Chaos And Bifurcation Controlin DC-DC Converter

DC-DC converters do not work well when they exhibit chaos and bifurcation for some circuit parameters. Objects of this thesis are three basic DC-DC converters, that is, the Buck converter, the Boost converter and the Buck-Boost converter. This thesis studies how to control chaos and bifurcation in converters to periodic orbits or the constant by using an improved correlation method, state feedback methods, a delayed differential feedback method, a controller in the form of difference of cubes and an active disturbance rejection control(ADRC) technique. The main content includes three parts as follows.(1)Based on the piecewise linear model and the discrete mapping model, the existence of chaos and bifurcation in converters is confirmed by studying bifurcation diagrams, Poincare sections, phase portraits, switching logic diagrams, inductor current waveforms and output voltage waveforms of chaotic state.(2)The improved correlation method, the state feedback methods, the delayed differential feedback method and the controller in the form of difference of cubes can control chaotic state of converters to various periodic orbits when the input voltage is fixed. The improved correlation method controls the chaotic Buck converter and the chaotic Boost converter to the period-1, period-2, period-4, period-8 orbits, and the chaotic Buck-Boost converter to the period-2, period-3, period-4, period-6, period-8, period-9 orbits, by improving correlation between the inductor current and the output voltage in converters. The state feedback methods are established by combining state feedback with parameter perturbation. The first kind of state feedback method controls the chaotic Buck converter to the period-1, period-2, period-4, period-8 orbits. The second kind of state feedback method controls the chaotic Boost converter to the period-2, period-8, period-10, period-14 orbits. These two state feedback methods have different mathematical expressions. The delayed differential feedback method is established by combining time delay with differential feedback. This method controls the chaotic Boost converter and the chaotic Buck-Boost converter to the period-1 orbit. The controller in the form of difference of cubes is established by taking difference of cubes between the output voltage and the inductor current. This controller controls the chaotic Buck-Boost converter to the period-2, period-3, period-4, period-6, period-8 orbits.These methods need not determine targeting orbits beforehand. They are independent of internal circuit parameters of converters and achieve chaos control for converters by adjusting an external parameter. Moreover, these methods can also be used to control chaos in other power electronic circuits.(3)The ADRC technique controls chaos and bifurcation in the Buck converter to the constant when the input voltage is fixed or variable. The ADRC technique estimates and compensates variation of the input voltage by treating this variation as total disturbances. The system output tracks the set point with the zero error by using the ADRC technique. Furthermore, the closed-loop system with the ADRC technique has good robustness to variation of the input voltage. The above results provide an effective way for controlling chaos and bifurcation in power electronic circuits.