Robust fractional order controller based on improved particle swarm optimization algorithm for the wind turbine equipped with a doubly fed asynchronous machine

Abstract

In this paper, an improvement of the particle swarm optimization algorithm is proposed. The aim of this algorithm is to determine the optimal parameters of a robust fractional order controller which guarantees stability and robustness of required nominal performances. Controllers with fractional order are first obtained by a previous transformation of the multi-objective optimization problem into an equivalent single-optimization problem, and then solved by the proposed improved particle swarm optimization algorithm. In order to examine the stability and performance robustness, this controller is applied on an ill-conditioned wind turbine equipped with a doubly fed asynchronous machine, where the system dynamics is modeled by an unstructured output multiplicative uncertainty model. The simulation results show the effectiveness of the proposed synthesis method, where the control is compared (for the same design frequency-domain specifications) for both the robust fractional order controller such as that designed through the standard particle swarm optimization algorithm and that obtained by resolving the multi-objective optimization problem.

Robustified fractional-order controller based on adjustable fractional weights for a doubly fed induction generator

“…Noting that, in the ( d − q ) -axis, both current components I ds and I qs are considered as constant in the steady state. Consequently, their derivatives are equal to zero (Belfedal et al, 2010; Sedraoui and Boudjehem, 2012). Thus, the rotor voltage vector V r = [ V dr V qr ] T is considered as a set-control vector that is provided by a proposed fractional controller.…”

“…Moreover, let us consider y = [ V ds V qs ] T and x s = [ ϕ dr ϕ qr ] T as the output vector and the state-variable vector of the plant-model that modelled the DFIG, respectively. By using the numerical data that is summarized in Table 2 (Belfedal et al, 2010; Sedraoui and Boudjehem, 2012), the state-space representation is determined by applying the MATLAB® function Linmod2 on the Simulink system, which is etablished from Equations (29) and (30). The transfer matrix of the nominal plant-model is determined by…”

“…These variables define the adjustable fractional weights that are included later in the mixed-sensitivity problem. The controller-structure is proposed, in this paper, as a commonly cascade fractional-order proportional-integral-derivative (PID) controller (Sedraoui and Boudjehem, 2012; Sedraoui et al, 2012):…”

“…Afterward, the output uncertainty model that modelled the real dynamic of the DFIG is considered in this paper. It is defined as (Belfedal et al, 2010; Sedraoui and Boudjehem, 2012):…”

“…Among them are the Schur Model Reduction (SMR) method (Safonov and Chiang, 1989), Optimal Hankel Model Reduction (OHMR) method (Safonov et al, 1990) and others. Unfortunately, the obtained robustness properties are gradually aggravated with the frequency evolution (Apkarian and Noll, 2006; Apkarian and Tuan, 2000; Sedraoui and Boudjehem, 2012). As result, designing such controllers is not easy in practice.…”