Stability margins of the systems of optimal and modal control. (English. Russian original) Zbl 1145.93376
Autom. Remote Control 68, No. 8, 1296-1308 (2007); translation from Avtom. Telemekh. 2007, No. 8, 4-17 (2007).
Summary: Consideration was given to the systems of \(H _{\infty }\)-suboptimal and modal control and the causes of their small phase and magnitude margins.
MSC:
| 93C73 | Perturbations in control/observation systems |
| 93D99 | Stability of control systems |
| 93B36 | \(H^\infty\)-control |
Keywords:
control systems under parametric perturbations; \(H_\infty\)-suboptimal control; stabilizing controllersReferences:
| [1] | Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002. |
| [2] | Bhattcharyya, S.P., Chapellat, H., and Keel, L.H., Robust Control. The Parametric Approach, New York: Prentice Hall, 1995. · Zbl 0838.93008 |
| [3] | Letov, A.M., Analytical Design of Controllers. I–IV, Avtom. Telemekh., 1960, no. 4, pp. 436–441; no. 5, pp. 561–568; no. 6, pp. 661–665; 1961, no. 4, pp. 425–435. |
| [4] | Kalman, R.E., Contributions to the Theory of Optimal Control, Bullet Soc. Mat. Mech., 1960, vol. 5, no. 1, pp. 102–119. · Zbl 0112.06303 |
| [5] | Anderson, B.D.O. and Moor, J.B., Linear System Optimization with Prescribed Degree of Stability, Proc. Inst. Eng., 1969, vol. 116, no. 2, pp. 100–106. |
| [6] | Aleksandrov, A.G., Frequency Characteristics of the Optimal Linear Control Systems, Avtom. Telemekh., 1969, no. 9, pp. 176–181. |
| [7] | Aleksandrov, A.G., Degree of Robustness of the System with Restorers of Phase Variables, in ”Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1977, no. 2, pp. 105–118. |
| [8] | Doyle, J.C., Guaranteed Margins for LQG-regulators, IEEE Trans. Automat. Control, 1978, vol. AC-23, no. 4, pp. 756–757. · doi:10.1109/TAC.1978.1101812 |
| [9] | Doyle, J.C. and Stein, G., Robustness with Observes, IEEE Trans. Automat. Control, 1979, vol. 24, no. 1, pp. 607–611. · Zbl 0412.93030 · doi:10.1109/TAC.1979.1102095 |
| [10] | Aleksandrov, A.G., Analytical Design of the Controller Transfer Matrices by the Frequency Performance Criteria. I, Avtom. Telemekh., 1971, no. 12, pp. 12–20. |
| [11] | Safonov, M.G. and Athans, M., Gain and Phase Margin for Multi-loop LQG Regulators, IEEE Trans. Automat. Control, 1977, vol. AC-22, no. 2, pp. 173–179. · Zbl 0356.93016 · doi:10.1109/TAC.1977.1101470 |
| [12] | Chestnov, V.N., On Possible Instability of the Controlled Systems and Design of Controllers with Regard for the Parametric Perturbations, in ”Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1984, pp. 26–35. |
| [13] | Aleksandrov, A.G., Degree of Robustness and Frequency Performance of Automatic Control, in ”Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1976, no. 1, pp. 14–26. |
| [14] | Doyle, J.C., Glover, K., Khagonekar, P.P., and Franis, B.A., State-space Solution to Standard H 2 and H Control Problem, IEEE Trans. Automat. Control, 1989, vol. 34, no. 8, pp. 831–846. · Zbl 0698.93031 · doi:10.1109/9.29425 |
| [15] | Aleksandrov, A.G., Robustness Criteria for the Nonstationary Control Systems, in ”Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1980, pp. 3–14. |
| [16] | Aleksandrov, A.G., Analytical Design of the Controller Transfer Matrices by the Frequency Performance Criteria. II, Avtom. Telemekh., 1972, no. 2, pp. 17–29. |
| [17] | Lhentomaki, N.A., Sandell, N.R., and Athans, M., Robustness Results in Linear-quadratic Gaussian Based Multivariable Control Design, IEEE Trans. Automat. Control, 1981, vol. 26, no. 1, pp. 75–92. · Zbl 0459.93024 · doi:10.1109/TAC.1981.1102565 |
| [18] | Aleksandrov, A.G. and Khlebalin, N.A., Analytical Design of Controllers under Incomplete Information about the Parameters of the Controlled Plant, in ”Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1981, pp. 138–147. |
| [19] | Alexandrov, A.G., Guaranteed Stabilized Plant, in Eur. Control Conf. ECC’03, Cambridge, 2003. |
| [20] | Chestnov, V.N., Synthesis of Controllers for Multivariate Systems with a Given Radius of Stability Margin by the H -Optimization Method, Avtom. Telemekh., 1999, no. 7, pp. 100–109. · Zbl 1062.93019 |
| [21] | Agafonov, P.A. and Chestnov, V.N., Simultaneous Maintenance of the Input and Output Stability Margins of the Multivariable Plant Based of the H Approach, Avtom. Telemekh., 2004, no. 9, pp. 110–119. |
| [22] | Keel, L. and Bhattacharyya, S.P., Robust, Fragile, or Optimal?, IEEE Trans. Automat. Control, 1997, vol. 42, no. 8, pp. 1098–1105. · Zbl 0900.93075 · doi:10.1109/9.618239 |
| [23] | Doyle, J.C., Franis, B.A., and Tannenbaum, A.R., Feedback Control Theory, New York: MacMillan, 1992. |
| [24] | Anderson, B.D.O., From Youla-Kucera to Identification, Adaptive and Nonlinear Control, in 13 World Congr. of IFAC, 1996, San Francisco, USA, pp. 39–59. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
