Article
Full entry |
PDF
(1.6 MB)
Feedback
PDF
(1.6 MB)
Feedback
Keywords:
measurement feedback solution; fixed pole
measurement feedback solution; fixed pole
Summary:
This paper is concerned with the flexibility in the closed loop pole location when solving the $H_2$ optimal control problem (also called the $H_2$ optimal disturbance attenuation problem) by proper measurement feedback. It is shown that there exists a precise and unique set of poles which is present in the closed loop system obtained by any measurement feedback solution of the $H_2$ optimal control problem. These “$H_2$ optimal fixed poles” are characterized in geometric as well as structural terms. A procedure to design $H_2$ optimal controllers which simultaneously freely assign all the remaining poles, is also provided.
References:
[1] Basile G., Marro G.: Controlled and Conditioned Invariants in Linear System Theory. Prentice Hall, Englewood Cliffs, N.J. 1992 MR 1149379 | Zbl 0758.93002
[2] Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM Stud. Appl. Math. 15 (1994) MR 1284712 | Zbl 0816.93004
[3] Del-Muro-Cuellar B., Malabre M.: Fixed poles of disturbance rejection by dynamic measurement feddback: a geometric approach. Automatica 37 (2001), 2, 231–238 DOI 10.1016/S0005-1098(00)00157-6 | MR 1832029
[4] Chen B. M., Saberi A., Sannuti, P., Shamash Y.: Construction and parametrization of all static and dynamic ${H}_2$ optimal state feedback solutions, optimal fixed modes, and fixed decoupling zeros. IEEE Trans. Automat. Control 38 (1993), 2, 248–261 DOI 10.1109/9.250513 | MR 1206805
[5] Malabre M., Kučera V.: Infinite structure and exact model matching problem: a geometric approach. IEEE Trans. Automat. Control AC-29 (1984), 3, 266–268 DOI 10.1109/TAC.1984.1103502
[6] Morse A. S.: Output controllability and system synthesis. SIAM J. Control 9 (1971), 2, 143–148 DOI 10.1137/0309012 | MR 0290819 | Zbl 0222.93006
[7] Saberi A., Sannuti, P., Chen B. M.: ${H}_2$ Optimal Control. Prentice Hall, Englewood Cliffs, N.J. 1995
[8] Saberi A., Sannuti, P., Stoorvogel A. A.: ${H}_2$ optimal controllers with measurement feedback for continuous-time systems-flexibility in closed-loop pole placement. Automatica 32 (1996), 8, 1201–1209 MR 1409674 | Zbl 1035.93503
[9] Schumacher J. M.: Compensator synthesis using $(C,A,B)$-pairs. IEEE Trans. Automat. Control AC-25 (1980), 6, 1133–1138 DOI 10.1109/TAC.1980.1102515 | MR 0601495 | Zbl 0483.93035
[10] Stoorvogel A. A.: The singular ${H}_2$ control problem. Automatica 28 (1992), 3, 627–631 DOI 10.1016/0005-1098(92)90189-M | MR 1166033
[11] Stoorvogel A. A., Saberi, A., Chen B. M.: Full and reduced-order observer-based controller design for ${H}_2$-optimization. Internat. J. Control 58 (1993), 4, 803–834 DOI 10.1080/00207179308923030 | MR 1239695
[12] Willems J. C.: Almost invariant subspaces: An approach to high gain feedback design. Part I: Almost controlled invariant subspaces. IEEE Trans. Automat. Control AC-26 (1981), 1, 235–252 DOI 10.1109/TAC.1981.1102551 | MR 0609263 | Zbl 0463.93020
[13] Willems J. C., Commault C.: Disturbance decoupling by measurement feedback with stability or pole placement. SIAM J. Control Optim. 19 (1981), 4, 409–504 DOI 10.1137/0319029 | MR 0618240 | Zbl 0467.93036
[14] Wonham W. M.: Linear Multivariable Control: A Geometric Approach. Third edition. Springer Verlag, New York 1985 MR 0770574 | Zbl 0609.93001
Search
Partner of
