Study On Nonlinear Dynamical Behaviors And Their Control In Higher Order Switching Power Converters

Nonlinear science, as a comprehensive and interdisciplinary subject for studying the generality of nonlinear phenomena, reveals the nonlinear nature of the world and promotes the process of changing the world constantly. Power electronics field has its own nonlinear problems as in the other disciplinary fields. Switching power converter is an important component in power electronics circuit and system, which belongs to a class of piecewise switching system with strong nonlinearity and time-varying characteristics. Therefore, studying on the power converters based on nonlinear theories and methods are beneficial to reveal the nonlinear nature of the power converters, to guide the engineering practice by optimizing the stability and reliability design of the converters, to establish the theoretical foundations of the power electronics, and to enrich the contents and methods of nonlinear science.Since the nonlinear phenomenon in power converter was reported in 1980s, the domestic and foreign researchers have widely carried out the study on the nonlinear dynamical behaviours and their control of power converters from the multi-dimensional viewpoints of computer simulation, theoretical analysis, and circuit experiments, resulting in a nonlinear study branch in power electronics. But the existing nonlinear studies are almost for lower order converters, while few work for higher converters. Based on this situation, higher order converters are selected as the research objects, and their modelling, descriptions, analysis and control of nonlinear dynamical behaviours are carried out in this dissertation with the aim to reveal the nonlinear nature of higher order converters, and to guide the design and application of higher order converters. The concrete work is as follows:(1) Review on nonlinear study in switching power converters and the basis of nonlinear dynamics. Chapter one analyzes the research significance of nonlinear study in power converters, gives an overview on the related research backgrounds from three aspects including nonlinear modelling, nonlinear dynamical behaviours, and control of nonlinear phenomena, and based on which, puts forward the research value and contents of this dissertation. Chapter two introduces the basis of nonlinear dynamics including bifurcation and chaos theory, summarizes the research methods in nonlinear dynamics, and presents some commonly used numerical methods and their applications to nonlinear study of power converters.(2) Nonlinear modelling of higher switching power converters. Modelling is the essential prerequisite of nonlinear study on power converters, which has two widely used methods including state-space average approach and discrete-time mapping approach. Aiming at strong nonlinearity and complexity of higher order power converters, an integrative modelling method by integrating these two approaches is proposed and is applied to the modelling and stability analysis of a peak-current-mode controlled Cuk converter in chapter three. The closed-form iterative mapping model is constructed, and analytical expression of the stability criterion is achieved. Furthermore, the relationship between the stability and the circuit parameters is studied. The results of simulation verify the validity of the proposed modelling method and stability analysis.(3) Nonlinear dynamical behaviours and their analysis in higher power converters. Chaotic phenomena can frequently appear in no less than two-order non-autonomous converters (one-order discontinuous current mode non-autonomous converter as well) or in no less than three-order autonomous converters. So four-order converters can present rich nonlinear dynamical behaviours such as bifurcation and chaos. Intermittent subharmonics and chaos in a peak-current-mode controlled SEPIC converter coupled with intruding interference is studied in chapter four. The intermittent phenomena are observed by means of numerical simulation and circuit simulation. Furthermore the relation between the circuit parameters and the threshold amplitude of interference is discussed. By mapping time-bifurcation into parameter-bifurcation, discrete-time mapping model and the analysis method of characteristic multiplier of Jacobian matrix are applied to theoretical analysis. The theoretical results are consistent with the simulation results and indicate that the intermittent type and period are decided by the strength and frequency of the intruding interference. Furthermore, a weak periodic signal detection method is proposed based on intermittency of switching converters. Stability analysis and complex dynamical behaviors of a sliding-mode controlled SEPIC converter, which is an autonomous higher order converter, are studied in chapter five. Based on sliding-mode variable structure theory, sliding-mode control of the SEPIC converter is achieved, the equivalent average model is obtained, and stability of the equilibrium point is analyzed. Analysis of the Jacobian matrix and its characteristic eigenvalues proves that the converter loses stability via a super critical Hopf bifurcation with the reference current increased, and that the circuit parameters can make important influence on the stability. Simulation results demonstrate the theoretical analysis, and show the route to chaos via Hopf bifurcation, single limit cycle, double limit cycle, and quasi-periodicity.(4) Control of nonlinear dynamical behaviours in higher order switching power converters. Applications of nonlinear study results to engineering practice must require the researchers to study on the control of nonlinear phenomena. Generally speaking, traditional control techniques and some special chaos control techniques can be used to control of bifurcation and chaos in power converters. But up to present, control of nonlinear dynamical behaviours is seldom investigated, so some explorations on this topic are implemented in chapter six. Firstly, time-delayed feedback control method is effectively applied to control chaos in non-autonomous higher order converter, with a peak-current-mode controlled SEPIC converter as a case study, and the value range of the feedback gain is obtained by bifurcation diagram. Secondly, external periodic signal method is successfully used to control chaos in autonomous power converter, with a sliding-mode controlled SEPIC converter as an example. Lastly, variable linear feedback control method is used to realize the Hopf bifurcation control in a sliding-mode controlled SEPIC converter, and the theoretical analysis is carried out based on sliding-mode theory, which is in agreement with the simulation results.