LCL Filter Plant Control

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Joined Nov 24, 2019
Hi everyone! I don't know if this is the place to ask Control Theory related questions, but it's for modelling a power electronics circuit so I thought I could at least try. I have to design a grid connected inverter in Simulink using the PLECS toolbox and I ran into some problems when designing the current controller. My teacher told me that I should treat the LCL filter in the PLECS model as my plant. However, I don't have a lot of experience with control theory and the transfer function of the filter is giving a behavior I haven't really seen before. locus.jpg
This is the root locus of the plant's transfer function. As you can see, the dominant poles are barely stable and there's no gain values that could push them further into the unity circle (this is in z-domain btw). I'm supposed to use a PI controller for it, but the plant has a response like nothing I've seen before. I tried doing it both analytically and through the control system designer in Matlab, but I basically only get a very small range of values for Kp and Ki that only barely improve the system's response (I think something between 0.1 and 0.7 for Kp, anything more and it's unstable). Using values in that range gives me a huge settling time too. I really haven't worked with a plant that gives such a response. I'll attach the .m file I used, as well as the Simulink model. Any help would be appreciated. Thanks a lot!