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This study deals with the current control of three-phase inverters connected to the grid by means of LCL filters. The control action is given by the feedback of the filter states, in coordinates αβ0, and of the internal states of resonant controllers. The control gains are computed by means of an optimal linear quadratic regulator that is robust to uncertain and time-varying parameters related to the grid impedance at the point of common coupling. As contributions, one has the detailed proof of a robust discrete linear quadratic control, showing its applicability also for the time-varying case, the experimental validation of the results in terms of the total harmonic distortion and harmonic limits for the grid injected current, according to the IEEE 1547 standard, and the analysis of the ℋ ∞ norm of the closedloop system for several values of grid inductance, indicating a value of grid inductance for which one has best performance for the time-invariant case. For comparison, a conventional state feedback controller is designed and implemented, showing the limitation of the non-robust strategy.

This study proposes a design procedure and experimental validation for a robust H 2 state feedback controller applied to a DC-DC boost converter modelled as a linear system affected by time-varying parameters lying in known intervals. The parameters considered as time-varying are the input voltage, the load resistance and the operating point duty cycle. A polytopic representation of the system is derived and the controller is designed by means of a convex optimisation problem based on linear matrix inequalities. The conventional H 2 controller is extended to cope with alpha-stability and robust linear quadratic regulator design, providing different strategies to trade-off the magnitude of the control gains and the response of the closed-loop system. Tight correspondences between numerical simulations and the experimental results prove the viability of the application of this technique for this kind of plant. Finally, a robust performance analysis illustrates the capacity of the closed-loop system to reject energy bounded disturbances, with interpretation for the cases of time-varying and time-invariant parameters.

This study provides a digital H 1 controller design suitable for uninterruptible power supply inverters, yielding results that comply with the IEC 62040-3 Standard. An augmented state space model for the system is given, taking into account the delay from the digital implementation of the control signal, and resonant controllers that ensure asymptotic tracking of the reference and good rejection of load disturbances. It is shown a case where an H 1 optimal state feedback controller cannot provide good results because of the high control gains. To solve this problem, an H 1 suboptimal controller is proposed, taking into account a prescribed bound for the H 1 norm of the closed-loop system and a parameter for limitation of the norm of the control gain vector. This suboptimal controller provides gains that lead to suitable results, complying with the constraints from the IEC 62040-3 Standard. These results are compared with those from a widely used state feedback controller, providing superior performance, even with a much simpler design procedure. Simulation and experimental results have a good correspondence. Finally, the study illustrates that the H 1 norm of the closed-loop system can be seen as the output impedance over the frequency. From this information, using the small gain theorem, one can get the admittance value of the linear loads that preserve stability when connected to the uninterruptible power supply.

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