Predictive Control & Youla-Kucera Parametrisation
Predictive control has become a very succesful control design, mainly due
tu direct constraint handling capabilities. Its main drawback is stability.
This research tries to solve the stability problem by applying the following
simple idea. Assume that a system is already controlled by some nominal
controller and the closed-loop is already stable. By the use of the Youla-Kucera
paramtrisation, a general formula for all stabilising controllers can be
found. Within these a controller (or an optimal YK polynomial) is searched
that minimises a quadratic function and simultaneously satisfies constraints.
The first approach is to use finite horizon cost function. However,
by applying this idea to a finite horizon cost function the overall Youla-Kucera
predictive controller (YKPC) becomes time-variant. The stability analysis
of such a system is performed. Stability proofs lead to minimum possible
horizon lenghts. These are given as number of unstable poles (control horizon)
and number of unstable zeros (output horizon) plus the degree of optimised
Another possibilty how to overcome stability problem is to use infinite
horizon cost function. In that case the controller is time-invariant when
constraints are inactive. Constrained stability is as in the previous case
assured if the corresponding optimisation problem is feasible.
The third approach to stability is based on the following idea. Let
us assume that the loop is already closed and controlled by a controller.
The question is what is the minimum number of control moves, or control
error moves that still lead to stable closed-loop behaviour and to a time-invariant
controller. Again, the minimum number if steps is directly related to the
number of unstable poles and zeros.
Journals and book chapters
Fikar, M., Kucera, V.: On minimum finite length control problem. Int. J.
Control, 73(2), 152-158, 2000. Abstract
Fikar, M., Engell, S., Dostál, P.: Design of Predictive LQ Controller.
Kybernetika 35(4), 459-472, 1999. Abstract
Fikar, M., Engell, S.: Receding horizon predictive control based upon Youla-Kucera
parametrisation. European Journal of Control, 3 (4), 304 - 316, 1997. Abstract
Fikar, M., Jorgensen, S. B.: Multivariable Constrained Control Based upon
all Stabilizing Controllers, In: D. W. Clarke (Ed.) Advances in Model-Based
Predictive Control, Oxford University Press, 1994, 260 - 275. Abstract
Fikar, M. Jorgensen, S. B.: Multivariable constrained adaptive predictive
control based on pole placement design. In: Wawrick, Kárný
(Eds.) Mutual Impact of Computing Power and Control Theory, Plenum Pub.
Corp., London, 1993, 301 - 310.
Fikar, M., Morari, M., Mikleš, J.: On Youla-Kuèera parametrisation
approach to predictive control. ECC99, Karlsruhe, CD-ROM Proceedings, F163, 1999.
Fikar, M., Kucera, V.: On stable finite length control problem. Proceedings
of the 12th Int. Conference Process Control '99, Tatranske Matliare, Slovakia,
31.5-3.6.1999, Vol. 1, 11-15. Abstract,
Fikar, M., Engell, S., Dostál, P.: Design of Infinite Horizon Predictive
LQ Controller. Proceedings ECC'97, Bruxelles, Paper No. 698, 1997. Abstract,
M. Fikar, On Minimum Degree Finite Length Control Error Problem, Technical
Report MF9901, Control Engineering Laboratory, FEE, Ruhr-University
Bochum, 1999. Abstract,
M. Fikar, On Minimum Degree Finite Length Control Problem, Technical
Report KAMF9802, Department of Process Control, FCT STU,
Fikar, M.: Control of Multivariable Systems. Parametrization of all Stabilizing
controllers. PhD thesis, Dep. of Process Control CHTF STU, 1994. Abstract,