Please see http://dx.doi.org/10.1109/TIE.2014.2334669 [Ufnalski, B.; Kaszewski, A.; Grzesiak, L.M., "Particle Swarm Optimization of the Multioscillatory LQR for a Three-Phase Four-Wire Voltage-Source Inverter With an LC Output Filter," in IEEE Transactions on Industrial Electronics, vol. 62, no. 1, pp. 484-493, Jan. 2015] for more details. And remember that OPTIMALITY DOES NOT IMPLY ROBUSTNESS! Selecting a sufficient penalty for control signal dynamics is crucial in this control system. The good news is that this is the only parameter to be guessed and checked in the proposed tuning procedure. More reference frames compared in http://dx.doi.org/10.1109/EPE.2013.6631891 [Kaszewski, A.; Ufnalski, B.; Grzesiak, L.M., "The LQ controller for the 3-phase 4-leg inverter with an LC output filter — Choosing the right reference frame," in 15th European Conference on Power Electronics and Applications (EPE 2013), pp. 1-9, 2-6 Sept. 2013] are on its way to File Exchange. Keep your stick on the ice!
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