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A passivity-based approach to reset control systems stability. (English) Zbl 1208.93118
This work gives a stability analysis of reset compensators in feedback interconnection with passive nonlinear systems. Reset control systems can be regarded as a special case of hybrid systems with impulsive motion. The reset actions amounts to setting the integrator output equal to zero whenever its input is zero. So there is take place a faster system response without excessive overshot. The stability problem of reset control systems is considered using passivity theory on the base of functional analysis. Several examples of full and partial reset compensators are analyzed.
93D15Stabilization of systems by feedback
93B52Feedback control
93C10Nonlinear control systems
46N10Applications of functional analysis in optimization and programming
[1]Clegg, J. C.: A nonlinear integrator for servomechanisms, Transactions A.I.E.E., part II 77, 41-42 (1958)
[2]Horowitz, I. M.; Rosenbaum: Nonlinear design for cost of feedback reduction in systems with large parameter uncertainty, International journal of control 24, No. 6, 977-1001 (1975) · Zbl 0312.93019 · doi:10.1080/00207177508922051
[3]Krishman, K. R.; Horowitz, I. M.: Synthesis of a nonlinear feedback system with significant plant-ignorance for prescribed system tolerances, International journal of control 19, No. 4, 689-706 (1974) · Zbl 0276.93019 · doi:10.1080/00207177408932666
[4]O. Beker, Analysis of reset control systems, Ph.D. Thesis, University of Massachusetts Amherst, 2001
[5]Beker, O.; Hollot, C. V.; Chait, Y.; Han, H.: Fundamental properties of reset control systems, Automatica 40, 905-915 (2004) · Zbl 1068.93050 · doi:10.1016/j.automatica.2004.01.004
[6]Hespanha, J. P.; Morse, A. S.: Switching between stabilizing controllers, Automatica 38, No. 11, 1905-1917 (2002) · Zbl 1011.93533 · doi:10.1016/S0005-1098(02)00139-5
[7]Nešić, D.; Zaccarian, L.; Teel, A. R.: Stability properties of reset systems, Automatica 44, 2019-2026 (2008)
[8]A. Baños, J. Carrasco, A. Barreiro, Reset times-dependent stability of reset system, in: Proceedings of the European Control Conference 2007, Kos, Greece, July 2–5, 2007, pp. 3074–3079
[9]A. Baños, J. Carrasco, A. Barreiro, Reset times-dependent stability of reset system with unstable base system, in: IEEE International Symposium on Industrial Electronics, Vigo, Spain, June 4–7, 2007, pp. 163–168
[10]W.H.T.M. Aangenent, G. Witvoet, W.P.M.H. Heemels, M.J.G. van de Molengraft, M. Steinbuch, An LMI-based L2 gain performance analysis for reset control systems, in: Proceedings of the 2008 American Control Conference, 2008
[11]Willems, J. C.: Dissipative dynamical systems – part I: General theory, Archive for rational mechanics amd analysis 45, 321-351 (1972) · Zbl 0252.93002 · doi:10.1007/BF00276493
[12]Van Der Schaft, A.: L2-gain and passivity techniques in nonlinear control, (2000) · Zbl 0937.93020
[13]Haddad, W. M.; Chellaboina, V.; Nersesov, S. G.: Impulsive and hybrid dynamical systems: stability, dissipativity, and control, Princeton series in applied mathematics (2006)
[14]M. Zefran, F. Bullo, M. Stein, A notion of passivity for hybrid systems, in: Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, USA, 2001
[15]Camlibel, M. K.; Heemels, W. P. M.H.; Schumacher, J. M.: On linear passive complementary systems, European journal of control 8, No. 3, 220-237 (2002)
[16]A. Pogromski, M. Jirstrand, P. Spangeus, On stability and passivity of a class of hybrid systems, in: Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, USA, 1998, pp. 3705–3710
[17]Bemporad, A.; Bianchini, G.; Brogi, Filippo: Passivity analysis and passification of discrete-time hybrid systems, IEEE transactions on automatic control 53, No. 4, 1004-1009 (2008)
[18]L. Zacarian, D. Nešić, A.R. Teel, First order reset elements and the Clegg integrator revisited, in: Proceedings of the 2005 American Control Conference, 2005
[19]Lozano, R.; Brogliato, B.; Egeland; Maschke, O.: Dissipative systems analysis and control, (2000)
[20]Rockafellar, R. T.; Wets, J. -B.: Variational analysis, Series of comprehensive studies in mathematics 317 (1998)
[21]Wright, R. A.; Kravaris, C.: On-line identification and nonlinear control of an industrial ph process, Journal of process control 11, 361-374 (2001)
[22]Khalil, Hassan K.: Nonlinear systems, (2002) · Zbl 1003.34002