Chapter Eleven

 

 

Annotated Bibliography

11.1 OVERVIEW

The history of anti-windup research ranges from the early approaches dating back to the 1950s (where fixes to malfunctioning analog controllers typically corresponded to ad hoc solutions proposed and implemented by industrialists) to the numerous recently reported results (where systematic solutions to suitable formalizations of the problem provide constructive tools with guaranteed performance and stability properties).

In the past fifty years, anti-windup research migrated from the initial ad hoc attempts to more general and systematic constructions and further, to formal definitions of the underlying problem and modern high-performance solutions. Many instances of the anti-windup problem are still unsolved and are the subject of ongoing research activity. Although it is not the aim of this book to provide a survey of the existing literature on anti-windup, the rest of this chapter underlines the main phases characterizing this research strand and lists a number of relevant publications for each one.

11.2 PROBLEM DISCOVERY

The anti-windup problem has been known since the very early developments of automatic control. Already in the 1940s, when industries started implementing analog controllers, actuator saturation constituted one of the main pitfalls in control design. The emerging methodology was mainly due to engineering experience within the industrial environment that remained undocumented, at least until the 1950s. However, it should be noted that the control problem for systems with input saturation nonlinearities partially motivated the large research activity in absolute stability theory, which has been an important research topic since the 1940s. The following list of papers corresponds to the first research publications that appeared in this field, mainly reflecting adhoc schemes and dating from the 1950s to the late 1970s.

[PD1] J.C. Lozier. A steady-state approach to the theory of saturable servo systems. IRE Transactions on Automatic Control, 1:19–39, May 1956.

[PD2] H.A. Fertik and C.W. Ross. Direct digital control algorithm with anti-windup feature. ISA Transactions, 6(4):317–328, 1967.

[PD3] L.C. Kramer and K.W. Jenkins. A new technique for preventing direct digital control windup. In Proceedings of the Joint Automatic Control Conference, pages 571–577, St. Louis (MO), USA, August 1971.

[PD4] R.K. Cox and J.P. Shunta. Tracking action improves continuous control. Chemical Engineering Progress, 69(9):56–61, 1973.

[PD5] P. Vandenbussche. Digital transposition and extension of classical analogical control algorithms. In Proceedings of the 6th IFAC World Congress, pages 5.6/1–4, Boston and Cambridge (MA), USA, August 1975.

[PD6] J. Khanderia and W.L. Luyben. Experimental evaluation of digital algorithms for antireset windup. Industrial Engineering Chemistry, Process Design and Development, 15(2):278–285, 1976.

[PD7] N.J. Krikelis. State feedback integral control with “intelligent” integrators. International Journal of Control, 32(3):465–473, 1980.

[PD8] R.M. Phelan. Automatic Control Systems. Ithaca (NY), USA, Cornell University Press, 1977.

11.3 THE FIRST CONSTRUCTIVE TECHNIQUES

From the late 1970s until the late 1980s, a new phase of anti-windup research occurred. Based on the increasing demand for constructive and general anti-windup techniques, several important schemes appeared in the literature. Even though most of these new schemes still were not formally addressing stability and performance, at least they provided techniques that were applicable to a broader class of control systems, with a high probability of achieving successful anti-windup.

[FC1] J. Debelle. A control structure based upon process models. Journal A, 20(2):71–81, 1979.

[FC2] R. Hanus. A new technique for preventing control windup. Journal A, 21(1):15–20, 1980.

[FC3] A.H. Glattfelder and W. Schaufelberger. Stability analysis of single loop control systems with saturation and antireset-windup circuits. IEEE Transactions on Automatic Control, AC–28(12):1074–1081, 1983.

[FC4] I. Horowitz. A synthesis theory for a class of saturating systems. International Journal of Control, 38(1):169–187, 1983.

[FC5] P. Kapasouris and M. Athans. Multivariable control systems with saturating actuators antireset windup strategies. In Proceedings of the American Control Conference, pages 1579–1584, Boston (MA), USA, June 1985.

[FC6] R. Hanus, M. Kinnaert, and J.L. Henrotte. Conditioning technique, a general anti-windup and bumpless transfer method. Automatica, 23(6):729–739, 1987.

[FC7] A. Zheng, M. V. Kothare, and M. Morari. Anti-windup design for internal model control. International Journal of Control, 60(5):1015–1024, 1994.

[FC8] K.J. Åström and B. Wittenmark. Computer Controlled Systems: Theory and Design. Englewood Cliffs (NJ), USA, Prentice-Hall, 1984.

11.4 CALL FOR SYSTEMATIZATION

A landmark paper signaling the final step in the early anti-windup schemes was presented by Doyle et al. at the 1987 American Control Conference. In this paper, the authors pointed to the need for more rigorous and general solutions to the anti-windup problem by means of simple examples where the inadequacy of some of the early schemes was demonstrated. The reaction exploded in the following years, starting in 1988, with the well-known survey paper by Hanus, where most of the existing techniques were reported and commented on. One year later, a large number of papers on anti-windup were presented at the 1989 American Control Conference. The following papers characterize this period of passage:

[CS1] J.C. Doyle, R.S. Smith, and D.F. Enns. Control of plants with input saturation nonlinearities. In Proceedings of the American Control Conference, pages 1034–39, Minneapolis (MN), USA, June 1987.

[CS2] K.J. Åström and L. Rundqwist. Integrator windup and how to avoid it. In Proceedings of the American Control Conference, volume 2, pages 1693–1698, Pittsburgh (PA), USA, June 1989.

[CS3] R.S. Baheti. Simple anti-windup controllers. In Proceedings of the American Control Conference, volume 2, pages 1684–1686, Pittsburgh (PA), USA, June 1989.

[CS4] P.J. Campo, M. Morari, and C.N. Nett. Multivariable anti-windup and bumpless transfer: A general theory. In Proceedings of the American Control Conference, volume 2, pages 1706–1711, Pittsburg (PA), USA, June 1989.

[CS5] R. Hanus and M. Kinnaert. Control of constrained multivariable systems using the conditioning technique. In Proceedings of the American Control Conference, volume 2, pages 1712–1718, Pittsburgh (PA), USA, June 1989.

[CS6] M.F. Weilenmann, H.P. Geering, L. Guzzella, and A.H. Glattfelder. A comparison of several controllers for plants with saturating power amplifiers. In Proceedings of the American Control Conference, volume 2, pages 1719–1724, Pittsburgh (PA), USA, June 1989.

[CS7] P.J. Campo and M. Morari. Robust control of processes subject to saturation nonlinearities. Computers and Chemical Engineering, 14(4/5):343–358, 1990.

[CS8] K.S. Walgama, S. Rönnbäck, and J. Sternby. Generalisation of conditioning technique for anti-windup compensators. IEE Proceedings on Control Theory and Applications, 139(2):109–118, March 1992.

The following papers represent interesting surveys of the anti-windup techniques dating from the 1970s to the early 1990s.

[SUR1] R. Hanus. Antiwindup and bumpless transfer: A survey. In Proceedings of the 12th IMACS World Congress, volume 2, pages 59–65, Paris, France, July 1988.

[SUR2] K.S. Walgama and J. Sternby. Inherent observer property in a class of anti-windup compensators. International Journal of Control, 52(3):705–724, 1990.

[SUR3] M. Morari. Some control problems in the process industries. In H.L. Trentelman and J.C. Willems, editors, Essays on Control: Perspectives in the Theory and Its Applications, pages 55–77. Boston (MA), USA, Birkhauser, 1993.

[SUR4] M.V. Kothare, P.J. Campo, M. Morari, and N. Nett. A unified framework for the study of anti-windup designs. Automatica, 30(12):1869–1883, 1994.

[SUR5] C. Bohn and D.P. Atherton. An analysis package comparing PID anti-windup strategies. IEEE Control Systems Magazine, 15(2):34–40, April 1995.

[SUR6] Y. Peng, D. Vrancic, and R. Hanus. Anti-windup, bumpless, and conditioning transfer techniques for PID controllers. IEEE Control Systems Magazine, 16(4):48–57, 1996.

[SUR7] C. Edwards and I. Postlethwaite. Anti-windup and bumpless-transfer schemes. Automatica, 34(2):199–210, 1998.

[SUR8] A.R. Teel. A nonlinear control viewpoint on anti-windup and related problems. In Proceedings of the 4th Nonlinear Control Systems Design Symposium (NOLCOS), pages 115–120, Enschede, The Netherlands, July 1998.

11.5 MODERN ANTI-WINDUP SCHEMES

In the last decade, improvements in technology and the advent of increasingly sophisticated control systems pointed to the need for more accurate and rigorous solutions to windup problems. In addition, the qualitative goals of anti-windup design (already formulated in the 1950s by industrialists) were interpreted and formalized within precise mathematical frameworks, so that constructive designs with guaranteed stability and performance properties could be sought. A comprehensive description and discussion of the many recently proposed modern anti-windup solutions can be found in the following two recent survey papers:

[SM1] S. Tarbouriech and M.C. Turner. Anti-windup design: An overview of some recent advances and open problems. IET Control Theory and Application, 3(1):1–19, 2009.

[SM2] S. Galeani, S. Tarbouriech, M.C. Turner, and L. Zaccarian. A tutorial on modern anti-windup design. European Journal of Control, 15(3–4):418–440, 2009.

In the remainder of this section, a classification is given of modern anti-windup schemes where the different contributions are grouped based on the underlying compensation architecture.

Reference and measurement governors

[RG1] E.G. Gilbert and K.T. Tan. Linear systems with state and control constraints: The theory and application of maximal output admissible sets. IEEE Transactions on Automatic Control, 36(9):1008–1020, September 1991.

[RG2] T.J. Graettinger and B.H. Krogh. On the computation of reference signal constraints for guaranteed tracking performance. Automatica, 28(6):1125–1141, 1992.

[RG3] E.G. Gilbert, I. Kolmanovsky, and K.T. Tan. Discrete-time reference governors and the nonlinear control of systems with state and control constraints. International Journal of Robust and Nonlinear Control, 5(5):487–504, 1995.

[RG4] A. Bemporad, A. Casavola, and E. Mosca. Nonlinear control of constrained linear systems via predictive reference management. IEEE Transactions on Automatic Control, 42(3):340–349, March 1997.

[RG5] A. Bemporad. Reference governor for constrained nonlinear systems. IEEE Transactions on Automatic Control, 43(3):415–419, March 1998.

[RG6] J. McNamee and M. Pachter. The construction of the set of stable states for contrained systems with open-loop unstable plants. In Proceedings of the American Control Conference, pages 3364–3368, Philadelphia (PA), USA, June 1998.

[RG7] D. Angeli and E. Mosca. Command governors for constrained nonlinear systems. IEEE Transactions on Automatic Control, 44(4):816–820, April 1999.

[RG8] E.G. Gilbert and I. Kolmanovsky. Fast reference governors for systems with state and control constraints and disturbance inputs. International Journal of Robust and Nonlinear Control, 9(15):1117–1141, 1999.

[RG9] J. McNamee and M. Pachter. Efficient nonlinear reference governor algorithms for constrained tracking control systems. In Proceedings of the American Control Conference, pages 3549–3553, San Diego (CA), USA, June 1999.

[RG10] J.S. Shamma. Anti-windup via constrained regulation with observers. Systems and Control Letters, 40:1869–1883, 2000.

H_∞ based anti-windup designs

[H1] S. Miyamoto and G. Vinnicombe. Robust control of plants with saturation nonlinearity based on coprime factor representation. In Proceedings of the 35th Conference on Decision and Control, pages 2838–2840, Kobe, Japan, December 1996.

[H2] P. Weston and I. Postlethwaite. Linear conditioning schemes for systems containing saturating actuators. In Proceedings of the 4th Nonlinear Control Systems Design Symposium (NOLCOS), pages 702–707, Enschede, The Netherlands, July 1998.

[H3] C. Edwards and I. Postlethwaite. An anti-windup scheme with closed-loop stability considerations. Automatica, 35(4):761–765, 1999.

[H4] S. Crawshaw and G. Vinnicombe. Anti-windup synthesis for guaranteed L₂ performance. In Proceedings of the Conference on Decision and Control, pages 1063–1068, Sidney, Australia, December 2000.

[H5] P.F. Weston and I. Postlethwaite. Linear conditioning for systems containing saturating actuators. Automatica, 36(9):1347–1354, 2000.

[H6] S. Crawshaw and G. Vinnicombe. Anti-windup for local stability of unstable plants. In Proceedings of the American Control Conference, pages 645–650, Anchorage (AK), USA, May 2002.

[H7] S. Crawshaw and G. Vinnicombe. Anti-windup synthesis for guaranteed L₂ performance. In Proceedings of the American Control Conference, pages 657–661, Anchorage (AK), USA, May 2002.

[H8] S. Crawshaw. Global and local analysis of coprime factor-based anti-windup for stable and unstable plants. In Proceedings of the European Control Conference, Cambridge, UK, September 2003.

[H9] G. Herrmann, M.C. Turner, and I. Postlethwaite. Some new results on anti-windup-conditioning using the Weston-Postlethwaite approach. In Proceedings of the 43rd Conference on Decision and Control, pages 5047–5052, Atlantis (BA), USA, December 2004.

[H10] M.C. Turner, G. Herrmann, and I. Postlethwaite. Further results on full-order anti-windup synthesis: Exploiting the stability multiplier. In Proceedings of the IFAC Non Linear Control Systems Symposium, pages 1385–1390, Stuttgart, Germany, September 2004.

[H11] M.C. Turner, G. Herrmann, and I. Postlethwaite. Incorporating robustness requirements into antiwindup design. IEEE Transactions on Automatic Control, 52(10):1842–1855, 2007.

Model recovery anti-windup designs

[MR1] J.K. Park and C.H. Choi. Dynamic compensation method for multivariable control systems with saturating actuators. IEEE Transactions on Automatic Control, 40(9):1635–1640, 1995.

[MR2] J.K. Park and C.H. Choi. Dynamical anti-reset windup method for discrete-time saturating systems. Automatica, 33(6):1055–1072, 1997.

[MR3] A.R. Teel and N. Kapoor. The L₂ anti-windup problem: Its definition and solution. In Proceedings of the European Control Conference, Brussels, Belgium, July 1997.

[MR4] A.R. Teel and N. Kapoor. Uniting local and global controllers. In Proceedings of the European Control Conference, Brussels, Belgium, July 1997.

[MR5] A.R. Teel. Anti-windup for exponentially unstable linear systems. International Journal of Robust and Nonlinear Control, 9:701–716, 1999.

[MR6] C. Barbu, R. Reginatto, A.R. Teel, and L. Zaccarian. Anti-windup for exponentially unstable linear systems with inputs limited in magnitude and rate. In Proceedings of the American Control Conference, pages 1230–1234, Chicago (IL), USA, June 2000.

[MR7] L. Zaccarian and A.R. Teel. A benchmark example for anti-windup synthesis in active vibration isolation tasks and an L₂ anti-windup solution. European Journal of Control, 6(5):405–420, 2000.

[MR8] J.K. Park, C.H. Choi, and H. Choo. Dynamic anti-windup method for a class of time-delay control systems with input saturation. International Journal of Robust and Nonlinear Control, 10:457–488, 2000.

[MR9] L. Zaccarian, A.R. Teel, and J. Marcinkowski. Anti-windup for an active vibration isolation device: Theory and experiments. In Proceedings of the American Control Conference, pages 3585–3589, Chicago (IL), USA, June 2000.

[MR10] L. Zaccarian and A.R. Teel. Anti-windup, bumpless transfer and reliable designs: A model-based approach. In Proceedings of the American Control Conference, pages 4902–4907, Arlington (VA), USA, June 2001.

[MR11] L. Zaccarian and A.R. Teel. Nonlinear L₂ anti-windup design: An LMI-based approach. In Proceedings of the Nonlinear Control Systems Design Symposium (NOLCOS), pages 1298–1303, Saint Petersburg, Russia, July 2001.

[MR12] C. Barbu, R. Reginatto, A.R. Teel, and L. Zaccarian. Anti-windup for exponentially unstable linear systems with rate and magnitude limits. In V. Kapila and K. Grigoriadis, editors, Actuator Saturation Control, chapter 1, pages 1–31. New York, Marcel Dekker, 2002.

[MR13] A. Bemporad, A.R. Teel, and L. Zaccarian. L₂ anti-windup via receding horizon optimal control. In Proceedings of the American Control Conference, pages 639–644, Anchorage (AK), USA, May 2002.

[MR14] F. Morabito, A.R. Teel, and L. Zaccarian. Results on anti-windup design for Euler-Lagrange systems. In Proceedings of the IEEE Conference on Robotics and Automation, pages 3442–3447, Washington (DC), USA, May 2002.

[MR15] L. Zaccarian and A.R. Teel. A common framework for anti-windup, bumpless transfer and reliable designs. Automatica, 38(10):1735–1744, 2002.

[MR16] G. Grimm, A.R. Teel, and L. Zaccarian. The L₂ anti-windup problem for discrete-time linear systems: Definition and solutions. In Proceedings of the American Control Conference, pages 5329–5334, Denver (CO), USA, June 2003.

[MR17] A. Bemporad, A.R. Teel, and L. Zaccarian. Anti-windup synthesis via sampled-data piecewise affine optimal control. Automatica, 40(4):549–562, 2004.

[MR18] F. Morabito, S. Nicosia, A.R. Teel, and L. Zaccarian. Measuring and improving performance in anti-windup laws for robot manipulators. In B. Siciliano, A. De Luca, C. Melchiorri, and G. Casalino, editors, Advances in Control of Articulated and Mobile Robots, chapter 3, pages 61–85. New York, Springer Tracts in Advanced Robotics, 2004.

[MR19] F. Morabito, A.R. Teel, and L. Zaccarian. Nonlinear anti-windup applied to Euler-Lagrange systems. IEEE Transactions on Robotics and Automation, 20(3):526–537, 2004.

[MR20] D. Neši, A.R. Teel, and L. Zaccarian. L₂ anti-windup for linear dead-time systems. In Proceedings of the American Control Conference, pages 5280–5285, Boston (MA), USA, June 2004.

[MR21] L. Zaccarian and A.R. Teel. Nonlinear scheduled anti-windup design for linear systems. IEEE Transactions on Automatic Control, 49(11):2055–2061, 2004.

[MR22] L. Zaccarian, E. Weyer, A.R. Teel, Y. Li, and M. Cantoni. Anti-windup for marginally stable plants applied to open water channels. In Proceedings of the Asian Control Conference, pages 1702–1710, Melbourne (VIC), Australia, July 2004.

[MR23] S. Galeani, A.R. Teel, and L. Zaccarian. Output feedback compensators for weakened anti-windup of additively perturbed systems. In Proceedings of the IFAC World Congress, Prague, Czech Republic, July 2005.

[MR24] L. Zaccarian, D. Neši, and A.R. Teel. L₂ anti-windup for linear dead-time systems. Systems and Control Letters, 54(12):1205–1217, 2005.

[MR25] L. Zaccarian and A.R. Teel. The L₂ (l₂) bumpless transfer problem: Its definition and solution. Automatica, 41(7):1273–1280, 2005.

[MR26] S. Galeani and A.R. Teel. On a performance-robustness trade-off intrinsic to the natural anti-windup problem. Automatica, 42(11):1849–1861, 2006.

[MR27] S. Galeani, S. Onori, A.R. Teel, and L. Zaccarian. Nonlinear L₂ anti-windup for enlarged stability regions and regional performance. In Proceedings of the Symposium on Nonlinear Control Systems (NOLCOS), pages 539544, Pretoria, South Africa, August 2007.

[MR28] S. Galeani, S. Onori, A.R. Teel, and L. Zaccarian. Regional, semiglobal, global nonlinear anti-windup via switching design. In Proceedings of the European Control Conference, pages 5403–5410, Kos, Greece, July 2007.

[MR29] S. Galeani, S. Onori, and L. Zaccarian. Nonlinear scheduled control for linear systems subject to saturation with application to anti-windup control. In Proceedings of the Conference on Decision and Control, pages 1168–1173, New Orleans (LA), USA, December 2007.

[MR30] S. Galeani, A.R. Teel, and L. Zaccarian. Constructive nonlinear anti-windup design for exponentially unstable linear plants. Systems and Control Letters, 56(5):357–365, 2007.

[MR31] L. Pagnotta, L. Zaccarian, A. Constantinescu, and S. Galeani. Anti-windup applied to adaptive rejection of unknown narrow band disturbances. In Proceedings of the European Control Conference, pages 150–157, Kos, Greece, July 2007.

[MR32] G. Grimm, A.R. Teel, and L. Zaccarian. The L₂ anti-windup problem for discrete-time linear systems: definition and solutions. Systems and Control Letters, 57(4):356–364, 2008.

[MR33] F. Forni, S. Galeani, and L. Zaccarian. Model recovery anti-windup for plants with rate and magnitude saturation. In Proceedings of the European Control Conference, Budapest, Hungary, August 2009.

Direct linear LMI-based anti-windup designs

[MI1] V.M. Marcopoli and S.M. Phillips. Analysis and synthesis tools for a class of actuator-limited multivariable control systems: A linear matrix inequality approach. International Journal of Robust and Nonlinear Control, 6:10451063, 1996.

[MI2] M. Saeki and N. Wada. Design of anti-windup controller based on matrix inequalities. In Proceedings of the 35th Conference on Decision and Control, pages 261–262, Kobe, Japan, December 1996.

[MI3] M.V. Kothare and M. Morari. Multivariable anti-windup controller synthesis using multi-objective optimization. In Proceedings of the American Control Conference, pages 3093-3097, Albuquerque (NM), USA, June 1997.

[MI4] M.V. Kothare and M. Morari. Stability analysis of anti-windup control schemes: A review and some generalizations. In Proceedings of the 4th European Control Conference, Brussels, Belgium, July 1997.

[MI5] B.G. Romanchuk and M.C. Smith. Incremental gain analysis of piece-wise linear systems and application to the antiwindup problem. Automatica, 35(7):1275–1283, 1999.

[MI6] E.F. Mulder and M.V. Kothare. Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions. In Proceedings of the American Control Conference, pages 3239–3243, Chicago (IL), USA, June 2000.

[MI7] M. Saeki and N. Wada. Synthesis of a static anti-windup compensator via linear matrix inequalities. In Proceedings of the 3rd IFAC Symposium on Robust Control Design, Prague, Czech Republic, June 2000.

[MI8] G. Grimm, Jay Hatfield, I. Postlethwaite, A.R. Teel, M.C. Turner, and L. Za-ccarian. Experimental results in optimal linear anti-windup compensation. In Proceedings of the Conference on Decision and Control, pages 2657–2662, Orlando (FL), USA, December 2001.

[MI9] G. Grimm, I. Postlethwaite, A.R. Teel, M.C. Turner, and L. Zaccarian. Case studies using linear matrix inequalities for optimal anti-windup synthesis. In Proceedings of the European Control Conference, Porto, Portugal, September 2001.

[MI10] G. Grimm, I. Postlethwaite, A.R. Teel, M.C. Turner, and L. Zaccarian. Linear matrix inequalities for full and reduced order anti-windup synthesis. In Proceedings of the American Control Conference, pages 4134–4139, Arlington (VA), USA, June 2001.

[MI11] E.F. Mulder, M.V. Kothare, and M. Morari. Multivariable anti-windup controller synthesis using linear matrix inequalities. Automatica, 37(9): 14071416, September 2001.

[MI12] Y.Y. Cao, Z. Lin, and D.G. Ward. An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation. IEEE Transactions on Automatic Control, 47(1):140–145, 2002.

[MI13] Y.Y. Cao, Z. Lin, and D.G. Ward. Antiwindup design for linear systems subject to input saturation. Journal of Guidance Navigation and Control,25(3):455–463, 2002.

[MI14] G. Grimm, A.R. Teel, and L. Zaccarian. Results on linear LMI-based external anti-windup design. In Proceedings of the Conference on Decision and Control, pages 299–304, Las Vegas (NV), USA, December 2002.

[MI15] G. Grimm, A.R. Teel, and L. Zaccarian. Robust LMI-based linear anti-windup design: optimizing the unconstrained response recovery. In Proceedings of the Conference on Decision and Control, pages 293–298, Las Vegas (NV), USA, December 2002.

[MI16] E.F. Mulder and M.V. Kothare. Static anti-windup controller synthesis using simultaneous convex design. In Proceedings of the American Control Conference, pages 651–656, Anchorage (AK), USA, June 2002.

[MI17] J.M. Gomes da Silva Jr and S. Tarbouriech. Anti-windup design with guaranteed regions of stability: An LMI-based approach. In Proceedings of the Conference on Decision and Control, pages 4451–4456, Maui (HI), USA, December 2003.

[MI18] G. Grimm, J. Hatfield, I. Postlethwaite, A.R. Teel, M.C. Turner, and L. Za-ccarian. Antiwindup for stable linear systems with input saturation: An LMI-based synthesis. IEEE Transactions on Automatic Control, 48(9): 1509–1525, September 2003.

[MI19] G. Grimm, I. Postlethwaite, A.R. Teel, M.C. Turner, and L. Zaccarian. Case studies using LMIs in anti-windup synthesis for stable linear systems with input saturation. European Journal of Control, 9(5):459–469, 2003.

[MI20] G. Grimm, A.R. Teel, and L. Zaccarian. Establishing Lipschitz properties of multivariable algebraic loops with incremental sector nonlinearities. In Proceedings of the Conference on Decision and Control, Maui (HI), USA, December 2003.

[MI21] S. Tarbouriech, J.M. Gomes da Silva Jr., and G. Garcia. Delay-dependent anti-windup loops for enlarging the stability region of time delay systems with saturating inputs. ASME Journal of Dynamic Systems, Measurement and Control, 125:265–267, June 2003.

[MI22] G. Grimm, A.R. Teel, and L. Zaccarian. Linear LMI-based external anti-windup augmentation for stable linear systems. Automatica, 40(11):1987–1996, 2004.

[MI23] G. Grimm, A.R. Teel, and L. Zaccarian. Robust linear anti-windup synthesis for recovery of unconstrained performance. International Journal of Robust and Nonlinear Control, 14(13–15): 1133–1168, 2004.

[MI24] A. Syaichu-Rohman and R.H. Middleton. Anti-windup schemes for discrete time systems: An LMI-based design. In Proceedings of the Asian Control Conference, pages 554–561, Melbourne (VIC), Australia, July 2004.

[MI25] M.C. Turner and I. Postlethwaite. A new perspective on static and low order anti-windup synthesis. International Journal of Control, 77(1):27–44, 2004.

[MI26] F. Wu and B. Lu. Anti-windup control design for exponentially unstable LTI systems with actuator saturation. Systems and Control Letters, 52(3–4):304–322, 2004.

[MI27] J.M. Gomes da Silva Jr and S. Tarbouriech. Anti-windup design with guaranteed regions of stability: An LMI-based approach. IEEE Transactions on Automatic Control, 50(1):106–111, 2005.

[MI28] S. Galeani, M. Massimetti, A.R. Teel, and L. Zaccarian. Reduced order linear anti-windup augmentation for stable linear systems. International Journal of Systems Science, 37(2):115–127, 2006.

[MI29] S. Galeani, S. Onori, A.R. Teel, and L. Zaccarian. Further results on static linear anti-windup design for control systems subject to magnitude and rate saturation. In Proceedings of the Conference on Decision and Control, pages 6373–6378, San Diego (CA), USA, December 2006.

[MI30] M. Massimetti, L. Zaccarian, T. Hu, and A.R. Teel. LMI-based linear anti-windup for discrete time linear control systems. In Proceedings of the Conference on Decision and Control, pages 6173–6178, San Diego (CA), USA, December 2006.

[MI31] J.M. Biannic, C. Roos, and S. Tarbouriech. A practial method for fixed-order anti-windup design. In Proceedings of the 17th IFAC Symposium on Nonlinear Control Systems, pages 527–532, Pretoria, South Africa, August 2007.

[MI32] S. Galeani, S. Onori, A.R. Teel, and L. Zaccarian. A magnitude and rate saturation model and its use in the solution of a static anti-windup problem. Systems and Control Letters, 57(1): 1–9, 2008.

[MI33] T. Hu, A.R. Teel, and L. Zaccarian. Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance. Automatica, 44(2):512–519, 2008.

[MI34] C. Roos and J.M. Biannic. A convex characterization of dynamically-constrained anti-windup controllers. Automatica, 44(9):2449–2452, 2008.

Other schemes

[OS1] S.F. Graebe and A.L.B. Ahlén. Dynamic transfer among alternative controllers and its relation to antiwindup controller design. IEEE Transactions on Control Systems Technology, 4(1):92–99, January 1996.

[OS2] T.A. Kendi and F.J. Doyle III. An anti-windup scheme for multivariable nonlinear systems. Journal of Process Control, 7(5):329–343, 1997.

[OS3] S. Valluri and M. Soroush. Input constraint handling and windup compensation in nonlinear control. In Proceedings of the American Control Conference, pages 1734–1738, Albuquerque (NM), USA, June 1997.

[OS4] N. Kapoor, A.R. Teel, and P. Daoutidis. An anti-windup design for linear systems with input saturation. Automatica, 34(5):559–574, 1998.

[OS5] W. Niu and M. Tomizuka. A robust anti-windup controller design for motion control systems with asymptotic tracking subject to actuator saturation. In Proceedings of the 37th Conference on Decision and Control, pages 915920, Tampa (FL), USA, December 1998.

[OS6] Y. Peng, D. Vrani, R. Hanus, and S.S.R. Weller. Anti-windup designs for multivariable controllers. Automatica, 34(12):1559–1565, 1998.

[OS7] N. Kapoor and P. Daoutidis. An observer-based anti-windup scheme for non-linear systems with input constraints. International Journal of Control, 72(1):18–29, 1999.

[OS8] Q. Hu and G.P. Rangaiah. Anti-windup schemes for uncertain nonlinear systems. IEE Proceedings on Control Theory Applications, 147(3):321–329, May 2000.

[OS9] J.A. De Dona, G.C. Goodwin, and M.M. Seron. Anti-windup and model predictive control: Reflections and connections. European Journal of Control, 6(5):467–477, 2002.

[OS10] A. Rantzer. A performance criterion for anti-windup compensators. European Journal of Control, 6(5):449–452, 2002.

[OS11] P. Hippe. Windup prevention for unstable systems. Automatica, 39(11):1967–1973, 2003.

[OS12] A.H. Glattfelder and W. Schaufelberger. Control Systems with Input and Output Constraints. London, UK, Springer-Verlag, 2003.

[OS13] P. Hippe. Windup in Control: Its Effects and Their Prevention. Surrey, UK, Springer-Verlag, 2006.

Anti-windup applications

[AP1] N. Kapoor and A.R. Teel. A dynamic windup compensation scheme applied to a turbofan engine. In Proceedings of the 36th Conference on Decision and Control, pages 4689 – 4694, San Diego (CA), USA, December 1997.

[AP2] A.R. Teel and J.B. Buffington. Anti-windup for an F–16's daisy chain control allocator. In Proceedings of the AIAA GNC Conference, pages 748–754, New Orleans (LA), USA, August 1997.

[AP3] A.R. Teel, O.E. Kaiser, and R.M. Murray. Uniting local and global controllers for the Caltech ducted fan. In Proceedings of the American Control Conference, volume 3, pages 1539–1543, Albuquerque (NM), USA, June 1997.

[AP4] K.J. Park, H. Lim, T. Basar, and C.H. Choi. Anti-windup compensator for active queue management in TCP networks. Control Engineering Practice, 11(10):1127–1142, October 2003.

[AP5] G. Herrmann, MC Turner, I. Postlethwaite, and G. Guo. Practical implementation of a novel anti-windup scheme in a HDD-dual-stage servo-system. IEEE/ASME Transactions on Mechatronics, 9(3):580–592, 2004.

[AP6] C. Barbu, S. Galeani, A.R. Teel, and L. Zaccarian. Nonlinear anti-windup for manual flight control. International Journal of Control, 78(14): 11111129, September 2005.

[AP7] C. Roos and J.M. Biannic. Aircraft-on-ground lateral control by an adaptive LFT-based anti-windup approach. In Proceedings of the IEEE Conference on Control Applications, pages 2207–2212, Munich, Germany, October 2006.

[AP8] A.R. Teel, L. Zaccarian, and J. Marcinkowski. An anti-windup strategy for active vibration isolation systems. Control Engineering Practice, 14(1): 1727, 2006.

[AP9] C. Roos, J. Biannic, S. Tarbouriech, and C. Prieur. On-ground aircraft control design using an LPV anti-windup approach. In D. Bates and M. Hagstrom, editors, Nonlinear Analysis and Synthesis Techniques for Aircraft Control, pages 117–145. Springer-Verlag, London, LNCIS, 2007.

[AP10] L. Zaccarian, E. Weyer, A.R. Teel, Y. Li, and M. Cantoni. Anti-windup for marginally stable plants and its application to open water channel control systems. Control Engineering Practice, 15(2):261–272, 2007.

[AP11] G. Herrmann, B. Hredzak, MC Turner, I. Postlethwaite, and G. Guo. Discrete robust anti-windup to improve a novel dual-stage large-span track-seek/following method. IEEE Transactions on Control Systems Technology, 16(6):1342–1351, 2008.

11.6 ADDITIONAL REFERENCES

Some of the results presented in this book are taken from references not directly related to anti-windup design but that become relevant in some anti-windup design contexts. These additional references are organized here in two groups, the first one comprising papers addressing nonlinear systems with saturation specifically. These are listed next.

[SAT1] P. Kapasouris, M. Athans, and G. Stein. Design of feedback control systems for stable plants with saturating actuators. In Proceedings of the Conference on Decision and Control, pages 469–479, Austin (TX), USA, December 1988.

[SAT2] A.R. Teel. Global stabilization and restricted tracking for multiple integrators with bounded controls. Systems and Control Letters, 18:165–171, 1992.

[SAT3] H.J. Sussmann, E.D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control, 39(12):2411–2424, 1994.

[SAT4] K.D. Hammett, W.C. Reigelsperger, and S.S. Banda. High angle of attack short period flight control design with thrust vectoring. In Proceedings of the 1995 American Control Conference, pages 170–174, Seattle (WA), USA, June 1995.

[SAT5] A.R. Teel. Semi-global stabilizability of linear null controllable systems with input nonlinearities. IEEE Transactions on Automatic Control, 40(1):96–100, January 1995.

[SAT6] J.M. Berg, K.D. Hammett, C.A. Schwartz, and S.S. Banda. An analysis of the destabilizing effect of daisy chained rate-limited actuators. IEEE Transactions on Control Systems Technology, 4(2):171–176, March 1996.

[SAT7] A. Megretski. L₂ BIBO output feedback stabilization with saturated control. In Proceedings of the 13th Triennial IFAC World Congress, pages 435440, San Francisco (CA), USA, 1996.

[SAT8] A.R. Teel. On L₂ performance induced by feedbacks with muiltiple saturations. ESAIM: Control, Optimization, and Calculus of Variations, 1:225–240, September 1996 (http://www.emath.fr/cocv/).

[SAT9] A.A. Stoorvogel, A. Saberi, and G. Shi. On achieving L_p (l_p) performance with global internal stability for linear plants with saturating actuators. In Proceedings of the 38th Conference on Decision and Control, pages 27622767, Phoenix (AZ), USA, December 1999.

[SAT10] A. Bemporad, M. Morari, V. Dua, and E.N. Pistikopoulos. The explicit linear quadratic regulator for constrained systems. Automatica, 38(1):3–20, 2002.

[SAT11] T. Hu, Z. Lin, and B.M. Chen. An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica, 38(2):351–359, 2002.

[SAT12] A. Syaichu-Rohman and R.H. Middleton. On the robustness of multivari-able algebraic loops with sector nonlinearities. In Proceedings of the Conference on Decision and Control, pages 1054–1059, Las Vegas (NV), USA, December 2002.

[SAT13] A. Syaichu-Rohman, RH Middleton, and MM Seron. A multivariable nonlinear algebraic loop as a QP with application to MPC. In Proceedings of the European Control Conference, 2003.

[SAT14] H. Fang, Z. Lin, and T. Hu. Analysis and control design of linear systems in the presence of actuator saturation and L₂ disturbances. Automatica, 40(7):1229–1238, 2004.

[SAT15] T. Hu, A.R. Teel, and L. Zaccarian. Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions. IEEE Transactions on Automatic Control, 51(11): 1770–1786, November 2006.

The second group involves more general references, most of them focusing in various ways on nonlinear systems or on computational tools or on specific application studies cited in the examples discussed in the book.

[G1] M. Grant and S. Boyd. CVX: MATLAB software for disciplined convex programming. (http://stanford.edu/boyd/cvx).

[G2] B. Armstrong, O. Khatib, and J. Burdick. The explicit dynamic model and inertial parameters of the PUMA 560 arm. In Proceedings of the IEEE Conference on Robotics and Automation, pages 510–518, San Francisco (CA), USA, April 1986.

[G3] A.S. Morse, D.Q. Mayne, and G.C. Goodwin. Applications of hysteresis switching in parameter adaptive control. IEEE Transactions on Automatic Control, 37(9):1343–1354, September 1992.

[G4] P.I. Corke and B. Armstrong-H6louvry. A search for consensus among model parameters reported fot the PUMA 560 robot. In Proceedings of the IEEE International Conference on Robotics and Automation, 1608–1613, San Diego (CA), USA, May 1994.

[G5] P. Gahinet and P. Apkarian. A linear matrix inequality approach to H_∞ control. International Journal of Robust and Nonlinear Control, 4:421–448, 1994.

[G6] T. Iwasaki and R.E. Skelton. All controllers for the general H_∞ control problem: LMI existence conditions and state space formulas. Automatica, 30(8):1307–17, August 1994.

[G7] G. Mester. Adaptive force and position control of rigid-link flexible-joint SCARA robots. In Proceedings of the IEEE Industrial Electronics Conference, volume 3, pages 1639–1644, Bologna, Italy, September 1994.

[G8] P. Gahinet. Explicit controller formulas for LMI-based H_∞ synthesis. Auto-matica, 32(7):1007–1014, July 1996.

[G9] M. Jankovic, R. Sepulchre, and PV Kokotovic. Constructive Lyapunov stabilization of nonlinear cascade systems. IEEE Transactions on Automatic Control, 41(12):1723–1735, 1996.

[G10] F. Mazenc and L. Praly. Adding integrations, saturated controls, and stabilization of feedforward systems. IEEE Transactions on Automatic Control, 41(11):1559–1578, November 1996.

[G11] S. Majhi and D.P. Atherton. Modified Smith predictor and controller for processes with time delay. IEE Proceedings on Control Theory Applications, 146(5):359–366, September 1999.

[G12] A.R. Teel. Asymptotic convergence from L_p stability. IEEE Transactions on Automatic Control, 44(11):2169–2170, November 1999.

[G13] D.Q. Mayne, J.B. Rawlings, C.V. Rao, and P.O.M. Scokaert. Constrained model predictive control: Stability and optimality. Automatica, 36(6):789–814, 2000.

[G14] W. Desch, H. Logemann, EP Ryan, and ED Sontag. Meagre functions and asymptotic behaviour of dynamical systems. Nonlinear Analysis, 44(8): 10871109,2001.

[G15] J. Lofberg. YALMIP: A toolbox for modeling and optimization in MAT-AB. In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.

[G16] Y. Wang and S. Boyd. Fast model predictive control using online optimization. In Proceedings of the IFAC World Congress, pages 6974–6997, 2008.

[G17] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. Philadelphia (PA), USA, Society for Industrial and Applied Mathematics, 1994.

[G18] F.H. Clarke. Optimization and Nonsmooth Analysis. Philadelphia (PA), USA, Society for Industrial and Applied Mathematics, 1990.

[G19] P. Gahinet, A. Nemirovski, A.J. Laub, and M. Chilali. LMI Control Toolbox. The Math Works Inc., 1995.

[G20] H.K. Khalil. Nonlinear Systems, 3rd ed. Englewood Cliffs (NJ), USA, Prentice Hall, 2002.

[G21] M. Morari and E. Zafiriou. Robust Process Control. Englewood Cliffs (NJ), USA, Prentice Hall, 1989.