OPEN ACCESS
This paper presents a design method for preview controller of discrete-time linear systems with multiple input delays based on the discrete lifting technology for single input delay plants. The design approach is featured by the infinite dimensionality of the actuator dynamics and the discrete-time feature of the delay-accumulation feedback operator. Specifically, an augmented error system was constructed to transform the tracking problem into a regulation problem, and the delays were eliminated by a new discrete lifting technique. On this basis, a controller with preview compensation and delay compensation was developed based on the preview control technology. The proposed controller was proved through a case study as suitable for multiple input delays system like robot trajectory control.
discrete-time system, input delays, preview control, lifting method
Cao M., Liao F. (2015). Design of an optimal preview controller for linear discrete-time descriptor systems with state delay. International Journal of Systems Science, Vol. 46, No. 5, pp. 932-943. https://doi.org/10.1080/00207721.2013.801097
Czarnetzki S., Kerner S., Urbann O. (2009). Observer-based dynamic walking control for biped robots. Robotics and Autonomous Systems, Vol. 57, No. 8, pp. 839-845. https://doi.org/10.1016/j.robot.2009.03.007
Fridman E. (2014). Introduction to Time-Delay Systems: Analysis and Control, Birkhauser.
Furukawa T., Shimemura E. (1983). Predictive control for systems with time delay. International Journal of Control, Vol. 37, No. 2, pp. 399-412. https://doi.org/10.1080/00207178308932979
Gershon E., Shaked U. (2014). H∞ preview tracking control of retarded state-multiplicative stochastic systems. International Journal of Robust and Nonlinear control, Vol. 24, No. 15, pp. 2119-2135. https://doi.org/10.1002/rnc.1646
Kajita S., Kanehiro F., Kaneko K., Fujiwara K., Harada K., Yokoi K., Hirukawa H. (2003). Biped walking pattern generation by using preview control of zero-moment point. Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan, September 14-19, Vol. 2, pp. 1620-1626. https://doi.org/10.1109/ROBOT.2003.1241826
Katayama T., Ohki T., Inoue T., Kato T. (1985). Design of an optimal controller for a discrete-time system subject to previewable demand. International Journal of Control, Vol. 41, No. 3, pp. 677-699. https://doi.org/10.1080/0020718508961156
Li L., Liao F. C. (2018). Output feedback preview tracking control for discrete-time polytopic time-varying systems. International Journal of Control. https://doi.org/10.1080/00207179.2018.1467046
Liao F., Cao M., Hu Z., An P. (2012). Design of an optimal preview controller for linear discrete-time causal descriptor systems. International Journal of Control, Vol. 85, No. 10, pp. 1616-1624. https://doi.org/10.1080/00207179.2012.695804
Liao F., Liao Y., Deng J. (2016). The application of predictor feedback in designing a preview controller for discrete-time systems with input delay. The application of predictor feedback in designing a preview controller for discrete-time systems with input delay, Vol. 2016, pp. 3023915.
Liao F., Takaba K., Katayama T., Katsuura J. (2003). Design of an optimal preview servomechanism for discrete-time systems in multirate setting. Dynamics of Continuous, Discrete, and Impulsive Systems Series B: Applications and Algorithms, 10, No. 5, pp. 727-744. https://doi.org/10.1215/S0012-7094-03-12017-7
Liao Y., Liao F. (2017). A design method of preview controller for linear continuous-time systems with multiple input delays. Control, Automation and Systems (ICCAS), 17th International Conference on. IEEE, pp. 454-459. https://doi.org/10.23919/ICCAS.2017.8204482
Liao Y., Liao F. (2017). Design of preview controller for discrete-time linear systems with time delay by using the lifting-predictor method. Control and Decision, Vol. 32, No. 8, pp. 1359-1367. https://doi.org/10.13195/j.kzyjc.2016.0672
Liao Y., Liao F. (2018). Design of preview controller for linear continuous-time systems with input delay. International Journal of Control, Automation and Systems, Vol. 16, No. 3, pp. 1080-1090. https://doi.org/10.1007/s12555-016-0209-1
Manitius A. Z., Olbrot A. W. (1979). Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, Vol. 24, No. 4, pp. 541-553. https://doi.org/10.1109/tac.1979.1102124
Marzbanrad J., Ahmadi G., Jha R. (2004). Optimal preview active control of structures during earthquakes. Engineering Structures, Vol. 26, No. 10, pp. 1463-1471. https://doi.org/10.1016/j.engstruct.2004.05.010
Marzbanrad J., Hojjat Y., Zohoor H., Nikravesh S. K. (2003). Optimal preview control design of an active suspension based on a full car model. Scientia Iranica, Vol. 10, No. 1, pp. 23-36.
MondiéS., Michiels W. (2003). Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Transactions on Automatic Control, Vol. 48, No. 12, pp. 2207-2212. https://doi.org/10.1109/tac.2003.820147
Sharp R. S. (2007). Optimal preview speed-tracking control for motorcycles. Multibody System Dynamics, Vol. 18, pp. 397-411. https://doi.org/10.1007/s11044-007-9079-x
Shimmyo S., Sato T., Ohnishi K. (2013). Biped walking pattern generation by using preview control based on three-mass model. IEEE Transactions on Industrial Electronics, Vol. 60, No. 11, pp. 5137-5147. https://doi.org/10.1109/tie.2012.2221111