An analog circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor

Abstract

This invention relates to a simulation circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor (PMSM), belonging to the field of PMSM simulation circuit experiments. The circuit consists of multipliers, amplifiers, a DC power supply, resistors, and capacitors, specifically including: six identical fractional-order integrator circuits, six identical inverting proportional operational amplifier circuits, four multipliers, and six integral drift leakage resistors. The six integrator circuits are used to map the state variables of the bidirectional coupled PMSM. The outputs of the six inverting proportional operational amplifier circuits are connected to the power supply, and the corresponding voltage state variables have a mapping relationship with the state variables of the bidirectional coupled PMSM. The integral drift leakage resistors are connected in parallel with the unit circuits to avoid saturation cutoff caused by integral drift. The multipliers are connected to the amplifiers in the integrator circuits through resistors. This invention improves the accuracy of characterizing the state behavior of the bidirectional coupled PMSM.

Description

Technical Field

[0001] This invention belongs to the field of simulation circuit experiments for permanent magnet synchronous motors, and relates to a simulation circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor. Background Technology

[0002] In recent years, permanent magnet synchronous motors (PMSMs), as one of the modern high-performance AC servo systems, have been widely used in industrial robots, machine tools, vehicles, and pumping devices due to their high resolution, wide speed range, and stable low-speed operation. However, for high-inertia, high-power loads, a single / isolated PMSM cannot meet the driving force and output power requirements under fixed conditions. Therefore, how to achieve synchronous control of multiple PMSMs to jointly drive the load has become a major research focus in the field of servo systems. Furthermore, if the system parameters of the PMSM are in the unstable region of dynamic characteristics, over time, temperature, wear, and internal and external disturbances will further generate harmful vibrations. Moreover, due to the diversity and harsh conditions of actual working conditions, control design that ensures high synchronization and tracking capabilities while also meeting given constraints and reducing communication speed becomes extremely difficult.

[0003] Constructing electronic circuits at the physical level is an effective method, allowing for precise scanning of the parameter space and examination of corresponding values ​​for the nonlinear characteristics of electromechanical systems. Consequently, it has attracted significant research attention for experimental verification and rapid application development. Sabarathinam and Thamilmaran modeled a series of Duffing-type MEMS resonators using analog circuit experiments and verified their inherent chaotic oscillatory behavior. El-Sayed et al. applied electronic circuits to characterize a 4D system. However, these studies did not address the coupling between adjacent systems and the fractional-order characteristics. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a simulation circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor, which takes into account the coupling of adjacent systems and the fractional-order characteristics, thereby improving the accuracy of characterizing the state behavior of the bidirectional coupled permanent magnet synchronous motor.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] An analog circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor consists of multipliers, amplifiers, a DC power supply, resistors, and capacitors. Specifically, it includes: six identical fractional-order integrator circuits (IC1 to IC6), six identical inverting proportional operational amplifier circuits (IPOC1 to IPOC6), four multipliers, and six integral drift leakage resistors (R3, R8, R30, R44, R59, and R72).

[0007] Six integrator circuits are used to map the state variables (x1, x2, x3, y1, y2, and y3) of the bidirectional coupled permanent magnet synchronous motor; each integrator circuit includes a unit circuit, an amplifier (U1A, U3A, U5A, U7A, U9A, or U11A), and resistors (R14, R9, R34, R45, R60, or R73); each unit circuit consists of three sets of parallel resistors and capacitors of different sizes connected in series; the unit circuit uses... Connect the negative input terminal and the output terminal of the amplifier (U1A, U3A, U5A, U7A, U9A, or U11A); the positive input terminal of the amplifier (U1A, U3A, U5A, U7A, U9A, or U11A) is grounded through a resistor (R14, R9, R34, R45, R60, or R73); the negative input terminal of the amplifier (U1A, U3A, U5A, U7A, U9A, or U11A) is connected to a power supply.

[0008] The negative input terminal of the inverting proportional operational amplifier circuit is connected to the output terminal of the amplifier (U1A, U3A, U5A, U7A, U9A or U11A) in the integrating circuit; the output terminals of the six inverting proportional operational amplifier circuits are respectively connected to the power supply, and the corresponding voltage state variables are x1, x2, x3, y1, y2 or y3, which have a mapping relationship with the state variables x1, x2, x3, y1, y2 or y3 of the bidirectional coupled permanent magnet synchronous generator;

[0009] The integral drift leakage resistor (R3, R8, R30, R44, R59 or R72) is connected in parallel with the unit circuit to avoid saturation cutoff caused by integral drift.

[0010] The multiplier is connected to the negative input terminal of the amplifier (U3A, U5A, U9A, or U11A) in the integrator circuit via a resistor (R15, R24, R51, or R54).

[0011] Furthermore, the inverting proportional operational amplifier circuit includes an amplifier (U2A, U4A, U6A, U8A, U10A, or U12A) and three resistors. One resistor is used to connect the negative input terminal and the output terminal of the amplifier (U2A, U4A, U6A, U8A, U10A, or U12A). Another resistor is used to connect the negative input terminal of the amplifier (U2A, U4A, U6A, U8A, U10A, or U12A) to the output terminal of the amplifier in the integrating circuit. The last resistor is used to ground the positive input terminal of the amplifier (U2A, U4A, U6A, U8A, U10A, or U12A).

[0012] Furthermore, the negative terminal of the input of the amplifier U1A is connected to a power supply with voltage state variables of -x1, x2 and z1 respectively through resistors (R1, R13 and R2);

[0013] The negative terminal of the input of the amplifier U3A is connected to a power supply with voltage state variables of -x2, x1, z0, y2 and -x2 through resistors (R7, R16, R25, R63 and R64), and is also connected to multiplier A1 through resistor R15. Multiplier A1 is connected to a power supply with voltage state variables of x3 and -x1.

[0014] The negative terminal of the input of the amplifier U5A is connected to a power supply with voltage state variables of -x3, z0, y3 and -x3 through resistors (R23, R17, R65 and R66), and is also connected to multiplier A2 through resistor R24. Multiplier A2 is connected to a power supply with voltage state variables of x2 and x1.

[0015] The negative terminal of the input of the amplifier U7A is connected to a power supply with voltage state variables -y1, y2 and z2 through resistors (R40, R41 and R42);

[0016] The negative terminal of the input of the amplifier U9A is connected to a power supply with voltage state variables of -y2, y1, z0, x2 and -y2 through resistors (R50, R52, R56, R67 and R68), and is also connected to multiplier A3 through resistor R51. Multiplier A3 is connected to a power supply with voltage state variables of y3 and -y1.

[0017] The negative terminal of the input of the amplifier U11A is connected to a power supply with voltage state variables of -y3, z0, x3 and -y3 through resistors (R53, R55, R69 and R70), and is also connected to multiplier A2 through resistor R24. Multiplier A2 is connected to a power supply with voltage state variables of y2 and y1.

[0018] Furthermore, applying Kirchhoff's circuit laws, the circuit equations for this analog circuit are determined as follows:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Where H(s) represents the transfer function of the unit circuit, and α represents the fractional order value starting at the origin and satisfying 0 < α < 1.

[0026] Furthermore, the expression for the transfer function H(s) of the unit circuit is:

[0027]

[0028] Among them, C o For specific capacitance, C a C b and C c R is the capacitor selected in the unit circuit. a R b and R c s represents the resistor selected in the unit circuit, and s represents the complex frequency.

[0029] The beneficial effects of the present invention are as follows: by considering the coupling and fractional-order characteristics of adjacent systems, the present invention simulates a bidirectional coupled permanent magnet synchronous motor, thereby improving the accuracy of characterizing the state behavior of the bidirectional coupled permanent magnet synchronous motor.

[0030] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0032] Figure 1 This is a block diagram of a permanent magnet synchronous motor. Figure 1 (a) is a block diagram of an isolated permanent magnet synchronous motor. Figure 1 (b) is a block diagram of a graded bidirectional coupled permanent magnet synchronous motor;

[0033] Figure 2 The results are 0-1 test results of the transient time trajectory x1 of the bidirectional coupled permanent magnet synchronous motor at α = 0.99 and α = 0.91, where p(n) and q(n) represent the dynamic characteristics of the translational components, and M(n) and K represent the mean square displacement and asymptotic growth rate, respectively.

[0034] Figure 3 The results are 0-1 test results of the transient time trajectory y1 of the bidirectional coupled permanent magnet synchronous motor at χ = ​​0.2 and χ = 0.6, where p(n) and q(n) represent the dynamic characteristics of the translational components, and M(n) and K represent the mean square displacement and asymptotic growth rate, respectively.

[0035] Figure 4 This is a simulation circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor.

[0036] Figure 5The simulation circuit phase diagram of the bidirectional coupled active permanent magnet synchronous motor is given at χ = ​​0.2 and α = 0.997.

[0037] Figure 6 The phase diagram of the analog circuit of the bidirectional coupled driven permanent magnet synchronous motor is given by χ = 0.2 and α = 0.997. Detailed Implementation

[0038] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0039] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0040] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0041] Please see Figures 1-6 This invention provides a method for designing an analog circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor, specifically including the following parts:

[0042] 1. System Modeling: Constructing a fractional-order model of a bidirectional coupled permanent magnet synchronous motor.

[0043] The mathematical model of an isolated integer-order permanent magnet synchronous motor can be expressed as follows:

[0044]

[0045] in, R, L d L q , ψ r B, J and n p Let represent the d- / q-axis current, angular velocity (rad / s), time (s), d- / q-axis voltage (V), load torque (Nm), stator winding resistance (Ω), d- / q-axis winding inductance (H), permanent magnet flux (Wb), viscous damping coefficient (N / rad / s), and polar moment of inertia (kgm), respectively. 2 ) and number of magnetic pole pairs.

[0046] Through scaling transformation, the time scaling factor τ is defined as τ = L / R, and the normalized time t is... The scalar κ is κ = B / (n p τψ r The normalized angular velocity ω is Normalized d-axis current i d for and the normalized q-axis current i q for Define L = L d =L q Therefore, equation (1) can be transformed into

[0047]

[0048] Where u q ,u d ,T L σ and γ represent the q-axis / d-axis stator voltage, normalized load torque, and system parameters, respectively. Meanwhile, let γ = -ψ r / (κL), σ=Bτ / J, and

[0049] Clearly, the dielectric and the current and voltage related to energy transmission in electromechanical equipment exhibit fractional-order characteristics. The corresponding fractional-order permanent magnet synchronous motors (PMSMs) possess long memory dependence, rich performance characteristics, and high design freedom. Furthermore, to avoid dynamic isolation between the active and driven PMSMs, a linear resistor is designed to connect the PMSMs instead of the resistor connected in series with the current slave. A schematic diagram of the fractional-order bidirectional coupled PMSM is shown below. Figure 1 As shown in (b).

[0050] Using Kirchhoff's circuit laws, a fractional-order mathematical model of a bidirectional coupled active permanent magnet synchronous motor is given as follows:

[0051]

[0052] Where C, χ, and α represent the Caputo fractional derivative with the origin at the origin, the resistive coupling parameter, and fractional values ​​respectively, satisfying 0 < α < 1, x1 = ω, x2 = i q and x3=i d .

[0053] Then, the fractional-order mathematical model of the driven permanent magnet synchronous motor with bidirectional coupling was obtained as follows:

[0054]

[0055] Comment 1: The master and slave permanent magnet synchronous motors with different system parameters operate in different attraction basins. They eventually cycle on different tracks. Synchronization is intended to change the configuration of the slave system, enabling it to move from the original track to the master system's track with high precision and speed. Furthermore, if α = 1 and χ = 0, the fractional-order mathematical model of the bidirectionally coupled permanent magnet synchronous motor degenerates into the integer-order model of the isolated permanent magnet synchronous motor.

[0056] By subtracting equation (4) from equation (3) and adding control input, the step-by-step synchronization model of the bidirectional coupled master-slave permanent magnet synchronous motor is derived as follows:

[0057]

[0058] The synchronization error is defined as E i =x i -y i i = 1, 2, 3, u i i = 2, 3 represents the control inputs that will be designed next.

[0059] 2. Dynamics analysis and analog circuit construction

[0060] The system parameters of the bidirectional coupled permanent magnet synchronous motor are given as follows:

[0061] Working condition 1: σ=10, γ=25, T L =6, u q =0 and u d =0, all initial conditions are 0.

[0062] Working condition 2: σ=5, γ=20, T L =3, u q =0 and u d =0, all initial conditions are 0.

[0063] To compare with traditional tools such as bifurcation diagrams and Lyapunov exponents, the 0-1 test, as a binary test, can simply and directly determine the dynamic characteristics of a bidirectional coupled permanent magnet synchronous motor based on time series data. Figure 2The 0-1 test results of the transient time trajectory of the bidirectional coupled permanent magnet synchronous motor are shown at α=0.99 and α=0.91. Figure 2 The Brownian motion in (a1) indicates that the bidirectionally coupled permanent magnet synchronous motor enters transient chaos at α = 0.99. Figure 2 The bounded motion of (a2) implies that this bidirectionally coupled permanent magnet synchronous motor produces periodic motion at α = 0.91. This also means that during transient chaos, Figure 2 The mean square displacement of (b1) increases exponentially, while Figure 2 M(n) in (b2) changes periodically during regular motion. As a function of the discrete time of transient chaos and periodic motion, the asymptotic growth rate is as follows: Figure 2 (c1)- Figure 2 As shown in (c2), where K≈1 represents transient chaos and K≈0 represents periodic states.

[0064] Similarly, to obtain quantitative and visual information, a 0-1 test was performed using the transient time trajectory y1 of a bidirectional coupled permanent magnet synchronous motor. Figure 3 The periodic or chaotic states under two different resistive coupling parameters were distinguished. It is easy to see that the bidirectional coupled permanent magnet synchronous motor exhibits transient chaos when χ = 0.2, and jumps to the periodic state when χ = 0.6.

[0065] To obtain the analytical solution for the dynamics, a frequency approximation is used in the circuit implementation to characterize the fractional-order system. The angular velocity range is

[10] . -2 10 2 ] rad / s, with a maximum deviation of 0.1dB for 1 / s 0.997 The linear approximate transfer function is written as

[0066]

[0067] Where s represents the complex frequency.

[0068] To facilitate the construction of the unit circuit for F(s), the corresponding transfer function is defined as follows:

[0069]

[0070] Among them, C o C is the specific capacitance; a C b and C c R is the capacitor selected in the unit circuit. a R b and R c The resistor selected in the unit circuit.

[0071] Based on equation (6), C can be derived. a =9.95382×10-9 F, C b =4.25812×10 -7 F, C c =4.16317×10 -7 F, R a =9.93105×10 8 Ω, R b =10529.4Ω and R c = 4.88467Ω. The electronic circuit of a bidirectional coupled permanent magnet synchronous motor consists of a multiplier, amplifier, DC power supply, resistors, and capacitors, such as... Figure 4 As shown.

[0072] The six unit circuits established are for achieving 1 / s 0.997 This includes UC1 (capacitors C1-C3, resistors R26-R28), UC2 (capacitors C4-C6, resistors R18, R19, R29), UC3 (capacitors C7-C9, resistors R35, R36, R43), UC4 (capacitors C10-C12, resistors R49, R57, R58), UC5 (capacitors C13-C15, resistors R61, R62, R71), and UC6 (capacitors C16-C18, resistors R74-R76). The values ​​of the resistors and capacitors are related to R... a R b R c C a C b and C c same.

[0073] Six integrating circuits under ±15V DC supply voltage: IC1 (unit circuit UC1, amplifier U1A, resistor R14), IC2 (unit circuit UC2, amplifier U3A, resistor R9), IC3 (unit circuit UC3, amplifier U5A, resistor R34), IC4 (unit circuit UC4, amplifier U7A, resistor R45), IC5 (unit circuit UC5, amplifier U9A, resistor R60), and IC6 (unit circuit UC6, amplifier U11A, resistor R73) are used to map the six state variables of the integrating bidirectional coupled permanent magnet synchronous motor.

[0074] Six inverting proportional operational amplifier circuits are used for inverting the DC power supply at ±15V: IPOC1 (resistors R4-R6, amplifier U2A), IPOC2 (resistors R10-R12, amplifier U4A), IPOC3 (resistors R20-R22, amplifier U6A), IPOC4 (resistors R31-R33, amplifier U8A), IPOC5 (resistors R37-R39, amplifier U10A), and IPOC6 (resistors R46-R48, amplifier U12A).

[0075] The four multipliers (A1, A2, A3, A4) are selected as AD633. Resistors R3, R8, R30, R44, R59, and R72 are used as integration drift leakage resistors to prevent saturation cutoff caused by integration drift. The time scaling scale is set to τ = 10⁻¹⁰. 3 t.

[0076] The voltage state variables x1, x2, x3, y1, y2, y3, etc., have a mapping relationship with the state variables x1, x2, x3, y1, y2, y3 of the bidirectional coupled permanent magnet synchronous generator.

[0077] By applying Kirchhoff's circuit laws and constitutive relations Figure 4 The circuit equations in the diagram are:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] Since the linear operating range of most amplifiers is in the range of [-10, 10] V, the voltage state variable is equal to the state variable x of the bidirectional coupled permanent magnet synchronous motor. i ,y i The values ​​of i = 1, 2, 3 reduced by a factor of 10. Based on this, the phase diagram of the analog circuit of the bidirectional coupled permanent magnet synchronous motor when α = 0.997 and χ = 0.2 is as follows. Figures 5-6 As shown, it can be clearly seen that the bidirectional coupled permanent magnet synchronous motor simulated by this invention has inherent chaotic oscillations under certain conditions.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A simulation circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor, characterized in that, The circuit consists of multipliers, amplifiers, DC power supplies, resistors, and capacitors. Specifically, it includes: six identical fractional-order integrator circuits (IC1~IC6), six identical inverting proportional operational amplifier circuits (IPOC1~IPOC6), four multipliers, and six integral drift drain resistors (R3, R8, R30, R44, R59, and R72). Six integrator circuits are used to map the state variables of the integral bidirectional coupled permanent magnet synchronous motor. , , , , and The integrating circuit includes a unit circuit, amplifiers U1A, U3A, U5A, U7A, U9A or U11A, and resistors (R14, R9, R34, R45, R60 or R73). The unit circuit consists of three sets of parallel resistors and capacitors of different sizes connected in series. The unit circuit connects the negative input terminal and the output terminal of the amplifiers (U1A, U3A, U5A, U7A, U9A or U11A). The positive input terminal of the amplifiers U1A, U3A, U5A, U7A, U9A or U11A is grounded through resistors (R14, R9, R34, R45, R60 or R73). The negative input terminal of the amplifiers U1A, U3A, U5A, U7A, U9A or U11A is connected to a power supply and interacts with the state variables of the bidirectionally coupled permanent magnet synchronous generator. , , , , or There is a mapping relationship; The negative input terminal of the inverting proportional operational amplifier circuit is connected to the output terminal of amplifiers U1A, U3A, U5A, U7A, U9A, or U11A in the integrating circuit; the output terminals of the six inverting proportional operational amplifier circuits are respectively connected to the power supply, and the corresponding voltage state variables are x1, x2, x3, y1, y2, or y3, which correspond to the state variables of the bidirectional coupled permanent magnet synchronous generator. , , , , or There is a mapping relationship; The integral drift leakage resistor (R3, R8, R30, R44, R59 or R72) is connected in parallel with the unit circuit to avoid saturation cutoff caused by integral drift. The multiplier is connected to the negative input terminal of amplifiers U3A, U5A, U9A, or U11A in the integrator circuit via resistors (R15, R24, R51, or R54).

2. The analog circuit for the fractional-order bidirectional coupled permanent magnet synchronous motor according to claim 1, characterized in that, The inverting proportional operational amplifier circuit includes an amplifier (U2A, U4A, U6A, U8A, U10A, or U12A) and three resistors. One resistor is used to connect the negative input terminal and the output terminal of the amplifier (U2A, U4A, U6A, U8A, U10A, or U12A). Another resistor is used to connect the negative input terminal of the amplifier (U2A, U4A, U6A, U8A, U10A, or U12A) to the output terminal of the amplifier in the integrating circuit. The last resistor is used to ground the positive input terminal of the amplifier (U2A, U4A, U6A, U8A, U10A, or U12A).

3. The analog circuit for the fractional-order bidirectional coupled permanent magnet synchronous motor according to claim 1, characterized in that, The negative terminal of the input of the amplifier U1A is connected to a power supply with voltage state variables of -x1, x2 and z1 through resistors R1, R13 and R2 respectively; The negative terminal of the input of the amplifier U3A is connected to a power supply with voltage state variables of -x2, x1, z0, y2 and -x2 through resistors R7, R16, R25, R63 and R64 respectively, and is also connected to multiplier A1 through resistor R15. Multiplier A1 is connected to a power supply with voltage state variables of x3 and -x1. The negative terminal of the input of the amplifier U5A is connected to a power supply with voltage state variables of -x3, z0, y3 and -x3 through resistors R23, R17, R65 and R66 respectively, and is also connected to multiplier A2 through resistor R24. Multiplier A2 is connected to a power supply with voltage state variables of x2 and x1. The negative terminal of the input of the amplifier U7A is connected to a power supply with voltage state variables -y1, y2 and z2 through resistors R40, R41 and R42 respectively; The negative input terminal of the amplifier U9A is connected to a power supply with voltage state variables -y2, y1, z0, x2 and -y2 respectively through resistors R50, R52, R56, R67 and R68. It is also connected to multiplier A3 through resistor R51. Multiplier A3 is connected to a power supply with voltage state variables y3 and -y1. The negative input terminal of the amplifier U11A is connected to a power supply with voltage state variables -y3, z0, x3 and -y3 respectively through resistors R53, R55, R69 and R70. It is also connected to multiplier A2 through resistor R24. Multiplier A2 is connected to a power supply with voltage state variables y2 and y1.

4. The analog circuit for the fractional-order bidirectional coupled permanent magnet synchronous motor according to claim 3, characterized in that, Applying Kirchhoff's circuit laws, the circuit equations for this analog circuit are as follows: in, The transfer function represents the unit circuit. α It represents the fractional order value starting at the origin and satisfying 0 < α < 1.

5. The analog circuit for a fractional-order bidirectional coupled permanent magnet synchronous motor according to claim 4, characterized in that, Transfer function of unit circuit The expression is: in, For specific capacitance, , and The capacitor selected in the unit circuit. , and The resistor selected in the unit circuit. Represents a complex frequency.

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