optimal projection theory of D.C. Hyland and D.S. Bernstein (1984). It is noted that suboptimal methods may, in certain cases, be simpler to implement than optimal methods. Thus, the choice of direct versus indirect methods can be viewed as a tradeoff between design simplicity and actual control-system performance. >

Multivariable internal model control for a full-scale industrial distillation column

A multivariable internal model control system was developed for a full-scale distillation column. The basis for the design of the control is a two-input/two-output matrix of linear transfer functions describing column dynamics. The control system is designed to perform dual composition control of the overhead and bottom products. Hardware constraints dictate multirate sampling of the product concentrations. In addition, the column exhibits inverse response to changes in reflux flow. The multirate sampling is addressed by a unique implementation of a feedforward decoupling control. A reduced-order controller design technique is developed to handle the non-minimum-phase behavior of part of the column. Simulations demonstrate the improvement in control obtained from this approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reduced Order Controller Design for Discrete Time Systems

This paper is concerned with robust discrete control system design techniques and model reduction. A new LQG/LTR † † We follow standard abbreviations: LQR Linear Quadratic Gaussian LTR Loop Transfer Recovery KBF Kalman-Bucy Filter LQR Linear Quadratic Regulator procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has a desired loop shape, and then recovered by a realizable LQG controller. To do this, results that show the effects of the weighting matrices (noise intensities) on LQR (KBF) return difference and inverse-return difference are derived and a procedure to recover the QR loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization where an error bound is discussed. The second is a frequency weighting technique where it is possible to vary the approximation accuracy with frequency. For this method, a bound on the weighted reduction error is derived. The controller design and reduction techniques are illustrated by designing a reduced order controller for an 8th order lumped inertia flexible mechanical system.

Integrated design of space structures using lattice plate finite elements

Lattice plate finite elements based on a continuum model of a large plate-like lattice space structure are used to examine the effect of variation of several fundamental structural parameters on the natural frequencies and mode shapes of the structure. Reduced-order controller design models are developed using modal cost analysis to rank the modes for each set of structural parameter values. The linear-quadratic-Gaussian controller design method is used to develop feedback control systems for each set of structural parameter values. The resulting system performance is then evaluated by examining the steady-state regulation cost of the structure as a function of the structural design parameters.

Frequency-weighted optimal Hankel-norm approximation of stable transfer functions

This paper shows how to introduce arbitrary frequency weighting into the optimal Hankel-norm approximation problem for scalar, finite-dimensional, linear, time-invariant systems. The procedure has applications to the closed-form design of reduced-order controllers.

An output error method for reduced order controller design

An efficient computational technique is presented for the design of reduced order controllers for linear discrete-time systems. The technique is based on the minimization of the output error between the closed-loop system and a specified reference model.

Low-sensitivity dynamic compensators for linear stochastic systems with random parameters

This paper presents procedures for the low-trajectory sensitivity design of reduced-order output feedback dynamic controllers for linear stochastic systems with uncertain parameters having zero-mean random variations around their expected values. Both the finite and infinite terminal time designs are discussed. Matrices are conveniently partitioned to reduce computational effort. Several special cases are considered, leading to simpler problem designs. Two numerical examples are included.

Explicit Solutions of Linear Matrix Equations

Explicit Solutions of Linear Matrix Equations