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This paper investigates the delay-dependent stability of the LFC scheme considering two time-varying delays, a new less conservative delay-dependent stability criterion is proposed to study the delay margin of LFC system with PI controller based on Lyapunov-Krasovskii (LK) functional method and linear matrix inequality (LMI) technique. In the presented stability analysis procedure, the time derivative of the LK functional is bounded tightly using the Jesen inequality and the extended reciprocally convex matrix inequality. The proposed stability criterion is tested on the one-area and multi-area LFC systems, and the delay margins with respect to different value of gains of PI controllers are computed to investigate the quantitative effect of the controller gains on the delay margin, and are obtained for different load disturbance to discuss the effect of the exogenous load disturbance.

An optimal control of boost converter based on model-free adaptive controller (MFAC) and fuzzy particle swarm optimization algorithm (FPSOA) is proposed to realize a better response performance and robustness under model mismatch and the parameter time variation. The data-based MFAC is investigated to design the boost converter, which avoids the precise modeling and greatly reduces the influence of model mismatch. Additionally, the FPSOA is used for online optimization of the controller parameters to improve the response performance and robustness. Comparing with the traditional optimal control methods of boost converter, the proposed method avoids the contradiction of establishing accurate model and complex systems design. It inhibits the influences of the parameter time variation and model mismatch, and has a better dynamic and static performance. Finally, the test is implemented on a semi-physical simulation platform for power electronic control systems. The comparison of MFAC and classic state feedback exact linearization control in various model mismatch situations are used to show the effectiveness of the obtained results.

In the field of power electronics, PID error control technology which does not need to establish accurate mathematical model of controlled system. And its' design of control system is simple and practical, so it is widely used in power electronics DC/DC converter. As the typical circuit of DC/DC converter, Buck converter has strong nonlinear and time-varying. The traditional PID controller parameter tuning method cannot satisfy the control performance. Therefore, this paper adopt fuzzy particle swarm optimization algorithm, the control parameters of PID controller in Buck converter is optimized and the optimization result is given in the ITAE performance index. Finally, the optimization of this algorithm is analyzed and compared with the simulation results.