Skip to main content

2017 | OriginalPaper | Buchkapitel

2. Theoretical Foundation of Finite Frequency Control

verfasst von : Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

Erschienen in: Finite Frequency Analysis and Synthesis for Singularly Perturbed Systems

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Finite frequency control strategy has been proven to be an important method for modern control system. Combined with the particular frequency characteristics of the plant, many control specifications in the full frequency domain can be simplified into finite frequency ones. Commonly used tools in the frequency division are the weighting function and general Kalman-Yakubovich-Popov (GKYP) Lemma. In this chapter, some background information and useful lemmas in the field of finite frequency control have been investigated in detail.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Davidson, T., Luo, Z., Sturm, J.: Linear matrix inequality formulation of spectral mask constraints. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 6, pp. 3813–3816 (2001) Davidson, T., Luo, Z., Sturm, J.: Linear matrix inequality formulation of spectral mask constraints. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 6, pp. 3813–3816 (2001)
3.
Zurück zum Zitat Genin, Y., Hachez, Y., Nesterov, Y., Van Dooren, P.: Convex optimization over positive polynomials and filter design. In: Proceedings of UKACC International Conference on Control (2000) Genin, Y., Hachez, Y., Nesterov, Y., Van Dooren, P.: Convex optimization over positive polynomials and filter design. In: Proceedings of UKACC International Conference on Control (2000)
4.
Zurück zum Zitat Hara, S., Iwasaki, T.: Robust PID control using generalized KYP synthesis. IEEE Control Syst. Mag. 26(1), 80–91 (2006)MathSciNetCrossRef Hara, S., Iwasaki, T.: Robust PID control using generalized KYP synthesis. IEEE Control Syst. Mag. 26(1), 80–91 (2006)MathSciNetCrossRef
5.
Zurück zum Zitat Iwasaki, T., Hara, S., Yamauchi, H.: Dynamical system design from a control perspective: finite frequency positive realness approach. IEEE Trans. Autom. Control 48(8), 1337–1354 (2003)MathSciNetCrossRef Iwasaki, T., Hara, S., Yamauchi, H.: Dynamical system design from a control perspective: finite frequency positive realness approach. IEEE Trans. Autom. Control 48(8), 1337–1354 (2003)MathSciNetCrossRef
6.
Zurück zum Zitat Iwasaki, T., Hara, S., Fradkov, A.L.: Time domain interpretations of frequency domain inequalities on finite ranges. Syst. Control Lett. 54(7), 681–691 (2005)MathSciNetCrossRefMATH Iwasaki, T., Hara, S., Fradkov, A.L.: Time domain interpretations of frequency domain inequalities on finite ranges. Syst. Control Lett. 54(7), 681–691 (2005)MathSciNetCrossRefMATH
7.
Zurück zum Zitat Iwasaki, T., Meinsma, G., Fu, M.: Generalized S-procedure and finite frequency KYP lemma. Math. Prob. Eng. 6(2–3), 305–320 (2009)MathSciNetMATH Iwasaki, T., Meinsma, G., Fu, M.: Generalized S-procedure and finite frequency KYP lemma. Math. Prob. Eng. 6(2–3), 305–320 (2009)MathSciNetMATH
8.
Zurück zum Zitat Iwasaki, T., Hara, S.: Robust control synthesis with general frequency domain specifications: static gain feedback case. Proc. Am. Control Conf. 5, 4613–4618 (2004) Iwasaki, T., Hara, S.: Robust control synthesis with general frequency domain specifications: static gain feedback case. Proc. Am. Control Conf. 5, 4613–4618 (2004)
9.
Zurück zum Zitat Iwasaki, T., Hara, S.: Generalized KYP lemma: unified frequency domain inequalities with design applications. IEEE Trans. Autom. Control 50(1), 41–59 (2005)MathSciNetCrossRef Iwasaki, T., Hara, S.: Generalized KYP lemma: unified frequency domain inequalities with design applications. IEEE Trans. Autom. Control 50(1), 41–59 (2005)MathSciNetCrossRef
10.
Zurück zum Zitat Jonsson, U.: Robustness analysis of uncertain and nonlinear systems. Ph.D. Dissertation, Department of Automatic Control, Lund Institute of Technology (1996) Jonsson, U.: Robustness analysis of uncertain and nonlinear systems. Ph.D. Dissertation, Department of Automatic Control, Lund Institute of Technology (1996)
11.
Zurück zum Zitat Luse, D.W., Ball, J.A.: Frequency-scale decoposition of \(H_\infty \) disk problems. SIAM J. Control Optimization 27, 814–835 (1989)MathSciNetCrossRefMATH Luse, D.W., Ball, J.A.: Frequency-scale decoposition of \(H_\infty \) disk problems. SIAM J. Control Optimization 27, 814–835 (1989)MathSciNetCrossRefMATH
12.
Zurück zum Zitat Megretski, A., Rantzer, A.: System analysis via integral quadratic constraints. IEEE Trans. Autom. Control 42(6), 819–830 (1997)MathSciNetCrossRefMATH Megretski, A., Rantzer, A.: System analysis via integral quadratic constraints. IEEE Trans. Autom. Control 42(6), 819–830 (1997)MathSciNetCrossRefMATH
13.
Zurück zum Zitat Megretski, A., Treil, S.: Power distribution inequalities in optimization and robustness of uncertain systems. J. Math. Syst. Estim. Control 3(3), 301–319 (1993)MathSciNetMATH Megretski, A., Treil, S.: Power distribution inequalities in optimization and robustness of uncertain systems. J. Math. Syst. Estim. Control 3(3), 301–319 (1993)MathSciNetMATH
14.
Zurück zum Zitat Nesterov, Y.: Squared functional systems and optimization problems. In: Frenk, H., et al. (eds.) High Performance Optimization, pp. 405–440. Kluwer Academic Publishers, Dordrecht (2000)CrossRef Nesterov, Y.: Squared functional systems and optimization problems. In: Frenk, H., et al. (eds.) High Performance Optimization, pp. 405–440. Kluwer Academic Publishers, Dordrecht (2000)CrossRef
15.
Zurück zum Zitat Oloomi, H., Shafai, B.: A system theory criterion for positive real matrices. SIAM J. Control 5(171–182), 2008 (1967)MathSciNet Oloomi, H., Shafai, B.: A system theory criterion for positive real matrices. SIAM J. Control 5(171–182), 2008 (1967)MathSciNet
16.
Zurück zum Zitat Pipeleers, G., Vandenberghe, L.: Generalized KYP lemma with real data. IEEE Trans. Autom. Control 56(12), 2942–2946 (2011)MathSciNetCrossRef Pipeleers, G., Vandenberghe, L.: Generalized KYP lemma with real data. IEEE Trans. Autom. Control 56(12), 2942–2946 (2011)MathSciNetCrossRef
19.
Zurück zum Zitat Willems, J.C.: Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans. Autom. Control 16(6), 621–634 (1971)MathSciNetCrossRef Willems, J.C.: Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans. Autom. Control 16(6), 621–634 (1971)MathSciNetCrossRef
20.
Zurück zum Zitat Yakubovich, V.A.: The S-procedure in nonlinear control theory. Vestn. Leningrad Univ. 1, 62–77 (1971)MathSciNetMATH Yakubovich, V.A.: The S-procedure in nonlinear control theory. Vestn. Leningrad Univ. 1, 62–77 (1971)MathSciNetMATH
21.
Zurück zum Zitat Yakubovich, V.A.: Nonconvex optimization problem: the infinite-horizon linear-quadratic control problem with quadratic constraints. Syst. Control Lett. 19(1), 13–22 (1992). (2010)MathSciNetCrossRefMATH Yakubovich, V.A.: Nonconvex optimization problem: the infinite-horizon linear-quadratic control problem with quadratic constraints. Syst. Control Lett. 19(1), 13–22 (1992). (2010)MathSciNetCrossRefMATH
Metadaten
Titel
Theoretical Foundation of Finite Frequency Control
verfasst von
Chenxiao Cai
Zidong Wang
Jing Xu
Yun Zou
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-45405-4_2

Neuer Inhalt