Research On Fractional-Order Circuit And Its Time-frequency Domain Comprehensive Analysis Method

For nearly four decades,fractional calculus has been widely used in science and technology and other fields.Compared with integer calculus,the introduction of fractional calculus shows a certain degree of superiority.Especially in the field of circuits,people have come to realize that fractional calculus can better describe some of the unique phenomena in the circuit.And in the circuit design and practical application,the fractional-order circuit has greater flexibility than the integer order circuit,and contains more parameters.However,the principle of fractional-order circuit is not perfect,urgent need to improve and develop.In this paper,the principle of fractional-order circuit is analyzed systematically and some unique results are obtained through the relevant experimental simulation.The principle system of fractional-order circuit is improved,and the fractional equivalent circuit is analyzed and studied.A comprehensive analysis method based on time ?frequency domain is proposed and applied to the proof and research of fractional characteristic of electrolytic capacitor.The fractional-order capacitor is first analyzed as the most important element in the fractional-order circuit.Several different ways to achieve fractional-order capacitor have been presented.And a relatively accurate method of RC circuit approximation is obtained through experimental simulation.The universality of fractional-order capacitor is proposed,and its model is given.The model is applied to the 0.5 order capacitor which the RC circuit approachesThen the principle and application of fractional-order equivalent circuit is analyzed in this paper.The fractional-order RC,RL and RLC circuits are analyzed.Including impedance,amplitude,phase,and the pure imaginary impedance.Compared with the integer order circuit.And the influence of the fractional order on the impedance of the fractional-order circuit and the influence of the pure imaginary impedance are analyzed by the experimental simulation,and many unique characteristics are obtained.Then,the application of two kinds of fractional-order equivalent circuits,including the the equivalent circuit model of the lithium ion battery and biomechanics,and proposed its superiority to the integer order equivalent circuit.Finally,this paper presents three different fractional-order circuit analysis methods,time domain analysis method,frequency domain analysis method and a comprehensive analysis method which more suitable for the practical application or model analysis.And analyzes the difference between the integer order circuit and the fractional-order circuit in the time domain and the frequency domain.The time-frequency synthesis method proposed in this paper is a unique analysis method,which not only considers the accuracy of time domain fitting,but also effectively retains the frequency characteristics of the actual system,can be effectively applied to the actual circuit and a variety of gray box model analysis.Then,this method is applied to the proof and analysis of fractional characteristics of electrolytic capacitors,and the fractional characteristics of electrolytic capacitors are proved.The order of fractional-order capacitor at different frequencies is obtained.A variable model of electrolytic capacitor is obtained.A lot of experimental results are analyzed,and many unique conclusions obtained.