Lyapunov approach based design of a gain adaptive interval type-2 fuzzy controller for servo systems

Article type: Research Article

Authors: De (Maity), Ritu Rani^{a; *} | Mudi, Rajani K.^a | Dey, Chanchal^b

Affiliations: [a] Department of Instrumentation and Electronics Engineering, Jadavpur University, Kolkata, India | [b] Instrumentation Engineering, Department of Applied Physics, University of Calcutta, Kolkata, India

Correspondence: [*] Corresponding author. Ritu Rani De(Maity), Department of Instrumentation and Electronics Engineering, Jadavpur University, Kolkata, India. E-mail: ritu_maity_8@yahoo.co.in .

Abstract: This paper focuses on the development of a stable Mamdani type-2 fuzzy logic based controller for automatic control of servo systems. The stability analysis of the fuzzy controller has been done by employing the concept of Lyapunov. The Lyapunov approach results in the derivation of an original stability analysis that can be used for designing the rule base of our proposed online gain adaptive Interval Type-2 Fuzzy Proportional Derivative controller (IT2-GFPD) for servo systems with assured stability. In this approach a quadratic positive definite Lyapunov function is used and sufficient stability conditions are satisfied by the adaptive type-2 fuzzy logic control system. Illustrative simulation studies with linear and nonlinear models as well as experimental results on a real-time servo system validate the stability and robustness of the developed intelligent IT2-GFPD. A comparative performance study of IT2-GFPD with other controllers in presence of noise and disturbance also proves the superiority of the proposed controller.

Keywords: Type-2 fuzzy control, Lyapunov stability, self-tuning, servo position control and real time experimentation

DOI: 10.3233/JIFS-200802

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 3, pp. 4187-4205, 2021