IEE Colloquium on Symbolic Computation for Control
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 Location: London, UK
 Conference date: 2 April 1996
 Conference number: 1996/078
 The following topics were dealt with: symbolic algebra tools; control education; control system design; and control system analysis
10 items found

Symbolic algebra tools for control teaching
 Author(s): N. Munro
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The paper describes various interactive facilities implemented in Mathematica, which have been used for several years in the teaching of Advanced Control to final year undergraduates in the Department of Electrical Engineering and Electronics at UMIST. The first facility, known as the LinModels Package, is a symbolic algebra package, which provides the various transformations needed to manipulate linear system models from one form to another. In particular, system models can be readily transformed between any of the following standard forms; statespace, transferfunction (matrix), left or right matrixfraction form, and Rosenbrock's system matrix in statespace or polynomial form. In the case of transformation from transferfunction to statespace form, a simple yet reliable minimal realization algorithm is automatically invoked. Similarly, with transformations to matrixfraction form the resulting system models are leastorder. The second facility, known as the Analysis Package provides a range of wellestablished analysis tools which provide the following features; the Kalman tests for controllability and observability, Rosenbrock's input and output decoupling zeros tests for models in statespace or polynomial matrix form, the Smith form of a polynomial matrix, the McMillan form of a rational polynomial matrix, and Bristol's Relative Gain Array for system sesitivity analysis. (7 pages)

Experiences from a Prologbased environment for modelling and simulation: an example of the application of logic programming in control engineering
 Author(s): E.B. Tanyi and D.A. Linkens
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The paper describes the use of Prolog in the implementation of a Knowledgebased Environment for Modelling and Simulation (KEMS). The basis of the implementation is the AI frame paradigm which provides a conceptual foundation for the design of the model base, the simulation code generator and the knowledge acquisition module which are the Prologbased components of KEMS. The experiences derived from KEMS provide a springboard from which the wider applications of logic programming in control engineering are discussed. Six application areas are identified, including modelling, the design of frontends for CAD packages, the design of objectoriented databases, the prototyping of engineering concepts, knowledgebased control and the design of decisionsupport systems. (6 pages)

Control system analysis with Mathematica
 Author(s): H.A. Barker ; P.W. Grant ; M. Zhuang
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It is shown that the linkage between Mathematica and MATLAB allows the graphical user interface of the associated simulation software SIMULINK to be used as a graphical user interface for Mathematica. This facility for defining the dynamic system models to be analysed by Mathematica has several significant advantages. In particular, the models are constructed by means of a comprehensive and welldeveloped graphical interface familiar to the control engineer, and the results of analysis obtained with Mathematica can be compared directly with the results of simulation obtained with SIMULINK. A Mathematicabased toolbox for the analysis and design of linear control systems is then described. It is shown that both continuous and digital systems may be analysed by Laplace and ztransforms and that familiar tools such as root locusand frequency responsediagrams are also available. Finally, an application of Mathematica to the analysis of nonlinear systems by means of multidimensional transforms is described, and results presented which by manual methods would take an inordinate amount of time to obtain. (5 pages)

MIMOQCAD: a Mathematica based multivariable control system CAD package
 Author(s): S.G. Breslin ; M.J. Grimble ; C.H. Houpist
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Quantitative Feedback Theory (QFT) was developed by Horowitz (1963, 1992) as a methodology for designing robust control systems. It is a frequency based technique where compensators can be designed to achieve a set of performance and stability objectives over specified ranges of plant parameter uncertainty. The QFT technique has been neglected for many years for several reasons, one of which has been the lack of efficient CAD software. This situation has been remedied by the release of a number of software packages which has sparked a renewed interest in the technique. The paper describes one such package, MIMOQCAD, a Mathematica based package which automates the QFT design methodology for both multiinput, singleoutput (MISC) and multiinput, multioutput (MIMO) systems. (5 pages)

Symbolic computation for dynamic sliding mode controller design
 Author(s): X.Y. Lu and S.K. Spurgeon
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In general, nonlinear controller design will involve three stages; symbolic computation to produce a controller, numerical simulation of the closedloop system and graphical display of the simulation results. The integration of these three phases can be seen in the work of Blankenship et al. (1995) where several tool boxes have been developed. In principle all three stages can be performed in any symbolic package such as MACSYMA, Mathematica, MAPLE, or REDUCE. The applications experience of the authors indicates that numerical integrators in those packages are far from enough. Thus it is necessary to interface with other languages or packages such as MATLAB or the Fortran NAG Library in order to exploit their numerical simulation functions and routines. The paper describes the preliminary development of a nonlinear sliding mode controller design package. (5 pages)

Symbolic algebra and physicalmodelbased control
 Author(s): P.J. Gawthrop and D.J. Ballance
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Physicalmodelbased control has been introduced to provide a general methodology for building systemspecific controllers which make use of systemspecific information about the system to be controlled. Partiallyknown and nonlinear systems form two categories of systems to which such a methodology is particularly appropriate. Because each control algorithm has to be specially constructed for each system, it is essential to provide software to help in this process. The use of computer algebra is a vital part of such software. The purpose of the paper is to present the computer algebra aspects of physicalmodelbased control. (5 pages)

The application of symbolic computation in the analysis of systems having parametric uncertainty
 Author(s): E. Kontogiannis and N. Munro
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In the analysis of systems with parametric uncertainty, complex symbolic computations are often encountered. Therefore, computer implementations require the use of symbolic environments. The Parametric Systems Toolbox (PST): a collection of files written in the MATLAB environment as a part of a current project, in the Control Systems Centre at UMIST, investigating the analysis and design of such systems; is demonstrated. The importance of symbolic computation in this type of system analysis is discussed. (6 pages)

Some applications of Maple in linear systems analysis
 Author(s): J. Jones ; N.P. Karampetakis ; A.C. Pugh
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Many problems in linear systems analysis are seen to be very computationally attractive. By this we mean that it is in general beneficial to implement the corresponding problem computationally rather than solving the problem by hand in terms of certain governing factors. Such factors may include the time, accuracy and cost of obtaining such a solution. The advent of complete symbolic computational packages, such as Maple and Mathematica, have made the computational implication of such problems particularly attractive. Perhaps understandably, however, neither one of these symbolic computer packages contain existing procedures or indeed packages for specialized work in linear systems. However, they are clearly flexible enough for the implementation of such work to be carried out. This is the motivation of the paper and we present a package of procedures, developed for use in Maple, for solving numerous and common problems in linear systems. (5 pages)

On using Mathematica to implement the zero set technique
 Author(s): M. Sandler and E. Zeheb
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The paper deals with an implementation of the zero set technique in the Mathematica programming language. In particular, use is made of the language's elegant list handling functions in performing algebraic and calculus operations on the representation of a polynomial. Two simple examples are presented, as is the complete code. (5 pages)

The use of symbolic computation for the problem of stabilisation via small order feedback controllers
 Author(s): J. Leventides
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The problem of stabilising a MIMO plant via output feedback controllers of a given degree was recently tackled via linearisation around some special degenerate compensators. This can be numerically implementated as an ɛperturbation method. The solution is in the form of a perturbation series which can be constructed by repetitively solving a set of linear equations, coming from the expansions (in ɛ and s) of the original pole placement equations. This expansion can be done almost trivially in any symbolic language using standard symbolic commands. The code is only a few lines long and can be done by the nonexpert. There is no need to understand the algebra of the problem, which involves tensor, polynomial algebra and some combinatorics since the load of the expansion is taken solely by the symbolic package. (4 pages)