Design Of Linear Control Systems Research Articles

Trade‐offs in linear control system design: A practical example

AbstractIn this paper two modern control techniques, the H2 and H∞ control design methods, are presented. After a brief theoretical explanation they are applied to a practical example: the control of the air flow rate through an axial ventilator. Modern control techniques are model‐based. In the first part of the paper it is explained how a model can be obtained both of the process and of the disturbances acting on it. On the basis of the model, several controllers can be designed. The example clearly illustrates some of the trade‐offs of modern control design. The H2 and H∞ controllers are also compared with a classical PI controller.

A microcomputer implementation of multivariable factorization theory

Factorization theory forms the basis of a powerful new method for the design of linear control systems. Techniques which simplify the implementation of this approach are examined: in particular, it is shown that under certain conditions, the multivariable design problem may be divided into a number of smaller independent subproblems. A microcomputer design system employing these techniques has been used to solve substantial multivariable design problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty

Robust H/sub infinity / control design for linear systems with uncertainty in both the state and input matrices is treated. A state feedback control design which stabilizes the plant and guarantees an H/sub infinity /-norm bound constraint on disturbance attenuation for all admissible uncertainties is presented. The robust H/sub infinity / control problem is solved via the notion of quadratic stabilization with an H/sub infinity /-norm bound. Necessary and sufficient conditions for quadratic stabilization with an H/sub infinity /-norm bound are derived. The results can be regarded as extensions of existing results on H/sub infinity / control and robust stabilization of uncertain linear systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimization technique for the design of a linear optimal power system stabilizer

A systematic optimization method for choosing the weighting matrix in linear optimal control system design, under the conditions of prespecified closed-loop dominant eigenvalue locations and feedback gain limit constraints, is presented. With the proposed method the desired weighting matrix can be obtained very quickly and conveniently without the heavy burden of choosing a suitable weighting matrix by trial and error. The analysis shows that a reduced-order feedback controller can be designed with the elements of the weighting matrix chosen in an optimal and coordinated manner. Simulation results of the linear optimal power system stabilizer designed by the proposed optimization technique are also given. The results show the correctness and effectiveness of the proposed method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computer-aided design of control systems using nonparametric models

A method based on the use of the impulse response as a nonparametric or graphical model is proposed for the analysis and design of linear time-invariant control systems. It can be used for systems too complex to be represented adequately by parametric models. The technique is restricted here to single-input single-output systems, but can be extended to more inputs and outputs.

Trade-offs in linear control system design

For some time now, many practitioners and researchers in the control area have been aware that unstable open loop poles, non-minimum phase zeros, and/or time delays make control systems design difficult. In this paper we examine the nature of these difficulties by discussing the results of Freudenberg and Looze (1987, 1988) and Sung and Hara (1988) on integral constraints on sensitivity functions. One of the key conclusions here is a set of rules of thumb, giving limitations on the closed loop bandwidth which are imposed by unstable open loop poles, non-minimum phase zeros and/or time delays.

On a Convex Parameter Space Method for Linear Control Design of Uncertain Systems

This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors’ knowledge, this is one of the first numerical procedures able to handle and solve this interesting design problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.

An approach to design of control systems with parametric-coordinate feedback

A method of control design for linear systems and some nonlinear systems is considered. The class of systems is characterized by the presence of coordinate and parametric feedback control signals. The system can be presented as consisting of two control channels: one controlling the system in a specified domain and the other to drive the system into this domain. The proposed method for binary system design is based on the solution of the Lyapunov-Bellman equations. The Lyapunov-Bellman function (or the optimal Lyapunov function, namely, the solution of the correspondent equation) is used to design the second channel of control. The analytical design problem of this channel is formulated as an optimal control problem under a cost functional of special type. >

Computer-aided design and analysis of linear multivariable control systems using the systematic design approach

A new approach for the design of multivariable feedback control systems in the frequency domain is presented. The techniques handle stability, performance, and robustness aspects of the design problem satisfactorily. The overall approach is systematic and intuitively appealing. A new computer-aided control system design package called SFPACK is developed. This package has implemented the new frequency response design techniques. The package is interactive and command-driven, and it is used as a teaching tool for helping the students to understand the concepts of the design approach. The MAT-LAB-derived control environment in SFPACK is extended to provide the user with an expert system development environment.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Development of a new generation of interactive CACSD environments

A description is given of the development of a novel interactive computer-aided control system design (CACSD) package for the design of linear multivariable control systems. The package incorporates the stable factorization design technique and other recent design methodologies, such as the systematic design approach. To provide a high level of interactive design environment for the user, knowledge-based expert system development tools are provided within the package. In addition, the user is provided with the facilities to write user-defined functions and procedures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Linear controller design: limits of performance via convex optimization

In this tutorial, an approach to the analysis and design of linear control systems based on numerical convex optimization over closed-loop maps is presented. Convexity makes numerical solution effective: it is possible to determine whether or not there is a controller that achieves a given set of specifications. Thus, the limit of achievable performance can be computed. To provide a context for the material presented, a brief overview of control engineering is given. A broad outline of various approaches to control design for linear and time-invariant systems is presented, including their advantages and disadvantages, for purposes of comparison with the approach presented. It is shown that many performance specifications have natural and useful geometric interpretations, and the notion of a closed-loop convex design specification is defined. The performance requirement that the closed-loop system be stable is discussed. It is shown that many performance specifications can be expressed as convex constraints on closed-loop performance specifications, and how some of these can be expressed as convex constraints on closed-loop transfer matrices is examined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two-delay robust digital control and its applications-avoiding the problem on unstable limiting zeros

In the design of linear control systems, the existence of unstable zeros makes it difficult to construct many control systems. When the usual digital control scheme is used, unstable zeros appear in the discrete-time model due to the existence of limiting zeros even though the continuous-time plant is minimal phase. To avoid this unstable zero problem, two new digital control schemes, called two-delay output control and two-delay input control, are proposed. These control systems are proved to have no finite zeros. Asymptotic inverse systems, pole assignable unknown input observers, and output feedback controllers having the LTR (loop transfer recovery) property are developed using the two-delay output control. Zero assignable control systems and model matching control systems are developed using the two-delay input control.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Magnitude and symmetric optimum criterion for the design of linear control systems: what is it and how does it compare with the others?

The magnitude and symmetric optimization techniques are two related methods for designing optimal linear control systems in th frequency domain. Both methods have been used in industry for some time, yet they do not appear to have been well-documented in the English control engineering literature. The development of the criterion is examined, including general solutions for typical controllers. As a basis for comparison, time-domain response optimization techniques, such as minimizing the integral time absolute error, along with state space techniques, i.e. pole placement, are briefly reviewed. Personal computer simulation results of a normalized position control system are given to illustrate these methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Symbolic computation application for the design of linear multivariable control systems

The application of symbolic computation to the algebraic design of linear multivariable control systems is presented. A software package for manipulating polynomial and rational function matrices and for solving the linear matrix equations referred to as unilateral and bilateral equations is implemented on the basis of the symbolic manipulation system known as REDUCE. Several basic functions in the package are explained and their usage is demonstrated by using an example of the design of a discrete-time control system.

Parallel and large-scale matrix computations in control: some ideas

The design and analysis of time-invariant linear control systems give rise to a variety of interesting linear-algebra problems. Numerically effective methods now exist for several of these problems. However, algorithms for large-scale computations and efficient parallel algorithms for these problems are virtually nonexistent. In this paper, we propose several efficient general-purpose parallel algorithms for single-input and multiinput eigenvalue assignment problems. A desirable feature of these algorithms is that they are composed of simple linear-algebraic operations such as matrix-vector multiplication, solution of a linear system, and computations of the eigensystem and singular values of a symmetric matrix, for which efficient parallel algorithms have already been developed and parallel software libraries are being built based on these algorithms. The proposed algorithms thus have potential for implementations on some existing and future parallel processors. We also propose a numerical method for the Sylvester matrix equation arising in the construction of a Luenberger observer. The method does not need reduction to “condensed” forms and is thus suitable for large and sparse matrices. The method also exhibits a certain parallelism.

Integrated engineering workstations in electrical engineering laboratories

The authors provide a description of integrated engineering workstations (IEWs) used in undergraduate electrical engineering laboratories. The IEWs are used for the design, analysis, and testing of engineering systems. Examples of laboratory experiments and software programs are presented. Two CAED (computer-aided engineering and design) software packages are described, BUCOP and BUDSP, which have enhanced the educational process at Bucknell on many different levels. The undergraduate developers of the packages have learned how to design and verify software systems. BUCOP and BUDSP have also stimulated the curiosity and creativity of students in the design of linear control systems and digital filters. Students now have a better understanding of realistic complex control and signal processing systems and are more aware of CAED capabilities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust controller design methodology for multivariable chemical processes: Structured perturbations

In this work, a methodology for the design of robust multivariable linear time invariant control systems with structured perturbations is presented. Useful properties of the μ-function are used to develop an algorithm that extends previous results on unstructured uncertainties. The complet methodology allows the specification of the dominant time constant for each control loop. The frequency response of an ideal controller is first computed allowing the synthesis of different controller structures (PI, PID, etc.). The specified time constants are then de-tuned in order to meet a desired upper bound over the multivariable stability margin. Some implementation aspects are discussed and the control design of a triple effect evaporator is considered to illustrate the feasibility of the methodology.

Parallel and Large Scale Matrix Computations in Control: Some Ideas

The design and analysis of time-invariant linear control systems give rise to a variety of interesting linear algebra problems. Numerically effective methods now exist for several of these problems. However, algorithms for large scale computations and efficient parallel algorithms for these problems are virtually nonexistent. In this paper, we propose several efficient generalpurpose parallel algorithms for single-input and multi-input eigenvalue assignment problems. A desirable feature of these algorithms is that they are composed of simple linear algebraic operations such as matrix-vector multiplication, solution of a linear system, and computations of eigensystem and singular values of a symmetric matrix, for which efficient parallel algorithms have already been developed and parallel software libraries are being built based on these algorithms. The proposed algorithms thus have potential for implementations on some existing and future parallel processors. We also propose a numerical method for Sylvester matrix equation arising in the construction of Luenberger observer. The method does not need reduction to”condensed” forms and is thus suitable for large and sparse matrices. The method also exhibits certain parallelism.

Rational linear algebraic tracking control system design

Basic issues and methods in tracking control system design are considered, with emphasis on the logical nature of the design process. The controller transfer functions are not required to share the same poles, resulting in added design freedom. Classical root-locus-based design is placed in perspective, and practical ways of choosing the overall system transfer function to meet tracking performance objects are discussed in detail.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Controller Design For Nonlinear Systems Based on Simultaneous Stabilization Theory and Describing Function Models

A new systematic and algebraic linear control system design procedure for use with highly nonlinear plants is developed. This procedure is based on simultaneous stabilization theory and sinusoidal-input describing function models of the nonlinear plant, and is presently applicable to single-input single-output, time-invariant, deterministic, stable, and continuous-time systems which are representable in standard state-variable differential equation form. Three software utilities to implement the controller design procedure are also outlined. This method and the associated software is applied to a position control problem of the sort encountered in robotics, and the results are compared with those previously obtained using both linear and nonlinear PID control.