**7. Conclusions**

In this paper, a robust multilayer MPC, which can achieve decoupling control of the output voltage and capacitor voltage balancing simultaneously in di fferent layers against the parameter uncertainties or mismatches of the LC filter, is proposed for the full-bridge NPC inverter-based CDAs. The errors caused by the parameter mismatches or uncertainties of the LC filter and the load current are regarded as lumped disturbance and estimated by the designed Luenberger observer. Based on the estimated disturbance, a two-layer MPC is proposed, where the output voltage tracking and the capacitor voltage balancing are achieved in the first layer and the second layer, respectively. Finally, the steady state performance, the dynamic performance and the robust performance are verified on the designed 2 kW experiment prototype.

Compared with existing methods, the proposed robust two-layer MPC uses only one observer to observe the lumped disturbance caused by the parameter mismatch and the load current, which simplifies the control system and reduces the calculation of the system. The layered structure further reduces the computation without a ffecting the dynamic performance of the MPC. However, the control delay is not considered, which may a ffect the control e ffect and calls for further research.

**Author Contributions:** Conceptualization, X.W.; formal analysis, A.L.; funding acquisition, M.L.; investigation, X.W.; methodology, A.L.; project administration, M.L.; software, K.L.; validation, K.W.; writing—original draft, X.W.; writing—review and editing, H.W. and A.L.

**Funding:** The Program for Guangdong Introducing Innovative and Entrepreneurial Teams: 2017ZT07G23; Research on High-power and High-e fficiency Electro-acoustic Transduction Mechanism and Control Method: 51837005; Research on Topology, Passive Current Sharing Mechanism and Control for Multiphase Resonant Converter with Coupled Resonant Tank: 51977069.

**Conflicts of Interest:** The authors declare no conflict of interest.
