Abstract
Windup effects can be subdivided into controller windup and plant windup. Controller windup can be prevented by stabilizing the compensator during saturation and plant windup by an additional dynamic element. When using a compensating design, i. e., the zeros and poles of the plant are compensated by the poles and zeros of the controller, plant windup does not occur. The compensating control is parametrized by one parameter allowing nearly arbitrary disturbance attenuation. This type of control is restricted to minimum-phase systems. But it has a number of advantages. It simplifies the SISO and especially the MIMO design of compensators with integral action considerably, it has good robustness properties and it allows a diagonal decoupling of the reference behavior for arbitrary MIMO system. Two examples demonstrate the results achievable.
Zusammenfassung
Windup Effekte kann man aufteilen in Regler-Windup und Strecken-Windup. Der Regler-Windup lässt sich durch eine Stabilisierung des Reglers während der Stellbegrenzung und ein eventuell vorhandener Strecken-Windup durch ein dynamisches Zusatz-Netzwerk vermeiden. Bei Verwendung eines kompensierenden Reglerentwurfs, d. h., die Nullstellen und Pole der Strecke werden durch Pole und Nullstellen des Reglers kompensiert, ist der Strecken-Windup automatisch vermieden. Die kompensierende Regelung wird durch einen einzigen Faktor parametriert, und mit ihm lässt sich die Störunterdrückung beliebig verbessern. Diese Art von Regelung ist natürlich auf minimalphasige Strecken beschränkt. Auf der anderen Seite besitzt dieser Ansatz eine Reihe von Vorteilen. Er vereinfacht den Entwurf von Eingrössen- und speziell von Mehrgrössen-Regelungen mit I-Anteil erheblich, er hat gute Robustheits-Eigenschaften und er erlaubt die diagonale Entkopplung des Führungsverhaltens für beliebige Mehrgrössen-Systeme. Zwei Beispiele demonstrieren die erzielbaren Ergebnisse.
About the author
Dr.-Ing. Peter Hippe worked as Akademischer Direktor at Lehrstuhl für Regelungstechnik of the Universität Erlangen-Nürnberg till September 2006. Main fields of interest: Control systems with plant input restrictions, design of state controllers and of MIMO compensators in the frequency domain.
References
1. D. S. Bernstein and A. N. Michel. A chronological bibliography on saturating actuators. International Journal Robust Nonlinear Control 5, 375–380, 1995.10.1002/rnc.4590050502Search in Google Scholar
2. E. J. Davison. The robust control of a servomechanism problem for linear time-invariant multivariable systems. IEEE Transactions on Automatic Control 21, 25–34, 1976.10.1109/TAC.1976.1101137Search in Google Scholar
3. J. C. Doyle, R. S. Smith and D. F. Enns. Control of plants with input saturation nonlinearities. In: Proceedings of the 1987 American Control Conference, pp. 1034–1039. Minneapolis, MN, 1987.Search in Google Scholar
4. P. L. Falb and W. A. Wolovich. Decoupling in the design and synthesis of multi-variable control systems. IEEE Transactions on Automatic Control 12, 651–659, 1967.10.1109/TAC.1967.1098737Search in Google Scholar
5. S. Galeani, S. Tarbouriech, M. C. Turner and L. Zaccarian. A tutorial on modern anti-windup design. European Journal of Control 15, 418–440, 2009.10.23919/ECC.2009.7074421Search in Google Scholar
6. C. Gökçek, P. T. Kabamba and S. M. Meerkov. An LQR/LQG theory for systems with saturating actuators. IEEE Transactions on Automatic Control 46, 1529–1542, 2001.10.1109/9.956049Search in Google Scholar
7. R. Hanus, M. Kinnaert and J. L. Henrotte. Conditioning technique, a general antiwindup and bumpless transfer method. Automatica 23, 729–739, 1987.10.1016/0005-1098(87)90029-XSearch in Google Scholar
8. P. Hippe. Design of MIMO compensators for systems with unmeasurable disturbances: the polynomial approach. Automatica 28, 1003–1009, 1992.10.1016/0005-1098(92)90154-8Search in Google Scholar
9. P. Hippe. Windup in Control – Its Effects and Their Prevention. Springer, Berlin Heidelberg New York London, 2006.Search in Google Scholar
10. P. Hippe. Prevention of windup caused by saturating sensors. Automatisierungstechnik 63, 968–976, 2015.10.1515/auto-2015-0056Search in Google Scholar
11. P. Hippe. Windup in Control Owing to Sensor saturation. Springer, Berlin Heidelberg New York London, 2021.10.1007/978-3-030-73133-5Search in Google Scholar
12. P. Hippe and J. Deutscher. Design of Observer-based Compensators – From the Time to the Frequency Domain. Springer, Berlin Heidelberg New York London, 2009.10.1007/978-1-84882-537-6Search in Google Scholar
13. P. Hippe and Ch. Wurmthaler. Systematic closed-loop design in the presence of input saturations. Automatica 35, 689–695, 1999.10.1016/S0005-1098(98)00199-XSearch in Google Scholar
14. S. Rönnbäck, K.S. Walgama and J. Sternby. An extension to the generalized anti-windup compensator. Proceedings of the 13th IMACS World Congress on Scientific Computation, Dublin, Ireland, 1991.Search in Google Scholar
15. A. Saberi, Z. Lin and A. R. Teel. Control of linear systems with saturating actuators. IEEE Transactions on Automatic Control 41, 368–378, 1996.10.1109/ACC.1995.529254Search in Google Scholar
16. S. Tarbouriech, G. Garcia and A. H. Glattfelder. Advanced strategies in control systems with input and output constraints, Vol. 336 of Lecture Notes in Control and Information Sciences. Springer, Berlin Heidelberg New York London, 2007.10.1007/978-3-540-37010-9Search in Google Scholar
17. M. C. Turner, G. Herrmann and I. Postlethwaite. Anti-windup compensation and the control of input-constrained systems, Vol. 267 of Mathematical Methods for Robust and Nonlinear Control, Springer, Berlin Heidelberg New York London, 143–173.10.1007/978-1-84800-025-4_5Search in Google Scholar
18. S. Tarbouriech, G. Garcia, J. M. Gomes da Silva Jr. and I. Queinnec. Piecewise Linear Control Systems: A Computational Approach. Springer, Berlin Heidelberg New York London, 2011.Search in Google Scholar
19. J. R. Teel and N. Kapoor. The L2 anti-windup problem: its definition and solution. Proceedings of the Fourth European Control Conference, Brussels, Belgium, 1997.10.23919/ECC.1997.7082381Search in Google Scholar
20. M. C. Turner and L. Zaccarian. Special Issue on Anti-windup, International Journal of Systems Science 37, 2006.10.1080/00207720612331392435Search in Google Scholar
21. L. Zaccarian and A. R. Teel. Modern Anti-Windup Synthesis: Control Augmentation for Actuator Saturation. Princeton University Press, Princeton and Oxford, 2011.10.23943/princeton/9780691147321.001.0001Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
