0
Technical Brief

Multirate Output Feedback Based Stochastic Sliding Mode Control

[+] Author and Article Information
A. J. Mehta

Associate Professor
Department of Electrical Engineering,
Institute of Infrastructure Technology
Research and Management,
Ahmedabad 380026, Gujarat, India
e-mail: draxaymehta@gmail.com

B. Bandyopadhyay

Chair Professor
Systems and Control Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, India
e-mail: bijnan@ee.iitb.ac.in

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 20, 2015; final manuscript received June 13, 2016; published online August 11, 2016. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 138(12), 124503 (Aug 11, 2016) (6 pages) Paper No: DS-15-1386; doi: 10.1115/1.4033947 History: Received August 20, 2015; Revised June 13, 2016

In this paper, a multirate output feedback (MROF) based discrete-time sliding mode control for the stochastic system with slowly varying bounded uncertainty is proposed. The states are estimated by the multirate Kalman filter and are used for designing the stochastic sliding mode controller which guarantee the stability under the bounded uncertainty and the uncertain noise covariance. The proposed algorithm has advantage of computational and implementation simplicity as it requires only the past output and input information. The stochastic sliding band (SSB) is also calculated which is found to be wider as compared to the state feedback case. Finally, the design procedure for stochastic sliding mode controller is demonstrated with an illustrative example.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Utkin, V. I. , 1977, “ Variable Structure Systems With Sliding Mode,” IEEE Trans. Autom. Control, 22(2), pp. 212–222. [CrossRef]
Utkin, V. I. , 1992, Sliding Modes in Control Optimization, Springer-Verlag, New York.
Hung, J. Y. , Gao, W. , and Hung, J. C. , 1993, “ Variable Structure Control: A Survey,” IEEE Trans. Ind. Electron., 40(1), pp. 2–22. [CrossRef]
Edwards, C. , and Spurgeon, S. K. , 1998, Sliding Mode Control: Theory and Applications, Taylor and Francis, London, UK.
Young, K. D. , Utkin, V. I. , and Ozguner, U. , 1999, “ A Control Engineer's Guide to Sliding Mode Control,” IEEE Trans. Control Syst. Technol., 7(3), pp. 328–342. [CrossRef]
Milosavljevic, C. , 1985, “ General Conditions for the Existence of Quasi Sliding Mode on the Switching Hyperplane in Discrete Variable Structure Systems,” Autom. Remote Control, 46, pp. 307–314.
Sarpturk, S. Z. , Istefanopulos, Y. , and Kaynak, O. , 1987, “ On the Stability of Discrete-Time Sliding Mode Control Systems,” IEEE Trans. Control Systems, 32(10), pp. 930–932.
Gao, W. , Wang, Y. , and Homaifa, A. , 1995, “ Discrete-Time Variable Structure Control System,” IEEE Trans. Ind. Electron., 42(2), pp. 117–122. [CrossRef]
Bartoszewicz, A. , 1995, “ A Comment on a ‘Time-Varying Sliding Surface for Fast and Robust Tracking Control of Second-Order Uncertain Systems',” Automatica, 31(12), pp. 1893–1895. [CrossRef]
Bartoszewicz, A. , 1998, “ Discrete-Time Quasi Sliding Mode Control Strategies,” IEEE Trans. Ind. Electron., 45(4), pp. 633–637. [CrossRef]
Bartoszewicz, A. , and Nowacka-Leverton, A. , 2009, Time-Varying Sliding Modes for Second and Third Order Systems, Springer–Verlag, Berlin/Heidelberg.
Kranc, G. M. , 1957, “ Input-Output Analysis of Multi-Rate Feedback System,” IRE Trans. Autom. Control, 3(1), pp. 21–28. [CrossRef]
Jury, E. , 1967, “ A Note on Multirate Sampled-Data Systems,” IRE Trans. Autom. Control, 12(3), pp. 319–320. [CrossRef]
Hagiwara, T. , and Araki, M. , 1988, “ Design of a Stable State Feedback Controller Based on the Multi-Rate Sampling of Plant Output,” IEEE Trans. Autom. Control, 33(9), pp. 812–819. [CrossRef]
Colaneri, P. , Scattolini, R. , and Schiavoni, N. , 1990, “ Stabilization of Multi-Rate Sampled-Data Linear Systems,” Automatica, 26(2), pp. 377–380. [CrossRef]
Werner, H. , and Furuta, K. , 1995, “ Simultaneous Stabilization by Piecewise Constant Periodic Output Feedback,” Control Theory Adv. Technol., 10(4), pp. 1763–1775.
Werner, H. , 1998, “ Multimodel Robust Control by Fast Output Sampling—An LMI Approach,” Automatica, 34(12), pp. 1625–1630. [CrossRef]
Janardhanan, S. , and Bandyopadhyay, B. , 2006, “ Output Feedback Sliding Mode Control for Uncertain Systems Using Fast Output Sampling Technique,” IEEE Trans. Ind. Electron., 53(5), pp. 1677–1682. [CrossRef]
Janardhanan, S. , and Bandyopadhyay, B. , 2007, “ Multirate Output Feedback Based Robust Quasi-Sliding Mode Control of Discrete-Time Systems,” IEEE Trans. Autom. Control, 52(3), pp. 499–503. [CrossRef]
Mehta, A. , and Bandyopadhyay, B. , 2006, “ Multirate Output Feedback Based Frequency Shaped Sliding Mode Control,” IEEE International Conference on Industrial Technology (ICIT2006), pp. 2658–2662.
Mehta, A. , and Bandyopadhyay, B. , 2009, “ Frequency Shaped Sliding Mode Control Using Output Sampled Measurements,” IEEE Trans. Ind. Electron., 56(1), pp. 28–35. [CrossRef]
Mehta, A. , and Bandyopadhyay, B. , 2010, “ The Design and Implementation of Output Feedback Based Frequency Shaped Sliding Mode Controller for the Smart Structure,” 2010 IEEE Symposium on Industrial Electronics (ISIE2010), Bari, Italy, July 4–7, pp. 353–358.
Mehta, A. , and Bandyopadhyay, B. , 2015, Frequency Shaped and Observer Based Discrete-Time Sliding Mode Control, Springer, Heidelberg, Germany.
Shah, D. , and Mehta, A. , 2015, “ Output Feedback Discrete-Time Networked Sliding Mode Control,” International Workshop on Recent Advances in Sliding Modes (RASM2015), Istanbul, Turkey, Apr. 9–11, pp. 1–7.
Yaz, E. , and Azemi, A. , 1993, “ Sliding Mode Observer for Nonlinear Models With Unbounded Noise and Measurement Uncertainties,” Dyn. Control, 3(3), pp. 217–235. [CrossRef]
Yaz, E. , and Azemi, A. , 1993, “ Variable Structure Observer With a Boundary Layer for Correlated Noise/Disturbance Models and Disturbance Minimization,” Int. J. Control, 57(5), pp. 1191–1206. [CrossRef]
Zeng, F. , Cheng, M. , and Gao, W.-B. , 1994, “ Variable Structure Control of Stochastic System,” Syst. Control Lett., 22(3), pp. 209–222. [CrossRef]
Er, M. J. , and Anderson, B. D. O. , 1992, “ Performance Study of Multi-Rate Output Controllers Under Noise Disturbance,” Int. J. Control, 56(3), pp. 531–545. [CrossRef]
Drazenovic, B. , 1969, “ The Invariance Conditions in Variable Structure Systems,” Automatica, 5(3), pp. 287–295. [CrossRef]
Kwakernaak, H. , and Sivan, R. , 1972, Linear Optimal Control Systems, Wiley Interscience, New York.
Sangsuk-Iam, S. , and Bullock, T. E. , 1990, “ Analysis of Discrete-time Kalman Filtering Under Incorrect Noise Covariances,” IEEE Trans. Autom. Control, 35(12), pp. 531–545. [CrossRef]
Su, W. C. , Drakuunov, S. V. , and Ozguner, U. , 2000, “ An O(T2) Boundary Layer in Sliding Mode for Sampled-Data Systems,” IEEE Trans. Autom. Control, 45(3), pp. 482–485. [CrossRef]
Kennedy, W. J. , and Gentle, J. F. , 1980, Statistical Computing, Dekker, New York.

Figures

Grahic Jump Location
Fig. 1

Response for (a) state x1(k) and its estimation x̂1(k), (b) state x2(k) and its estimation x̂2(k), (c) control input u(k), and (d) sliding variable s(k)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In