LQR and predictive control tuned via BDU

• Autorzy: Ramos C. , Sanchis J. , Martinez M. , Herrero J. M.
• Języki publikacji: EN

Abstrakty

EN

This work presents the BDU technique (Bounded Data Uncertainties) and the tuning of the linear quadratic regulator (LQR) via this technique, which considers models with bounded uncertainties. The BDU method is based on constrained game-type formulations, and allows the designer to explicitly incorporate a priori information about bounds on the sizes of the uncertainties into the problem statement. Thus, on the one hand, the uncertainty effect is not over-emphasized, avoiding an overly conservative design and, on the other hand, the uncertainty effect is not under-emphasized, avoiding an overly sensitive to errors design. A feature of this technique consists of its geometric interpretation. The structure of the paper is the following, in the first section, some problems about the least-squares method in the presence of uncertainty are introduced. The BDU technique is shown in the second section and the LQR controller in the third. After that a new guided way of tuning the LQR is offered, taking into account the uncertainties bounds via the BDU. The consequence of this method is that both recursive and algebraic Riccati equations are modified. Finally, some examples are shown and the main conclusions and future work are commented.

Słowa kluczowe

EN

LQR controller; Riccati equation; control system synthesis; predictive control; least squares method

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2005
• Tom: Vol. 31, no 1
• Strony: 15--25
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Ramos C.

• Department of Systems Engineering and Control, Polytechnic University of Valencia, Camino de Vera 14, P.O. Box 22012 E-46071 Valencia, Spain

autor

Sanchis J.

autor

Martinez M.

autor

Herrero J. M.

Bibliografia

• [1] Chandrasekaran S., GOLUB M., Gu M., Sayed A. H., Worst-case parameter estimation with bounded model uncertainties, American Control Conference, 1997.
• [2] Chandrasekaran S., GOLUB M., Gu M., Sayed A. H., Parameter estimation in the presence of bounded data uncertainties, SIMAX, No. 19, 1998, 235-252.
• [3] Golub G. H., Van Loan Cii. F., Matrix Computations, Johns Hopkins University Press, 1996.
• [4] Lawson C. L., Hanson R. J., Solving least-squares problems, SIAM, 1995.
• [5] Nascimento V. H., Sayed A. H., Optimal slate regulation for uncertain state-space models, American Control Conference, Vol. 1, San Diego 1999, 419-424.
• [6] Ramos C., Sanchis J., Martínez M., Herrero J. M., Sintonizado del LQR y Control Predictivo mediante BDU, XI Congreso Latinoamericano de Control, Preprints ISBN 959-237-117-2, 2004.
• [7] Sayed A. H., Nascimento V. H., Design criteria for imcertain models with structured and unstructured uncertainties. Robustness in Identification and Control, Vol. 245, Springer Veriag, tendon 1999, 159-173.
• [8] Sayed A. H., Nascimento V. H., Chandrasekaran S., Estimation and control with bounded data uncertainties. Linear Algebra and its Applications, Vol. 284, Elsevier, 1998, 259-306.
• [9] Skogestad S., Postlethwaite L, Multivariable feedback control. Analysis and Design, John Wiley and Sons, 1996.
• [10] Tikiionov A. N., Regularization of incorrectly posed problems, Soviet Math, Vol. 4, 1963, 1624-1627.