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Foundation of Control Systems Design

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Control Systems Design

Abstract

The need for a new conceptual foundation for the design of control systems is explained. A new foundation is proposed, comprising a definition of control and three principles of systems design: the principle of inequalities, the principle of matching and the principle of uniform stability. A design theory is built on this foundation. The theory brings into sharper focus, hitherto elusive but central, concepts of tolerance to disturbances and over-design. It also gives ways of characterising a good design. The theory is shown to be the basis of design methods that can cope with, important and commonly occurring, design problems involving critical systems and other problems, where strict bounds on responses are required. The method of inequalities, that can be used to design such systems, is discussed.

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References

  • Arunsawatwong, S., (1996) Stability of retarded delay differential systems, Int. J. Contr., 65:347–364.

    MathSciNet  MATH  Google Scholar 

  • Arunsawatwong, S., (1998) Stability of Zakian I MN recursions for linear delay differential equations, BIT, 38:219–233.

    MathSciNet  MATH  Google Scholar 

  • Birch, B.J. and Jackson, R., (1959) The behaviour of linear systems with inputs satisfying certain bounding conditions, J. Electroncs & Control, 6:366–375.

    Google Scholar 

  • Bode, H.W., (1960) Feedback — the history of an idea, Proceedings of the Symposium on Active Networks and Feedback Systems, 4.

    Google Scholar 

  • Boyd, S.P. and Barratt, C.H., (1991) Linear Controller Design: Limits of Performance, (Englewood Cliffs, New Jersey, U.S.A.: Prentice Hall).

    MATH  Google Scholar 

  • Desoer, C.A. and Chan, W.S., (1975) The feedback interconnection of linear time-invariant systems, J. Franklin Inst., 300:335–351.

    MathSciNet  MATH  Google Scholar 

  • Kuhn, T.S., (1970) The structure of scientific revolutions 2nd ed., (Chicago: University Chicago Press).

    Google Scholar 

  • Lane, P.G., (1995) The principle of matching: a necessary and sufficient condition for inputs restricted in magnitude and rate of change, Int. J. Contr., 62:893 915.

    MathSciNet  MATH  Google Scholar 

  • Liu, T.K., Satoh, T., Ishihara, T., and Inooka, H., (1994) An application of genetic algorithms to control system design, Proceedings of the 1st Asian Control Conference, Tokyo, 701–704.

    Google Scholar 

  • Liu, T.K., Ishihara, T., and Inooka, H., (1997) Application of a multiobjective genetic algorithm to control systems design based on the method of inequalities” Proceedings of the 2nd Asian Control Conference, Seoul, 289–292.

    Google Scholar 

  • Maciejowski, J.M., (1989) Multivariable Feedback Design (Wokingham, U.K.: Addison-Wesley).

    MATH  Google Scholar 

  • Mayne D.Q., and Sahba M., (1985) An efficient algorithm for solving inequalities, J. Opt. Theory & Appl., 45:407–423.

    MathSciNet  MATH  Google Scholar 

  • Maxwell, J.C., (1868) On governors, Proc. Roy. Soc., 16:270–283.

    MATH  Google Scholar 

  • Newton, G.C., Gould, L.A., and Kaiser, J.F., (1957) Analytical design of linear feedback controls, (New York: Wiley).

    Google Scholar 

  • Nyquist, H. (1932) Regeneration theory, Bell Syst. Tech. J., 11:126–147.

    MATH  Google Scholar 

  • Papoulis, A., (1970) Maximum response with input energy constraints and the mathched filter principle, IEEE Trans. Circuit Theory, 17:175–182.

    Article  Google Scholar 

  • Royden, H.L., (1968) Real Analysis, 2nd ed. (London: Collier Macmillan).

    Google Scholar 

  • Rosenbrock, H.H., (1960) An automatic method for finding greatest or least value of a function, Comput. J., 3:175–184.

    Article  MathSciNet  Google Scholar 

  • Rutland, N.K., (1992) Illustration of a new principle of design: vehicle speed control, Int. J. Contr., 55:1319–1334.

    MathSciNet  MATH  Google Scholar 

  • Rutland, N.K., (1994a) Illustration of the principle of matching with inputs restricted in magnitude and rate of change: vehicle speed control revisited, Int. J. Contr., 60:395–412.

    MathSciNet  MATH  Google Scholar 

  • Rutland, N.K., (1994b) The principle of matching: practical conditions for systems with inputs restricted in magnitude and rate of change, IEEE Trans. Automatic Control, AC-39:550–553.

    Google Scholar 

  • Rutland, N.K. and Lane, P.G., (1995) Computing the 1-norm of the impulse response of linear time-invariant systems, Syst. Control Lett., 26:211–221.

    Article  MathSciNet  MATH  Google Scholar 

  • Whidborne, J.F., Postlethwaite, I., and Gu, D.-W., (1994) Robust controller design using H loop-shaping and the method of inequalities, IEEE Trans. Control Syst. Technology, 2(4):455–461.

    MathSciNet  Google Scholar 

  • Zakian, V., (1975) Properties of I MN and J MN approximants and applications to numerical inversion of Laplace transforms and initial-value problems, J. Math. Anal. & Appl., 50:191–222.

    Article  MathSciNet  MATH  Google Scholar 

  • Zakian, V., (1979a) New formulation for the method of inequalities, Proc. IEE, 126:579–584.

    Google Scholar 

  • Zakian, V., (1979b) Computation of the abscissa of stability by repeated use of the Routh test, IEEE Trans. Automatic Control, AC-24: 604–607.

    MathSciNet  Google Scholar 

  • Zakian, V., (1986a) A performance criterion, Int. J. Contr., 43:921–931.

    MathSciNet  MATH  Google Scholar 

  • Zakian, V., (1986b) On performance criteria, Int. J. Contr., 43:1089–1092.

    MathSciNet  MATH  Google Scholar 

  • Zakian, V., (1987a) Input spaces and output performance, Int. J. Contr., 46:185–191.

    MATH  Google Scholar 

  • Zakian, V., (1987b) Design formulations, Int. J. Contr., 46: 403–408.

    MATH  Google Scholar 

  • Zakian, V., (1989) Critical systems and tolerable inputs, Int. J. Contr., 49:1285–1289.

    MathSciNet  MATH  Google Scholar 

  • Zakian, V., (1991) Well matched systems, IMA J. Math. Control Inf., 8:29–38 (see also Corrigendum, 1992, 9:101).

    Article  MathSciNet  MATH  Google Scholar 

  • Zakian, V., (1996) Perspectives on the principle of matching and the method of inequalities, Int. J. Contr., 65: 147–175.

    MathSciNet  MATH  Google Scholar 

  • Zakian, V. and Al-Naib, U., (1973) Design of dynamical and control systems by the method of inequalities, Proc. IEE, 120:1421–1427.

    Google Scholar 

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© 2005 Springer-Verlag London Limited

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Zakian, V. (2005). Foundation of Control Systems Design. In: Zakian, V. (eds) Control Systems Design. Springer, London. https://doi.org/10.1007/1-84628-215-2_1

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  • DOI: https://doi.org/10.1007/1-84628-215-2_1

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-913-5

  • Online ISBN: 978-1-84628-215-7

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