Abstract
This paper summarizes the authors’ recent results on finite frequency characterization of easily controllable plants under control effort constraint, the aim being the development of a new approach for plant/control design integration. We first show by a motivating example that the closed-loop bandwidth achievable with a reasonable control effort is closely related to the frequency range for which the plant is high-gain and exhibits positive-realness. We then present an LMI characterization of the finite frequency Kalman—Yakubovich—Popov (KYP) lemma and derive several related conditions. Finally, the conditions for the finite frequency positive-real (FFPR) and the finite frequency high-gain (FFHG) properties are shown.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. D. O. Anderson and S. VongpanitlerdNetwork Analysis and Synthesis.Prentice Hall, 1973.
T. Asai, S. Hara, and T. Iwasaki, “Simultaneous parametric uncertainty modeling and robust control synthesis by LFT scaling,”Automaticavol. 36, pp. 1457–1467, 2000.
M. Fan, A. Tits, and J. Doyle, “Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics,”IEEE Trans. Auto. Contr.vol. 36, no. 1, pp. 25–38, 1991.
K. M. Grigoriadis and F. Wu “IntegratedH oo plant/controller design via linear matrix inequalities,“ inProc. IEEE Conf. Decision Contr., 1997.
K. M. Grigoriadis, G. Zhu, and R. E. Skelton, “Optimal redesign of linear systems,”ASME J. Dyn. Syst. Meas. Contr.vol. 118, pp. 596–605, 1996.
S. Hara, T. Iwasaki, and F. Shimizu “Finite frequency characterization of easily controllable mechanical systems under control effort constraint,” inProc. IFAC World Congress2002.
T. Iwasaki and S. Hara,“Integrated design of dynamical systems: Requirements for easily controllable structures,” inPre-print of TITech COE/Super Mechano-Systems Workshop’ 991999, pp. 68–72.
T. Iwasaki, S. Hara, and H. Yamauchi “Structure/control design integration with finite frequency positive real property,” inProc. American Contr. Conf.2000.
T. Iwasaki, S. Hara, and H. Yamauchi “Dynamical system design from a control perspective: Finite frequency positive-realness approach,” submitted toIEEE Trans. Auto. Contr.2002.
T. Iwasaki, G. Meinsma, and M. Fu, “Generalized S-procedure and finite frequency KYP lemma,”Mathematical Problems in Engineeringvol. 6, pp. 305–320, 2000.
T. Iwasaki and G. Shibata, “LPV system analysis via quadratic separator for uncertain implicit systems,”IEEE Trans. Auto. Contr.vol. 46, no. 8, pp. 1195–1208, 2001.
I. Kajiwara and A. Nagamatsu, “An approach of optimal design for simultaneous optimization of structure and control systems using sensitivity analysis,”J. SICEvol. 26, no. 10, pp. 1140–1147, 1990.
K. Ono and T. Teramoto, “Design methodology to stabilize the natural modes of vibration of a swing-arm positioning mechanism,”ASME Adv. Info. Storage Syst.vol. 4, pp. 343–359, 1992.
J. Onoda and R. Haftka, “An approach to structure/control simultaneous optimization for large flexible spacecraft,”AIAA Journalvol. 25, no. 8, pp. 1133–1138, 1987.
A. Rantzer, “On the Kalman¡ªYakubovich¡ªPopov lemma,”Sys. Contr. Lett., vol. 28, no. 1, 1996.
C. Sultan and R. E. Skelton, “Integrated design of controllable tensegrity structures,” in Proc. Int. Mech. Eng. Congress, Dallas, TX, 1997.
J. C. Willems, “Least squares stationary optimal control and the algebraic Riccati equation,”IEEE Trans. Auto. Contr., vol. 16, pp. 621–634, 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hara, S., Iwasaki, T. (2003). Finite Frequency Characterization of Easily Controllable Plant toward Structure/Control Design Integration. In: Hashimoto, K., Oishi, Y., Yamamoto, Y. (eds) Control and Modeling of Complex Systems. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0023-9_12
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0023-9_12
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6577-1
Online ISBN: 978-1-4612-0023-9
eBook Packages: Springer Book Archive