Earticle

This paper expands a sliding mode fuzzy controller which sliding surface gain is optimized by Gradient Descent Optimization Algorithm (GDOA). The main goal is to guarantee acceptable trajectories tracking between the second order nonlinear system (robot manipulator) actual and the desired trajectory. The fuzzy controller in proposed sliding mode fuzzy controller is based on Mamdani’s fuzzy inference system (FIS) and it has one input and one output. The input represents the function between sliding function, error and the rate of error. The outputs represent torque, respectively. The GDOA is the most prominent iterative method for solving sparse systems of nonlinear equations. The GDOA is a composite of simple, elegant ideas that almost anyone can understand. Pure sliding mode fuzzy controller has difficulty in handling unstructured model uncertainties. To solve this problem applied GDOA to sliding mode fuzzy controller for adjusting the sliding surface gain ( ). Since the sliding surface gain ( ) is adjusted by GDOA, it is nonlinear and continuous. GDOA sliding mode fuzzy controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in GDOA sliding mode fuzzy controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0.1%, rise time=0.6 second, steady state error = 1.1e-9 and RMS error=1.8e-9).