Your browser does not support JavaScript!

Experimental results on implicit and explicit time-discretization of equivalent control-based sliding mode control

Experimental results on implicit and explicit time-discretization of equivalent control-based sliding mode control

For access to this article, please select a purchase option:

Buy chapter PDF
(plus tax if applicable)
Buy Knowledge Pack
10 chapters for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
Recent Trends in Sliding Mode Control — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This chapter presents a set of experimental results concerning the sliding mode control of an electropneumatic system. The controller is implemented via a micro-processor as a discrete-time input. Three discrete-time control strategies are considered for the implementation of the discontinuous part of the sliding mode controller: explicit discretizations with and without saturation, and an implicit discretization (i.e., very easy to implement as a projection on the interval [-1, 1]). While the explicit implementation is known to generate numerical chattering, the implicit one is expected to significantly reduce chattering while keeping the accuracy. The experimental results reported in this work remarkably confirm that the implicit discrete-time sliding mode supersedes the explicit ones with several important features: chattering in the control input is almost eliminated (while the explicit and saturated controllers behave like high-frequency bang-bang inputs), the input magnitude depends only on the perturbation size and is “independent” of the controller gain and sampling time. On the contrary the explicit controller shows obvious chattering for all sampling times, its magnitude increases as the controller gain increases, and it does not reduce when the sampling period augments. The tracking errors are comparable for both methods, though the implicit method keeps the precision when the control gain increases, which is not the case for the explicit one. Introducing a saturation in the explicit controller does not allow to significantly improve the explicit controller behavior if one does not take care of the saturation width.

Chapter Contents:

  • Abstract
  • 3.2.1 Introduction
  • Explicit versus implicit discrete sliding mode control
  • 3.2.2 Dynamics of the plant and controllers
  • Implicit controller design
  • Plant dynamics and controllers
  • 3.2.3 Experimental results
  • Comparison of the tracking errors e
  • Comparison of control inputs u (3.2.21) and v (3.2.24), (3.2.25), and (3.2.27)
  • Summary
  • 3.2.4 Numerical analysis of the saturation controller
  • 3.2.5 Conclusion
  • Appendix 1 Some basic convex analysis tools
  • Acknowledgments
  • References

Inspec keywords: variable structure systems; numerical analysis; discrete time systems; electropneumatic control equipment

Other keywords: discrete-time sliding mode; electropneumatic system; saturation width; explicit time-discretization; tracking errors; discrete-time input; implicit time-discretization; controller gain; discrete-time control strategies; equivalent control-based sliding mode control; microprocessor; numerical chattering; explicit controller behavior

Subjects: Other numerical methods; Discrete control systems; Electrohydraulic and electropneumatic control equipment; Multivariable control systems

Preview this chapter:
Zoom in

Experimental results on implicit and explicit time-discretization of equivalent control-based sliding mode control, Page 1 of 2

| /docserver/preview/fulltext/books/ce/pbce102e/PBCE102E_ch3.2-1.gif /docserver/preview/fulltext/books/ce/pbce102e/PBCE102E_ch3.2-2.gif

Related content

This is a required field
Please enter a valid email address