Symbolic analysis method and apparatus of fractional order switching converter under continuous current mode

Abstract

The present invention discloses a symbolic analysis method and apparatus of a fractional order switching converter operating under continuous current mode. On the basis of the harmonic balance principle, the method converts a process of solving non-integer-order calculus operation into a processing of matrix operation and linear equation group solution by converting state variable fractional order differential operation in the converter into differential operators and combining all of the differential operators into a diagonal semiotic matrix. Compared with an existing analysis method of establishing an Oustaloup filter approximate model in Matlab / Simulink which is frequently used for a fractional order switching converter, the method can analytically analyze state variable ripple peak-to-peak values of the converter and the influence of order change of an energy storage element on the working condition of the converter, can rapidly obtain analytical solution of a steady state period of state variables, and can also be used for analyzing harmonic components of the state variables.

Description

technical field

[0001] The invention relates to the field of modeling and analysis of fractional-order switching converters, in particular to a symbolic analysis method and device for fractional-order switching converters working in current continuous mode. Background technique

[0002] In the past, the commonly used modeling and analysis methods for switching converters include: models based on state space averaging, discrete iterative mapping models, piecewise linear models based on circuit principles (KCL, KVL), and methods that combine harmonic balance and disturbance methods, etc. The analysis objects of these methods are integer-order switching converters, that is, the capacitors and inductors in the converter are all integer-order components. However, the existing reference 1 "Westerlund S. Dead Matter Has Memory![ M].Kalmar,Sweden:Causal Consulting,2002,Chap.7."And reference 2 "Podlubny I.Fractional Differential Equations[M].San Diego:Academic Press,1999,Chap.2."It i...

Examples

Embodiment

[0105] See Figure 5 , Figure 5 It is a flowchart of a symbolic analysis method for a fractional-order switching converter operating in the inductor current continuous mode in the first embodiment. As shown in the figure, the specific implementation steps of the symbolic analysis method of the open-loop fractional-order switching converter in the CCM (Continuous Conduction Mode, continuous current mode) state provided by the present invention are as follows:

[0106] Step S1, system state description of fractional order switching converter

[0107] The system state of the fractional order DC-DC converter working in the CCM state can be described as:

[0108]

[0109] In the above formula, x=[i L v C ] T Represents the state variable of the system (usually the current i on the i-th inductor Li , the voltage v on the i-th capacitor Ci ), k represents the order of the corresponding system state variables on the corresponding inductance L and capacitance C components, ...

Embodiment 2

[0165] The second embodiment discloses a symbol analysis device for fractional-order switching converters working in inductive continuous mode, which specifically includes a system state description module, a calculus operator definition module, a system state conversion module, a nonlinear part expansion module, and a state variable And switch function Fourier expansion module, state variable solution module, state variable solution module, state variable expression acquisition module. The following is a detailed description:

[0166] 201. System status description module

[0167] This module is used to describe the system state of the fractional-order switching converter operating in the inductive continuous mode as:

[0168]

[0169] In the above formula, x=[i L v C ] T Represents the state variables of the system, including the current i on the ith inductor Li , the voltage v on the i-th capacitor Ci , k represents the order of the corresponding system state vari...

technical field

[0001] The invention relates to the field of modeling and analysis of fractional-order switching converters, in particular to a symbolic analysis method and device for fractional-order switching converters working in current continuous mode. Background technique

[0002] In the past, the commonly used modeling and analysis methods for switching converters include: models based on state space averaging, discrete iterative mapping models, piecewise linear models based on circuit principles (KCL, KVL), and methods that combine harmonic balance and disturbance methods, etc. The analysis objects of these methods are integer-order switching converters, that is, the capacitors and inductors in the converter are all integer-order components. However, the existing reference 1 "Westerlund S. Dead Matter Has Memory![ M].Kalmar,Sweden:Causal Consulting,2002,Chap.7."And reference 2 "Podlubny I.Fractional Differential Equations[M].San Diego:Academic Press,1999,Chap.2."It i...

Examples

Embodiment

[0105] See Figure 5 , Figure 5 It is a flowchart of a symbolic analysis method for a fractional-order switching converter operating in the inductor current continuous mode in the first embodiment. As shown in the figure, the specific implementation steps of the symbolic analysis method of the open-loop fractional-order switching converter in the CCM (Continuous Conduction Mode, continuous current mode) state provided by the present invention are as follows:

[0106] Step S1, system state description of fractional order switching converter

[0107] The system state of the fractional order DC-DC converter working in the CCM state can be described as:

[0108]

[0109] In the above formula, x=[i L v C ] T Represents the state variable of the system (usually the current i on the i-th inductor Li , the voltage v on the i-th capacitor Ci ), k represents the order of the corresponding system state variables on the corresponding inductance L and capacitance C components, ...

Embodiment 2

[0165] The second embodiment discloses a symbol analysis device for fractional-order switching converters working in inductive continuous mode, which specifically includes a system state description module, a calculus operator definition module, a system state conversion module, a nonlinear part expansion module, and a state variable And switch function Fourier expansion module, state variable solution module, state variable solution module, state variable expression acquisition module. The following is a detailed description:

[0166] 201. System status description module

[0167] This module is used to describe the system state of the fractional-order switching converter operating in the inductive continuous mode as:

[0168]

[0169] In the above formula, x=[i L v C ] T Represents the state variables of the system, including the current i on the ith inductor Li , the voltage v on the i-th capacitor Ci , k represents the order of the corresponding system state vari...

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