Robust H∞ Static Output Feedback Control with Actuator Saturation
Publication: Journal of Engineering Mechanics
Volume 125, Issue 2
Abstract
There are several key issues to be considered in the design of active control systems for civil structures, including robustness to pertubations of the structural parameters stability in the presence of nonlinear actuator saturation effects, and the use of output feedback methods when it is either impossible or impractical to obtain the full state of the system. This research presents a design algorithm to create robust H∞ static output feedback controllers for seismically excited civil structures, which account for all these effects in a single design. Robust static acceleration feedback H∞ controllers are created for a five-story structure with a bounded, structural parameter uncertainty model. A nonconvex optimization problem is formulated and solved using an iterative solution method to obtain the desired control gains. A primary advantage of this method is that an intuitive, feasible starting point is available using the open loop (uncontrolled) system and the worst case attenuation constant for the uncertain system. Simulation results using seismic excitations show controllers obtained using this design method to be effective with minimal control effort.
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References
1.
Boyd, S. P., el Ghaoui, L., Feron, E., and Balakrishnan, V. ( 1994). “Linear matrix inequalities in system and control theory.” Studies in applied mathematics, Vol. 15, SIAM, Philadelphia, Pa.
2.
Chase, J. G., and Smith, H. A. (1996). “Robust H∞ control considering actuator saturation. I: Theory.”J. Engrg. Mech., ASCE, 122(10), 976–983.
3.
Chase, J. G., Smith, H. A., and Suzuki, T. (1996). “Robust H∞ control considering actuator saturation. II: Applications.”J. Engrg. Mech., ASCE, 122(10), 984–993.
4.
Dyke, S. J., Spencer, B. F., Quast, P., and Sain, M. K. (1995). “Role of control-structure interaction in protective system design.”J. Engrg. Mech., ASCE, 121(2), 322–338.
5.
Dyke, S. J., Spencer, B. F., Quast, P., Sain, M. K., Kaspari, D. C., and Soong, T. T. (1996). “Acceleration feedback control of MDOF structures.”J. Engrg. Mech., ASCE, 122(9), 907–917.
6.
Glover, K., and Doyle, J. C. ( 1988). “State-space formulae for all stabilizing controllers that satisfy an H∞ norm bound and relations to risk sensitivity.” Systems and Control Letters, 11, 167–172.
7.
Gu, G., and Misra, P. ( 1994). “Disturbance attenuation and H∞ optimization with linear output feedback control.” J. Guidance, Control, and Dyn., 17(1), 145–152.
8.
Hausner, G. W., et al. (1997). “Structural control: past, present, and future.”J. Engrg. Mech., ASCE, 123(9), 897–971.
9.
Jabbari, F., Schmitendorf, W. E., and Yang, J. N. (1995). “H∞ control for seismic excited buildings with acceleration feedback.”J. Engrg. Mech., ASCE, 121(9), 994–1001.
10.
Kose, I. E., Schmitendorf, W. E., Jabbari, F., and Yang, J. N. (1996). “H∞ active seismic response control using static output feedback.”J. Engrg. Mech., ASCE, 122(7), 651–659.
11.
Peres, P. L. D., Geromel, J. C., and Souza, S. R. ( 1993). “H∞ robust control by static output feedback.” Proc., 1993 Am. Control Conf., American Automatic Control Conference, Evanston, Ill., 620–621.
12.
Savkin, A. V., and Petersen, I. R. ( 1994). “Robust H∞ control of uncertain linear systems with structured uncertainty.” Proc., 1994 Am. Control Conf., American Automatic Control Conference, Evanston, Ill., 3176–3177.
13.
Skelton, R. E., Stroustrup, J., and Iwasaki, T. ( 1994). “The H∞ control problem using static output feedback.” Int. J. Robust and Nonlinear Control, 4, 449–455.
14.
Spencer, B. F., Dyke, S. J., Sain, M. K., and Quast, P. (1993). “Acceleration feedback control strategies for aseismic protection.”J. Engrg. Mech., ASCE, 120(1), 135–158.
15.
Stoustrup, J., and Niemann, H. H. ( 1993). “The great H∞ problem with static output feedback.” Proc., Am. Control Conf., American Automatic Control Conference, Evanston, Ill., 600–604.
16.
Vandenberghe, L., and Boyd, S. P. ( 1995). “Primal-dual potential reduction method for problems involving matrix inequalities.” Math. Programming Series B, 69(1), 205–236.
17.
Veilette, R. J., Medanic, J. V., and Perkins, W. R. ( 1989). “Robust stabilization and disturbance rejection for systems with structured uncertainty.” Proc., 28th Conf. on Decision and Control, IEEE, New York, 936–941.
18.
Xie, L., Fu, M., and de Souza, C. E. ( 1992). “H∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback.” IEEE Trans. on Automatic Control, 37(8), 1253–1256.
19.
Xie, L. ( 1996). “Output feedback H∞ control of systems with parameter uncertainty.” Int. J. Control, 63(4), 741–750.
20.
Yeh, H. H., Banda, S. S., Heise, S. A., and Bartlett, A. C. ( 1990). “Robust control design with real parameter uncertainty and unmodeled dynamics.” J. Guidance, 13(6), 1117–1125.
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Published In
Journal of Engineering Mechanics
Volume 125 • Issue 2 • February 1999
Pages: 225 - 233
History
Published online: Feb 1, 1999
Published in print: Feb 1999
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