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

• Published in: Expert systems with applications Vol. 40; no. 1; pp. 188 - 199
• Main Authors: Precup, Radu-Emil, Rădac, Mircea-Bogdan, Tomescu, Marius L., Petriu, Emil M., Preitl, Stefan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.01.2013; Elsevier
• Subjects: Algorithms; Applied sciences; Computer science; control theory; systems; Control system analysis; Control systems; Control theory; Control theory. Systems; Convergence; Discrete-time input affine SISO systems; Dynamical systems; Exact sciences and technology; Feedback; Iterative feedback tuning; Nonlinear dynamics; Optimal control; PI-fuzzy controllers; Real-time experimental results; Stability; Stability analysis; Real-time experimental results; Stability; Iterative feedback tuning; Discrete-time input affine SISO systems; PI-fuzzy controllers; Convergence; Input output; Integral proportional control; Evolutionary algorithm; Position control; Lyapunov method; Feedback regulation; Updating; Nonlinear dynamical systems; Direct method; Fuzzy control; Direct current; Angular position; Numerical convergence; Real time; Affine transformation; Hyperstability; Fuzzy logic; Measure theory; Experimental result; Optimal control; Discrete time; SISO system; Sugeno integral
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2012.07.023

► 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. ► Discrete-time input affine SISO systems are considered. ► Lyapunov’s direct method is applied to tune Takagi–Sugeno–Kang PI-fuzzy controllers. ► An IFT-based tuned PI-fuzzy controller for a servo system shows performance improvement. 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.