Fuzzy predictive control of three-tank system based on a modeling framework of hybrid systems

Abstract

In this article, a fuzzy predictive control scheme is proposed for controlling liquid level in a three-tank system in the presence of disturbances and uncertainties. The three-tank system is considered as a hybrid system, and a hybrid model of the system is obtained using the mixed logical dynamical modeling approach. Nonlinear parts of the system are linearized based on a piecewise affine linear method. Then, a model predictive control is designed based on the hybrid model and applied to the three-tank system. Although the performance of the model predictive control method is satisfactory in normal condition, it suffers from the problem of bias in output in the presence of disturbance and uncertainty. In this article, a fuzzy supervisor is utilized to adjust the main predictive controller such that the effects of disturbance and uncertainties are degraded by using zero-offset tracking. The proposed fuzzy predictive control scheme has advantages of simplicity and efficiency in normal operation, and strong robustness in the presence of disturbances and uncertainties. Simulation results demonstrate the effectiveness and superiority of the method.

Keywords

Predictive control supervisory control fuzzy logic control three-tank process hybrid system mixed logical dynamical model piecewise affine approach

Get full access to this article

View all access options for this article.

References

Heemels

WPMH

De Schutter

Bemporad

. Equivalence of hybrid dynamical models. Automatica 2001; 37: 1085–1091.

Sontag

. Nonlinear regulation: the piecewise linear approach. IEEE T Automat Contr 1981; 26: 346–358.

Bemporad

Morari

. Control of systems integrating logic, dynamics, and constraints. Automatica 1999; 35: 407–427.

Lazar

. Model predictive control of hybrid systems: stability and robustness. PhD Thesis, Technische Universiteit Eindhoven, Eindhoven, 2006.

Maruthai

Gunna

Ranganathan

. Integrated fuzzy logic based intelligent control of three-tank system. Serbian J Electr Eng 2009; 6: 1–14.

Biswas

Abdelwahed

. A hybrid control system design and implementation for a three-tank testbed. In: Proceedings of IEEE conference on control applications, Toronto, Canada, 28–31 August 2005, pp.645–650. New York: IEEE.

Nandola

Bhartiya

. A multiple model approach for predictive control of nonlinear hybrid systems. J Process Contr 2008; 18: 131–148.

Mignone

. Control and estimation of hybrid systems with mathematical optimization. PhD Thesis, Swiss Federal Institute of Technology, Zürich, 2002.

Precup

Mosincat

Radac

. Experiments in iterative feedback tuning for level control of three-tank system. In: Proceedings of 15th IEEE Mediterranean electrotechnical conference, Valletta, 26–28 April 2010, pp.564–569. New York: IEEE.

10.

Yang

Cocquempot

Jiang

. Robust fault tolerant tracking control with application to hybrid nonlinear systems. IET Control Theory A 2009; 3: 211–224.

11.

Deng

Hao

. The Smith-PID control of three-tank-system based on fuzzy theory. J Comput 2011; 6: 514–523.

12.

Precup

Tomescu

Radac

. Iterative performance improvement of fuzzy control systems for three tank systems. Expert Syst Appl 2012; 39: 8288–8299.

13.

Lunze

Askari-Marnani

Cela

. Tank control reconfiguration. In: Aström

Albertos

Blanke

. (eds) Control of complex systems: Springer-Verlag, 2001, pp.241–283. London: Springer-Verlag.

14.

Heiming

Lunze

. Definition of the three-tank benchmark problem for controller reconfiguration. In: Proceedings of the European control conference, Karlsruhe, Germany 31 August–3 September 1999. Zurich: European Control Association.

15.

Delavari

Ranjbar

Ghaderi

. Fractional order control of a coupled tank. Nonlinear Dynam 2010; 61: 383–397.

16.

Ikeda

. Nonlinear parametric vibrations of an elastic structure with a rectangular liquid tank. Nonlinear Dynam 2003; 33: 43–70.

17.

Geyer

. Low complexity model predictive control in power electronics and power systems. PhD Thesis, Swiss Federal Institute of Technology, Zürich, 2005.

18.

Groetsch

. Inverse problems and Torricelli’s law. Coll Math J 1993; 24: 210–217.

19.

Torrisi

Bemporad

. HYSDEL—a tool for generating computational hybrid models for analysis and synthesis problems. IEEE T Contr Syst T 2004; 12: 235–249.

20.

Bemporad

. Hybrid toolbox v.1.2.6, http://control.ee.ethz.ch/∼hybrid/

21.

Nagelkerke

NJD

. A note on a general definition of the coefficient of determination. Biometrika 1991; 78: 691–692.

22.

Sarailoo

Rahmani

Rezaie

. Modeling of three-tank system with nonlinear valves based on hybrid system approach. J Control Eng Technol 2013; 3: 20–23.

23.

Ławryńczuk

. Accuracy and computational efficiency of suboptimal nonlinear predictive control based on neural models. Appl Soft Comput 2011; 11: 2202–2215.

24.

Ławryńczuk

. On improving accuracy of computationally efficient nonlinear predictive control based on neural models. Chem Eng Sci 2011; 66: 5253–5267.

25.

Gerkšič

Pregelj

. Tuning of a tracking multi-parametric predictive controller using local linear analysis. IET Control Theory A 2012; 6: 669–679.

26.

Huang

. Design and input-to-state practically stable analysis of the mixed H2/H_∞ feedback robust model predictive control. IET Control Theory A 2012; 6: 498–505.

27.

Wang

Zhang

Sun

. Using subset sequence to approach the maximal terminal region for model predictive control. IET Control Theory A 2012; 6: 596–601.

28.

Antsaklis

Koutsoukos

. Model predictive control past present and future. Comput Chem Eng 1999; 23: 667–682.

29.

Camacho

Ramirez

Limon

. Model predictive control techniques for hybrid systems. Annu Rev Control 2010; 34: 21–31.

30.

Makhorin

. GLPK (GNU Linear Programming Kit), version 4.42. 2007, http://www.gnu.org/software/glpk/.