Design of Discrete-Time Backstepping Sliding- Mode Control for LCL-Type Grid-Connected Inverter

This study designs a discrete-time backstepping sliding-mode control (DTBSMC) method for an LCL-type grid-connected inverter. Firstly, the dynamic model of a discrete-time three-order system is derived, and a discrete-time backstepping control method cascading with the sliding-mode control theory is designed via Lyapunov stability verification. Moreover, the system state equation is transformed into a special form by using a time-varying mapping for overcoming the difficulty of a non-causal problem. Besides, through the recursively subsystem design for the high-order LCL-type inverter, the asymptotic system stability can be ensured by step-by-step virtual control designs. In addition, the proposed method can combine both the advantages of the backstepping control method and sliding-mode control theory. Therefore, the inverter system can have strong robustness under the condition of a power grid with varied grid impedances. Finally, the effectiveness of the proposed DTBSMC method is verified by numerical simulations and experimental results in comparison with a traditional proportional-resonant (PR) method and a backstepping control method.