Adaptive second‐order terminal PID sliding mode control design for integer‐order approximation of wind turbine system for maximum power extraction

Abstract

The main purpose of this paper is to extract the maximum power from the variable speed wind turbine (VSWT), which is modelled using fractional calculus. The use of the fractional-order operator can harden the practical implementation and numerical simulation of the fractional-order systems. To apply the fractional calculus theory, we assume that the orders of all fractional derivatives of the system have a small deviation from the nearest integers. By defining this small deviation as a perturbation parameter, an integer-order approximation method is presented for approximating the fractional-order system into a perturbed integer-order system in the time domain. Then, a new adaptive second-order sliding mode control (SOSMC) method is proposed using the terminal proportional integral derivative (TPID) sliding surface to achieve maximum power extraction and reduce mechanical loads and chattering. A TPID sliding surface is employed to ensure better tracking, have a zero steady-state error, decrease the mechanical stresses, and eliminate the chattering phenomenon. The stability of the adaptive SOSMC based on the obtained integer-order approximation is analyzed using the Lyapunov stability criterion. The simulation results of the proposed method are presented and compared with some designed controllers for wind turbines (WTs) modelled with fractional and integer derivatives. The obtained results show the effectiveness of the proposed strategy.