Nonlinear Behavior and Chaos Control of T-Type Inverters Regulated with Quasi-PIR Controller

To suppress grid-current distortion induced by grid-side DC disturbance, a quasi-proportional integral resonant (quasi-PIR) control strategy is introduced into a single-phase second-order T-type grid-connected inverter. The nonlinear dynamical behavior of the system is systematically investigated. Based on the stroboscopic mapping theory, a discrete iterative model of the system is established. Nonlinear analysis tools, including bifurcation diagrams, folding diagrams, time-domain diagrams, Lyapunov exponents, and normalized distance analysis, are employed to reveal and quantitatively characterize the nonlinear evolution of the system with the outer-loop proportional gain [Formula: see text] as the bifurcation parameter. The Lyapunov exponent is used to identify the transition from periodic motion to chaos, while the normalized distance between adjacent trajectories is introduced to evaluate the sensitivity of the system to initial conditions. In addition, the effects of other control parameters and main-circuit parameters on the system nonlinearity are examined through bifurcation analysis. The system dynamics are further analyzed using the eigenvalues of the Jacobian matrix and parameter stability regions, enabling a quantitative characterization of the stability boundaries. To address the inherent nonlinear instabilities commonly observed in T-type inverters, an improved proportional cosinoidal delayed feedback control strategy is proposed. The feedback signal is constructed from the difference between the system output and its one-period delayed value, which is processed through a proportional gain and a cosine function to generate the control input. Bifurcation diagrams and eigenvalue trajectories indicate that the proposed control strategy significantly enlarges the stability domains of key parameters, including the outer-loop proportional gain [Formula: see text], the inner-loop proportional gain [Formula: see text], and the DC-link voltage [Formula: see text]. Finally, hardware-in-the-loop experimental results validate the effectiveness of the proposed control strategy, providing strong support for the stable operation of quasi-PIR-regulated T-type grid-connected inverters.