Abstract
The aim of the work for this paper is the design of an optimal backstepping controller for a nonlinear pendulum system to stabilize the position of pendulum’s ball suspended in the desired position. The Cuckoo optimization algorithm (COA) has been utilized to get and tune the gain variables of the proposed backstepping controller in order to find the best torque action for the system. The numerical simulation results using (MATLAB package) show the robustness and the effectiveness of the proposed backstepping based COA controller in terms of obtaining the best torque control action without a saturation state that will stabilize the pendulum system performance. The simulation results show also that the proposed control system when compared with the other controller results has the capability of minimizing the pendulum’s ball position tracking error to the zero value at the steady state response and speeding up the system response. Moreover, the fitness evaluation value is reduced.
Highlights
In various nonlinear control system issues, the backstepping control method is recently popular since it gives a nonlinear robust controller with good performance
Various types of backstepping control algorithms have been used for controlling various nonlinear systems such as adaptive backstepping controller [3], the integral backstepping controller [4], the optimal backstepping controller [5], the fuzzy backstepping controller [6], backstepping sliding mode controller [7], backstepping based PID controller [8], backstepping /nonlinear H∞ controller [9], and adaptive type-2 fuzzy backstepping controller [10]
) and the maximum simulation time ( ) equals 10 are described as follows: To investigate the optimal backstepping controller as shown in Figure 2 for controlling the output position of the pendulum ball, cuckoo tuning control methodology has been used to find and tune the optimal parameters of the backstepping controller ( ) and ( ). These parameters lead to finding the optimal control action and minimizing the position tracking error with the minimum number of fitness evaluation, the parameters of the control methodology based on Cuckoo Optimization Algorithm (COA) algorithm is defined in Description and Symbol
Summary
In various nonlinear control system issues, the backstepping control method is recently popular since it gives a nonlinear robust controller with good performance. The Backstepping approach is a recursive procedure using a systematic design approach and Lyapunov function for particular forms of the nonlinear dynamical systems This methodology guarantees both global and local asymptotic convergence for regulation and tracking properties [1, 2]. A robust nonlinear controller is needed for reaching stable limit cycles when the ground, changes, or manipulated objects are unknown [11]. This motivates the design of a robust nonlinear controller for controlling a simple pendulum. The contribution of this paper is described as follows: Utilizing the COA which has the ability of fast off-line searching in global regions to obtain and tune the best gain variables for the backstepping controller.
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