Nonlinear Control of Multiple Equilibrium Systems and Unknown Sinusoidal Disturbance by Using Backstepping Technique and Neural-Fuzzy Controller

Abstract

Controlling nonlinear systems have always been a challenging problem. Complexity is mostly the result of nonlinear systems behavior dependence on initial conditions and input. Linearization techniques are such kinds of nonlinear systems analysis tools, which can give suitable results in neighborhood of equilibrium points. In addition, phase portraits are very efficient for visualizing the behavior of system in equilibrium points’ neighborhood. In this paper, designing a controller for a low order dynamic system with multiple equilibrium points in presence of a sinusoidal disturbance with unknown amplitude and unknown bounded frequency is investigated. The proposed controller is based on a combination of the backstepping method, Lyapunov based techniques and neuro-fuzzy strategies. At first, the mathematical dynamic model is presented and all equilibrium points are found. Lyapunov-based techniques and backstepping method are combined in order to control the system under influence of sinusoidal disturbance with unknown amplitude but fixed frequency. Finally, a neuro-fuzzy controller is designed and added to main controller to tolerate the frequency variation of the disturbance. Simulation results are presented to demonstrate the performance of the controller in omission of a sinusoidal disturbance with random variable frequency and amplitude.