Abstract
A parameterization of the class of linear state-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is applied to give a method for maximal order reduction of proper transfer function matrices. By making the maximum number of closed-loop modes unobservable, while retaining arbitrary assignment of the remaining modes, a lower-order transfer function matrix is obtained. The method establishes that results concerning the existence, number, and cancellation of zeros of proper transfer-function matrices may be applied in the response insensitivity problem. The main result is a class of maximal order reducing fixed-gain state-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements.
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References
Al-Nasr, N., 1982, On zeros of time-invariant multivariable linear systems containing input derivatives, International Journal of Control 35: 749–753.
Amin, M.H., and Hassan, M.M., 1988, Determination of invariant zeros, International Journal of Control 47: 1011–1041.
Antsaklis, P., 1980, Maximal order reduction and supremal (A, B)-invariant and controllability subspaces, IEEE Transactions on Automatic Control 25: 44–49.
Davidson, E.J., and Wang, S.H., 1974, An algorithm for the calculation of transmission zeros of linear multivariable systems, Automatica, 10: 643–658.
Emami-Naeini, A., and van Dooren, P., 1982, Computation of zeros of linear multivariable systems, Automatica, 18: 415–430.
Fahmy, M.M., and O’Reilly, J., 1982, On eigenstructure assignment in linear multivariable systems, IEEE Transactions on Automatic Control 27: 690–693.
Fahmy, M.M., and O’Reilly, J., 1983, Eigenstructure assignment in linear multivariable systems- A parametric solution, IEEE Transactions on Automatic Control 28: 990–994.
MacFarlane, A.G.J., and Karcanias, N., 1976, Poles and zeros of linear multivariable systems: a survey of the algebraic, geometric and complex variable theory, International Journal of Control 24: 33–74.
Mita, T., 1977, On maximal unobservable subspace, zeros and their applications, International Journal of Control 25: 885–899.
O’Reilly, J., and Fahmy, M.M., 1985, The minimum number of degrees of freedom in state feedback control, International Journal of Control 41: 749–768.
Owens, T.J., 1988, Parametric state feedback control with model reduction, International Journal of Control 47: 1299–1306.
Owens, T.J., 1988, Parametric state feedback control with exact model matching, in CONTROL 88, IEE Conference Publication No. 285.
Owens, T.J., 1988, Parametric output feedback control with response insensitivity, International Journal of Control 48: 1213 1239.
Owens, T.J., and O’Reilly, J., 1987, Parametric state feedback control with response insensitivity, International Journal of Control 45: 791–809.
Roppenecker, G., 1983, Minimum norm output feedback design under specified eigenvalue areas, Systems and Control Letters 3: 101–103.
Roppenecker, G., 1986, On parametric state feedback design, International Journal of Control 43: 793–804.
Rosenbrock, H.H., 1974 Computer-aideddesign of control systems, Academic Press.
van Dooren, P.M., 1981, The generalized eigenstructure problem in linear systems theory, IEEE Transactions on Automatic Control 26: 111–129.
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© 1990 Birkhäuser Boston
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Owens, T.J. (1990). Maximal order reduction of proper transfer function matrices. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Robust Control of Linear Systems and Nonlinear Control. Progress in Systems and Control Theory, vol 4. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4484-4_14
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DOI: https://doi.org/10.1007/978-1-4612-4484-4_14
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8839-8
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