Skip to main content

On establishing classic performance measures for reset control systems

  • Conference paper
  • First Online:
Book cover Perspectives in robust control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 268))

Abstract

Reset controllers are linear controllers that reset some of their states to zero when their inputs reach a threshold. We are interested in their feedback connection with linear plants, and in this context, the objective of this paper is twofold. First, to motivate the use of reset control through theory, simulations and experiments, and secondly, to summarize some of our recent results which establish classic performance properties ranging from quadratic and BIBO stability to steady-state and transient performance.

This material is based upon work supported by the National Science Foundation under Grant No.CMS-9800612.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Horowitz I.M., Synthesis of Feedback Systems, Academic Press, New York, 1963.

    MATH  Google Scholar 

  2. Beker O., Hollot C.V. and Chait Y., “Plant with Integrator: An Example of Reset Control Overcoming Limitations of Linear Feedback,” ECE Department Technical Note #ECE07.13.2000, University of Massachusetts Amherst, also submitted to IEEE Transactions on Automatic Control, 2000.

    Google Scholar 

  3. Horowitz I.M. and Rosenbaum P., “Nonlinear Design for Cost of Feedback Reduction in Systems with Large Parameter Uncertainty,” International Journal of Control, Vol. 24, No. 6, pp. 977–1001, 1975.

    Article  Google Scholar 

  4. Zheng Y., Theory and Practical Considerations in Reset Control Design, Ph.D. Dissertation, University of Massachusetts, Amherst, 1998.

    Google Scholar 

  5. Zheng Y., Chait Y., Hollot C.V., Steinbuch M. and Norg M., “Experimental Demonstration of Reset Control Design,” IFAC Journal of Control Engineering Practice, Vol. 8, No. 2, pp. 113–120, 2000.

    Article  Google Scholar 

  6. Clegg J.C., “A Nonlinear Integrator for Servomechanism,” AIEE Transactions Part II, Application and Industry, Vol. 77, pp. 41–42, 1958.

    Google Scholar 

  7. Tsypkin Y.Z., Relay Control Systems, Cambridge University Press, Cambridge, UK, 1984.

    MATH  Google Scholar 

  8. Decarlo R.A., “Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial,” IEEE Proceedings, Vol. 76, No. 3, pp. 212–232, 1988.

    Article  Google Scholar 

  9. Branicky M.S., “Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems,” IEEE Transactions on Automatic Control, Vol. 43, pp. 475–482, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  10. Bainov D.D. and Simeonov P.S., Systems with Impulse Effect: Stability, Theory and Application, Halsted Press, New York, 1989.

    Google Scholar 

  11. Haddad W.M., Chellaboina V. and Kablar N.A., “Nonlinear Impulsive Dynamical Systems Part I: Stability and Dissipativity,” Proceedings of Conference on Decision and Control, pp. 4404–4422, Phoenix, AZ, 1999.

    Google Scholar 

  12. Singer N.C. and Seering W.P., “Preshaping Command Inputs to Reduce System Vibration,” Transactions of the ASME, Vol. 76, No. 3, pp. 76–82, 1990.

    Google Scholar 

  13. Bobrow J.E., Jabbari F. and Thai K., “An Active Truss Element and Control Law for Vibration Suppression,” Smart Materials and Structures, Vol. 4., pp. 264–269, 1995.

    Article  Google Scholar 

  14. Bupp R.T., Bernstein D.S., Chellaboina V. and Haddad W.M., “Resetting Virtual Absorbers for Vibration Control,” Proceedings of the American Control Conference, pp. 2647–2651, Albuquerque, NM, 1997.

    Google Scholar 

  15. Haddad W.M., Chellaboina V. and Kablar N.A., “Active Control of Combustion Instabilities via Hybrid Resetting Controllers,” Proceedings of the American Control Conference, pp. 2378–2382, Chicago, IL, 2000.

    Google Scholar 

  16. Hu H., Zheng Y., Chait Y. and Hollot C.V., “On the Zero-Input Stability of Control Systems Having Clegg Integrators,” Proceedings of the American Control Conference, pp. 408–410, Albuquerque, NM, 1997.

    Google Scholar 

  17. Beker O., Hollot C.V., Chen Q. and Chait Y., “Stability of A Reset Control System Under Constant Inputs,” Proceedings of the American Control Conference, pp. 3044–3045, San Diego, CA, 1999.

    Google Scholar 

  18. Chen Q., Hollot C.V., Chait Y. and Beker O., “On Reset Control Systems with Second-Order Plants,” Proceedings of the American Control Conference, pp. 205–209, Chicago, IL, 2000.

    Google Scholar 

  19. Chen Q., Reset Control Systems: Stability, Performance and Application, Ph.D. Dissertation, University of Massachusetts, Amherst, 2000.

    Google Scholar 

  20. Chen Q., Hollot C.V. and Chait Y., “BIBO Stability of a Class of Reset Control Systems,” Proceedings of the 2000 Conference on Information Sciences and Systems, p. TP8-39, Princeton, NJ, 2000.

    Google Scholar 

  21. Middleton R.H., “Trade-offs in Linear Control System Design,” Automatica, Vol. 27, No. 2, pp. 281–292, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  22. dSPACE Experiment Guide, dSPACE Inc., Paderborn, Germany, 1999.

    Google Scholar 

  23. Ye H., Michel A.N. and Hou L., “Stability Analysis of Systems with Impulse Effects,” IEEE Transactions on Automatic Control, Vol. 43, No. 12, pp. 1719–1723, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  24. Slotine J-J.E. and Li W., Applied Nonlinear Control, Prentice-Hall, New Jersey, 1991.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

S.O. Reza Moheimani BSc, MengSc, PhD

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London Limited

About this paper

Cite this paper

Hollot, C.V., Beker, O., Chait, Y., Chen, Q. (2001). On establishing classic performance measures for reset control systems. In: Moheimani, S.R. (eds) Perspectives in robust control. Lecture Notes in Control and Information Sciences, vol 268. Springer, London. https://doi.org/10.1007/BFb0110618

Download citation

  • DOI: https://doi.org/10.1007/BFb0110618

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-452-9

  • Online ISBN: 978-1-84628-576-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics