Maximum power tracking of variable‐speed wind energy conversion systems based on a near‐optimal servomechanism control system

Abstract

In this article, integral servomechanism based state‐dependent Riccati equation (SDRE) nonlinear output feedback control for wind energy conversion systems (WECSs) has been proposed. The numerical off‐line solving the proposed SDRE control requires to formulate algebraic Riccati equation and algebraic Lyapunov equation. This method approximates the solution of SDRE with Taylor series expansions which are solved with MATLAB solvers. The maximum power point tracking is achieved by defining relation between the optimal angular shaft speed and maximum power providing optimal tip speed ratio in variable‐speed WECSs. The proposed control can significantly reduce the angular shaft speed errors of the permanent magnet synchronous generator (PMSG)‐based WECSs without use of disturbance observers to compensate model uncertainties, modeling errors and noise as in the conventional SDRE control method. The simulation results demonstrate the superior results under mean average errors and root mean square error evaluation methods of the angular shaft speed of PMSG. The performance of the proposed integral servomechanism based SDRE control system has been improved by 80.67% and 80.05% in both scenarios compared to the conventional SDRE control based on compensation technique with disturbance observers.

Output Regulation-Based Optimal Control System for Maximum Power Extraction of a Machine-Side Power Converter in Variable-Speed WECS

“…Let's consider the dynamic system's equations of the PMSG in the WECS in the d-q reference frame where electromagnetic torque is the function of quadrature current [29],…”

“…Particularly, the servomechanism-based state-dependent Riccati equation (SDRE) control approximated with Taylor series expansion has been proposed to account for nonlinearities in the internal dynamics of the PMSG. In the control design, the multivariable nonlinear structure is captured with the SDRE method transforming it into pointwise linear dynamics [29]. While servomechanism has been incorporated into the SDRE approach, it has not been thoroughly tested with a linear quadratic regulator (LQR).…”

Approximate optimal control design for quadrotors: A computationally fast solution

“…Using 7) and 15), and equating the coefficients of the powers of 𝜃 to zero yield the following equations:…”

“…The power series provides an approximate solution and the resultant control law works faster than the conventional SDRE controller. 15 To relieve the computational burden of the finite-time SDRE technique, a suboptimal control algorithm named the finite-time 𝜃-D method, is proposed in this paper. It is an extension of the infinite-time 𝜃-D method [16][17][18] to the finite-time optimal control problem.…”

“…At every time instant it needs to solve a state‐dependent Riccati equation and perform matrix inversion operations twice, which demands intensive computation resources and is hard to implement in real time. The power series provides an approximate solution and the resultant control law works faster than the conventional SDRE controller 15 . To relieve the computational burden of the finite‐time SDRE technique, a suboptimal control algorithm named the finite‐time $$$ \theta $$$‐$$$ D $$$ method, is proposed in this paper.…”