Journal of Optimization Theory and Applications

, Volume 59, Issue 2, pp 183–207 | Cite as

Dynamically similar control systems and a globally minimum gain control technique: IMSC

Contributed Papers

Abstract

The concept of dynamically similar control systems is introduced. The necessary and sufficient conditions to minimize a quadratic modal gain measure are given for dynamically similar closed-loop control systems. The globally minimum modal gain is obtained when the independent modal space control (IMSC) is used. Corollaries of the results for the control of infinite-dimensional structural distributed parameter systems (DPS) are given. Based on the results, a modal interaction parameter (MIP) is defined for all control systems. The minimum value of MIP is zero and uniquely corresponds to the IMSC. A nonzero value of MIP corresponds to all other coupled control (CC) designs and implies suboptimality relative to the IMSC design. The relative optimality of the real-space gain matrices of the IMSC and the CC designs depends on the actuator locations for the IMSC. Based on this, a real-space interaction parameter (RIP) is defined. A positive value of RIP renders IMSC optimal in its real-space gain matrix. The MIP and RIP are indications of suboptimality of a particular control technique and can be used to tune-up the control design via actuator locations. Actuator distribution criteria are suggested for both CC and IMSC designs, based on the values of MIP and RIP, respectively.

Key Words

Distributed parameter system control modal control control gain optimization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Meirovitch, L., andÖz, H.,Modal-Space Control of Distributed Gyroscopic Systems, Journal of Guidance, Control and Dynamics, Vol. 3, No. 2, pp. 140–150, 1980.Google Scholar
  2. 2.
    Meirovitch, L., Baruh, H., andÖz, H.,A Comparison of Control Techniques for Large Flexible Systems, Journal of Guidance, Control, and Dynamics, Vol. 6, No. 4, pp. 302–310, 1983.Google Scholar
  3. 3.
    Meirovitch, L., andBaruh, H.,Control of Self-Adjoint Distributed Parameter Systems, Journal of Guidance, Control, and Dynamics, Vol. 5, No. 1, pp. 60–66, 1982.Google Scholar
  4. 4.
    Öz, H., andMeirovitch, L.,Stochastic Independent Modal-Space Control of Distributed Parameter Systems, Journal of Optimization Theory and Applications, Vol. 40, No. 1, pp. 121–154, 1983.Google Scholar
  5. 5.
    Meirovitch, L., andBaruh, H.,On the Problem of Observation Spillover in Distributed Parameter Systems, Journal of Optimization Theory and Applications, Vol. 39, No. 2, pp. 611–620, 1981.Google Scholar
  6. 6.
    Balas, M. J.,Active Control of Flexible Systems, Journal of Optimization Theory and Applications, Vol. 25, No. 3, pp. 415–536, 1978.Google Scholar
  7. 7.
    Meirovitch, L., andBenninghof, J. K.,Control of Traveling Waves in Flexible Structures, Proceedings of 4th VPI/AIAA Symposium on Dynamics and Control of Large Structures, Blacksburg, Virginia, 1980.Google Scholar
  8. 8.
    Meirovitch, L., Baruh, H., Montgomery, R. C., andWilliams, J. P.,Nonlinear Natural Control of an Experimental Beam, Journal of Guidance, Control, and Dynamics, Vol. 7, No. 4, pp. 437–442, 1984.Google Scholar
  9. 9.
    Hallauer, W. L., Skidmore, G. R., andMesquita, L. L.,Experimental-Theoretical Study of Active Vibration Control, Proceedings of the International Modal Analysis Conference, Orlando, Florida, pp. 39–45, 1982.Google Scholar
  10. 10.
    Baruh, H., andSilverberg, L.,Robust Natural Control of Distributed Systems, Journal of Guidance, Control, and Dynamics, Vol. 8, No. 6, pp. 717–724, 1985.Google Scholar
  11. 11.
    Lindberg, R. E., andLongman, R. W.,On the Number and Placement of Actuators for Independent Modal-Space Control, Paper No. 82-1436, AIAA/AAS Astrodynamics Conference, Gatlinburg, Tennessee, 1982.Google Scholar
  12. 12.
    Öz, H.,A New Concept of Optimality for Control of Flexible Structures, Ohio State University, Aeronautical and Astronautical Engineering Research Report in Dynamics Control, No. AAE-RR-DC-101-1988.Google Scholar
  13. 13.
    Meirovitch, L., andSilverberg, L.,Globally Optimal Control of Self-Adjoint Distributed Systems, Optimal Control Applications and Methods, Vol. 4, pp. 365–386, 1983.Google Scholar
  14. 14.
    Chen, C. T.,Linear System Theory and Design, Holt, Rinehart, and Winston, New York, New York, 1984.Google Scholar
  15. 15.
    Öz, H., Farag, K., andVenkayya, V. B., Efficiency of Structure-Control Systems, Journal of Guidance, Control, and Dynamics (to appear).Google Scholar
  16. 16.
    Dorny, N.,A Vector Space Approach to Models and Optimization. John Wiley and Sons, New York, New York, 1975.Google Scholar
  17. 17.
    Luenberger, D.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • H. Öz
    • 1
  1. 1.Department of Aeronautical and Astronautical EngineeringOhio State UniversityColumbus

Personalised recommendations