Abstract
This chapter is dedicated to the presentation of a panel of the different anti-windup techniques which can be found in the literature. We try to explain the philosophy pursued by the anti-windup compensation together with a bit of history allowing us to show the development of the various techniques. We focus on the modern anti-windup loop design in opposition to ad hoc solutions. Quick overviews both in regional and global stability frameworks are presented.
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Notes
- 1.
For simplicity, the time dependence in the vector will be omitted.
- 2.
The matrix I p −D pu D c is, however, never explicitly used in what follows.
References
Angeli, D., Mosca, E.: Command governors for constrained nonlinear systems. IEEE Trans. Autom. Control 44(4), 816–820 (1999)
Åström, K.J., Rundqwist, L.: Integrator windup and how to avoid it. In: American Control Conference, Pittsburgh, PA, pp. 1693–1698 (1989)
Barbu, C., Reginatto, R., Teel, A.R., Zaccarian, L.: Anti-windup for exponentially unstable linear systems with inputs limited in magnitude and rate. In: American Control Conference, Chicago, IL, June 2000
Bemporad, A., Teel, A.R., Zaccarian, L.: Anti-windup synthesis via sampled-data piecewise affine optimal control. Automatica 40(4), 549–562 (2004)
Bernstein, D.S., Michel, A.N.: A chronological bibliography on saturating actuators. Int. J. Robust Nonlinear Control 5, 375–380 (1995)
Biannic, J.-M., Tarbouriech, S.: Optimization and implementation of dynamic anti-windup compensators with multiple saturations in flight control systems. Control Eng. Pract. 17, 703–713 (2009)
Biannic, J.-M., Tarbouriech, S., Farret, D.: A practical approach to performance analysis of saturated systems with application to fighter aircraft flight controllers. In: IFAC Symposium on Robust Control Design (ROCOND), Toulouse, France, July 2006
Biannic, J.-M., Roos, C., Tarbouriech, S.: A practical method for fixed-order anti-windup design. In: IFAC Symposium on Nonlinear Control Systems (NOLCOS), Pretoria, South Africa (2007)
Boada, J., Prieur, C., Tarbouriech, S., Pittet, C., Charbonnel, C.: Anti-windup design for satellite control with microthrusters. In: AIAA Guidance, Navigation, and Control Conference, Chicago, IL, USA (2009)
Boada, J., Prieur, C., Tarbouriech, S., Pittet, C., Charbonnel, C.: Multi-saturation anti-windup structure for satellite control. In: American Control Conference, Baltimore, USA, June 2010
Brieger, O., Kerr, M., Leissling, D., Postlethwaite, I., Sofrony, J., Turner, M.C.: Anti-windup compensation of rate saturation in an experimental aircraft. In: American Control Conference, New York (2007)
Burgat, C., Tarbouriech, S.: Intelligent anti-windup for systems with input magnitude saturation. Int. J. Robust Nonlinear Control 8, 1085–1100 (1998)
Campo, P.J., Morari, M., Nett, C.N.: Multivariable anti-windup and bumpless transfer: a general theory. In: American Control Conference, Pittsburgh, pp. 1706–1711 (1989)
Cao, Y.Y., Lin, Z., Ward, D.G.: An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation. IEEE Trans. Autom. Control 47(1), 140–145 (2002)
Crawshaw, S.: Global and local analyses of coprime-factor based anti-windup for stable and unstable plants. In: European Control Conference, Cambridge (2003)
Edwards, C., Postlethwaite, I.: Anti-windup and bumpless-transfer schemes. Automatica 34(2), 199–210 (1998)
Fertik, H.A., Ross, C.W.: Direct digital control algorithm with anti-windup feature. ISA Trans. 6, 317–328 (1967)
Galeani, S., Tarbouriech, S., Turner, M.C., Zaccarian, L.: A tutorial on modern anti-windup design. Eur. J. Control 15(3–4), 418–440 (2009)
Gatley, S.L., Turner, M.C., Postlethwaite, I., Kumar, A.: A comparison of rate-limit compensation schemes for pilot-induced-oscillation avoidance. Aerosp. Sci. Technol. 10(1), 37–47 (2006)
Gilbert, E.G., Kolmanovsky, I.: Fast reference governors for systems with state and control constraints and disturbance inputs. Int. J. Robust Nonlinear Control 9(15), 1117–1141 (1999)
Glattfelder, A.H., Schaufelberger, W.: Control Systems with Input and Output Constraints. Springer, London (2003)
Gomes da Silva Jr., J.M., Tarbouriech, S.: Anti-windup design with guaranteed regions of stability: an LMI-based approach. In: Conference on Decision and Control, Hawaii, USA (2003)
Gomes da Silva Jr., J.M., Tarbouriech, S.: Anti-windup design with guaranteed region of stability: an LMI-based approach. IEEE Trans. Autom. Control 50(1), 106–111 (2005)
Gomes da Silva Jr., J.M., Tarbouriech, S.: Anti-windup design with guaranteed regions of stability for discrete-time linear systems. Syst. Control Lett. 55(3), 184–192 (2006)
Gomes da Silva Jr., J.M., Tarbouriech, S., Reginatto, R.: Analysis of regions of stability for linear systems with saturating inputs through an anti-windup scheme. In: IEEE Conference on Control Applications (CCA), Glasgow, UK (2002)
Grimm, G., Postlethwaite, I., Teel, A.R., Turner, M.C., Zaccarian, L.: Linear matrix inequalities for full and reduced order anti-windup synthesis. In: American Control Conference, Arlington, VA, pp. 4134–4139 (2001)
Grimm, G., Hatfield, J., Postlethwaite, I., Teel, A.R., Turner, M.C., Zaccarian, L.: Anti-windup for stable linear systems with input saturation: an LMI based synthesis. IEEE Trans. Autom. Control 48(9), 1509–1525 (2003)
Grimm, G., Teel, A.R., Zaccarian, L.: The \(\mathcal{L}_{2}\) anti-windup problem for discrete-time linear systems: definition and solutions. In: American Control Conference, Denver, CO, pp. 5329–5334 (2003)
Grimm, G., Teel, A.R., Zaccarian, L.: Robust linear anti-windup synthesis for recovery of unconstrained performance. Int. J. Robust Nonlinear Control 14(13–14), 1133–1168 (2004)
Hanus, R., Kinnaert, M.: Control of constrained multivariable systems using conditioning technique. In: American Control Conference, Pittsburgh, pp. 1712–1718 (1989)
Hanus, R., Kinnaert, M., Henrotte, J.L.: Conditioning technique, a general anti-windup and bumpless transfer method. Automatica 23, 729–739 (1987)
Herrmann, G., Turner, M.C., Postlethwaite, I.: Practical implementation of a novel anti-windup scheme in a HDD-dual-stage servo-system. IEEE/ASME Trans. Mechatron. 9(3), 580–592 (2004)
Herrmann, G., Turner, M.C., Postlethwaite, I.: Some new results on anti-windup conditioning using the Weston–Postlethwaite approach. In: Conference on Decision and Control (2004)
Herrmann, G., Turner, M.C., Postlethwaite, I.: Discrete-time and sampled-data anti-windup synthesis: stability and performance. Int. J. Syst. Sci. 37(2), 91–113 (2006)
Hippe, P.: Windup in Control. Its Effects and Their Prevention. AIC/Springer, Berlin (2006)
Horrowitz, I.: A synthesis theory for a class of saturating systems. Int. J. Control 38(1), 169–187 (1983)
Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design. Birkhäuser, Boston (2001)
Hu, T., Teel, A.R., Zaccarian, L.: Regional anti-windup compensation for linear systems with input saturation. In: American Control Conference, Portland, OR, pp. 3397–3402 (2005)
Hu, T., Teel, A.R., Zaccarian, L.: Anti-windup synthesis for linear control systems with input saturation: achieving regional, nonlinear performance. Automatica 64(2), 512–519 (2008)
Kapila, V., Grigoriadis, K. (eds.): Actuator Saturation Control. Dekker, New York (2002)
Kapoor, N., Teel, A.R., Daoutidis, P.: An anti-windup design for linear systems with input saturation. Automatica 34(5), 559–574 (1998)
Kerr, M., Villota, E., Jayasuriya, S.: Robust anti-windup design for input constrained SISO systems. In: 8th International Symposium on QFT and Robust Frequency Domain Methods (2007)
Khalil, H.K.: Nonlinear Systems. MacMillan, London (1992)
Kothare, M.V., Morari, M.: Stability analysis of anti-windup control scheme: a review and some generalizations. In: European Control Conference, Brussels, Belgium (1997)
Kothare, M.V., Morari, M.: Multiplier theory for stability analisys of anti-windup control systems. Automatica 35, 917–928 (1999)
Kothare, M.V., Campo, P.J., Morari, M., Nett, C.N.: A unified framework for the study of anti-windup designs. Automatica 30(12), 1869–1883 (1994)
Krikelis, N.J.: State feedback integral control with inteligent integrator. Int. J. Control 32, 465–473 (1980)
Lin, Z., Mantri, R., Saberi, A.: Semi-global output regulation for linear systems subject to input saturation—a low and high gain design. Control Theory Adv. Technol. 10(4), 2209–2232 (1995)
Lozier, J.C.: A steady-state approach to the theory of saturable servo systems. IRE Trans. Autom. Control, 19–39 (1956)
Lu, B., Wu, F., Kim, S.: Linear parameter varying anti-windup compensation for enhanced flight control performance. AIAA J. Guid. Control Dyn. 28(3), 494–504 (2005)
Lurie, B.J.: The absolutely stable Nyquist stable nonlinear feedback system design. Int. J. Control 40(6), 1119–1130 (1984)
Marcopoli, V.R., Phillips, S.M.: Analysis and synthesis tools for a class of actuator-limited multivariable control systems: a linear matrix inequality approach. Int. J. Robust Nonlinear Control 6(9–10), 1045–1063 (1996)
Miyamoto, S., Vinnicombe, G.: Robust control of plants with saturation nonlinearity based on coprime factor representation. In: Conference on Decision and Control, Kobe, Japan, pp. 2838–2840 (1996)
Mulder, E.F., Kothare, M.V.: Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions. In: American Control Conference, pp. 3239–3243 (2000)
Mulder, E.F., Kothare, M.V., Morari, M.: Multivariable anti-windup controller synthesis using linear matrix inequalities. Automatica 37(9), 1407–1416 (2001)
Park, J.-K., Lim, H., Basar, T., Choi, C.-H.: Anti-windup compensator for active queue management in TCP networks. Control Eng. Pract. 11(10), 1127–1142 (2003)
Queinnec, I., Tarbouriech, S., Garcia, G.: Anti-windup design for aircraft control. In: IEEE Conference on Control Applications (CCA), Munich, Germany (2006)
Romanchuk, B.G.: Some comments on anti-windup synthesis using LMI’s. Int. J. Robust Nonlinear Control 9(10), 717–734 (1999)
Roos, C.: Contribution à la commande des systèmes saturés en présence d’incertitudes et de variations paramétriques. Application au pilotage de l’avion au sol. PhD thesis, University of Toulouse, ISAE, France, December 2007
Roos, C., Biannic, J.-M., Tarbouriech, S., Prieur, C.: On-Ground Aircraft Control Design Using an LPV Anti-windup Approach. LNCIS, vol. 365. Springer, Berlin (2007). Chap. 7
Saberi, A., Lin, Z., Teel, A.: Control of linear systems with saturating actuators. IEEE Trans. Autom. Control 41(3), 368–377 (1996)
Saeki, M., Wada, N.: Synthesis of a static anti-windup compensator via linear matrix inequalities. Int. J. Robust Nonlinear Control 12, 927–953 (2002)
Schuster, E., Walker, M.L., Humphreys, D.A., Krstic, M.: Plasma vertical stabilization with actuation constraints in the DIII-D tokamak. Automatica 41(7), 1173–1179 (2005)
Shamma, J.S.: Anti-windup via constrained regulation with observers. Syst. Control Lett. 40(4), 261–268 (2000)
Stoorvogel, A.A., Saberi, A. (eds.): Special issue: control problems with constraints. Int. J. Robust Nonlinear Control 9(10) (1999)
Suárez, R., Alvarez-Ramirez, J., Solis-Daun, J.: Linear systems with bounded inputs: global stabilization with eigenvalue placement. Int. J. Robust Nonlinear Control 7(9), 835–845 (1997)
Tarbouriech, S., Turner, M.C.: Anti-windup design: an overview of some recent advances and open problems. IET Control Theory Appl. 3(1), 1–19 (2009)
Tarbouriech, S., Prieur, C., Gomes da Silva Jr., J.M.: An anti-windup strategy for a flexible cantilever beam. In: IFAC World Congress, Prague, CZ (2005)
Tarbouriech, S., Gomes da Silva Jr., J.M., Bender, F.A.: Dynamic anti-windup synthesis for discrete-time linear systems subject to input saturation and \(\mathcal{L}_{2}\) disturbances. In: IFAC Symposium on Robust Control Design (ROCOND), Toulouse, France (2006)
Tarbouriech, S., Prieur, C., Gomes da Silva Jr., J.M.: Stability analysis and stabilization of systems presenting nested saturations. IEEE Trans. Autom. Control 51(8), 1364–1371 (2006)
Tarbouriech, S., Queinnec, I., Garcia, G.: Stability region enlargement through anti-windup strategy for linear systems with dynamics restricted actuator. Int. J. Syst. Sci. 37(2), 79–90 (2006)
Tarbouriech, S., Garcia, G., Glattfelder, A.H. (eds.): Advanced Strategies in Control Systems with Input and Output Constraints. LNCIS, vol. 346. Springer, Berlin (2007)
Teel, A.R.: Anti-windup for exponentially unstable linear systems. Int. J. Robust Nonlinear Control 9, 701–716 (1999)
Teel, A.R., Buffington, J.B.: Anti-windup for an F-16’s daisy chain control allocator. In: AIAA GNC Conference, New Orleans, LA, USA, pp. 748–754 (1997)
Teel, A.R., Kapoor, N.: The \(\mathcal{L}_{2}\) anti-windup problem: Its definition and solution. In: European Control Conference, Brussels, Belgium, July 1997
Teel, A.R., Kapoor, N.: Uniting local and global controllers. In: European Control Conference, Brussels, Belgium, July 1997
Teel, A.R., Zaccarian, L., Marcinkowski, J.J.: An anti-windup strategy for active vibration isolation systems. Control Eng. Pract. 14(1), 17–27 (2006)
Turner, M.C., Postlethwaite, I.: A new perspective on static and low order anti-windup synthesis. Int. J. Control 77(1), 27–44 (2004)
Turner, M.C., Tarbouriech, S.: Anti-windup for linear systems with sensor saturation: sufficient conditions for global stability and \(\mathcal{L}_{2}\) gain. In: Conference on Decision and Control, San Diego, USA (2006)
Turner, M.C., Zaccarian, L. (eds.): Special issue: anti-windup. Int. J. Syst. Sci. 37(2), 65–139 (2006)
Turner, M.C., Herrmann, G., Postlethwaite, I.: Accounting for uncertainty in anti-windup synthesis. In: American Control Conference, Bostron, MA, pp. 5292–5297 (2004)
Turner, M.C., Herrmann, G., Postlethwaite, I.: Incorporating robustness requirements into anti-windup design. IEEE Trans. Autom. Control 52(10), 1842–1855 (2007)
Tyan, F., Bernstein, D.S.: Anti-windup compensator synthesis for systems with saturating actuators. Int. J. Robust Nonlinear Control 5(5), 521–537 (1995)
Villota, E., Kerr, M., Jayasuriya, S.: A study of configurations for anti-windup control of uncertain systems. In: Conference on Decision and Control, San Diego, California (2006)
Walgama, K.S., Ronnback, S., Sternby, J.: Generalization of conditioning technique for anti-windup compensators. IEE Proc. D 139(2), 109–118 (1992)
Walsh, M.J., Hayes, M.J.: A robust throughput rate control mechanism for an 802.15.4 wireless sensor network—an anti-windup approach. In: American Control Conference, New York (2007)
Weston, P.F., Postlethwaite, I.: Analysis and design of linear conditioning schemes for systems containing saturating actuators. In: IFAC Nonlinear Control System Design Symposium (1998)
Weston, P.F., Postlethwaite, I.: Linear conditioning for systems containing saturating actuators. Automatica 36(9), 1347–1354 (2000)
Wu, W., Jayasuriya, S.: A new QFT design methodology for feedback systems under input saturation. ASME J. Dyn. Syst. Meas. Control 123(2), 225–232 (2001)
Wu, F., Lu, B.: Anti-windup control design for exponentially unstable LTI systems with actuator saturation. Syst. Control Lett. 52, 305–322 (2004)
Wu, F., Soto, M.: Extended anti-windup control schemes for LTI and LFT systems with actuator saturations. Int. J. Robust Nonlinear Control 14, 1255–1281 (2004)
Wurmthaler, C., Hippe, P.: Closed-loop design for stable and unstable plants with input saturation. In: European Control Conference, Gröningen, The Netherlands, pp. 1084–1088 (1993)
Zaccarian, L., Teel, A.R.: A common framework for anti-windup, bumpless transfer and reliable designs. Automatica 38(10), 1735–1744 (2002)
Zaccarian, L., Teel, A.R.: Nonlinear scheduled anti-windup design for linear system. IEEE Trans. Autom. Control 49(11), 2055–2061 (2004)
Zaccarian, L., Teel, A.R.: Modern Anti-windup Synthesis. Princeton University Press, Princeton (2011)
Zaccarian, L., Li, Y., Weyer, E., Cantoni, M., Teel, A.R.: Anti-windup for marginally stable plants and its application to open water channel control systems. Control Eng. Pract. 15(2), 261–272 (2007)
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Tarbouriech, S., Garcia, G., Gomes da Silva, J.M., Queinnec, I. (2011). An Overview of Anti-windup Techniques. In: Stability and Stabilization of Linear Systems with Saturating Actuators. Springer, London. https://doi.org/10.1007/978-0-85729-941-3_6
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