Skip to main content
SpringerLink
Log in

Anti-windup TS Fuzzy PI-like Control for Discrete-Time Nonlinear Systems with Saturated Actuators

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper deals with piecewise constant set-points tracking control of nonlinear discrete-time systems represented by Takagi-Sugeno models under actuators’ saturation. To this end, a fuzzy Proportional Integral-like (PI-like) discrete-time control scheme is considered, which consists of a proportional state feedback, an integral action over the tracking error, and an anti-windup action. All the control gains are obtained through a convex optimization procedure formulated in term of Linear Matrix Inequalities (LMIs). The proposed method yields a Parameter Distributed Compensation (PDC) PI-like control and a non-PDC anti-windup action structure. Due to the actuators’ saturation, a local approach is considered with a fuzzy Lyapunov function to ensure the local closed-loop stability, to provide an estimate of the region of attraction, and to compute the amplitude bounds of set-points changes. This latter issue allows delivering operational security by providing a bounded range for the set-points variation. To validate and illustrate the performance of the proposed tracking control approach, real-time experiments has been performed on an industrial oriented process consisting on the nonlinear level control of two interactive tanks.

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
Fig. 9

Similar content being viewed by others

References

  1. Blažič, S., Škrjanc, I., Matko, D.: Globally stable model reference adaptive control based on fuzzy description of the plant. International Journal of Systems Science 33(12), 995–1012 (2002)

    Article  MathSciNet  Google Scholar 

  2. Bouallegue, S., Hagg, J., Ayadi, M., Benrejeb, M.: PID type fuzzy logic controller tuning based on particle swarm optimization. Engineering Applications of Artificial Intelligence 25, 484–493 (2012)

    Article  Google Scholar 

  3. Chen, S.Y., Hung, Y.H., Gong, S.S.: Speed control of vane-type air motor servo system using proportional-integral-derivative-based fuzzy neural network. International Journal of Fuzzy Systems 18(6), 1065–1079 (2016)

    Article  MathSciNet  Google Scholar 

  4. Dragos, C.A., Preitl, S., Petriu, E.M., Radac, M.B., Stînean, A.I.: Alternative control solutions for vehicles with continuously variable transmission. a case study. In: 2011 \(15^{th}\) International Conference on System Theory, Control and Computing, pp. 1–6 (2011)

  5. Du, H., Zhang, N.: Fuzzy control for nonlinear uncertain electrohydraulic active suspensions with input constraint. IEEE Transactions on Fuzzy Systems 17(2), 343–356 (2009)

    Article  Google Scholar 

  6. Estrada-Manzo, V., Lendek, Z., Guerra, T.: An alternative lmi static output feedback control design for discrete-time nonlinear systems represented by takagi-sugeno models. ISA Transactions 84, 104–110 (2019)

    Article  Google Scholar 

  7. Fan, X., Yi, Y., Ye, Y.: Mechatronics and Robotics Engineering for Advanced and Intelligent Manufacturing, vol. 3, chap. DOB Tracking Control for Systems with Input Saturation and Exogenous Disturbances via T-S Disturbance Modelling, pp. 445 – 455. Spring (2017)

  8. Fateh, M.M.: Robust voltage control of electrical manipulators in task-space. International Journal of Innovative Computing, Information and Control 6(6), 2691–2700 (2010)

    Google Scholar 

  9. Fattah, A.J., Abdel-Qader, I.: Performance and comparison analysis of speed control of induction motors using improved hybrid pid-fuzzy controller. In: 2015 IEEE International Conference on Electro/Information Technology, pp. 575–580 (2015)

  10. Gao, H., Liu, F., Wang, T., Yin, S.: Setpoints compensation for nonlinear industrial processes with disturbances based on fuzzy logic control. In: IECON 2014 - \(40^{th}\) Annual Conference of the IEEE Industrial Electronics Society, pp. 2611–2616 (2015)

  11. Gonzalez, A., Guerra, T.M.: An improved robust stabilization method for discrete-time fuzzy systems with time-varying delays. Journal of the Franklin Institute 351(11), 5148–5161 (2014)

    Article  MathSciNet  Google Scholar 

  12. Hamzaa, M.F., Yapa, H.J., Choudhury, I.A.: Cuckoo search algorithm based design of interval type-2 fuzzy PID controller for furuta pendulum system. Engineering Applications of Artificial Intelligence 62, 134–151 (2017)

    Article  Google Scholar 

  13. Johansson, K.H.: The quadruple-tank process: A multivariable laboratory process with an adjustable zero. IEEE Transactions on Control Systems Technology 8(3), 456–465 (2000)

    Article  Google Scholar 

  14. Jungers, M., Castelan, E.B.: Gain-scheduled output control design for a class of discrete-time nonlinear systems with saturating actuators. System and Control Letters 60(3), 315–325 (2011)

    Article  MathSciNet  Google Scholar 

  15. Kailath, T.: Linear Systems, 3rd edn. Prentice-Hall Inc., Englewood Cliffs, N.J. (1980)

  16. Klug, M., Castelan, E.B., Leite, V.J.S., Silva, L.F.P.: Fuzzy dynamic output feedback control through nonlinear Takagi-Sugeno models. fuzzy sets and systems. Fuzzy Sets and Systems 263, 92–11 (2015)

    Article  MathSciNet  Google Scholar 

  17. Kmetóvá, J., Vasickaninová, A., Dvoran, J.: Neuro-fuzzy control of exothermic chemical reactor. In: \(2013\) - International Conference on Process Control (PC), pp. 168–172 (2013)

  18. Kong, L., Yuan, J.: Disturbance-observer-based fuzzy model predictive control for nonlinear processes with disturbances and input constraints. ISA Transactions (2019). https://doi.org/10.1016/j.isatra.2018.12.041

    Article  Google Scholar 

  19. Laurain, T., Lauber, J., Palhares, R.M.: Avoiding matrix inversion in Takagi-Sugeno-Based advanced controllers and observers. IEEE Transactions on Fuzzy Systems 26(1), 216–225 (2018)

    Article  Google Scholar 

  20. Lendek, Z., Nagy, Z., Lauber, J.: Local stabilization of discrete-time TS descriptor systems. Engineering Applications of Artificial Intelligence 67, 409–418 (2018)

    Article  Google Scholar 

  21. Li, H., Wang, J., Shi, P.: Output-feedback based sliding mode control for fuzzy systems with actuators saturation. IEEE Transactions on Fuzzy Systems 24(6), 1282–1293 (2016)

    Article  Google Scholar 

  22. Lin, A.Y., Huang, H.N., Shiu, C.Y., Hwang, J.L.: Implementation of fuzzy controller for measuring instantaneous arterial blood pressure via tissue control method. IET Control Theory & Applications 2(1), 40–50 (2008)

    Article  Google Scholar 

  23. Lopes, A.N.D., Leite, V.J.S., Silva, L.F.P.: On the integral action of discrete-time fuzzy ts control under saturated actuator. In: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–8 (2018)

  24. Lv, X., Fei, J., Sun, Y.: Fuzzy PID controller design for uncertain networked control systems based on T-S fuzzy model with random delays. International Journal of Fuzzy Systems 21(2), 571–582 (2019)

    Article  MathSciNet  Google Scholar 

  25. Mehdi, N., Rehan, M., Malik, F.M., Bhatti, A.I., Tufail, M.: A novel anti-windup framework for cascade control systems: An application to underactuated mechanical systems. ISA Transactions 53(3), 802–815 (2014)

    Article  Google Scholar 

  26. Mishra, P., Kumar, V., Rana, K.P.S.: Stiction combating intelligent controller tuning: A comparative study. In: \(2015\) - International Conference on Advances in Computer Engineering and Applications (PC), pp. 534–541 (2015)

  27. Nguyen, A.T., Márquez, R., Dequidt, A.: An augmented system approach for LMI-based control design of constrained Takagi-Sugeno fuzzy systems. Engineering Applications of Artificial Intelligence 61, 96–102 (2017)

    Article  Google Scholar 

  28. Nouri, A., Salhi, I., Elwarraki, E., Beid, S.E., Essounbouli, N.: DSP-based implementation of self-tunning fuzzy controller for three-level boost converter. Electric Power Systems Research 17, 286–297 (2017)

    Article  Google Scholar 

  29. O’Dwyer, A.: Handbook of PI and PID controller tunning rules, 3rd edn. Imperial College Press, London (2009)

    Book  Google Scholar 

  30. Ounnas, D., Ramdani, M., Chenikher, S., Bouktir, T.: Optimal reference model based fuzzy tracking control for wind energy conversion system. International Journal of Renewable Energy research 6(3), 1129–1236 (2016)

    Google Scholar 

  31. Precup, R.E., Preitl, S., Petriu, E.M., Tar, J.K., Tomescu, M.K., Pozna, C.: Generic two-degree-of-freedom linear and fuzzy controllers for integral process. Journal of the Franklin Institute 346, 980–1003 (2009)

    Article  MathSciNet  Google Scholar 

  32. Preitl, S., Precup, R.E.: Sensitivity study of a class of fuzzy control systems. Periodica Polytechnica Electrical Engineering 50(3–4), 255–268 (2006)

    Google Scholar 

  33. Preitl, S., Precup, R.E., Preitl, Z.: Sensitivity analysis of low cost fuzzy controlled servo systems. In: \(2005\) - \(16^{th}\) IFAC World Congress, pp. 342–347 (2005)

    Article  Google Scholar 

  34. Qiao, W.Z., Mizumoto, M.: PID type fuzzy controller and parameters adaptive method. Fuzzy Sets and Systems 78, 23–35 (1996)

    Article  MathSciNet  Google Scholar 

  35. Sari, N.N., Jahanshahi, H., Fakoor, M.: Adaptive fuzzy PID control strategy for spacecraft attitude control. International Journal of Fuzzy Systems 21(3), 769–781 (2019)

    Article  MathSciNet  Google Scholar 

  36. Sousa, A.C., Leite, V.J.S., Rubio Scola, I.: Affordable control platform with MPC application. Studies in Informatics and Control 27, 265–274 (2018)

    Article  Google Scholar 

  37. Sun, Y., Xu, J., Qiang, H., Wang, W., Lin, G.: Hopf bifurcation analysis of maglev vehicle-guideway interaction vibration system and stability control based on fuzzy adaptive theory. Computers in Industry 108, 197–209 (2019)

    Article  Google Scholar 

  38. Tamilarasi, D., Sivakumaran, T.S.: Fuzzy PI control of symmetrical and asymmetrical multilevel current source inverter. International Journal of Fuzzy Systems 20(2), 426–443 (2018)

    Article  Google Scholar 

  39. Tanaka, K., Wang, H.O.: Fuzzy control systems design and analysis: A linear matrix inequality approach. John Wiley & Sons, New York (2001)

    Book  Google Scholar 

  40. Tarbouriech, S., Garcia, G., da Silva Jr., J.M.G., Queinnec, I., : Stability and Stabilization of Linear Systems with Saturating Actuators. Springer (2011)

  41. Wang, Y., Zou, L., Zhao, Z., Bai, X.: \({\cal{H}}_\infty\) fuzzy PID control for discrete time-delayed T-S fuzzy systems. Neurocomputing 332, 91–99 (2019)

    Article  Google Scholar 

  42. Yi, Y., Guo, L.: Constrained PI tracking control for the output pdfs based on T-S fuzzy model. International Journal of Innovative Computing, Information and Control 5(2), 349–358 (2009)

    Google Scholar 

  43. Yi, Y., Li, T., Guo, L.: Statistic tracking control for non-gaussian systems using T-S fuzzy model. In: 2008 - \(17^{th}\) IFAC World Congress, pp. 11564–11569 (2008)

    Article  Google Scholar 

  44. Yu, G.R., Huang, Y.J.: T-S fuzzy control of magnetic levitation systems using qea. In: 2009 - \(4^{th}\) International Conference on Innovative Computing, Information and Control (ICICIC), pp. 1110–1113 (2009)

  45. Yu, G.R., Huang, Y.J., Huang, L.W.: T-S fuzzy control for magnetic levitation systems using quantum particles swarm optimization. In: 2010 - SICE Annual Conference, pp. 48–53 (2010)

  46. Zaccarian, L., Teel, A.R.: Modern Anti-windup Synthesis: control augmentation for actuator saturation, 1st edn. Princeton University Press, Princeton, NJ (2011)

    Book  Google Scholar 

  47. Zhang, D., Nguang, K., Srinivassan, D., Yu, L.: Distributed filtering for discrete-time T-S fuzzy systems with incomplete measurements. IEEE Transactions on Fuzzy Systems pp. 1–10 (2017)

Download references

Author information

Authors and Affiliations

  1. Department of Mechatronics Engineering, Campus Divinópolis-CEFET-MG, R. Álvares Azevedo, 400, Divinópolis, MG, 35503-822, Brazil

    Adriano N. D. Lopes, Valter J. S. Leite & Luis F. P. Silva

  2. CReSTIC EA3804-Université de Reims Champagne-Ardenne, Moulin de la Housse, BP1039, 51687, Reims cedex 2, France

    Adriano N. D. Lopes & Kevin Guelton

Authors
  1. Adriano N. D. Lopes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Valter J. S. Leite
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis F. P. Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kevin Guelton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valter J. S. Leite.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lopes, A.N.D., Leite, V.J.S., Silva, L.F.P. et al. Anti-windup TS Fuzzy PI-like Control for Discrete-Time Nonlinear Systems with Saturated Actuators. Int. J. Fuzzy Syst. 22, 46–61 (2020). https://doi.org/10.1007/s40815-019-00781-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-019-00781-0

Keywords

Search

Navigation