Chaos in power electronic circuits

(1) The chaotic system is divided from which the basic theory of chaos is elaborated. Taking the buck converter as an example, the chaos phenomenon in the power electronic circuit is discussed, and the power converter is observed with the input voltage plant simulation Changes in the chaotic waveform. The waveforms in the article are all obtained by computer simulation using Ding 18 Soft Cow. It is convenient for readers to verify by themselves. Classification No. 17, Shu 72.1 Since the emergence of the study of mixed pure theory in the 1970s on a par with the theory of relativistic quantum mechanics, people have discovered that mixed pure phenomenon is almost everywhere. Many power supply designers often encounter creaking noises from power converters, or observe unclear and messy output waveforms on the wave. Generally, it is believed that the circuit has generated self-oscillation. In fact, after research, the converter is in chaos at this time. (4) Until now, there is no corresponding mathematical theory that can effectively predict the chaos of a given circuit. Therefore, to fully understand the chaotic phenomenon of power converters, to develop a set of reliable power supply design techniques to eliminate or use chaos, is of great guiding significance for the correct design and debugging of power converters.

The 10th generation de-chaotic system In 1963, 012 derived the famous chaotic equation from the simplified atmospheric model. This group of differential equations exhibits a strange phenomenon, namely chaotic phenomenon. The system of differential equations is like formula 1. In this system, the ruler and call are variable parameters. The change of thousands of parameters can cause the system to change from periodic state to pure state. The date of the system soap appeared cycle 1 was received 1999, 716 National Natural Science Foundation of China 〃Yin Yiguang female 27-year-old Ph.D. Ecology; when the parameter 5 changed from 0.2 to 2.0, the system changed from the periodic state to the wave pure state, 2, The trajectories of hybrid systems are attracted to certain regions of the state space, which is called singular attractors in chaos theory.

These trajectories are messy, but they never intersect itself. It never repeats the points it has traveled before, but returns infinitely to the vicinity of every point it has previously passed. The reason for this strange phenomenon is the result of dissipative and nonlinear interaction. Due to the effect of dissipation, the chaotic system is now stable and shrinks in phase volume as a whole and in a large range, and the result of the nonlinear effect makes the orbit partially unstable, and this instability makes the orbit partially separated. The overall stability of the dissipative effect and the local qualitative effect of the anisotropic effect form a mixture; Tun 2. In other words, the life attractor is the essence of chaos. A large number of theoretical analysis and experimental results show that the system that may produce chaotic behavior is a time-ordered forced system. The order non-autonomous system excitation source contains time parameters. The order nonlinear system and order autonomous system excitation sources do not contain time parameters. Order nonlinear system. As mentioned above, the system is a rank-order autonomous system. In the system, the number of changes occurs at once, and it can produce chaos.

2 Chaos phenomenon in the buck 00 converter 21 buck 0, the working principle of the converter 1 The redundant converter is a non-autonomous system of external order, circuit box 3. Assume that the components in the circuit are ideal, that is, comparison Device 0 person 2 has infinite gain switch 3 when closed! (1) Enter one, and the beneficial device is like a spoon positive input terminal to test the voltage plant. Connected to the inverting input terminal of comparator 0 and person 2, the positive buck of the comparator, the input terminal of the converter is an independent ramp voltage source factory resistance, circuit box, linearly from the low voltage in the cycle factory Change to electric Kig.3i.lflii.am, f pressure, and then return instantaneously, assuming that the buckmnverter 3 state switch in the plant 1 section; This is called the Jinguan condition. Transform; wave. The output pressure is adjusted by continuous sampling to adjust the pulse width of the comparator output, so as to control the switching of the switch 3. However, in some cases, the circuit will send out a strange phenomenon called, the ramp wave card cycle throw. The output voltage 1 heart follows the ramp voltage 1 change, and the switch is turned on and off multiple times. At this time, the circuit may generate chaos. This is highly undesirable.

22 Theoretical analysis of the voltage transmission plant; left = 12 with 1 =, 12 as the undetermined coefficient, the initial conditions give North 23 numerical calculation and simulation results. In each ramp voltage cycle, when the switching conditions are met, the state of switch 3 will be change. Defining this moment as formula 4 is a transcendental equation, so there is no analytical solution. This is a major obstacle to theoretical analysis, but the numerical solution of the series at the moment of switching can be obtained by means of numerical calculation. The voltage and current values ​​of a given group are used as initial conditions. It is assumed that when = 0, the switch 3 is in the off state, 1 =., Using formula 2 and formula 3, the 7-inch approximation is often calculated based on the above theoretical analysis, using 8 software to pass Computer simulations have obtained the chaotic waveform of the converter controlling the voltage when the input voltage plant is 1 = 35. 4. During a ramp voltage cycle, the switch turns on and off many times. The phase space of the output voltage; and the inductor current; 5, from which it is clearly observed that some of the singular attractors are not given all the shapes due to the limited experimental conditions, and the circuit is in a pure state.

3 Conclusion The switch-mode power converter has an efficiency of 1 weight. The obvious advantages such as small size are widely used in the field of electronic technology. However, because the control circuit of the adjustment element of the converter is relatively complicated, it has shortcomings such as large ripple coefficient and poor transient response. Therefore, it is difficult to be applied in a high-precision analog circuit. The results of research in recent years have shown that the power converter itself is a strongly nonlinear discrete system, and chaotic behavior cannot be avoided. Therefore, it is difficult to improve the system performance by using the conventional feedback control method. Therefore, the research on the existence mechanism and control method of chaos in power converters is a huge amount of money. It may be a new way to improve power The application in the field of science will be a great theoretical and practical meaning of the great theoretical and technical changes in the field of power electronics. In this paper, the buck type working in the ideal state is selected, and the 01 redundant converter is the object of research. Through theoretical analysis and computer simulation, the chaotic phenomenon produced by the converter under specific circuit parameters is observed.

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