Period-doubling bifurcation analysis and chaos control for load torque using FLC

Chaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

[1]  M. Radisic,et al.  A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems. , 2019, Biomaterials.

[2]  S. Xie,et al.  Calculating Floquet Multipliers for Periodic Solution of Non-smooth Dynamical System , 2019, DEStech Transactions on Computer Science and Engineering.

[3]  Kun Zhang,et al.  The Stability Analysis of DC-DC Conversion Systems Based on Monodromy Matrix , 2019, 2019 Chinese Control And Decision Conference (CCDC).

[4]  Sajal K. Das,et al.  High performance nonlinear controller design for AC and DC machines: partial feedback linearization approach , 2018 .

[5]  Sahapong Somwong,et al.  Automatic Fruit Syrup Mixing Machine , 2020, 2020 8th International Electrical Engineering Congress (iEECON).

[6]  Frede Blaabjerg,et al.  Floquet-Theory-Based Small-Signal Stability Analysis of Single-Phase Asymmetric Multilevel Inverters With SRF Voltage Control , 2020, IEEE Transactions on Power Electronics.

[7]  Junguo Wang,et al.  Chaos and Stability of Spur Gear Transmission System for Locomotive Based on Energy Method and Floquet Theory , 2018, Shock and Vibration.

[8]  Omid Mehrjooee,et al.  Dynamic modeling and extended bifurcation analysis of flexible-link manipulator , 2020 .

[9]  J. Nathan Kutz,et al.  Poincaré maps for multiscale physics discovery and nonlinear Floquet theory , 2020 .

[10]  D. Breda,et al.  Floquet Theory and Stability of Periodic Solutions of Renewal Equations , 2020 .

[11]  Xu Yang,et al.  Lyapunov Exponent-Based Study of Chaotic Mechanical Behavior of Concrete under Compression , 2019 .

[12]  Shijian Cang,et al.  Chaotic and subharmonic oscillations in a DC–DC boost converter with PWM voltage–current hybrid controller and parallel MR load , 2020 .

[13]  Liliya A. Demidova,et al.  A Study of Chaotic Maps Producing Symmetric Distributions in the Fish School Search Optimization Algorithm with Exponential Step Decay , 2020, Symmetry.

[14]  Shuai Yuan,et al.  Influence of multiple time delays on bifurcation of fractional-order neural networks , 2019, Appl. Math. Comput..

[15]  Qiang Lai,et al.  Coexisting attractors, circuit implementation and synchronization control of a new chaotic system evolved from the simplest memristor chaotic circuit , 2020, Commun. Nonlinear Sci. Numer. Simul..

[16]  Changjin Xu,et al.  Bifurcation control of a fractional-order delayed competition and cooperation model of two enterprises , 2019, Science China Technological Sciences.

[17]  Damian Giaouris,et al.  A new method on the limit cycle stability analysis of digitally controlled interleaved DC–DC converters , 2019, Control Engineering Practice.

[18]  Paulo B. Gonçalves,et al.  Influence of transient escape and added load noise on the dynamic integrity of multistable systems , 2019, International Journal of Non-Linear Mechanics.

[19]  H. Yau,et al.  Analyses and Control of Chaotic Behavior in DC-DC Converters , 2018, Mathematical Problems in Engineering.

[20]  A. Wawrzaszek,et al.  Hopf Bifurcations, Periodic Windows and Intermittency in the Generalized Lorenz Model , 2019, Int. J. Bifurc. Chaos.

[21]  Viet-Thanh Pham,et al.  Analysis and Stabilization of Chaos in Permanent Magnet DC Motor Driver , 2017, Int. J. Bifurc. Chaos.

[22]  Nitesh Tiwari,et al.  Design and Control of BuckConverter using PID and Fuzzy LogicController , 2018, 2018 International Conference on Power Energy, Environment and Intelligent Control (PEEIC).

[23]  Shijian Cang,et al.  Dynamical analysis and circuit implementation of a DC/DC single-stage boost converter with memristance load , 2018 .

[24]  Jan Cermak,et al.  Stability and chaos in the fractional Chen system , 2019, Chaos, Solitons & Fractals.

[25]  D. V. Senthilkumar,et al.  Frustration induced transient chaos, fractal and riddled basins in coupled limit cycle oscillators , 2019, Commun. Nonlinear Sci. Numer. Simul..

[26]  Babak Fahimi,et al.  On the Period-doubling Bifurcation in PWM controlled Buck Converter , 2018, 2018 IEEE Transportation Electrification Conference and Expo (ITEC).

[27]  Baran Hekimoglu,et al.  Optimal Tuning of Fractional Order PID Controller for DC Motor Speed Control via Chaotic Atom Search Optimization Algorithm , 2019, IEEE Access.

[28]  Qiang Lai,et al.  Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors , 2018, Chaos, Solitons & Fractals.

[29]  Damian Giaouris,et al.  Nonlinear Analysis and Control of Interleaved Boost Converter Using Real-Time Cycle to Cycle Variable Slope Compensation , 2017, IEEE Transactions on Power Electronics.

[30]  M. Farajzadeh,et al.  Mixing and heat transfer enhancement of power-law fluids inside helically coiled tube by chaotic advection , 2019 .

[31]  Metin U. Salamci,et al.  Effect of Delay of Immune System Response in Cancer Dynamics: Bifurcation and Chaos Analysis , 2018, 2018 26th Mediterranean Conference on Control and Automation (MED).

[32]  Y. Wang,et al.  Comparative study of full state variables and time-delay coordinates OGY chaos control for bi-stable vortex induced vibration energy harvesters , 2017, 2017 IEEE International Conference on Advanced Intelligent Mechatronics (AIM).

[33]  Yunis Torun,et al.  A New Breakthrough Detection Method for Bone Drilling in Robotic Orthopedic Surgery with Closed-Loop Control Approach , 2020, Annals of Biomedical Engineering.

[34]  Qingji Xue,et al.  Design of Music Toy Car Based on Smart Phone Via Bluetooth Remote Control , 2018, 2018 2nd IEEE Advanced Information Management,Communicates,Electronic and Automation Control Conference (IMCEC).

[35]  Hasan Erteza Gelani,et al.  AC vs. DC Home: An Efficiency Comparison , 2019, 2019 International Symposium on Recent Advances in Electrical Engineering (RAEE).

[36]  Shih-Yu Li,et al.  Adaptive synchronization of complicated chaotic systems with uncertainties via fuzzy modeling-based control strategy , 2018, Inf. Sci..

[37]  Qiang Lai,et al.  An Extremely Simple Chaotic System With Infinitely Many Coexisting Attractors , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[38]  Zhongliang Jing,et al.  Feedback control of unstable periodic motion for brushless motor with unsteady external torque , 2019, The European Physical Journal Special Topics.

[39]  Radu-Emil Precup,et al.  Stable fuzzy logic control of a general class of chaotic systems , 2014, Neural Computing and Applications.

[40]  Ilhami Colak,et al.  A Fuzzy Controller for Stabilization of Asynchronous Machine , 2018, 2018 7th International Conference on Renewable Energy Research and Applications (ICRERA).

[41]  Sen Li,et al.  Nonlinear Dynamics in the Switched Reluctance Motor Drive with Time-delay Feedback Control , 2019, 2019 IEEE Texas Power and Energy Conference (TPEC).

[42]  Hak-Keung Lam,et al.  Unactuated Force Control of 5-DOF Parallel Robot Based on Fuzzy PI , 2020 .

[43]  M. Tazerout,et al.  A Continuous Biodiesel Production Process Using a Chaotic Mixer-Reactor , 2019, Waste and Biomass Valorization.

[44]  José Manoel Balthazar,et al.  On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors , 2018 .

[45]  Azman Samsudin,et al.  Enhanced digital chaotic maps based on bit reversal with applications in random bit generators , 2020, Inf. Sci..

[46]  Cristina Morel,et al.  Generalization of the Filippov method for systems with a large periodic input , 2018, Math. Comput. Simul..

[47]  Dong-Hee Lee.  Combined Sensor–Sensorless Control of PMDC Motor for HD Camera of Unmanned Monitoring System , 2020 .

[48]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[49]  Ping Zhou,et al.  Stabilization of the unstable equilibrium points of the fractional-order BLDCM chaotic system in the sense of Lyapunov by a single-state variable , 2016 .

[50]  A. P. Misra,et al.  Chaos-based image encryption using vertical-cavity surface-emitting lasers , 2017, Optik.

[51]  Bo Zhang,et al.  Bifurcation Mechanism and Stabilization of V2C Controlled Buck Converter , 2019, IEEE Access.