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Controllers of a Given Radius of Stability Margin: Their Design by the H ∞-approach with Regard for External Disturbances

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Abstract

Output controllers for multivariate linear systems are designed such that they ensure, besides a given radius of stability margin for the physical input or output of the controlled object, a given radius of steady state characterized by the operation accuracy of a closed-loop system for adjusted variables. This design problem is reduced to a special H ∞-optimization problem and the result is purely of sufficient type. It is solved numerically in the state space by the linear matrix inequalities method of MATLAB.

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REFERENCES

  1. Doyle, J.C. and Stein, G., Multivariable Feedback Design: Concepts for a Classical/Modern Synthesis, IEEE Trans. Automat. Control, 1981, vol. 26, no. 1, pp. 4–16.

    Google Scholar 

  2. Aleksandrov, A.G., Sintez regulyatorov mnogomernykh system (Design of Controllers for Multivariate Systems), Moscow: Mashinostroenie, 1986.

    Google Scholar 

  3. Lehtomaki, N.A., Sandell, N.R., and Athans, M., Robustness Results in Linear-Quadratic Gaussian Based Multivariable Control Designs, IEEE Trans. Automat. Control, 1981, vol. 26, no. 1, pp. 75–92.

    Google Scholar 

  4. Aleksandrov, A.G., A Direct Analytical Method of Controller Design. Incomplete Observability Degree, Izv. Vuzov SSSR, Priborostroenie, 1978, no. 11, pp. 34–39.

  5. Doyle, J.C. and Stein, G., Robustness with Observers, IEEE Trans. Automat. Control, 1979, vol. 24, no. 1, pp. 607–611.

    Google Scholar 

  6. Stein, G. and Athans, M., The LQG/LTR Procedure for Multivariable Feedback Control Design, IEEE Trans. Automat. Control, 1987, vol. 32, no. 2, pp. 105–114.

    Google Scholar 

  7. Li, X. and Lee, E.B., Stability Robustness Characterization and Related Issues for Control Systems Design, Automatica, 1993, vol. 29, no. 2, pp. 479–484.

    Google Scholar 

  8. Keel, L.H. and Bhattacharya, S.P., Robust, Fragile, or Optimal? IEEE Trans. Automat. Control, 1997, vol. 42, no. 8, pp. 1098–1105.

    Google Scholar 

  9. Chestnov, V.N., Design of Controllers for Multivariate Systems for a Given Radius of Stability Margin by the H Optimization Procedure, Avtom. Telemekh., 1999, no. 7, pp. 100–109.

  10. Aleksandrov, A.G. and Chestnov, V.N., Design of Multivariate Systems of a Given Accuracy. I. Application of LQ-Optimization Procedures, Avtom. Telemekh., 1998, no. 7, pp. 83–95.

  11. Aleksandrov, A.G. and Chestnov, V.N., Design of Multivariate Systems of a Given Accuracy. II. Application of H 1-Optimization Procedures, Avtom. Telemekh., 1998, no. 8, pp. 124–138.

  12. Chestnov, V.N. and Agafonov, P.A., H 1-Control for Guaranteed Simultaneous Input and Output Stability Margins for a Multivariate System, Avtom. Telemekh., 2003, no. 9, pp. 110–119.

  13. Chestnov, V.N., Design of Multivariate Systems of a Given Accuracy by the Mean-Square Criterion, Avtom. Telemekh., 1998, no. 12, pp. 109–117.

  14. Boyd, S., Chaoui, L.E., Feron, E., and Balakrishnan, V., Linear Matrix Inequality in System and Control Theory, Philadelphia: SIAM, 1994.

    Google Scholar 

  15. Gahinet, P., Nemirovski, A., and Laub, A., LMI Control Toolbox. User's Guide, Massachusetts: Math works, 1995.

    Google Scholar 

  16. Chestnov, V.N., Agafonov, P.A., and Galkin, A.S., Design of Multivariate Systems of a Given RaDius of Stability Margin with Regard for Outer Disturbances, Tezisy doklada VII mezhdynar. Seminara "Ustoichivost' i kolebaniya nelineinykh sistem upravleniya" (Abst. VII Int. Seminar on Stability and Oscillation of Nonlinear Control Systems), Moscow, 2002, pp. 161, 162.

  17. — The Control Handbook, Levine, W.S., Ed., New York: IEEE Press, 1996.

    Google Scholar 

  18. Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A., State-Space Solution to Standard and H Control Problems, IEEE Trans. Automat. Control, 1989, vol. 34, no. 8, pp. 831–846.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Steel and Alloys, Moscow, Russia

    P. A. Agafonov

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    V. N. Chestnov

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  1. P. A. Agafonov
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  2. V. N. Chestnov
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Agafonov, P.A., Chestnov, V.N. Controllers of a Given Radius of Stability Margin: Their Design by the H ∞-approach with Regard for External Disturbances. Automation and Remote Control 65, 1611–1617 (2004). https://doi.org/10.1023/B:AURC.0000044270.56172.9d

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  • DOI: https://doi.org/10.1023/B:AURC.0000044270.56172.9d

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