Abstract
In this paper, we study the problem of state and control signal constraints in discrete-time sliding mode control. We introduce a sufficient condition for finite time convergence of the representative point to the sliding hyperplane, while respecting imposed restrictions. We propose a new control strategy based on the reaching law approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
1. Bartolini G., Ferrara A., Utkin V. I.: Adaptive sliding mode control in discrete-time systems. Automatica, 31, 769–773 (1995)
2. Bartoszewicz A.: Discrete-time quasi-sliding-mode control strategies. IEEE Trans. Ind. Electron., 45, 633–637 (1998)
3. Bartoszewicz A., Latosiński P.: Discrete time sliding mode control with reduced switching a new reaching law approach. Intern. Jour. Robust Nonlinear Control, 26, 47–68 (2016)
4. Bartoszewicz, A., Leśniewski, P.: Reaching law approach to the sliding mode control of periodic review inventory systems. IEEE Trans. Autom. Sci. Eng., 11, 810–817 (2014)
5. Bartoszewicz A., Leśniewski P.: Reaching law based sliding mode congestion control for communication networks. IET Control Theory Appl., 8, 1914–1920 (2014)
6. Bartoszewicz A., Leśniewski P.: New switching and nonswitching type reaching laws for SMC of discrete time systems. IEEE Trans. Control Syst. Technol., 24, 670–677 (2016)
7. Bartoszewicz A., Nowacka A.: Switching plane design for the sliding mode control of systems with elastic input constraints. Proceedings of institution of mechanical engineers, part I. Jour. Syst. Control Eng., 219, 393–403 (2005)
8. Bartoszewicz A., Nowacka A.: Reaching phase elimination in variable structure control of the third order system with state constraints. Kybernetika, 42, 111–126 (2006)
9. Bartoszewicz A., Nowacka-Leverton A.: ITAE optimal sliding modes for third order systems with input signal and state constraints. IEEE Trans. Autom. Control, 55, 1928–1932 (2010)
10. Chakrabarty S., Bandyopadhyay B.: A generalized reaching law for discrete sliding mode control. Automatica, 52, 83–86 (2015)
11. Chakrabarty S., Bandyopadhyay B.: A generalized reaching law with different convergence rates. Automatica, 63, 34–37 (2016)
12. Emelyanov S. V.: Variable structure control system. Nauka, Moscow (1967)
13. Fallaha C.J., Saad M., Kanaan H.Y., Al-Haddad K.: Sliding-mode robot control with exponential reaching law. IEEE Trans. Ind. Electron., 58, 600–610 (2011)
14. Furuta K.: Sliding mode control of a discrete system. Syst. Control Lett., 14, 145–152 (1990)
15. Gao W., Hung J. C.: Variable structure control of nonlinear systems: A new approach. IEEE Trans. Ind. Electron., 40, 45–55 (1993)
16. Gao W., Wang Y., Homaifa A.: Discrete-time variable structure control systems. IEEE Trans. Ind. Electron., 42, 117–122 (1995)
17. Golo G., Milosavljević Č.: Robust discrete-time chattering free sliding mode control. Syst. Control Lett., 41, 19–28 (2000)
18. Milosavljević Č.: General conditions for the existence of a quasisliding mode on the switching hyperplane in discrete variable structure systems. Autom. Remote Control, 46, 307–314 (1985)
19. Niu Y., Ho D. W. C., Wang Z.: Improved sliding mode control for discrete-time systems via reaching law. IET Control Theory and Appl., 4, 2245–2251 (2010)
20. Qu S., Xia X., Zhang J.: Dynamics of discrete-time sliding-mode-control uncertain systems with a disturbance compensator. IEEE Trans. Ind. Electron., 61, 3502–3510 (2014)
21. Utkin V. I.: Variable structure systems with sliding modes. IEEE Trans. Autom. Control, 22, 212–222 (1977)
22. Utkin V. I., Drakunow S. V.: On discrete-time sliding mode control. IFAC Conf. Nonlinear Control, 484–489 (1989)
23. Veselić B., Peruničić-Draženović B., Milosavljević Č.: Improved discrete-time sliding-mode position control using Euler velocity estimation. IEEE Trans. Ind. Electron., 57, 3840–3847 (2010)
24. Wang A., Jia X., Dong S.: A new exponential reaching law of sliding mode control to improve performance of permanent magnet synchronous motor. IEEE Trans. Magn., 49, 2409–2412 (2013)
25. Zhang X., Sun L., Zhao K., Sun L.: Nonlinear speed control for PMSM system using sliding-mode control and disturbance compensation techniques. IEEE Trans. Power Electron., 28, 1358–1365 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Pietrala, M., Jaskuła, M., Leśniewski, P., Bartoszewicz, A. (2017). Sliding Mode Control of Discrete Time Dynamical Systems with State Constraints. In: Mitkowski, W., Kacprzyk, J., Oprzędkiewicz, K., Skruch, P. (eds) Trends in Advanced Intelligent Control, Optimization and Automation. KKA 2017. Advances in Intelligent Systems and Computing, vol 577. Springer, Cham. https://doi.org/10.1007/978-3-319-60699-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-60699-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60698-9
Online ISBN: 978-3-319-60699-6
eBook Packages: EngineeringEngineering (R0)