**5. Conclusions**

In order to solve the problem of poor global control performance of the controller designed by small signal modeling and harmonic linearization, two universal controller design methods based on state feedback linearization are proposed for the LCL type VSI. Relation degree of the VSI system and that of the reduced order model are analyzed, respectively. Subsequently, the coupling matrixes are designed by adopting the Lie derivative. Through the nonlinear transformation, the original system is mapped to the Brunovsky standard type, and the new system linear controller can be used to

complete the control of the original complex system. Then, the parameters design ideas of two kinds of controllers are given. The proposed single closed-loop current controller has a simple structure, but it is highly dependent on the exact model of the system. The double closed loop controller sets the filter capacitor voltage as the inner loop control variable, by which a reduced order feedback linearization control can be achieved step by step, to improve the adaptability and robustness of the system. The simulation and experimental results show that the two controllers have good steady-state control performance and dynamic response performance. In practical application, the robustness of linear control system based on reduced-order feedback is better.

**Author Contributions:** L.Y. wrote the paper and designed the control method; C.F. contributed to the conception of the study and designed the simulation model; J.L. helped to perform the analysis with constructive discussions.

**Acknowledgments:** This work is supported by the National Natural Science Foundation of China (Grant No. 51607179) and the Fundamental Research Funds for the Central Universities (2017QNB01).

**Conflicts of Interest:** No potential conflict of interest was reported by the authors.
