Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems

Authors:
Radu-Emil Precup;Mircea-Bogdan Rdac;Marius L. Tomescu;Emil M. Petriu;Stefan Preitl
Affiliations:
Department of Automation and Applied Informatics, "Politehnica" University of Timisoara, Bd. V. Parvan 2, RO-300223 Timisoara, Romania;Department of Automation and Applied Informatics, "Politehnica" University of Timisoara, Bd. V. Parvan 2, RO-300223 Timisoara, Romania;Faculty of Computer Science, "Aurel Vlaicu" University of Arad, Complex Universitar M, Str. Elena Dragoi 2, RO-310330 Arad, Romania;School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward, Ottawa, ON, Canada K1N 6N5;Department of Automation and Applied Informatics, "Politehnica" University of Timisoara, Bd. V. Parvan 2, RO-300223 Timisoara, Romania
Venue:
Expert Systems with Applications: An International Journal
Year:
2013

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Abstract

This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi-Sugeno-Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov's direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov's hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included.