Bifurcation analysis and control in a DC–AC inverter with PID controller

Abstract Aiming at the rich bifurcation and chaotic characteristics in the inverter with proportion integral derivative (PID) controller, the discrete iterative model of such an inverter was derived based on the stroboscopic mapping theory; the nonlinear evolution and the cause of instability in this inverter are analyzed. It was observed that the low‐frequency oscillation following instability was due to the Hopf bifurcation, which will decrease the power supplied quality by the inverter. To address the potential issue of the system instability caused by nonlinear behaviors, an improved exponential time‐delay feedback control scheme was proposed. The controlled object's output current first subtracted its own delay a period of time to form a difference term, which was subsequently fed into an exponential link to make difference with the constant 1. The resulting value was then fed into a proportional link to obtain the control term, which was applied to the PID controlled inverter in a feedback manner. Moreover, the range of the feedback proportional coefficient was solved via the Jury criterion. Finally, the effectiveness of this scheme was verified through the comparative simulations, demonstrating that this scheme can not only increase the stability domain for each parameter by more than 50 % in the PID controlled inverter but also stabilize the quasi‐periodic behavior due to the low scale oscillation caused by the Hopf bifurcation at the switching frequency.