| Switching power converter is the core part of modern power electronics system and its operation directly relats to the working performance of power electronics system. Due to the non-linear characteristic of its devices and the switching action of the switch, feedback-controlled power converter performs as a strongly nonlinear and time-varying system, which runs with a variety of non-linear phenomena, such as period-doubling bifurcation, the border collision Bifurcation, chaos, etc., resulting in a problem that it's difficult for the system to work as expected. This dissertation, starting for a detailed study on power converter, conducted a research on the analyzing approaches on its non-linear behaviour and the chaos control strategy, aiming to provide a theoretical support for the stable, reliable and optimized operation of the power electronic system.①According to the common piecewise-linear characteristic of PWM control DC-DC converter system, an improved solution to its Jacobian matrix is put forward to obtain its general expression. In the existing literatures, the Jacobian-matrix expression usually derived with the data-sampled method is not adaptable to analytical analysis and not applicable in most of DC-DC converters. Based on linear perturbation method, the general expression of the Jacobian matrix of a single-switch PWM control DC-DC converter system is derived and based on the derived expression three concerning stability conclusions about fast-scale behaviour are given. The validity of the proposed method is confirmed by applying the conclusions to two typical PWM control DC-DC converters.②A research on the controllability analysis of time-delayed feedback controlled (TDFC) DC-DC converter are conducted. Study on TDFC control of chaos in DC-DC converter has been rarely addressed and few effective methods for determining TDFC control parameters been reported. The discrete model related to the TDFC controlled current-mode Boost converter system is established with the data-sampled method. In addition, through analyzing the duty cycle and state-variables separately, the prediction of chaos control effect and optimization of control parameters are achieved. The introduction of TDFC to the converter system leads to an infinite dimensional problem and hence it becomes difficult to establish the discrete iteration model of the controlled system. To solve the problem, the author conducted a transfer-function based period-doubling bifurcation analysis method for the TDFC controlled Buck converter system to determine the control-parameter range. Meanwhile, a quasi-TDFC control method with a good control effect is introduced and owning to the adjustable characteristics of its delay time and feedback gain, some new circuit-realization chaos control methods are easily achieved with some improvements of this method.③An improved chaos control method for PWM control DC-DC converter is put forward and its circuit-based realization and control-parameter optimization are given. Based on an evolution of the quasi-TDFC method, a differential-voltage feedback control and a first-order dynamic feedback control are put forward for the control of chaos in voltage-mode Buck converter and current-mode Boost converter, respectively. The simulation and experiment results show good control effects of the proposed methods. In addition, based on the analysis on the multi-pulse behaviour in the differential voltage feedback controlled Buck converter system a square-current feedback control is proposed for the control targets of the chaos control and multi-pulse suppression.④A self-stable chaos control concept is proposed for DC-DC converter and its theoretical basis, realization with circuits and control-parameter optimization are completed. Based on the cyclical nature of converter system, a steady-state frequency-domain model is derived to achieve the filter-based realization of of the self-stable chaos controller. With the voltage-mode Buck converter as the research object, analysis related to the controllability and control effect of the quasi-self-stable control and self-stable control is reported. The control parameters are optimized with the improved Jacobian-matrix solution. The simulation and experiment results confirm the feasibility of the proposed control strategy.⑤The concept of periodic equilibrium power converter is proposed and its analysis method and chaos control strategies are explored. According to the quasi-steady-state concept, periodic equilibrium power converter is considered as an equivalent of quasi direct-equilibrium system with a variable input-voltage. With the peak-current mode Boost PFC system as the study object, the eigenvalues of the controlled system are observed by applying the improved Jacobian-matrix solution. An improved district-divided multi-parameter control strategy for the chaos control of the peak-current mode Boost PFC system is proposed to achieve a better control effect. According to the high- and low-frequency characteristic of periodic equilibrium power converter, dual-band mode control strategy is put forward. A better control effect is achieved with the application of a dual-band mode feedback-control strategy to the the peak-current mode Boost PFC system, where self-stable control is introduced into the control prototype of periodic equilibrium power converter.
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