Skip to main content
Erschienen in: Soft Computing 9/2013

01.09.2013 | Methodologies and Application

Limit-cycle analysis of dynamic fuzzy control systems

verfasst von: Jau-Woei Perng

Erschienen in: Soft Computing | Ausgabe 9/2013

Einloggen

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

search-config
loading …

Abstract

The main purpose of this study is to predict limit cycles of a dynamic fuzzy control system by combining a stability equation, describing function and parameter plane. The stability of a linearized dynamic fuzzy control system is then analyzed using stability equations and the parameter plane method, with the assistance of a describing function method. This procedure identifies the amplitude and frequency of limit cycles that are clearly formed by the dynamic fuzzy controller in the parameter plane. Moreover, the suppression of the limit cycle by adjusting control parameters is proposed. Continuous and sampled-data systems are addressed, and the proposed approach can easily be extended to a fuzzy control system with multiple nonlinearities. Simulations are performed to demonstrate the effectiveness of the proposed scheme.

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 "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • 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
Zurück zum Zitat Abdelnour G, Cheung TY, Chang CH, Tinetti G (1993) Steady-state analysis of a three-term fuzzy controller. IEEE Trans Syst Man Cybern 23:607–610MATHCrossRef Abdelnour G, Cheung TY, Chang CH, Tinetti G (1993) Steady-state analysis of a three-term fuzzy controller. IEEE Trans Syst Man Cybern 23:607–610MATHCrossRef
Zurück zum Zitat Ackermann J, Bunte T (1997) Actuator rate limits in robust car steering control. In: Proceedings of the IEEE conference on decision and control, pp 4726–4731 Ackermann J, Bunte T (1997) Actuator rate limits in robust car steering control. In: Proceedings of the IEEE conference on decision and control, pp 4726–4731
Zurück zum Zitat Chang CH, Chang MK (1994) Analysis of gain margins and phase margins of a nonlinear reactor control system. IEEE Trans Nucl Sci 41:1686–1691CrossRef Chang CH, Chang MK (1994) Analysis of gain margins and phase margins of a nonlinear reactor control system. IEEE Trans Nucl Sci 41:1686–1691CrossRef
Zurück zum Zitat Chang W, Park JB, Joo YH, Chen G (2003) Static output-feedback fuzzy controller for Chen’s chaotic system with uncertainties. Inf Sci 151:227–244MathSciNetMATHCrossRef Chang W, Park JB, Joo YH, Chen G (2003) Static output-feedback fuzzy controller for Chen’s chaotic system with uncertainties. Inf Sci 151:227–244MathSciNetMATHCrossRef
Zurück zum Zitat Chen YL, Han KW (1970) Stability analysis of a nonlinear reactor control system. IEEE Trans Nucl Sci NS-17:18–25CrossRef Chen YL, Han KW (1970) Stability analysis of a nonlinear reactor control system. IEEE Trans Nucl Sci NS-17:18–25CrossRef
Zurück zum Zitat Cheng CC, Huang CH (1998) On the limit cycle of the underwater vehicle control system. In: Proceedings of the international symposium on underwater technology, pp 461–465 Cheng CC, Huang CH (1998) On the limit cycle of the underwater vehicle control system. In: Proceedings of the international symposium on underwater technology, pp 461–465
Zurück zum Zitat Chu YC, Dowling AP, Glover K (1998) Robust control of combustion oscillations. In: Proceedings of IEEE international conference on control applications, pp 1165–1169 Chu YC, Dowling AP, Glover K (1998) Robust control of combustion oscillations. In: Proceedings of IEEE international conference on control applications, pp 1165–1169
Zurück zum Zitat Cox CS, French IG (1986) Limit cycle prediction conditions for hydraulic control system. ASME J Dyn Syst Meas Control 108:17–23MATHCrossRef Cox CS, French IG (1986) Limit cycle prediction conditions for hydraulic control system. ASME J Dyn Syst Meas Control 108:17–23MATHCrossRef
Zurück zum Zitat D’Amico MB, Moiola JL, Paolini EE (2002) Hopf bifurcation for maps: a frequency-domain approach. IEEE Trans Circuits Syst I 49:281–288MathSciNetCrossRef D’Amico MB, Moiola JL, Paolini EE (2002) Hopf bifurcation for maps: a frequency-domain approach. IEEE Trans Circuits Syst I 49:281–288MathSciNetCrossRef
Zurück zum Zitat Genesio R, Tesi A, Villoresi F (1993) A frequency approach for analyzing and controlling chaos in nonlinear circuits. IEEE Trans Circuits Syst II 40:819–828MATHCrossRef Genesio R, Tesi A, Villoresi F (1993) A frequency approach for analyzing and controlling chaos in nonlinear circuits. IEEE Trans Circuits Syst II 40:819–828MATHCrossRef
Zurück zum Zitat Gordillo F, Aracil J, Alamo T (1993) Determining limit cycles in fuzzy control systems. In: Proceedings of IEEE international conference on fuzzy systems, pp 193–198 Gordillo F, Aracil J, Alamo T (1993) Determining limit cycles in fuzzy control systems. In: Proceedings of IEEE international conference on fuzzy systems, pp 193–198
Zurück zum Zitat Han KW (1977) Nonlinear control systems—some practical methods. Academic Cultural Company, CaliforniaMATH Han KW (1977) Nonlinear control systems—some practical methods. Academic Cultural Company, CaliforniaMATH
Zurück zum Zitat Han KW (1979) Digital and sampled-data control systems. Kuang-Mei Publishing Co., Lungtan Han KW (1979) Digital and sampled-data control systems. Kuang-Mei Publishing Co., Lungtan
Zurück zum Zitat Han KW, Thaler GJ (1966) Control system analysis and design using a parameter space method. IEEE Trans Autom Control 11:560–563CrossRef Han KW, Thaler GJ (1966) Control system analysis and design using a parameter space method. IEEE Trans Autom Control 11:560–563CrossRef
Zurück zum Zitat Hauksdottir AS, Sigurdaraottir G (1993) On the use of robust design methods in vehicle longitudinal controller design. ASME J Dyn Syst Meas Control 115:166–172CrossRef Hauksdottir AS, Sigurdaraottir G (1993) On the use of robust design methods in vehicle longitudinal controller design. ASME J Dyn Syst Meas Control 115:166–172CrossRef
Zurück zum Zitat Itovich GR, Moiola JL (2006) On period doubling bifurcations of cycles and the harmonic balance method. Chaos Solitons Fractals 27:647–665MathSciNetMATHCrossRef Itovich GR, Moiola JL (2006) On period doubling bifurcations of cycles and the harmonic balance method. Chaos Solitons Fractals 27:647–665MathSciNetMATHCrossRef
Zurück zum Zitat Kim E, Lee H, Park M (2000) Limit-cycle prediction of a fuzzy control system based on describing function method. IEEE Trans Fuzzy Syst 8:11–21CrossRef Kim E, Lee H, Park M (2000) Limit-cycle prediction of a fuzzy control system based on describing function method. IEEE Trans Fuzzy Syst 8:11–21CrossRef
Zurück zum Zitat Li J, Wang HO, Niemann D, Tanaka K (2000) Dynamic parallel distributed compensation for Takagi–Sugeno fuzzy systems: an LMI approach. Inf Sci 123:201–221MathSciNetMATHCrossRef Li J, Wang HO, Niemann D, Tanaka K (2000) Dynamic parallel distributed compensation for Takagi–Sugeno fuzzy systems: an LMI approach. Inf Sci 123:201–221MathSciNetMATHCrossRef
Zurück zum Zitat Marco MD, Forti M, Tesi A (2002) Existence and characterization of limit cycles in nearly symmetric neural networks. IEEE Trans Circuits Syst I 49:979–992CrossRef Marco MD, Forti M, Tesi A (2002) Existence and characterization of limit cycles in nearly symmetric neural networks. IEEE Trans Circuits Syst I 49:979–992CrossRef
Zurück zum Zitat Nagi F, Ahmed SK, Zainul Abidin AA, Nordin FH (2010) Fuzzy bang–bang relay controller for satellite attitude control system. Fuzzy Sets Syst 161:2104–2125MathSciNetMATHCrossRef Nagi F, Ahmed SK, Zainul Abidin AA, Nordin FH (2010) Fuzzy bang–bang relay controller for satellite attitude control system. Fuzzy Sets Syst 161:2104–2125MathSciNetMATHCrossRef
Zurück zum Zitat Nguang SK (2006) Robust H-infinity output feedback control design for fuzzy dynamic systems with quadratic D stability constraints: an LMI approach. Inf Sci 176:2161–2191MathSciNetMATHCrossRef Nguang SK (2006) Robust H-infinity output feedback control design for fuzzy dynamic systems with quadratic D stability constraints: an LMI approach. Inf Sci 176:2161–2191MathSciNetMATHCrossRef
Zurück zum Zitat Olsson H, Astrom KJ (2001) Friction generated limit cycles, IEEE Trans. Control Syst Technol 9:629–636CrossRef Olsson H, Astrom KJ (2001) Friction generated limit cycles, IEEE Trans. Control Syst Technol 9:629–636CrossRef
Zurück zum Zitat Padin MS, Robbio FI, Moiola JL, Chen G (2005) On limit cycle approximations in the van der Pol oscillator. Chaos Solitons Fractals 23:207–220MATHCrossRef Padin MS, Robbio FI, Moiola JL, Chen G (2005) On limit cycle approximations in the van der Pol oscillator. Chaos Solitons Fractals 23:207–220MATHCrossRef
Zurück zum Zitat Perng JW (2012) Describing function analysis of uncertain fuzzy vehicle control systems. Neural Comput Appl 21:555–563CrossRef Perng JW (2012) Describing function analysis of uncertain fuzzy vehicle control systems. Neural Comput Appl 21:555–563CrossRef
Zurück zum Zitat Precup RE, David RC, Petriu EM, Preitl S, Paul AS (2011) Gravitational search algorithm based tuning of fuzzy control systems with a reduced parametric sensitivity. Soft Computing in Industrial Applications, Springer, Berlin, pp 141–150 Precup RE, David RC, Petriu EM, Preitl S, Paul AS (2011) Gravitational search algorithm based tuning of fuzzy control systems with a reduced parametric sensitivity. Soft Computing in Industrial Applications, Springer, Berlin, pp 141–150
Zurück zum Zitat Sadeghi-Tehran P, Cara AB, Angelov P, Pomares H, Rojas I, Prieto A (2012) Self-evolving parameter-free rule-based controller. In: Proceedings of IEEE conference on fuzzy systems, pp 754–761 Sadeghi-Tehran P, Cara AB, Angelov P, Pomares H, Rojas I, Prieto A (2012) Self-evolving parameter-free rule-based controller. In: Proceedings of IEEE conference on fuzzy systems, pp 754–761
Zurück zum Zitat Shenton AT (1999) Parameter space design of PID limit cycle controllers. In: Proceedings of American control conference, pp 3342–3346 Shenton AT (1999) Parameter space design of PID limit cycle controllers. In: Proceedings of American control conference, pp 3342–3346
Zurück zum Zitat Siljak DD (1964) Analysis and synthesis of feedback control systems in the parameter plane. IEEE Trans Ind Appl 83:466–473CrossRef Siljak DD (1964) Analysis and synthesis of feedback control systems in the parameter plane. IEEE Trans Ind Appl 83:466–473CrossRef
Zurück zum Zitat Siljak DD (1969) Nonlinear systems—the parameter analysis and design. Wiley, New YorkMATH Siljak DD (1969) Nonlinear systems—the parameter analysis and design. Wiley, New YorkMATH
Zurück zum Zitat Tanaka K, Manabu S (1993) Fuzzy stability criterion of a class of nonlinear systems. Inf Sci 71:3–26MATHCrossRef Tanaka K, Manabu S (1993) Fuzzy stability criterion of a class of nonlinear systems. Inf Sci 71:3–26MATHCrossRef
Zurück zum Zitat Tao CW, Taur JS, Chang CW, Chang YH (2012) Simplified type-2 fuzzy sliding controller for wing rock system. Fuzzy Sets Syst 207:111–129MathSciNetMATHCrossRef Tao CW, Taur JS, Chang CW, Chang YH (2012) Simplified type-2 fuzzy sliding controller for wing rock system. Fuzzy Sets Syst 207:111–129MathSciNetMATHCrossRef
Zurück zum Zitat Xing J, Shi Z, Dai G (1996) Using describing function to analyze wriggling phenomenon of fuzzy control systems. In: Proceedings of IEEE conference on fuzzy systems, pp 1198–1204 Xing J, Shi Z, Dai G (1996) Using describing function to analyze wriggling phenomenon of fuzzy control systems. In: Proceedings of IEEE conference on fuzzy systems, pp 1198–1204
Metadaten
Titel
Limit-cycle analysis of dynamic fuzzy control systems
verfasst von
Jau-Woei Perng
Publikationsdatum
01.09.2013
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 9/2013
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-012-0971-9

Weitere Artikel der Ausgabe 9/2013

Soft Computing 9/2013 Zur Ausgabe