Optimized fuzzy fractional-order linear quadratic tracking control for a nonlinear system

Abstract

In this paper, a novel fuzzy fractional-order Linear Quadratic Tracking (LQT) controller optimized by a Multi-Objective gray Wolf Algorithm (MOGWA) is designed for a 6 Degree-Of-Freedom (DOF) quadcopter flying system. In order to reach this end, the state-space equations would be divided into two parts, one for attitude and altitude control and another for position control. The LQT method is implemented to determine the constant parameters of the designed controller by minimizing a quadratic form related to errors and control efforts. Then, to substantially improve the performance of the linear quadratic tracking scheme, the fractional-order derivatives of the system errors are considered as the control inputs, while the MOGWA is used for optimal determination of the related orders. A fuzzy system that employs triangular and trapezoidal membership functions as well as the center average defuzzifier and singleton fuzzifier, is designed to timely regulate the gains of the controller. The introduced strategy would be applied on the nonlinear quadcopter flying system, and the related diagrams would be revealed to illustrate the efficiency and ability of the introduced fuzzy optimal fractional-order linear quadratic tracking controller.

Keywords

• Fractional-order calculus
• Fuzzy system
• Multi-objective design
• Quadcopter flying robot