Farzin Piltan; Bamdad Boroomand; Arman Jahed; Hossein Rezaie

Performance-Based Adaptive Gradient Descent Optimal Coefficient Fuzzy Sliding Mode Methodology

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Author(s)

Farzin Piltan ^1,* Bamdad Boroomand ¹ Arman Jahed ¹ Hossein Rezaie ¹

1. Industrial Electrical and Electronic Engineering SanatkadeheSabze Pasargad. CO (S.S.P. Co), NO:16 , PO.Code 71347- 66773, Fourth floor , Dena Apr , Seven Tir Ave , Shiraz , Iran

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2012.11.05

Received: 12 Feb. 2012 / Revised: 1 Jun. 2012 / Accepted: 20 Aug. 2012 / Published: 8 Oct. 2012

Index Terms

Gradient Descent Optimal Algorithm, Sliding Mode Controller, Gradient Descent Optimal Fuzzy Sliding Mode Controller, Fuzzy Based Tuning Methodology, Lyapunov Based Stability

Abstract

Design a nonlinear controller for second order nonlinear uncertain dynamical systems is the main challenge in this paper. This paper focuses on the design and analysis of a chattering free Mamdani’s fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller for highly nonlinear dynamic six degrees of freedom robot manipulator, in presence of uncertainties. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure sliding mode controller. Pure sliding mode controller and error-based fuzzy sliding mode controller have difficulty in handling unstructured model uncertainties. To solve this problem applied fuzzy-based tuning method to error-based fuzzy sliding mode controller for adjusting the sliding surface gain. Since the sliding surface gain is adjusted by gradient descent optimization method. Fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in fuzzy-based tuning gradient descent optimal fuzzy sliding mode controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).

Cite This Paper

Farzin Piltan, Bamdad Boroomand, Arman Jahed, Hossein Rezaie, "Performance-Based Adaptive Gradient Descent Optimal Coefficient Fuzzy Sliding Mode Methodology", International Journal of Intelligent Systems and Applications(IJISA), vol.4, no.11, pp.40-52, 2012. DOI:10.5815/ijisa.2012.11.05

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