Design of Discrete-Time Backstepping Sliding- Mode Control for <italic>LCL</italic>-Type Grid-Connected Inverter

Abstract

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.

Keywords

• Backstepping
• sliding-mode control
• discrete-time
• non-causal problem
• LCL filter%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">LCL</italic> filter
• grid-connected inverter