In this paper, the authors propose a particle swarm optimization (PSO) for a discrete-time inverse optimal control scheme of a doubly fed induction generator (DFIG). For the inverse optimal scheme, a control Lyapunov function (CLF) is proposed to obtain an inverse optimal control law in order to achieve trajectory tracking. A posteriori, it is established that this control law minimizes a meaningful cost function. The CLFs depend on matrix selection in order to achieve the control objectives; this matrix is determined by two mechanisms: initially, fixed parameters are proposed for this matrix by a trial-and-error method and then by using the PSO algorithm. The inverse optimal control scheme is illustrated via simulations for the DFIG, including the comparison between both mechanisms.

This paper pressents an infinite-horizon optimal controller, based on a state-dependent Riccati equation approach to solve the tracking for nonlinear systems. The synthesized control law comes from solving the Hamilton-Jacobi-Bellman equation for state-dependent coefficient factorized nonlinear systems. The proposed controller results in a state feedback optimal control law plus a time varying term, which minimizes a quadratic performance index. In order to illustrate the tracking to a desired reference, the proposed optimal control law is applied to two systems with practical applications: the Van der Pol oscillator and a doubly fed induction generator. Simulation results illustrate the effectiveness of the control scheme.

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The authors propose robust non-linear controllers for a wind system. The proposed controllers are based on a combination of the block control linearisation and super-twisting algorithm, as a second-order sliding mode technique. The main control loop is designed to regulate the electromagnetic torque and stator power factor of a doubly-fed induction generator which is connected to the grid. The generator is mechanically coupled with a DC motor, which can emulate the wind turbine operation. Therefore, an auxiliary control loop is designed to control the DC motor velocity. Additionally, a grid-side converter controller is proposed to regulate the DC-link voltage into AC/DC/AC converter, and displacement factor of the energy flow between the rotor and the grid. A robust stability analysis of the complete closed-loop system under external disturbances is presented. The robustness of the proposed control schemes is validated in real time using a workbench, which consists of a motor-generator group, AC/DC/AC electronic drive and dSPACE DS 1104 controller boards.

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