A reset controller is a controller that operates most of the time as a linear system, except when some condition holds. The typical reset condition is the zero crossing of the tracking error signal, e(t) = 0. At this moment, the controller performs a zero resetting action on its state. It has been shown that reset control is able to overcome fundamental linear limitations. This article studies, within a frequency-domain framework, the generalisation of reset control systems based on including some anticipation on the reset condition.This has a favourable phase lead effect. The paper discusses different reset anticipations schemes, including multiple reset actions in the same period, computes Fourier harmonics and describing function of general reset controllers and shows explicitly the overcoming of frequency-domain limitations (Bode's gain–phase relation).

References

1. 1)
  - 13. Guo, Y., Wang, Y., Xie, L., Zheng, J.: ‘Stability analysis and design of reset systems: theory and an application’, Automatica, 2009, 45 pp. 492–497 (doi: 10.1016/j.automatica.2008.08.016).
2. 2)
  - 20. Baños, A., Dormido, S., Barreiro, A.: ‘Stability Analysis of reset control systems with reset band’, Third IFAC Conf. on Analysis and Design of Hybrid Systems, 2009.
3. 3)
  - 8. Beker, O., Hollot, C.V., Chait, Y.: ‘Plant with an integrator: anations of linear feedback’, IEEE Trans. Autom. Control, 2001.
4. 4)
  - 18. Baños, A., Dormido, S., Barreiros, A.: ‘Limit cycles analysis in reset control systems with reset band’, Nonlinear Anal.: Hybrid Syst., 2011, 5, (2), pp. 163–173 (doi: 10.1016/j.nahs.2010.07.004).
5. 5)
  - 1. Clegg, J.C.: ‘A nonlinear integrator for servomechanism’, Trans. A.I.E.E.m, Part II, 1958, 77, pp. 41–42.
6. 6)
  - 22. Guo, Y., Wang, Y., Xie, L., Zheng, J.: ‘Frequency-domain properties of reset systems with application in hard-disk-drive systems’, IEEE Trans. Control Syst. Technol., 2009, 17, (6).
7. 7)
  - 19. Baños, A., Dormido, S., Barreiros, A.: ‘Reset control systems with reset band: well-posedness and limit cycles analysis’, Mediterranean Control Conf.MED’11, Greece, 2011.
8. 8)
  - 7. Zheng, Y., Chait, Y., Hollot, C.V., Steinbuch, M., Norg, M.: ‘Experimental demonstration of reset control design, control engineering practice’, Control Eng. Pract., 2000, 8, pp. 113–120 (doi: 10.1016/S0967-0661(99)00131-8).
9. 9)
  - 6. Chait, Y., Hollot, C.: ‘On Horowitzs contributions to reset control’, Int. J. Robust Nonlinear Control, 2002, pp. 335–355.
10. 10)
  - 3. Krishnan, K.R., Horowitz, I.M.: ‘Synthesis of a nonlinear feedback system with significant plant-ignorance for prescribed system tolerances’, Int. J. Control, 1974, 19, (4), pp. 689–706 (doi: 10.1080/00207177408932666).
11. 11)
  - 9. Aangenent, W.H.T.M., Witvoet, G., Heemels, W.P.M.H., van de Molengraft, M.J.G., Steinbuch, M.: ‘Performance analysis of reset control systems’, Int. J. Robust Nonlinear Control, 2009.
12. 12)
  - 4. Beker, O., Hollot, C.V., Chait, Y.: ‘Plant with integrator: an example of reset control overcoming limitations of linear systems’, IEEE Trans. Autom. Control, 2001, 46, (11), pp. 1797–1799 (doi: 10.1109/9.964694).
13. 13)
  - 5. Beker, O., Hollotb, C.V., Chait, Y., Han, H.: ‘Fundamental properties of reset control systems’, Automatica, 2004, 40, pp. 905–915 (doi: 10.1016/j.automatica.2004.01.004).
14. 14)
  - 23. Aström, K.J., Murray, R.M.: ‘Feedback systems’ (Princeton University Press, 2008).
15. 15)
  - 10. Loquen, T., Tarbouriech, S., Prieur, C.: ‘Stability of reset control systems with nonzero reference’. Proc. 47th IEEE Conf. on Decision and Control, Cancun, Mexico, 9–11 December, 2008.
16. 16)
  - 16. Vidal, A., Baños, A.: ‘Reset compensation for temperature control: experimental applications on heat exchangers’, Chem. Eng. J., 2010, 159, (1–3), pp. 170–181 (doi: 10.1016/j.cej.2010.02.033).
17. 17)
  - 15. Vidal, A., Baños, A., Moreno, J.C., Berenguel, M.: ‘PI+CI compensation with variable reset: application on solar collector field’. 34th Annual Conf. on IEEE Industrial Electronics Society, Orlando, Florida, EE.UU.2008.
18. 18)
  - 17. Fernández, A., Barreiro, A., Baños, A., Carrasco, J.: ‘Reset control for passive bilateral teleoperation’, IEEE Trans. Ind. Electron., 2011, to appear.
19. 19)
  - 21. Baños, A., Barreiro, A.: ‘Delay-independent stability of reset systems’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 341–346 (doi: 10.1109/TAC.2008.2007865).
20. 20)
  - 11. Nešić, D., Zaccarian, L., Teel, A.R.: ‘Stability properties of reset systems’, Automatica, 2008, 44, (8), pp. 2019–2026 (doi: 10.1016/j.automatica.2007.11.014).
21. 21)
  - 12. Nešić, D., Zaccarian, L., Teel, A.R.: ‘First order reset elements and the Clegg integrator revisited’. Proc. American Control Conf., 2005, vol. 1, pp. 563–568.
22. 22)
  - 2. Horowitz, I.M., Rosenbaum, P.: ‘Nonlinear design for cost of feedback reduction in systems with large parameter uncertainty’, Int. J. Control, 1975, 24, (6), pp. 977–1001 (doi: 10.1080/00207177508922051).
23. 23)
  - 14. Baños, A., Carrasco, J., Barreiro, A.: ‘Reset times-dependent stability of reset control with unstable base systems’, IEEE Trans. Autom. Control, 2011, 56, (1) (doi: 10.1109/TAC.2010.2088892).

Frequency domain properties of reset systems with multiple reset anticipations

References

Related content