Tracking and rejection of periodic signals for discrete-time linear systems subject to control saturation

Tracking and rejection of periodic signals for discrete-time linear systems subject to control saturation

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This work addresses the tracking and rejection problem of periodic signals for discrete-time linear systems subject to control saturation. To ensure the periodic tracking/rejection an internal model-based controller is considered. Based on this control structure, conditions allowing the simultaneous synthesis of a stabilising state feedback gain and an anti-windup gain are proposed. Provided that references and disturbances belong to the interior of a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in an ellipsoidal set contract to the linearity region of the closed-loop system, where the presence of the internal model ensures the periodic tracking/rejection. To compute the gains, an LMI-based optimisation problem aiming at the maximisation of the set of admissible states and/or the set of admissible references/disturbances is proposed.


    1. 1)
      • 1. Zhang, B., Zhou, K., Wang, Y., Wang, D.: ‘Performance improvement of repetitive controlled PWM inverters: a phase-lead compensation solution’, Int. J. Circuit Theory Appl., 2010, 38, (5), pp. 453469.
    2. 2)
      • 2. Tomizuka, M., Tsao, T.C., Chew, K.K.: ‘Analysis and synthesis of discrete-time repetitive controllerTrans. ASME, J. Dyn. Syst. Meas. Control, 1989, 111, pp. 353358 (doi: 10.1115/1.3153060).
    3. 3)
      • 3. Liuzzo, S., Tomei, P.: ‘A global adaptive learning control for robotic manipulators’, Automatica, 2008, 44, (5), pp. 13791384 (doi: 10.1016/j.automatica.2007.10.025).
    4. 4)
      • 4. Chen, C.: ‘Linear system theory and design’ (Holt, Rinehart and Winston, New York, NY, 1970, 2nd edn.), p. 679.
    5. 5)
      • 5. Francis, B.A., Wonham, W.M.: ‘The internal model principle for linear multivariable regulators’, Appl. Math. Optim., 1975, 2, (2), pp. 170194 (doi: 10.1007/BF01447855).
    6. 6)
      • 6. Davison, E.: ‘The robust control of a servomechanism problem for linear time-invariant multivariable systems’, IEEE Trans. Autom. Control, 1976, 21, (1), pp. 2534 (doi: 10.1109/TAC.1976.1101137).
    7. 7)
      • 7. Inoue, T., Nakano, M., Iwa, S.: ‘High accuracy control of servomechanism for repeated contouring’. Proc. Tenth Annual Symp. Incremental Motion Control Systems and Devices, 1981, pp. 258292.
    8. 8)
      • 8. Hara, S., Yamamoto, Y., Omata, T., Nakano, M.: ‘Repetitive control system: a new type servo system for periodic exogenous signals’, IEEE Trans. Autom. Control, 1988, 33, (7), pp. 659668 (doi: 10.1109/9.1274).
    9. 9)
      • 9. Doh, T.-Y., Ryoo, J., Chung, M.: ‘Design of a repetitive controller: an application to the track-following servo system of optical disk drives’, IEE Proc. Control Theory Appl., 2006153, (3), pp. 323330 (doi: 10.1049/ip-cta:20045217).
    10. 10)
      • 10. Li, C., Zhang, D., Zhuang, X.: ‘A survey of repetitive control’. Proc. 2004 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, 2004 (IROS 2004), vol. 2, September–October 2004, pp. 11601166.
    11. 11)
      • 11. Tarbouriech, S., Pittet, C., Burgat, C.: ‘Output tracking problem for systems with input saturations via nonlinear integrating actions’, Int. J. Robust Nonlinear Control, 2000, 10, (6), pp. 489512 (doi: 10.1002/(SICI)1099-1239(200005)10:6<489::AID-RNC489>3.0.CO;2-D).
    12. 12)
      • 12. Cao, Y., Lin, Z., Ward, D.G.: ‘Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances’, Automatica, 2004, 40, (7), pp. 12211228 (doi: 10.1016/j.automatica.2004.02.012).
    13. 13)
      • 13. Tarbouriech, S., Queinnec, I., Pittet, C.: ‘Output-reference tracking problem for discrete-time systems with input saturations’, IEE Proc. Control Theory Appl., 2000, 147, (4), pp. 447455 (doi: 10.1049/ip-cta:20000552).
    14. 14)
      • 14. Flores, J.V., Gomes da Silva, Jr., J.M., Sbarbaro, D.: ‘Robust periodic reference tracking for uncertain linear systems subject to control saturations’. Proc. 48th IEEE Conf. on Decision and Control, 2009, Shanghai, China, December 2009, pp. 79607965.
    15. 15)
      • 15. Flores, J.V., Gomes Da Silva, Jr., J.M., , Pereira, L.F.A., Sbarbaro, D.: ‘Repetitive control design for MIMO systems with saturating actuators’, IEEE Trans. Autom. Control, 2012, 57, (1), pp. 192198 (doi: 10.1109/TAC.2011.2174829).
    16. 16)
      • 16. Sbarbaro, D., Tomizuka, M., de la Barra, B.L., ‘Repetitive control system under actuator saturation and windup prevention’, ASME, J. Dyn. Syst. Meas. Control, 2009, 131, (4), 044505 (8 pages) (doi: 10.1115/1.3117207).
    17. 17)
      • 17. Haykin, S., Van Veen, B.: ‘Signals and systems’ (Wiley, 2002, 2nd edn.).
    18. 18)
      • 18. Gomes da Silva, Jr., J.M., Tarbouriech, S.: ‘Anti-windup design with guaranteed regions of stability for discrete-time linear systems’, Syst. Control Lett., 2006, 55, pp. 184192 (doi: 10.1016/j.sysconle.2005.07.001).
    19. 19)
      • 19. Boyd, S., Ghaoui, E., Feron, E., Balakrishnan, V.: ‘Linear matrix inequalities in system and control theory’ (SIAM, Philadelphia, PA, 1994, 1st edn.).
    20. 20)
      • 20. Tarbouriech, S., Garcia, G., Gomes da Silva, Jr., J.M., Queinnec, I.: ‘Stability and stabilization of linear systems with saturating actuators’ (Springer, 2011, 1st edn.).
    21. 21)
      • 21. Montagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D.: ‘Convergent LMI relaxations for quadratic stabilizability and ℋ control of Takagi–Sugeno fuzzy systems’, IEEE Trans. Fuzzy Syst., 2009, 17, (4), pp. 863873 (doi: 10.1109/TFUZZ.2009.2016552).

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