CHEMICAL ENGINEERING TRANSACTIONS VOL. 51, 2016 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian Copyright © 2016, AIDIC Servizi S.r.l., ISBN 978-88-95608-43-3; ISSN 2283-9216 Complex Behavior Analysis and Chaos Control of Electronic Circuits Bangfeng Zhang ChongQing College of Electronic Engineering, ChongQing 401331, China zhangbangfeng023@sina.com In-depth analysis of the complex nature of the circuit, this paper discussed chaotic dynamics theory. The numerical simulation of power electronic circuits gives the complex dynamic behavior of the circuit. By theoretical analysis, to explore the root causes of the phenomenon, and through specific circuit experiment. Kinetic behavior of complex present in the circuit for establishing the corresponding chaos control method, we try to keep the original circuit structure and parameters on the basis of the system. It has excellent working stability studies which obtained the outcome. They will be a variety of power electronic circuits provide important theoretical guidance. Analyzes the general chaotic dynamical systems, in terms of the history of the development of chaos, chaos characteristics of the roads leading to chaos, chaos theory describes nonlinear systems related. Lists typical continuous dynamical systems and chaos typical discrete chaotic system dynamics, and specific analysis for studying complex phenomena of power electronic circuits provide a theoretical basis. 1. Introduction Power electronics are strong nonlinear circuits and systems category, which is a typical non-linear direction of scientific research, with a very complex dynamics, which involves very rich nonlinear phenomena such as bifurcation, chaos, intermittent (Sarathi, 2013; Sun, 2015). This making power electronic circuits job stability has been a huge challenge (Zamani and Vaidyanathan, 2015). Through the power electronic circuits in complex behavior research can reveal the nonlinear nature of the circuit, to improve the stability of the circuit, to provide a theoretical guarantee the reliability of this type of circuit design, circuit design to provide guidance to manufacturers of power electronic circuits to meet the needs of the national economy in various fields of high stability power electronic circuits (Vasan, 2014). With the rapid development of power electronics technology, particularly in the power electronic circuit complexity research carried out, more and more mysteries are unveiled to give a reasonable explanation, revealing the non-linear nature of power electronic circuits (Wang and Vaidyanathan, 2015), improves the performance of the circuit, making it more stable and provide a reliable guarantee for the theory of circuit design in this category, the study not only of theoretical significance also has several important practical application value research for power electronic circuits manufacturing company offers circuit design guidance, to avoid waste of resources and a decline in product quality due to improper design, saving a lot of manpower and material costs, the economic benefits are obvious, to meet the industrial, agricultural, military, civil and other fields of high-performance power electronic circuits it needs (Lang and Ding, 2013). This article describes the chaotic dynamical systems, in terms of the history of the development of chaos, chaos characteristics of the roads leading to chaos theory describes nonlinear systems related. Study the typical continuous chaotic system dynamics and discrete dynamics typical chaotic systems, and its detailed analysis of power electronic circuits Kinetics of complex behavior provides the theoretical basis of the analysis of the switching power converter complex behavior research methods, including numerical simulation methods, research methods of theoretical analysis, experimental research methods. In voltage control mode Buck converter as an example, the study of these three methods proved switching power converter complex behavior of accuracy and consistency. DOI: 10.3303/CET1651222 Please cite this article as: Zhang B.F., 2016, Complex behavior analysis and chaos control of electronic circuits, Chemical Engineering Transactions, 51, 1327-1332 DOI:10.3303/CET1651222 1327 http://www.aidic.it/cet/15/46/indice.html#A447A 2. Continuous chaotic system 2.1 Chaos features Chaotic phenomenon ubiquitous in nature, chaotic strange phenomenon, but there are these different from each other in many of the same characteristics of the phenomenon (Tamba, 2016). Chaos is the product of nonlinear systems, it is not a disorder of random motion, which is a non-periodic motion, it is generally stable and in part is unstable, it looks like disorder, in fact, there is a sequence. The following mainly from the high sensitivity to the initial value, the intrinsic randomness, fractal structure with unlimited self-similarity, universality, strange attractors, continuous power spectrum, Lyapunov exponent positive aspects to analyze the chaos characteristics (Huo, 2014; Chu,2015). The largest Lyapunov exponent values: max 0 1 lim ln m i m i d m d           (1) The maximum Lyapunov index calculation method can take two closely spaced points x (t), y (t), as shown in Figure 1. y(t0) y(t2) x(t1) y(t1) x(t0) d d d d d y`(t2) y`(t1) x(t2) Figure 1: The maximum Lyapunov index calculation method Their distance:    0 0d y t x t  (2) 2.2 Continuous chaotic system dynamics Typically, differential equations can be used to describe the continuous chaotic system dynamics (Vaidyanathan, 2015):     ,x t f x t k (3) f=f (f1, f2…fn)T is a continuous mapping n-dimensional space. K=(k1,k2,…kn)T∈Rm continuous time t corresponding to the state variables. f=f (f1, f2…fn)T was the control parameters of the system. Chua is a typical continuous chaotic systems dynamics, this study by the following typical continuous chaotic system, intrinsic dynamics of continuous chaotic systems. The circuit is composed of two capacitors, a resistor, an inductor and a nonlinear RLC circuit resistor, as shown in Figure 2. 1328 http://www.aidic.it/cet/15/46/indice.html#A488A L + - + - R1iL iR Uc2 C2 C1 Uc1 uR RN Figure 2: Circuit diagram of Chua’s circuit According to Chua's circuit diagram, using Kirchhoff's law, and the relationship between the voltage across the capacitor and the inductor current can be listed status Chua equation:       1 2 1 1 1 2 1 2 2 2 2 1 1 1 1 C C C C L C C L C du u u g x dt RC C du i u u dt RC C di u dt L               (4) Let x=uc1, y=uc2,z=RiL, then     1 2 1 1 x y x Rg x RC y x y z RC R z y L                 (5) g (x) function expression can be written the following expression:   1 0 1 0 1 0 1 ; 1 ; 1 ; 1 m x m m x g x m x x m x m m x            (6) 3. Experiments and results 3.1 Equilibrium Point and Stability Balance by the following equations: 0 0 0 ax yz y k by xz cz xy            (7) Solve the equations, you can find: (1) If c<(16bk2)/(4ab+1)2 , the system has three balance points. 1329 (2) If c=(16bk2)/(4ab+1)2, the system has four balance points. (3) If c>(16bk2)/(4ab+1)2, the system has five balance points. Through a simple analysis, we learned that five equilibrium points are unstable, and their respective characteristics shown in Table 1. Table 1: The balance point and its latent root Balance Points latent root Type P1(0.1,0,0) λ1=-19.994, λ2=-2.0006, λ3=10, Index-1 Unstable saddle points P2(6.3246,4.2813,13.5388) λ1=-17.3374 λ2,3=2.6687±8.9767i Index-2 Unstable saddle points P3(6.3246,-4.5976,-14.539) λ1=-17.4674 λ2,3=2.7337±9.2741i Index-2 Unstable saddle points P4(-6.3246,4.6682,-14.7622) λ1=-17.3254 λ2,3=2.6627±9.4935i Index-2 Unstable saddle points P5(-6.3246,-4.3520,13.7623) λ1=-17.1910 λ2,3=2.5955±9.1981i Index-2 Unstable saddle points 3.2 Numerical simulation Numerical simulation method has a very important role in the dynamics of complex behavior switching power converter, which can be done using a computer, using numerical simulation software, the research object modeling, and preparation of the corresponding simulation program be implemented. Typically, it is relatively easy to implement, just know that the study works, we can give the corresponding mathematical model. It is convenient and flexible, you only need to change the value of the parameters in the program, you can change the state of motion of nonlinear dynamical systems, it can directly observe different sports results of the system. Voltage mode control Buck converter is a very broad application of the switching power converter, its main circuit topology and voltage mode control waveforms as shown in Figure 3. + - + - Vcon VrefA VS D L C R + - V0 G u Vramp Vu VL iL (A) Buck converter basic circuit 1330 0 tn 0 tn+1ts u t Von Vramp dT T t (b) Voltage-mode control waveforms Figure 3: Voltage-mode control buck converter and its control waveforms Plus noise signal, and when the perturbation intensity D = 0.004, the window range in period 3 largest Lyapunov exponent is larger than the intermittent chaos Boost converter state, as shown in Figure 4. 4.8 4.85 4.9 4.95 0 0.2 0.4 0.6 0.8 1 I r ef / A λ m a x Figure 4: Lyapunov exponent is larger than the intermittent chaos Boost converter state Fault feature extraction analog circuit fault diagnosis system is an important part, since different extraction methods from the failure characteristics of the signal in the frequency domain, so the realization of simulation and process analysis of analog circuit fault diagnosis are slightly different, here are sampling from the effective implementation of the sampling points and the wavelet transform fault feature extraction, SVM fault diagnosis were achieved on the final results of fault diagnosis further comparative analysis. 4. Conclusions Analyzes the general chaotic dynamical systems, in terms of the history of the development of chaos, chaos characteristics of the roads leading to chaos, chaos theory describes nonlinear systems related. Lists typical continuous dynamical systems and chaos typical discrete chaotic system dynamics, and specific analysis for 1331 studying complex phenomena of power electronic circuits provide a theoretical basis. Kinetic behavior of complex present in the circuit for establishing the corresponding chaos control method, so try to keep the original circuit structure and parameters on the basis of the system has excellent working stability studies obtained the outcome will be a variety of power electronic circuits provide important theoretical guidance. Reference Chu J., Wang G.Y., 2015, Research and design of control system for vibration transmission machine. Chemical Engineering Transactions, 46, 1147-1152. DOI: 10.3303/CET1546192 Ding G., Wang L., Yang P., Shen P., Dang S., 2013, Diagnosis model based on least squares support vector machine optimized by multi-swarm cooperative chaos particle swarm optimization and its application, Journal of Computers, 8(4), 975-982. Huo X., Zhang A., Karimi H.R., 2014, March, Research on amplifier performance evaluation based on δ- support vector regression, In Abstract and Applied Analysis (Vol. 2014), Hindawi Publishing Corporation. Lang R.L., Xu Z.P., Gao F., DENG X., 2013, A knowledge acquisition method for fault diagnosis of airborne equipments based on support vector regression machine. Chinese Journal of Electronics, 22(2), 277-281. Sarathi Vasan A.S., Long B., Pecht M., 2013, Diagnostics and prognostics method for analog electronic circuits. Industrial Electronics, IEEE Transactions on, 60(11), 5277-5291. Sun Y.G., Qiang H.Y., Lin G.B., Ren J.D., Li W.L., 2015, Dynamic modeling and control of nonlinear electromagnetic suspension systems, Chemical Engineering Transactions, 46,1309-1044. DOI: 10.3303/CET1546174. Tamba V.K., Fotsin H.B., Kengne J., Ngouonkadi E.B.M., Talla P.K., 2016, Emergence of complex dynamical behaviors in improved Colpitts oscillators: antimonotonicity, coexisting attractors, and metastable chaos, International Journal of Dynamics and Control, 1-12. Vaidyanathan S., Volos C.K., Pham V.T., 2015, Analysis, control, synchronization and SPICE implementation of a novel 4-D hyperchaotic Rikitake dynamo system without equilibrium, Journal of Engineering Science and Technology Review, 8(2), 232-244. Vaidyanathan S., Volos C.K., Pham V.T., 2015, Analysis, adaptive control and adaptive synchronization of a nine-term novel 3-D chaotic system with four quadratic nonlinearities and its circuit simulation. Journal of Engineering Science and Technology Review, 8(2), 174-184. Vaidyanathan S., Rajagopal K., Volos C.K., Kyprianidis I.M., Stouboulos I.N., 2015, Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in LabVIEW, Journal of Engineering Science and Technology Review, 8(2), 130-141. Vasan A.S.S., Long B., Pecht M., 2014, Experimental validation of LS-SVM based fault identification in analog circuits using frequency features, In Engineering Asset Management 2011 (pp. 629-641). Springer London. Wang J., Shi J., He Q., 2015, October, Research on component-level health quantitative assessment based on SVM algorithm for analog electronic circuits, In Prognostics and System Health Management Conference (PHM), 2015 (pp. 1-5). IEEE. Zamani N., Ataei M., Niroomand, M, 2015, Analysis and control of chaotic behavior in boost converter by ramp compensation based on Lyapunov exponents assignment: theoretical and experimental investigation, Chaos, Solitons & Fractals, 81, 20-29. 1332 http://www.aidic.it/cet/15/46/indice.html#A488A http://www.aidic.it/cet/15/46/indice.html#A489A http://www.aidic.it/cet/15/46/192.pdf http://www.aidic.it/cet/15/46/indice.html#A447A http://www.aidic.it/cet/15/46/indice.html#A448A http://www.aidic.it/cet/15/46/indice.html#A449A http://www.aidic.it/cet/15/46/indice.html#A450A http://www.aidic.it/cet/15/46/indice.html#A451A http://www.aidic.it/cet/15/46/174.pdf http://www.aidic.it/cet/15/46/174.pdf