Research On Choas Dynamics In Typical Discrete Systems

Chaos system is an important part of chaos theory and application study.Control and anticontrol of chaos can be realized if the research on chaos behaviorand chaos mechanism are fully understood. The traditional nonlinear analysismethod which is based on the linear and deterministic perspective can not satisfy theincreasing high performance demands. With advances in these areas, this dissertationconducts a thorough investigation on the nonoliear characteristics of the chaoticsystems. Some new behaviors of chaos dynamics with typical discrete Logisticsystem and switching converters are obtained, which are tied tightly in togologicalconjugation with symbolic dynamics, relative entropy and information entropy, thevalidity and effectiveness of the proposed method are verified, which develop theprinciple of chaos theory and set a theoretical foundation for chaos application inengineering projects. Finally, the series switching converter based on voltage andcurrent dual-loop control is designed.In this thesis, relative entropy is applied in analysising the chaotic state oftypical chaos Logistic map, and we propose a new index which is based on symbolicdynamic and time irreversibility. First, the original numerical series of Logistic mapare translated into symbolic series, then the suitable length of symbolic series andcoding length are respectively selected, and time irreversibility of Logistic chaossystem is approved through a series ofderivations. The relative entropy can bequantified the distance deviating from the equilibrium state in chaostic Logisticsystem, and the relative entropy is increase with parameter μ and is irrelevant withinitial valuex0, which proves that not all the characteristic parameters are sensitiveto initial value. In the thesis, time irreversibility of switching converter based on relativeentropy is studied, and a new index is put forward which can quantitative thedistance deviating from the equilibrium state in chaostic converter. The converter ina state of discontinuous inductor current can be equivalent to the first-order discretedynamical system, taking the DCM boost converter as an example, the originalnumerical series of converter are translated into symbolic series based on topologicalconjugate in the form of coarse graining, the word probability can be obtained byusing sliding window method. Furthermore, relative entropy of DCM boostconverter can be obtained by calculating the forward and backword probability.Because relative entropy can be measured distance from equilibrium, so the changetrend of switching converter can be reasonably anticipated, the new ideas andmethods can be provided for revealing the nonlinear characteristic, and furtherlyproves that the relative entropy is feasible for analysising the converter characteristicin chaostic state.According to the distribution characteristics of converter numerical sequence,and combining the information theory, we develop the direction calculationtechnique of converter numerical sequences based on information theory. Theinformation entropy analysis results of the first-order DCM buck and boost converterin different parameters show that information entropy can distinguish periodic andchaotic behavior under the premise of entropy increase. Information entropyapproaches the maximum value with the increase of feedback parameters, wheninitial value change, the information entropy of its corresponding numericalsequence doesn’t change, so it is proved that the information entropy of converterchaos system isn’t sensitive to initial value. The numerical distribution of converterchaos system can be make reasonable prediction from a macroscopic view due to thedistribution characteristic, and the results will provide theoretic basis to the study ofchaos characteristic and chaos control of switching coverter. Finally, a series buck converter of voltage-loop and current-loop is introduced.The result of experiments shows that the circuit of series switching power supplybased on voltage and current dual-loop control can work in the voltage range from12V to90V, and is less influence to working state when capacitive load is accessed.The circuit have the function of quickly response, short circuit protection andovercurrent protection. The power supply have advantages of low-cost and workingstability, which can be used to different various industry alarms and blasting signallights in the wide voltage range.