Generalized Discretization of State-Space Model for Discrete-Time Small-Signal Analysis of Inverters With Arbitrary Control Delay

For inverter control, delay-reduction methods, such as multisampling and pulse-width modulation with sampling instant shift, are gaining in popularity. The outcome of the arbitrary ratio of the sampling-computation time to the control period greatly challenges z-domain modeling and analysis of the digital control system. Therefore, a generalized discretization method of the state-space model is elaborated by incorporating the definition of a delay-based input matrix. The discrete-time pulse-transfer-function matrix is then derived based on the proposed generalized state-space model (G-SSM), which avoids complicated algebraic calculation of residues and thus facilitates the input–output dynamic analysis via classical control tools, such as Bode diagram or root locus. Additionally, the G-SSM with a constant input matrix is constructed by introducing an augmented state vector, which eases the implementation of modern control theory, such as observer or pole placement. Applications of tools of classical and modern control theory are further investigated from the standpoint of stability identification and parameter tuning, which confirms the effectiveness of the G-SSM in governing the discrete-time small-signal analysis of the arbitrary-delay system. Finally, experiments are conducted on an LCL-filtered grid-tied inverter to validate the correctness of the theoretical expectations.