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Article

Keywords:
PID regulator; MIMO controlled plant
Summary:
A continuous version of optimal LQG design under presence of Wiener disturbances is solved for MIMO controlled plant. Traditional design tools fail to solve this problem due to unstability of the augmented plant. A class of all optimality criteria, which guarantee existence of an asymptotical solution, is defined using a plant deviation model. This class is utilized in design of an optimal state and an error feedback regulator which is presented here. The resultant optimal error regulator is interpreted as an optimal multivariable matrix PID regulator.
References:
[1] Ackermann J.: Sampled–Data Control Systems, Analysis and Synthesis, Robust System Design. Springer–Verlag, Berlin 1985 MR 0699111 | Zbl 0639.93001
[2] Åström K. J., Wittenmark B.: Computer–Controlled Systems, Theory and Design. Prentice–Hall, Englewood Cliffs, N. J. 1984
[3] Bryson A. E., Ho, Yu–Chi: Applied Optimal Control. Gin and Company, Waltham, MA 1969
[4] Dai L., Lin W.: Solutions to the output regulation problem of linear singular systems. Automatica 32 (1996), 1713–1718 DOI 10.1016/S0005-1098(96)80008-2 | MR 1427141 | Zbl 0873.93047
[5] Francis B. A., Wohman W. M.: The internal model principle of control theory. Automatica 12 (1976), 457–465 DOI 10.1016/0005-1098(76)90006-6 | MR 0429257
[6] Kalman R. E.: Canonical structure of linear dynamical systems. SIAM J. Control 1 (1962), 596–600 MR 0138865 | Zbl 0249.34005
[7] Kwanty G. H., Young D. K.: Variable structure servomechanism design and applications to overspeed protection control. Automatica 18 (1982), 385–400 DOI 10.1016/0005-1098(82)90068-1 | MR 0667558
[8] Mošna J., Melichar J., Pešek P.: Optimality versus complexity: Optimal matrix PID regulator. In: Preprints of the 3rd European IEEE Workshop CMP’98, Prague 1998, pp. 139–143
[9] Mošna J., Pešek: Sampled–data control: Optimal matrix PID regulator. In: The Eighteenth IASTED International Conference on Modeling, Identification and Control, Innsbruck 1999, pp. 305–308
[10] Vidyasagar M.: Control System Synthesis, A Factorization Approach. The MIT Press, Cambridge, MA 1987 MR 0787045 | Zbl 0655.93001
[11] Štecha J.: Robustness versus control quality in asymptotic reference tracking. In: Proceedings of the Fifteenth IASTED International Conference Modeling, Identification and Control, Innsbruck 1996, pp. 292–294
[12] Štecha J.: Robust and nonrobust tracking. Kybernetika 34 (1998), 203–216
[13] Young K. D.: Deviation variables in linear multivariable servomechanisms. IEEE Trans. Automat. Control AC-29 (1984), 567–569 DOI 10.1109/TAC.1984.1103585 | Zbl 0532.93034
[14] Žampa P.: On a new system theory and its new paradigms. In: Cybernetics and Systems’96, Austria Society for Cybernetic Studies, Vienna 1996, Volume 1, pp. 3–7
[15] Žampa P., Mošna J., Prautsch P.: New approach to optimal control theory. In: The 2nd IFAC Workshop on New Trends in Design of Control Systems, Smolenice 1997
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