Skip to main content

Advertisement

SpringerLink
Log in

A novel approach to robust \(\mathcal {H}_\infty \) integral control for TS fuzzy systems

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, a novel approach to the robust \(\mathcal {H}_\infty \) integral control for TS fuzzy systems is considered. The control design concept can significantly improve the system stability for such a system. Based on the \(\mathcal {H}_\infty \) control theory and linear matrix inequality approach, a set of sufficient conditions guarantee the stability of the system and the \(\mathcal {H}_\infty \) performance. The proposed RHFI controllers are able to work well with the complex nonlinearity and can overcome the effect of approximate rules in the fuzzy system in case of parametric uncertainty existing in the system. This enables the fuzzy system to give appropriate responses with a fewer number of membership functions. Finally, the proposed RHFI controllers are verified through a simulation example, i.e., DFIG wind energy system. The simulated results show that the stability of the system is satisfied and the \(\mathcal {H}_\infty \) performance is achieved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Andrikopoulos G, Nikolakopoulos G, Manesis S, Manesis S (2014) Advanced nonlinear PID-based antagonistic control for pneumatic muscle actuators. IEEE Trans Ind Electron 61(12):6926–6937

    Article  Google Scholar 

  • Assawinchaichote W (2012) A non-fragile \({H}_{\infty }\) output feedback controller for uncertain fuzzy dynamical systems with multiple time-scales. Int J Comput Commun Control 7(1):8–19

    Article  Google Scholar 

  • Assawinchaichote W (2014) Further results on robust fuzzy dynamic systems with LMI D-stability constraints. Int J Appl Math Comput Sci 24(4):785–794

    Article  MathSciNet  MATH  Google Scholar 

  • Beji L, Abichou A, Bestaoui Y (2004) Position and attitude control of an underactuated autonomous airship. Int J Differ Equ Appl 8(3):231–255

    MATH  Google Scholar 

  • Bououden S, Chadli M, Filali S, Hajjaji A (2012) Fuzzy model based multivariable predictive control of a variable speed wind turbine: LMI approach. Int J Renew Energy Res 37(1):434–439

    Article  Google Scholar 

  • Chang W, Wang W (2015) \({H}_\infty \) fuzzy control synthesis for a large-scale system with a reduced number of LMIs. IEEE Trans Fuzzy Syst 23(4):1197–1210

    Article  MathSciNet  Google Scholar 

  • Chang X (2012) Takagi–Sugeno fuzzy systems non-frgile H-infinity filtering. Springer, Berlin

    Book  MATH  Google Scholar 

  • Chang X (2014) Robust output feedback H-infinity control and filtering for uncertain linear systems. Springer, Berlin

    Book  Google Scholar 

  • Chang X, Yang G (2014) Nonfragile \({H}_\infty \) filter design for TS fuzzy systems in standard form. IEEE Trans Ind Electron 61(7):3448–3458

    Article  Google Scholar 

  • Chekkal S, Lahaçani N, Aouzellag D, Ghedamsi K (2014) Fuzzy logic control strategy of wind generator based on the dual-stator induction generator. Int J Electr Power Energy Syst 59:166–175

    Article  Google Scholar 

  • Dong H, Wang Z, Ho W, Gao H (2011) Robust \({H}_\infty \) filtering for Markovian jump systems with randomly occurring nonlinearities and sensor saturation: The finite-horizon case. IEEE Trans Signal Process 59(7):3048–3057

    Article  MathSciNet  Google Scholar 

  • Esfahani S (2016) Improvement on the problem of output feedback fuzzy \({H}_\infty \)-tracking control design for non-linear discrete-time systems with state and input delay. IET Control Theor Appl 10(1):24–34

    Article  MathSciNet  Google Scholar 

  • Gao Q, Feng G, Xi Z, Wang Y, Qiu J (2014) A new design of robust \({H}_\infty \) sliding mode control for uncertain stochastic TS fuzzy time-delay systems. IEEE Trans Cybern 44(9):1556–1556

    Article  Google Scholar 

  • Gassara H, Hajjaji A, Chaabane M (2010) Observer-based robust \({H}_\infty \) reliable control for uncertain TS fuzzy systems with state time delay. IEEE Trans Fuzzy Syst 18(6):1027–1040

    Article  MATH  Google Scholar 

  • Hao L, Park J, Ye D (2016) Fuzzy logic systems-based integral sliding mode fault-tolerant control for a class of uncertain non-linear systems. IET Control Theor Appl 10(3):300–311

    Article  MathSciNet  Google Scholar 

  • Hassan N, Assaad M, Tembine H (2013) Distributed \({H}_\infty \)-based power control in a dynamic wireless network environment. IEEE Commun Lett 17(6):1124–1127

    Article  Google Scholar 

  • Kamal E, Oueidat M, Aitouche A, Ghorbani R (2013) Robust scheduler fuzzy controller of DFIG wind energy systems. IEEE Trans Sustain Energy 4(3):706–715

    Article  Google Scholar 

  • Kim Y (2016) Robust data driven H-infinity control for wind turbine. Int J Franklin Inst. doi:10.1016/j.jfranklin.2016.06.009

  • Kugi A, Schlacher K, Novak R (2001) Nonlinear control in rolling mills: a new perspective. IEEE Trans Ind Appl 37(5):1394–1402

    Article  Google Scholar 

  • Kumar K, Jeevananthan S (2013) Design and implementation of reduced-order sliding mode controller plus proportional double integral controller for negative output elementary super-lift luo-converter. IET Power Electron 23(2):974–989

    Article  Google Scholar 

  • Li F, Zhang X (2012) A delay-dependent bounded real lemma for singular LPV systems with time-variant delay. Int J Robust Nonlinear Control 22(5):559–574

    Article  MathSciNet  MATH  Google Scholar 

  • Li F, Shi P, Wu L, Zhang X (2014) Fuzzy-model-based D-stability and nonfragile control for discrete-time descriptor systems with multiple delays. IEEE Trans Fuzzy Syst 22(4):1019–1025

    Article  Google Scholar 

  • Lin C, Wang G, Lee T, He Y (2007) LMI approach to analysis and control of Takagi–Sugeno fuzzy systems with time delay. Springer, Berlin

    MATH  Google Scholar 

  • Liu Z, Gao C, Kao Y (2015) Robust H-infinity control for a class of neutral-type systems via sliding mode observer. Int J Appl Math Comput 27:669–681

    MathSciNet  Google Scholar 

  • Ma M, Chen H, Liu X, Allgöwer F (2014) Moving horizon \({H}_{\infty }\) control of variable speed wind turbines with actuator saturation. IET Renew Power Gener 8(5):498–508

    Article  Google Scholar 

  • Niknam T, Khooban M (2013) Fuzzy sliding mode control scheme for a class of non-linear uncertain chaotic systems. IET Sci Measure Technol 7(5):249–255

    Article  Google Scholar 

  • Qiu L, Shi Y, Xu B, Yao F (2015) Robust stochastic stability and delayed-state-feedback stabilisation of uncertain Markovian jump linear systems with random time delays. IET Control Theor Appl 9(12):1878–1886

    Article  MathSciNet  Google Scholar 

  • Shi P, Li F, Wu L, Lim C (2016) Neural network-based passive filtering for delayed neutral-type semi-Markovian jump systems. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2016.2573853

  • Shi P, Zhang Y, Chadli M, Agarwal R (2016b) Mixed H-infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays. IEEE Trans Neural Netw Learn Syst 27(4):903–909

    Article  MathSciNet  Google Scholar 

  • Sun D, Hu S, Shao X, Liu C (2014) Global stability of a saturated nonlinear PID controller for robot manipulators. IEEE Trans Control Syst Technol 17(4):892–899

    Google Scholar 

  • Tang C, Guo Y, Jiang J (2011) Nonlinear dual-mode control of variable-speed wind turbine with doubly fed induction generators. IEEE Trans Control Syst Technol 19(4):744–756

    Article  Google Scholar 

  • Wang D, Wang W, Shi P (2009) H-infinity filtering of discrete-time switched systems with state delays via switched lyapunov function approach. IEEE Trans Autom Control 54(6):1428–1429

    Article  MathSciNet  MATH  Google Scholar 

  • Wang G, Nan Q, Li J (2015a) Fuzzy integers and methods of constructing them to represent uncertain or imprecise integer information. Int J Innov Comput Inf Control 11(4):1483–1494

    Google Scholar 

  • Wang T, Gao H, Qiu J (2015b) A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Trans Neural Netw Learn Syst 27(2):416–425

    Article  MathSciNet  Google Scholar 

  • Wu L, Luo W, Zeng Y, Li F, Zheng Z (2016) Fault detection for underactuated manipulators modeled by Markovian jump systems. IEEE Trans Ind Electron 63(7):4387–4399

    Article  Google Scholar 

  • Yang Q, Jagannathan S, Sun Y (2015) Robust integral of neural network and error sign control of MIMO nonlinear systems. IEEE Trans Neural Netw Learn Syst 26(12):3278–3286

    Article  MathSciNet  Google Scholar 

  • Ying X, Lin Y, Li W, Gu Y, Lei P, Liu H (2015) Sliding mode voltage control strategy for capturing maximum wind energy based on fuzzy logic control. Int J Electr Power Energy Syst 70:45–51

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronic and Telecommunication Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand

    Nattapat Chayaopas & Wudhichai Assawinchaichote

Authors
  1. Nattapat Chayaopas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wudhichai Assawinchaichote
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wudhichai Assawinchaichote.

Additional information

Communicated by Maria do Rosário de Pinho.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chayaopas, N., Assawinchaichote, W. A novel approach to robust \(\mathcal {H}_\infty \) integral control for TS fuzzy systems. Comp. Appl. Math. 37, 954–977 (2018). https://doi.org/10.1007/s40314-016-0379-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40314-016-0379-8

Keywords

Mathematics Subject Classification

Search

Navigation