Static anti-windup compensator based on BMI optimisation for discrete-time systems with cut-off constraints

• Autorzy: Horla Dariusz

Identyfikatory

DOI

10.24425/bpasts.2021.135837

• Języki publikacji: EN

Abstrakty

EN

In the paper, a design method of a static anti-windup compensator for systems with input saturations is proposed. First, an anti-windup controller is presented for system with cut-off saturations, and, secondly, the design problem of the compensator is presented to be a non-convex optimization problem easily solved using bilinear matrix inequalities formulation. This approach guarantees stability of the closed-loop system against saturation nonlinearities and optimizes the robust control performance while the saturation is active.

Słowa kluczowe

EN

anti-windup compensation; bilinear matrix inequalities; cut-off constraint

PL

kompensacja zjawiska windup; nierówność macierzy dwuliniowa; ograniczenie odcięcia

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2021
• Tom: Vol. 69, nr 1
• Strony: art. no. e135837
• Opis fizyczny: Bibliogr. 31 poz., rys.

Twórcy

autor

Horla Dariusz

• Poznan University of Technology, Faculty of Automatic Control, Robotics and Electrical Engineering, ul. Piotrowo 3a, 60-965 Poznan, Poland

• https://orcid.org/0000-0002-9456-6704

Bibliografia

• [1] E.F. Mulder, M.V. Kothare, L. Zaccarian, and A.R. Teel, “Multivariable Anti-windup Controller Synthesis using Bilinear Matrix Inequalities”, Eur. J. Control 6(5), 455–464 (2000).
• [2] J.G. VanAntwerp and R.D. Braatz, “A Tutorial on Linear and Bilinear Matrix Inequalities”, J. Process Control 10, 363–385 (2000).
• [3] C. Scherer and S. Weiland, “Linear Matrix Inequalities in Control”, DISC Course on Linear Matrix Inequalities in Control, Technische Universiteit Eindhoven, 2005.
• [4] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix Inequalities” in System and Control Theory, 2nd ed., SIAM, Philadelphia, 1994.
• [5] E. de Klerk, Aspects of Semidefinite Programming. Interior Point Algorithms and Selected Applications, Kluwer Academic Publishers, Dordrecht, 2002.
• [6] M. Kocvara and M. Stingl, “PENNON – A Generalized Augmented Lagrangian Method for Semidefinite Programming”, in High Performance Algorithms and Software for Nonlinear Optimization, eds. G. Di Pillo, A. Murli, pp. 297–315, Kluwer Academic Publishers, Dordrecht, 2003.
• [7] M. Kocvara and M. Stingl, “PENNON – A Code for Convex Nonlinear and Semidefinite Programming”, Optim. Method Softw. 18(3), 317–333 (2003).
• [8] D. Henrion, J. Löfberg, M. Kocvara, and M. Stingl, “Solving Polynomial Static Output Feedback Problems with PENBMI”, technical report LAAS-CNRS 05165, 2005.
• [9] Tomlab Optimization, [Online]. http://tomopt.com/tomlab/ (accessed 20.03.2020).
• [10] T.D. Quoc, S. Gumussoy, W. Michiels, and M. Diehl, “Combining Convex-Concave Decompositions and Linearization Approaches for solving BMIs, with Application to Static Output Feedback”, technical report, OPTEC K.U. Lueven Optimization in Engineering Center, 2011.
• [11] J. Löfberg, “YALMIP: A Toolbox for Modeling and Optimization in MATLAB”, in Proceedings of the CACSD Conference, Taipei, 2004.
• [12] CVX Research, Inc., CVX: Matlab Software for Disciplined Convex Programming, version 2.0, 2012 [Online]. http://cvxr.com/cvx
• [13] M. Grant and S. Boyd, “Graph implementations for nonsmooth convex programs”, in Recent Advances in Learning and Control, Lecture Notes in Control and Information Sciences, eds. V. Blondel, S. Boyd and H. Kimura, pp. 95–110, Springer-Verlag Limited, 2008.
• [14] A.A. Adegbege and W.P. Heath, “Internal Model Control Design for Input-constrained Multivariable Processes”, AICHE J. 57, 3459–3472 (2011).
• [15] M. Rehan, A. Ahmed, N. Iqbal, and M.S. Nazir, “Experimental Comparison of Different Anti-windup Schemes for an AC Motor Speed Control System”, in Proceedings of 2009 International Conference on Emerging Technologies, Islamabad, 2009.
• [16] N. Wada, M. Saeki, “Synthesis of a Static Anti-windup Compensator for Systems with Magnitude and Rate Limited Actuators”, in 3rd IFAC Symposium on Robust Control Design, Prague, 2000.
• [17] X. Sun, Z. Shi, Z. Yang, S. Wang, B. Su, L. Chen, and K. Li, “Digital Control System Design for bearingless permanent magnet synchronous motor”, Bull. Pol. Ac.: Tech. 66(5), 687–698 (2018).
• [18] M. Ran, Q. Wang, C. Dong, and M. Ni, “Simultaneous antiwindup synthesis for linear systems subject to actuator saturation”, J. Syst. Eng. Electron. 26(1), 119–126 (2015).
• [19] G. Liu, W. Ma, and A. Xue, ‘ ‘Static Anti-windup Control for Unstable Linear Systems with the Actuator Saturation”, Proceedings of the Chinese Automation Congress, Hangzou, 2019, pp. 2734–2739.
• [20] S. Solyom, “A synthesis method for static anti-windup compensators”, Proceedings of the European Control Conference, Cambridge, 2003, pp. 485–488.
• [21] H. Septanto, A. Syaichu-Rohman, and D. Mahayana, “Static Anti-Windup Compensator Design of Linear Sliding Mode Control for Input Saturated Systems”, Proceedings of the International Conference on Electrical Engineering and Informatics, Bandung, 2011, p. C5-2.
• [22] D. Horla, “Interplay of Directional Change in Controls and Windup Phenomena – Analysis and Synthesis of Compensators”, D. Sc. Monography, no. 471, Poznan University of Technology, Poznan, 2012.
• [23] N. Wada and M. Saeki, “Design of a static anti-windup compensator which guarantees robust stability”, Trans. Inst. Syst. Control Inf. Eng. 12(11), 664—670 (1999).
• [24] P.J. Campo and M. Morari, “Robust Control of Processes Subject to Saturation Nonlinearities”, Comput. Chem. Eng. 14(4-5), 343–358 (1990).
• [25] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control. Analysis and Design, 2nd ed., Wiley-Blackwell, Chichester, 2005.
• [26] F. Wu and M. Soto, “Extended Anti-windup Control Schemes for LTI and LFT Systems with Actuator Saturations”, Int. J. Robust Nonlinear Control 14(15), 1255–1281 (2004).
• [27] F. Amato, “Robust Control of Linear Systems Subject to Uncertain Time-Varying Parameters”, Lecture Notes in Control and Information Sciences, Springer, Berlin–Heidelberg, 2006.
• [28] F. Uhlig, “A recurring theorem about pairs of quadratic forms and extensions: a survey”, Linear Alg. Appl. 25, 219–237 (1979).
• [29] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2006.
• [30] D. Horla and A. Królikowski, “Discrete-time LQG Control with Actuator Failure”, in Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics, Noordwijkerhout, 2011, [CD-ROM].
• [31] J.M. Maciejowski, Multivariable Feedback Design, Addison Wesley Publishing Company, Cambridge, 1989.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).