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This article proposes a design procedure for $\mathcal {H}_{\infty }$ current controllers suitable for application in grid-connected converters (GCCs) subject to disturbances and uncertain parameters. Linear matrix inequalities provide robust state feedback controllers from a set of design parameters automatically tuned with the help of a genetic algorithm, oriented by a suitable objective function. Such strategy allows to overcome the problem of $\mathcal {H}_{\infty }$ high control gains, ensuring a good tradeoff between performance and robustness against uncertain grid parameters. The proposal contributes to improve the effective use of metaheuristics for automated control tuning in GCCs, avoiding time-consuming human–machine interaction in the design stage. A case study with experimental results is presented, demonstrating the viability and the superior performance of the proposed controllers with respect to similar techniques, and also the compliance with the IEEE 1547 Std for grid currents. [ABSTRACT FROM AUTHOR]

This paper provides robust $\mathcal {H}_{\infty }$ state feedback controllers suitable for implementation in three-phase grid-connected converters. This control strategy is known to provide optimal rejection of disturbances, but usually leads to high control gains, that may be difficult to be implemented in practice. To mitigate this problem, a linear matrix inequality condition based on slack variables is proposed, which allows to impose bounds on the control gains in a less conservative way than conventional quadratic stability. The performance is proven to be superior to similar $\mathcal {H}_{\infty }$ state feedback controllers in the literature, providing an upper bound for the converter output admittance and experimental grid currents complying with the IEEE Standard 1547. [ABSTRACT FROM AUTHOR]

This brief presents a numerically attractive approach to design fixed-order \mathcal H2/ \mathcal H\infty controllers for discrete-time linear parameter-varying (LPV) systems. In this approach, the controller order that is completely determined by the number of states and the parameter dependence is selected in advance. For a prefixed controller order, parameter-dependent sufficient linear matrix inequalities (LMIs) are presented, relying on an a priori computed full-order LPV controller that stabilizes the LPV system for all the possible parameter trajectories. Pólya’s theorem and polynomial approximations are used to obtain numerically tractable LMI problems that guarantee the feasibility of the parameter-dependent synthesis conditions. The practical viability of the approach is demonstrated by experimental validations on a lab-scale overhead crane with varying cable lengths. [ABSTRACT FROM AUTHOR]

This paper presents a linear matrix inequality-based procedure for the design of state feedback current controllers that are robust to uncertainties on grid inductance for grid-connected converters with LCL filters. The state feedback control law includes the filter state variables, the states of resonant controllers, and considers also the delay from digital control implementation. As the main contribution here, the proposed strategy allows to deal with resonant controllers of arbitrary dimension, and provides results complying with IEEE Standard 1547 requirements. The control synthesis condition takes into account the assignment of the closed-loop eigenvalues in a circular region with radius r, located inside the unit circle, and the control design relies only on the choice of the value of the radius in the interval 0 <; r ≤ 1, providing all the state feedback gains in a simple and efficient procedure. [ABSTRACT FROM AUTHOR]