Abstract
The dead-beat ripple-free tracking problem for multivariable multirate sampled-data systems is considered. A necessary and sufficient condition for the problem solvability is given in a constructive way. The proposed approach involves the associated time-invariant representation of periodic systems and polynomial matrix methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Araki, M and T. Hagiwara, “Pole assignment by multirate sampled-data output feedback”, Int. J. Control, vol.44, no.6, (1986), pp 1661–1673.
Araki, M and K. Yamamoto,“ Multivariable multirate sampled-data systems: state-space description, trasfer characteristics, and Nyquist criterion”, IEEE Trans. Autom. Control, vol.AC-31, no. 2, (1986)., pp 145–154.
Berg, M.C., N. Amit and J.D. Powell, “Multirate digital control system design”, IEEE Trans. Autom. Control. Vol. AC-33, (1988), pp. 1139–1150.
Colaneri, P., R. Scattolini and N. Shiavoni, “A design technique for multirate control with applications to a distillation column”, Proceed. 12th IMACS World Congress, vol. 2, Paris, 1989.
Meyer, D.G., “Toward a new CAD methods for MIMO multi-rate digital controllers”, Proceedings of the 27th Conference on Decision and Control. Austin, Texas, (1988) pp 1889–1891.
Tarn, T., X. Zeng and J.R. Zavgren jr, “Feedback stabilization of linear dynamic systems with multirate sampled output”, SIAM J. Control and Optim.. vol.26, no.4, (1988), pp 812–833.
Akashi, A. and M. Adachi, “Minimum time output regulation problem of linear discrete-time systems”, IEEE Trans. Autom Contr.. Vol. AC-22, (1977), pp. 939–942.
Akashi .A. and H. Imai,“ Output deadbeat controllers with stability for discrete-time multivariable linear systems”, IEEE Trans. Autom. Contr.. Vol. AC-23, (1978), pp.1036–1043.
Akashi,A., H. Imai, and M. Adachi, “ On time optimal control of linear discrete-time systems by geometric approach”, Int. J. Contr.. Vol. 28, (1978), pp. 733–742.
Ichikawa ,K., “Discrete-time fast regulator with fast observer”, Int. J. Contr... Vol. 28, (1978), pp. 733–742.
Isermann, R., Digital Control Systems. Springer-Verlag, Berlin, (1981)
Leden, B., “Multivariable dead-beat control”, Automatica, Vol. 13, (1977), pp.185–188
Leden, B., “Output dead-beat control -A geometric approach”, Int. J. Control. Vol. 26, (1977), 493– 507.
O’ Reilly, J., “The deadbeat control of linear multivariable systems with inaccessible state”, Int. J. Control, Vol. 31, (1980), 645–654.
O’ Reilly, J., “The discrete linear time-invariant time optimal control problem-an overview”, Automatica. Vol. 17, (1981), pp.363–370.
Seraji,H., “Deadbeat control of discrete-time systems using output feedback”, Int J. Contr.. Vol. 21, (1975), pp. 213–223.
Bradshaw, A. and Porter B., “Design of linear multivariable discrete-time tracking systems incorporating error-actuated controllers”, Int. J. Systems Sci., Vol 9, (1978), pp.185–191.
Doraiswami, R., “Robust control strategy for a linear time-invariant multivariable sampled-data servomechanism problem”, IEE Proc., Vol. 129, Part D, (1982), pp283–292.
Eichstaedt, B., “Multivariable closed-loop deadbeat control: a polynomial-matrix approach”, Automatica. Vol. 18, (1982), pp. 589–593.
Emami-Naeini, A. and G.F. Franklin,“ Deadbeat control and tracking of discrete-time systems”. IEEE Trans. Autom. Contr.. Vol. AC-27, (1982), pp.176–182.
Franklin, G.F. and A. Emami-Naeini, “Design of ripple-free multivariable robust servomechanisms”, IEEE Trans. Autom. Contr.,Vol. AC-31, (1986), pp.661–664.
Jetto, L., “Ripple-free tracking problem”, Int. J. Contr..Vol. 50, (1989), pp.349–359.
Kimura, H. and Y. Tanaka, Minimal-time minimal order deadbeat regulators with internal stability, IEEE Trans. Autom, Contr., Vol. AC-16, (1981), pp. 375–377.
Koschmann, J.E., and Farison J.B., “Controller design for discrete-systems subjected to disturbances”, Int. J. Contr., Vol. 16, (1978), pp.375
Kucera, V., “A dead-beat servo problem”, Int. J. Contr.. Vol.32, (1980), pp.107–113.
Kučera, V. and M. Sebek, “ On deadbeat controllers”, IEEE Trans. Autom. Contr..Vol. AC-29, (1984), pp.719–722,1984.
Sebek, M., “Multivariable deadbeat servo problem”, Kibernetica.Vol. 16, (1980), pp.443–453.
Wolovich, W.A., “Deadbeat error control of discrete multivariable systems”, Int. J. Contr.,Vol.37. (1983), pp.567–582.
Grasselli, O.M. and F. Lampariello, “Dead-beat control of linear periodic disrete-time systems”, Int. J. Contr., (1981), pp.31.39.
Grasselli, O.M. and S. Longhi,“ Output dead-beat controllers and function dead-beat observers for linear periodic discrete-time systems”, Int. J. Contr.. Vol43, (1986), pp.517–537.
Grasselli, O.M. and S. Longhi, “Disturbance localization with dead-beat control for linear periodic disrete-time systems”, Int. J. Contr.. Vol. 44, (1986), pp. 1319–1347.
Grasselli, O.M. and S. Longhi, “Disturbance localization with dead-beat control by measurement feedback for linear periodic discrete-time systems”, Automatica. Vol. 24, (1988), 375–385.
Grasselli, O.M. and S. Longhi, “Robust tracking and regulation of linear periodic multivariable discrete-time systems”, Rap. Int. 89.08, Dip di Ingegneria Elettronica, Seconda Universita di Roma “Tor Vergata”, 1989.
Jetto, L., “On deadbeat controller with ripple-free requirement for SISO discrete systems”,to appear on IEE Proceedings on Control Theory and Applications, part D, (1989).
Sirisena, H.R, “Ripple-free deadbeat control of SISO discrete systems”, IEEE Trans. Autom. Contr.,Vol.AC-30, (1985), pp.168–170.
Meyer, R.A. and C.S. Burrus, “A unified analysis of multirate and periodically time-varying digital filters”. IEEE Trans. Circ. and Systems. Vol. CAS-22, (1975), pp. 162–168.
Chen, C.T., Linear System Theory and Design. New York: Holt, Rinehart and Winston, (1984).
Francis, B.A. and T.T. Georgiou, Stability theory for linear time-invariant plants with periodic digital controllers, IEEE Trans. Autom. Control. Vol. 33, No. 9, (1988), 820–832.
Grasselli, O.M. and S. Longhi,“ Input and output decoupling zeros of linear periodic discrete-time systems”, Preprints of the IFAC Workshop on Systems Structure and Control: State Space and Polynomial methods. Prague. September 1989, 215–218.
Grasselli, O.M. and S. Longhi, “Algebraic-geometric techniques for linear periodic discrete-time systems”.Proc. of the Intern. Symp. on the Mathem. Theory of Netw. and Syst. (MTNS-89), Amsterdam, Junel989.Realization and Modeling in System Theory (M.A. Kaashoek, J.H. Van Schuppen and A.C.M. Ran Eds.), Vol. 1, Birkhauser Verlag.Basel, (1990).
Kailath, T., Linear Systems. Prentice-Hall, (1980).
Grasselli, O.M., “A canonical decomposition of linear periodic discrete-time systems”, Int. J. Control. vol. 40, (1984) 201–214.
Evans.D.S., “ Finite-dimensional realizations of discrete-time weighting patterns”.SIAM J. Appl. Math,22, (1972), 45–67.
Rosenbrock, H.H., Computer-Aided Control System Design. Academic Press, London, (1974).
Bengtsson, G., “Output regulation and internal models -A frequency domain approach”, Automatica. 13, (1977), 333–345.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Grasselli, O.M., Jetto, L., Longhi, S. (1991). Continuous Output Dead-Beat Control of Multivariable Multirate Sampled-Data Systems. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_37
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0439-8_37
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6760-7
Online ISBN: 978-1-4612-0439-8
eBook Packages: Springer Book Archive