Systematic and Robust Tuning of Proportional-Resonant Controllers for Current and Voltage Tracking

In the control and operation of power inverters, proportional-resonant (PR) controllers are used to track references and reject disturbances that can be described by a sum of sinusoidal signals of known frequency. The relevance of these controllers is increasing due to the increase in distortion and volatility of three-phase signals in the grid. However, as reported in the literature, the tuning of PR controllers is far from trivial due to their large number of parameters and the presence of pure imaginary poles in the associated transfer function. To address these issues, a time-domain framework based on linear matrix inequalities (LMIs) is presented for the tuning of PR controllers with applications to voltage and current tracking. The advantage of this approach is the straightforward combination with other techniques such as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{H}_{\infty}$</tex> control. The effectiveness of the approach is illustrated through numerical simulations, where the injection of a constant active power is achieved in the presence of distorted voltages.