H∞ Phase Control for Flexible Systems
A new weighted H∞ optimization method is proposed to design a robust controller for the flexible system, it solves the problem that the controller is unstable and poor robustness which using H∞ loop shaping method design. The idea of phase control is realized by the configuration of the closed-loop poles which corresponding to the flexible modes, and the closed-loop poles of the high-frequency parts are allowed to differ from the expected poles and weakening the strict positive real constraints. Combined with the phase control and H∞ optimization, the desired closed-loop poles can be realized by the controller. The new method has the advantage of flexibility, and a clear physical meaning in the design process. The feasibility of the proposed method is verified by two simulation examples.
KeywordsFlexible systems Phase control H∞ optimization Robustness Local positivity
Manuscript received April 7, 2018. This work was supported in part by the Doctoral Foundation of Liaoning Province (No. 20170520333), the Fundamental Research Funds for the Central Universities(No. N182304010), the Doctoral Foundation of Hebei Province (No. F2019501012).
- 2.Si, Z., Liu, Y.: High accuracy and high stability attitude control of a satellite with a rotating solar array. J. Astronaut. 31(12), 2697–2073 (2010)Google Scholar
- 3.Wu, Y., Li, J., Zeng, H., Duan, G.: Robust H-infinity control design for spacecrafts with large flexible netted antennas. Control Theory Appl. 30(3), 365–371 (2013)Google Scholar
- 8.McFarlaned, D., Glover, K.: Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Lecture Notes in Control and Information Sciences, 138. Springer, New York (1989)Google Scholar
- 9.Sun, X., Yang, X., Geng, Y., Yang, D.: H∞ loop-shaping attitude stabilization control fora large flexible satellite platform. Syst. Eng. Electron. 27(3), 490–493 (2005)Google Scholar
- 11.Glover, K., McFarlane, D.: Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Lecture Notes in Control and Information Sciences, vol. 138. Springer, New York (1990)Google Scholar
- 14.He, Z., Jiang, X., Meng, F.-W., Wang, G.: μ-synthesis in H-infinity loop-shaping design. Control Theory Appl. 29(3), 347–352 (2012)Google Scholar
- 15.Meng, F.-W., He, Z., Wang, G., Zhou, D.: Control design of flexible systems and H-infinity loop-shaping method. Control Theory Appl. 30(8), 1014–1020 (2013)Google Scholar
- 16.Franklin, G.F., Powell, J.D., Abbas, E.N.: Feedback Control of Dynamic Systems (4th edn). Pearson Education, Beijing (2003)Google Scholar
- 17.Doyle, J.C., Francis, B.A., Tannenbaum, A.R.: Feedback Control Theory, 208–213. Tsinghua University Press, Beijing (1993)Google Scholar
- 20.Guangxiong, W.A.N.G., Zhen, H.E.: Applied H∞ Control. Harbin Institute of Technology Press, Harbin (2010)Google Scholar