Permanent magnet synchronous motor current loop control method and device based on cascade sliding mode resonance

Abstract

The present invention relates to the field of permanent magnet synchronous motor current control, and specifically to a permanent magnet synchronous motor current loop control method and device based on cascade sliding mode resonance. The method and device first construct a permanent magnet synchronous motor mathematical model, and the nonlinear influence of the inverter is taken into account during the construction of the permanent magnet synchronous motor mathematical model; then construct a cascade sliding mode resonance controller, and the cascade sliding mode resonance controller designs a super spiral sliding mode control law based on high-order sliding mode theory during the construction; finally, a fixed time adaptive estimation law is designed in the cascade sliding mode resonance controller to estimate unknown disturbances, and a cascade sliding mode resonance control structure combining a super spiral controller and a resonance controller is formed to achieve the purpose of suppressing current loop harmonics and ensuring good robustness of the control system, realize the rapidity and robustness of the current loop response, and reduce the distortion of the output current of the permanent magnet synchronous motor, and effectively improve the control accuracy under the condition of motor system parameter changes.

Description

Technical Field

[0001] The present invention relates to the field of permanent magnet synchronous motor current control, and in particular to a permanent magnet synchronous motor current loop control method and device based on cascade sliding mode resonance. Background Art

[0002] Permanent magnet synchronous motors (PMSMs), with their high power density, high torque-to-inertia ratio, and high efficiency, are widely used in diverse applications, including electric vehicles, CNC machine tools, optoelectronic turntables, and ship propulsion. However, torque ripple has long been a key issue hindering the high-performance application of PMSMs. Even without design or manufacturing flaws, inverter nonlinearity inevitably exists in the motor servo system. Interference caused by inverter nonlinearity has a significant negative impact on servo system performance, leading to current distortion and, consequently, torque ripple, reducing tracking performance and stability. This phenomenon is particularly pronounced at low speeds.

[0003] Proportional-integral resonant control is a commonly used current loop control strategy for permanent magnet synchronous motors. It uses high gain at the resonant point to suppress current harmonics, thereby reducing torque ripple. However, this type of controller suffers from poor robustness and cannot eliminate the effects of coupling terms.

[0004] At the same time, during continuous operation of a permanent magnet synchronous motor, the temperature rise of the stator winding, changes in the degree of magnetic circuit saturation, and changes in the temperature of the permanent magnets will lead to changes in the stator resistance, inductance, and permanent magnet flux linkage. In addition, changes in load may also occur and cause changes in system parameters, which will affect the actual control effect of the system. Summary of the Invention

[0005] The embodiments of the present invention provide a permanent magnet synchronous motor current loop control method and device based on cascade sliding mode resonance, so as to at least solve the technical problem of low control accuracy of the existing permanent magnet synchronous motor current loop control method.

[0006] According to one embodiment of the present invention, a method for controlling a current loop of a permanent magnet synchronous motor based on cascaded sliding mode resonance is provided, comprising the following steps:

[0007] S101: Constructing a mathematical model of a permanent magnet synchronous motor, wherein the mathematical model of the permanent magnet synchronous motor takes into account the nonlinear effect of the inverter;

[0008] S102: constructing a cascade sliding mode resonant controller, wherein the cascade sliding mode resonant controller is designed with a super-helical sliding mode control law based on a high-order sliding mode theory during construction;

[0009] S103: Design a fixed-time adaptive estimation law in the cascade sliding mode resonant controller to estimate unknown disturbances.

[0010] Furthermore, factors affecting the nonlinearity of the inverter include: the inverter's dead time, device delay time, and voltage drop of the power device tube.

[0011] Furthermore, the device turn-on delay and turn-off delay time are much shorter than the dead time of the motor control; when the motor is in steady-state operation, the motor phase current is sinusoidal.

[0012] Furthermore, the non-periodic interference caused by parameter mismatch and voltage error between reference voltage and actual voltage will be suppressed by the super-spiral controller.

[0013] Furthermore, the non-periodic interference caused by parameter mismatch and voltage error between the reference voltage and the actual voltage is a slow time-varying disturbance.

[0014] Furthermore, the method further comprises the steps of:

[0015] S104: Prove the stability of the superhelical controller with fixed-time adaptive law based on Lyapunov stability theory.

[0016] According to another embodiment of the present invention, a permanent magnet synchronous motor current loop control device based on cascade sliding mode resonance is provided, comprising:

[0017] A model building unit is used to build a mathematical model of the permanent magnet synchronous motor, and the mathematical model of the permanent magnet synchronous motor takes the nonlinear effect of the inverter into consideration during the construction;

[0018] A controller construction unit is used to construct a cascade sliding mode resonant controller. The cascade sliding mode resonant controller is designed with a super-helical sliding mode control law based on high-order sliding mode theory during construction.

[0019] The estimation unit is used to design a fixed-time adaptive estimation law in a cascade sliding mode resonant controller to estimate unknown disturbances.

[0020] Furthermore, the device further comprises:

[0021] Proof unit, used to prove the stability of the superhelical controller with fixed-time adaptive law based on Lyapunov stability theory.

[0022] A storage medium stores a program file capable of implementing any one of the above-mentioned permanent magnet synchronous motor current loop control methods based on cascade sliding mode resonance.

[0023] A processor is used to run a program, wherein when the program is run, any one of the above-mentioned permanent magnet synchronous motor current loop control methods based on cascade sliding mode resonance is executed.

[0024] The permanent magnet synchronous motor current loop control method and device based on cascade sliding mode resonance in the embodiment of the present invention first constructs a mathematical model of the permanent magnet synchronous motor, and the nonlinear influence of the inverter is taken into account during the construction of the mathematical model of the permanent magnet synchronous motor; then a cascade sliding mode resonance controller is constructed, and a super-helical sliding mode control law based on high-order sliding mode theory is designed in the cascade sliding mode resonance controller during the construction; finally, a fixed-time adaptive estimation law is designed in the cascade sliding mode resonance controller to estimate unknown disturbances, and a cascade sliding mode resonance control structure that combines the super-helical controller and the resonance controller is formed to achieve the purpose of suppressing current loop harmonics and ensuring good robustness of the control system, thereby achieving rapid and robust current loop response and reducing the distortion of the output current of the permanent magnet synchronous motor, which can effectively reduce the influence of the nonlinearity of the inverter of the permanent magnet synchronous motor drive system, and effectively improve the control accuracy under the condition of changing motor system parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0026] Figure 1 This is a flow chart of a current loop control method for a permanent magnet synchronous motor based on cascade sliding mode resonance according to the present invention;

[0027] FIG2( a ) is a schematic diagram of phase a in a three-phase inverter according to the present invention;

[0028] FIG2( b ) is a schematic diagram of the dead time effect in the present invention;

[0029] Figure 3 is the error voltage waveform diagram of the present invention;

[0030] Figure 4 It is a schematic diagram of a traditional proportional-integral resonant controller;

[0031] Figure 5 Schematic diagram of the cascade sliding mode resonant controller in the present invention;

[0032] Figure 6 is the Bode diagram of the present invention;

[0033] Figure 7 This is a structural block diagram of a permanent magnet synchronous motor speed servo system based on a cascaded sliding mode resonant controller according to the present invention;

[0034] Figure 8 The total harmonic distortion rate diagram of the phase current under different motor speeds and different inverter dead time is shown in the present invention;

[0035] FIG9( a ) is a diagram showing the motor phase current, Fourier analysis of the phase current, and output torque waveforms when the motor speed is 100 r / min and the inverter nonlinearity is not applied under the simulation of the present invention;

[0036] 9( b ) is a diagram showing the motor phase current, Fourier analysis of the phase current, and output torque waveforms when the motor speed is 100 r / min and the inverter nonlinearity is applied under the simulation of the present invention;

[0037] Figure 10 The following are the shaft current response and three-phase current response of the PI algorithm to the step signal, as well as the Fourier analysis diagram of the three-phase current;

[0038] Figure 11 The shaft current response and three-phase current response of the PIR algorithm to the step signal and the Fourier analysis diagram of the three-phase current;

[0039] Figure 12 The shaft current response and three-phase current response of the algorithm of the present invention to the step signal and the Fourier analysis diagram of the three-phase current;

[0040] Figure 13 From left to right are the shaft current response diagrams of PI, PIR and the algorithm of the present invention to the sinusoidal signal;

[0041] Figure 14 This is a result diagram of the fixed-time adaptive law estimation proposed by the present invention;

[0042] Figure 15 The motor speed is 100r / min, the current loop is PIR, and the shaft current response diagram of the algorithm of the present invention under the condition of motor parameter changes;

[0043] Figure 16 This is a preferred flow chart of the permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance of the present invention;

[0044] Figure 17 This is a module diagram of a permanent magnet synchronous motor current loop control device based on cascade sliding mode resonance according to the present invention;

[0045] Figure 18 This is a preferred module diagram of the permanent magnet synchronous motor current loop control device based on cascade sliding mode resonance of the present invention. DETAILED DESCRIPTION

[0046] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0047] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0048] Example 1

[0049] According to an embodiment of the present invention, a current loop control method for a permanent magnet synchronous motor based on cascade sliding mode resonance is provided. Figure 1 , including the following steps:

[0050] S101: Constructing a mathematical model of a permanent magnet synchronous motor, wherein the mathematical model of the permanent magnet synchronous motor takes into account the nonlinear effect of the inverter;

[0051] S102: constructing a cascade sliding mode resonant controller, wherein the cascade sliding mode resonant controller is designed with a super-helical sliding mode control law based on a high-order sliding mode theory during construction;

[0052] S103: Design a fixed-time adaptive estimation law in the cascade sliding mode resonant controller to estimate unknown disturbances.

[0053] The permanent magnet synchronous motor current loop control method based on cascaded sliding mode resonance in the embodiment of the present invention first constructs a mathematical model of the permanent magnet synchronous motor, and the nonlinear influence of the inverter is taken into account during the construction of the mathematical model of the permanent magnet synchronous motor; then a cascaded sliding mode resonance controller is constructed, and a super-helical sliding mode control law based on high-order sliding mode theory is designed in the cascaded sliding mode resonance controller during the construction; finally, a fixed-time adaptive estimation law is designed in the cascaded sliding mode resonance controller to estimate unknown disturbances, and a cascaded sliding mode resonance control structure that combines the super-helical controller and the resonance controller is formed to achieve the purpose of suppressing current loop harmonics and ensuring good robustness of the control system, thereby achieving rapidity and robustness of the current loop response and reducing the distortion of the output current of the permanent magnet synchronous motor, which can effectively reduce the influence of the nonlinearity of the inverter of the permanent magnet synchronous motor drive system, and can effectively improve the control accuracy under the condition of changing motor system parameters.

[0054] Among them, the nonlinear factors affecting the inverter include: the inverter's dead time, device delay time and the voltage drop of the power device tube.

[0055] Among them, the device turn-on delay and turn-off delay time are much smaller than the dead time of motor control; when the motor is running in steady state, the motor phase current is sinusoidal.

[0056] Among them, the non-periodic interference caused by parameter mismatch and voltage error between reference voltage and actual voltage will be suppressed by the super-spiral controller.

[0057] Among them, the non-periodic interference caused by parameter mismatch and the voltage error between the reference voltage and the actual voltage is a slow time-varying disturbance.

[0058] Among them, see Figure 16 , the method further comprises the steps of:

[0059] S104: Prove the stability of the superhelical controller with fixed-time adaptive law based on Lyapunov stability theory.

[0060] The following is a detailed description of the permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance of the present invention using a specific embodiment:

[0061] In response to disturbances such as inverter nonlinearity and current loop parameter mismatch in a permanent magnet synchronous motor drive system, the present invention proposes a cascaded sliding mode resonant control structure that combines a superhelical controller and a resonant controller to suppress current loop harmonics and ensure good robustness of the control system, thereby achieving rapid and robust current loop response and reducing distortion in the output current of the permanent magnet synchronous motor. At the same time, a fixed-time adaptive law method is adopted to actively estimate and eliminate disturbances such as parameter uncertainty in real time to improve the dynamic performance and anti-interference capability of the permanent magnet synchronous motor current loop. In view of this, the present invention proposes a permanent magnet synchronous motor current loop control method and device based on cascaded sliding mode resonance, which can effectively reduce the impact of inverter nonlinearity in the permanent magnet synchronous motor drive system and effectively improve control accuracy under conditions of motor system parameter changes.

[0062] The adaptive law in the present invention, based on fixed-time convergence theory, compensates the disturbance estimate to the controller, further improving the anti-interference capability of the current loop. This adaptive law is characterized by not requiring the estimated values ​​of the dq-axis currents and ensuring that the disturbance estimate error converges to zero within a fixed time. Combining the advantages of sliding mode control and resonant control, the present invention effectively reduces the nonlinear effects of the inverter in the permanent magnet synchronous motor drive system while ensuring good dynamic response capabilities of the current loop and robustness to parameter changes.

[0063] The technical solution of the present invention specifically includes the following steps:

[0064] Step 1: Establish a mathematical model of the permanent magnet synchronous motor considering the nonlinear effect of the inverter;

[0065] The inverter's dead time, device delay time, and voltage drop across the power device are the main factors contributing to inverter nonlinearity. Figure 2(a) shows a schematic diagram of phase a in a three-phase inverter, including two insulated gate bipolar transistors (IGBTs) and two anti-parallel freewheeling diodes. For a pulse width modulation (PWM) voltage source inverter, complementary PWM signals are provided to the upper and lower bridge arms to achieve voltage output. However, to prevent a short circuit from occurring when the upper and lower bridge arms in the same phase are simultaneously turned on, a dead time is typically inserted at the rising edge of the drive signal. A schematic diagram of the dead time effect is shown in Figure 2(b).

[0066] Figure 2(a) shows the model of the bridge arm of phase a, where U dc Indicates the DC bus voltage, U CE Indicates the IGBT conduction voltage drop, U F is the voltage drop of the freewheeling diode. Figure 2(b) shows the ideal and actual a-phase upper and lower bridge arm drive signals and a-phase voltage, where T PWMis the carrier period, t d is the dead time, t on With t off Respectively represent the IGBT turn-on and turn-off delay time, is the action time of the a-phase switch tube after pulse width modulation calculation.

[0067] According to Figure 2(b), the average voltage from phase a to reference ground N per PWM cycle can be expressed as:

[0068]

[0069] Where sgn(·) represents the sign function, i a represents the a-phase current, T a Indicates the actual action time of the a-phase switch tube, which is different from the action time of the switch tube calculated by pulse width modulation The relationship is:

[0070]

[0071] Typically, the device turn-on and turn-off delays are much shorter than the motor control dead time. Therefore, to simplify the analysis, the device turn-on and turn-off delays are ignored. To further calculate the average phase voltage, including nonlinearity, it is necessary to understand the relationship between the line voltage and the phase voltage. This relationship is described as follows:

[0072] U aN =U aN′ +U NN′ (3)

[0073] Where U NN′ Represents the voltage between the neutral point N' and the reference ground N. At the same time, the following conditions are met in the permanent magnet synchronous motor with three-phase winding Y connection:

[0074] U aN′ +U bN′ +U cN ′=0 (4)

[0075] Where U bN′ and U cN′ The phase voltages of phases b and c can be defined according to equation (1). Therefore, the phase voltages including the inverter nonlinearity can be obtained from equations (1), (2) and (3) as follows:

[0076]

[0077] Where, T b and T c Respectively represent the actual action time of the b-phase and c-phase switching tubes, i b and i cRepresent the b-phase and c-phase currents respectively. Without considering the nonlinear effect of the inverter, the a-phase voltage can be expressed as:

[0078]

[0079] Where, T b and T c They represent the switching time of phase B and phase C respectively after pulse width modulation calculation. Therefore, the error voltage of phase A caused by inverter nonlinearity in one PWM cycle can be expressed as:

[0080]

[0081] When the motor is running in steady state, the motor phase current is sinusoidal and the error voltage is as follows: Figure 3 As shown:

[0082] Therefore, the error voltage can be regarded as Frequency in-phase current (ω e ), the error voltage of the six-step wave is expanded by Fourier, and we have:

[0083]

[0084] Furthermore, by setting ΔU aN′ , ΔU bN′ , ΔU cN′ Transformed into the synchronous rotating coordinate system, we can get ΔU d , ΔU q It is the sum of the DC component, the 6th harmonic component, and its integer multiples. These voltage distortions can cause inconsistencies between the inverter applied voltage and the current loop output voltage, as well as current distortion.

[0085] Therefore, considering the effects of inverter nonlinearity and parameter mismatch, the state equation of the surface-mount PMSM can be modeled as:

[0086]

[0087] Where i d 、i q They represent the dq axis current of the permanent magnet synchronous motor respectively; R, L and ψ f They represent the stator resistance, inductance and permanent magnet flux of the permanent magnet synchronous motor respectively; d ddc and d qdc They represent the non-periodic interference of d and q axes caused by the voltage error between the reference voltage and the actual voltage and the parameter mismatch; d dac and d qac They represent the harmonic interference caused by the inverter.

[0088] Step 2: Design a cascade sliding mode resonant controller;

[0089] Traditional proportional-integral resonant controllers such as Figure 4 The proposed cascade sliding mode resonant controller is shown in Figure 5 shown.

[0090] exist Figure 5 In the example, the resonant controller is connected in series with the output of the super-helical controller to suppress the 6th and 12th harmonics on the dq axis, i.e., the 5th, 7th, 11th, and 13th harmonic components in the phase current. The transfer function of the resonant controller is as follows:

[0091]

[0092] Where K r Represents the gain coefficient of the resonant controller; ω c is the cutoff frequency of the resonant controller; 6nω e (n=1,2,…,∞) is the resonant frequency.

[0093] Multiply the state equation in Eq. (9) by [1+G Σ (s)] -1 , which is equivalent to embedding the resonant internal model into (9).

[0094]

[0095] Where u′ d =[1+G ∑ (s)] -1 u d ,u′ q =[1+G Σ (s)] -1 u q . [1+G Σ (s)] -1 Bird Figure 6 As shown, where K r =50,ω c =50rad / s,ω e =10πad / s. It can be seen that [1+G Σ (s)] -1 The attenuation effect on the resonant frequency signal is very strong, while the effect on signals of other frequencies is relatively small. Based on this characteristic, Equation (11) can be simplified to:

[0096]

[0097] The non-periodic interference caused by parameter mismatch and voltage error between reference voltage and actual voltage will be suppressed by the super-helical controller. To achieve this control goal, the d-axis and q-axis current tracking errors are defined as follows:

[0098]

[0099] in They are the dq axis reference currents respectively, and the current tracking error e is d and e q As the state variable, the dq axis voltage u d and u q As the control input, the state space equation of the dq axis current can be expressed as follows:

[0100]

[0101] Where, E d and E q represents a known disturbance, D d and D q Denotes the unknown disturbance D d =-d ddc / L,D q =-d qdc / L. Define the sliding surface s d =e d , s q =e q , then the super-helical sliding mode control law designed based on the high-order sliding mode theory is as follows:

[0102]

[0103] Where, α>0, β>0, sig y (x)=|x| y sgn(x), y is a real number, and D d and D q The estimated value of will be given in step 3.

[0104] Step 3: Design a fixed-time adaptive estimation law to estimate the unknown disturbance;

[0105] To further improve the anti-interference capability of the current loop, an adaptive law based on fixed-time convergence theory is proposed to observe and compensate for unknown disturbances such as parameter mismatch. The adaptive law is as follows:

[0106]

[0107] Where, e dd and e dq are the estimated errors of the unknown disturbances in the dq axis, m, n, p and q are all positive odd numbers and satisfy m>n, p<q. Formula (16) is used to estimate the unknown disturbance, and the estimated error convergence time satisfies:

[0108]

[0109] The above-mentioned fixed convergence time calculation method is explained using the d-axis as an example.

[0110] Substituting the sliding mode control law (15) into the derivative of the sliding mode surface, we get:

[0111]

[0112] Therefore, the first term of formula (16) is satisfied, and the non-periodic interference caused by parameter mismatch and voltage error between reference voltage and actual voltage can be regarded as slow time-varying disturbance, that is, Therefore, the second term of formula (16) can be further expressed as:

[0113]

[0114] make but Formula (19) can be rewritten as:

[0115]

[0116] Where, Solving formula (20), the upper bound of the convergence time can be estimated as:

[0117]

[0118] The stability of the superhelical controller with a fixed-time adaptive law is demonstrated below based on Lyapunov stability theory:

[0119] Construct a quadratic Lyapunov function of the following form:

[0120]

[0121] Take a positive definite matrix Then V is continuous positive definite, and dividing s d = 0 and is differentiable everywhere.

[0122] Since the time derivative of η in, Assume that at any time This condition is met in permanent magnet synchronous motor systems.

[0123] Then, by solving the derivative of the quadratic Lyapunov function (22), we can obtain:

[0124]

[0125] In the formula, C=1 0.

[0126] make When the values ​​of α and β satisfy:

[0127] α>2,

[0128] Q is positive definite symmetric, so The above formula shows that the system current tracking error formula (13) can converge to zero under the control law formula (15).

[0129] In order to better illustrate the purpose and advantages of the present invention, the present invention is further described below with reference to the accompanying drawings.

[0130] Figure 7 This is the structural block diagram of the permanent magnet synchronous motor speed servo system based on the cascade sliding mode resonant controller.

[0131] The system consists of a permanent magnet synchronous motor, a three-phase inverter, space voltage vector pulse width modulation (SVPWM), a position sensor, a PI controller for the velocity loop, a cascaded sliding mode resonant controller (current controller), and a coordinate transformation module. The velocity loop uses a PI controller to generate the q-axis current setpoint, while the current loop uses a cascaded sliding mode resonant controller to generate the control voltage. The SVPWM control strategy is used to switch the power components of the three-phase inverter, ultimately driving the permanent magnet synchronous motor.

[0132] First, in order to evaluate the impact of inverter nonlinearity on the permanent magnet synchronous motor system, the current loop and speed loop are both traditional proportional integral controllers, and the IGBT conduction voltage drop U CE is 1.9V and the freewheeling diode voltage drop U F Under the condition of 2.5V, Figure 8 The total harmonic distortion (THD) of the phase current under different motor speeds and different inverter dead time is given. Figure 9 shows the total harmonic distortion (THD) of the phase current under different motor speeds and different inverter dead time. CE =1.9V, U F =2.5V, t d=5μs) without applying inverter nonlinearity, a Fourier analysis of the motor phase current, and a comparison of the output torque waveforms. Specifically, Figure 9(a) shows the motor phase current, a Fourier analysis of the phase current, and a waveform of the output torque without applying inverter nonlinearity under the simulation of the present invention at a motor speed of 100r / min; Figure 9(b) shows the motor phase current, a Fourier analysis of the phase current, and a waveform of the output torque under the simulation of the present invention at a motor speed of 100r / min with inverter nonlinearity applied. The results show that inverter nonlinearity seriously affects the smoothness of the permanent magnet synchronous motor phase current and output torque, and the longer the inverter dead time and the lower the motor operating speed, the more obvious the impact of inverter nonlinearity. This also demonstrates the accuracy of the model established in step 1.

[0133] To evaluate the proposed algorithm, a comparative simulation experiment was conducted. PI and PIR controllers were used for comparison with the proposed control algorithm. To ensure fairness, the speed loop used a PI controller with identical parameters.

[0134] Figure 10 、 11 12 are the dq axis current responses, three-phase current responses and Fourier analysis diagrams of the three-phase currents of PI, PIR and the algorithm of the present invention to the step signal respectively; Figure 13 From left to right, the results of PI, PIR and the algorithm of the present invention on the sinusoidal signal are shown in the figure. The q-axis current response diagram. Figure 10-12 It can be seen that the PI, PIR, and the algorithm of the present invention took 0.0295, 0.0255, and 0.0068 seconds to track the reference current, respectively. At the same time, the algorithm of the present invention has the smallest fluctuation range of 0.0134A in steady state, which is smaller than 0.023A of PI and 0.0176A of PIR. The total harmonic distortion rate of the phase current is the smallest, and the amplitude of the harmonics of the specific order caused by the nonlinearity of the inverter is greatly attenuated. And from Figure 13 It can be clearly seen that the proposed algorithm has the best ability among the three algorithms when tracking the sinusoidal reference.

[0135] Figure 14 The result diagram of the proposed fixed-time adaptive law estimation is shown in the figure. It can be seen from the figure that the adaptive law can quickly and accurately predict the unknown disturbance D q Make an estimate.

[0136] To further illustrate the robustness of the proposed technique to parameter mismatch, Figure 15 The q-axis current response of the proposed algorithm is shown for a motor with a speed of 100 rpm and a PIR current loop under varying motor parameters. The figure shows that the proposed method achieves shorter current amplitude changes and shorter recovery times than the traditional proportional-integral-resonance method when faced with varying motor parameters.

[0137] The above experimental results show that the permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance of the present invention can not only effectively reduce the influence of the nonlinearity of the inverter of the permanent magnet synchronous motor drive system, but also has good dynamic response capability and robustness to parameter changes.

[0138] Example 2

[0139] According to another embodiment of the present invention, a permanent magnet synchronous motor current loop control device based on cascade sliding mode resonance is provided. Figure 17 ,include:

[0140] The model building unit 201 is used to build a mathematical model of the permanent magnet synchronous motor, and the nonlinear effect of the inverter is taken into consideration during the construction of the mathematical model of the permanent magnet synchronous motor;

[0141] A controller construction unit 202 is used to construct a cascade sliding mode resonant controller, wherein the cascade sliding mode resonant controller is designed with a super-helical sliding mode control law based on a high-order sliding mode theory during construction;

[0142] The estimation unit 203 is used to design a fixed-time adaptive estimation law in the cascade sliding mode resonant controller to estimate the unknown disturbance.

[0143] The permanent magnet synchronous motor current loop control device based on cascade sliding mode resonance in the embodiment of the present invention first constructs a mathematical model of the permanent magnet synchronous motor, and the nonlinear influence of the inverter is taken into account during the construction of the mathematical model of the permanent magnet synchronous motor; then a cascade sliding mode resonance controller is constructed, and a super-helical sliding mode control law based on high-order sliding mode theory is designed in the cascade sliding mode resonance controller during the construction; finally, a fixed-time adaptive estimation law is designed in the cascade sliding mode resonance controller to estimate unknown disturbances, and a cascade sliding mode resonance control structure combining the super-helical controller and the resonance controller is formed to achieve the purpose of suppressing current loop harmonics and ensuring good robustness of the control system, thereby achieving rapidity and robustness of the current loop response and reducing the distortion of the output current of the permanent magnet synchronous motor, which can effectively reduce the influence of the nonlinearity of the inverter of the permanent magnet synchronous motor drive system, and can effectively improve the control accuracy under the condition of changing motor system parameters.

[0144] Among them, see Figure 18 , the device further comprises:

[0145] The proving unit 204 is used to prove the stability of the super spiral controller with a fixed time adaptive law based on Lyapunov stability theory.

[0146] The following is a detailed description of the permanent magnet synchronous motor current loop control device based on cascade sliding mode resonance of the present invention using a specific embodiment:

[0147] In response to disturbances such as inverter nonlinearity and current loop parameter mismatch in a permanent magnet synchronous motor drive system, the present invention proposes a cascaded sliding mode resonant control structure that combines a superhelical controller and a resonant controller to suppress current loop harmonics and ensure good robustness of the control system, thereby achieving rapid and robust current loop response and reducing distortion in the output current of the permanent magnet synchronous motor. At the same time, a fixed-time adaptive law method is adopted to actively estimate and eliminate disturbances such as parameter uncertainty in real time to improve the dynamic performance and anti-interference capability of the permanent magnet synchronous motor current loop. In view of this, the present invention proposes a permanent magnet synchronous motor current loop control method and device based on cascaded sliding mode resonance, which can effectively reduce the impact of inverter nonlinearity in the permanent magnet synchronous motor drive system and effectively improve control accuracy under conditions of motor system parameter changes.

[0148] The adaptive law in the present invention, based on fixed-time convergence theory, compensates the disturbance estimate to the controller, further improving the anti-interference capability of the current loop. This adaptive law is characterized by not requiring the estimated values ​​of the dq-axis currents and ensuring that the disturbance estimate error converges to zero within a fixed time. Combining the advantages of sliding mode control and resonant control, the present invention effectively reduces the nonlinear effects of the inverter in the permanent magnet synchronous motor drive system while ensuring good dynamic response capabilities of the current loop and robustness to parameter changes.

[0149] The technical solution of the present invention specifically includes the following steps:

[0150] Step 1: Establish a mathematical model of the permanent magnet synchronous motor considering the nonlinear effect of the inverter;

[0151] The inverter's dead time, device delay time, and voltage drop across the power device are the main factors contributing to inverter nonlinearity. Figure 2(a) shows a schematic diagram of phase a in a three-phase inverter, including two insulated gate bipolar transistors (IGBTs) and two anti-parallel freewheeling diodes. For a pulse width modulation (PWM) voltage source inverter, complementary PWM signals are provided to the upper and lower bridge arms to achieve voltage output. However, to prevent a short circuit from occurring when the upper and lower bridge arms in the same phase are simultaneously turned on, a dead time is typically inserted at the rising edge of the drive signal. A schematic diagram of the dead time effect is shown in Figure 2(b).

[0152] Figure 2(a) shows the model of the bridge arm of phase a, where U dc Indicates the DC bus voltage, U CE Indicates the IGBT conduction voltage drop, U F is the voltage drop of the freewheeling diode. Figure 2(b) shows the ideal and actual a-phase upper and lower bridge arm drive signals and a-phase voltage, where T PWMis the carrier period, t d is the dead time, t on With t off Respectively represent the IGBT turn-on and turn-off delay time, is the action time of the a-phase switch tube after pulse width modulation calculation.

[0153] According to Figure 2(b), the average voltage from phase a to reference ground N per PWM cycle can be expressed as:

[0154]

[0155] Where sgn(·) represents the sign function, i a represents the a-phase current, T a Indicates the actual action time of the a-phase switch tube, which is different from the action time of the a-phase switch tube calculated by pulse width modulation The relationship is:

[0156]

[0157] Typically, the device turn-on and turn-off delays are much shorter than the motor control dead time. Therefore, to simplify the analysis, the device turn-on and turn-off delays are ignored. To further calculate the average phase voltage, including nonlinearity, it is necessary to understand the relationship between the line voltage and the phase voltage. This relationship is described as follows:

[0158] U aN =U aN′ +U NN′ (3)

[0159] Where U NN′ Represents the voltage between the neutral point N' and the reference ground N. At the same time, the following conditions are met in the permanent magnet synchronous motor with three-phase winding Y connection:

[0160] U aN′ +U bN′ +U cN′ =0 (4)

[0161] Where U bN′ and U cN′ The phase voltages of phases b and c can be defined according to equation (1). Therefore, the phase voltages including the inverter nonlinearity can be obtained from equations (1), (2) and (3) as follows:

[0162]

[0163] Where, T b and T c Respectively represent the actual action time of the b-phase and c-phase switching tubes, i b and i cRepresent the b-phase and c-phase currents respectively. Without considering the nonlinear effect of the inverter, the a-phase voltage can be expressed as:

[0164]

[0165] Where, T b and T c They represent the switching time of phase B and phase C respectively after pulse width modulation calculation. Therefore, the error voltage of phase A caused by inverter nonlinearity in one PWM cycle can be expressed as:

[0166]

[0167] When the motor is running in steady state, the motor phase current is sinusoidal and the error voltage is as follows: Figure 3 As shown:

[0168] Therefore, the error voltage can be regarded as Frequency in-phase current (ω e ), the error voltage of the six-step wave is expanded by Fourier, and we have:

[0169]

[0170] Furthermore, by setting ΔU aN′ , ΔU bN′ , ΔU cN′ Transformed into the synchronous rotating coordinate system, we can get ΔU d , ΔU q It is the sum of the DC component, the 6th harmonic component, and its integer multiples. These voltage distortions can cause inconsistencies between the inverter applied voltage and the current loop output voltage, as well as current distortion.

[0171] Therefore, considering the effects of inverter nonlinearity and parameter mismatch, the state equation of the surface-mount PMSM can be modeled as:

[0172]

[0173] Where i d 、i q They represent the dq axis current of the permanent magnet synchronous motor respectively; R, L and ψ f They represent the stator resistance, inductance and permanent magnet flux of the permanent magnet synchronous motor respectively; d ddc and d qdc They represent the non-periodic interference of d and q axes caused by the voltage error between the reference voltage and the actual voltage and the parameter mismatch; d dac and d qac They represent the harmonic interference caused by the inverter.

[0174] Step 2: Design a cascade sliding mode resonant controller;

[0175] Traditional proportional-integral resonant controllers such as Figure 4 The proposed cascade sliding mode resonant controller is shown in Figure 5 shown.

[0176] exist Figure 5 In the example, the resonant controller is connected in series with the output of the super-helical controller to suppress the 6th and 12th harmonics on the dq axis, i.e., the 5th, 7th, 11th, and 13th harmonic components in the phase current. The transfer function of the resonant controller is as follows:

[0177]

[0178] Where K r Represents the gain coefficient of the resonant controller; ω c is the cutoff frequency of the resonant controller; 6nω e (n=1, 2, ..., ∞) is the resonant frequency.

[0179] Multiply the state equation in Eq. (9) by [1+G ∑ (s)] -1 , which is equivalent to embedding the resonant internal model into (9).

[0180]

[0181] Where u′ d =[1+G ∑ (s)] -1 u d , u′ q =[1+G ∑ (s)] -1 u q . [1+G ∑ (s)] -1 Bird Figure 6 As shown, where K r =50,ω c =50rad / s,ω e =10πrad / s. It can be seen that [1+G ∑ (s)] -1 The attenuation effect on the resonant frequency signal is very strong, while the effect on signals of other frequencies is relatively small. Based on this characteristic, Equation (11) can be simplified to:

[0182]

[0183] The non-periodic interference caused by parameter mismatch and voltage error between reference voltage and actual voltage will be suppressed by the super-helical controller. To achieve this control goal, the d-axis and q-axis current tracking errors are defined as follows:

[0184]

[0185] in They are the dq axis reference currents respectively, and the current tracking error e is d and e q As the state variable, the dq axis voltage u d and u q As the control input, the state space equation of the dq axis current can be expressed as follows:

[0186]

[0187] Where, E d and E q represents a known disturbance, D d and D q Denotes the unknown disturbance D d =-d ddc / L,D q =-d qdc / L. Define the sliding surface s d =e d , s q =e q , then the super-helical sliding mode control law designed based on the high-order sliding mode theory is as follows:

[0188]

[0189] Where, α>0, β>0, sig y (x)=|x| y sgn(x), y is a real number, and D d and D q The estimated value of will be given in step 3.

[0190] Step 3: Design a fixed-time adaptive estimation law to estimate the unknown disturbance;

[0191] To further improve the anti-interference capability of the current loop, an adaptive law based on fixed-time convergence theory is proposed to observe and compensate for unknown disturbances such as parameter mismatch. The adaptive law is as follows:

[0192]

[0193] Where, e dd and e dq are the estimated errors of the unknown disturbances in the dq axis, m, n, p and q are all positive odd numbers and satisfy m>n, p<q. Formula (16) is used to estimate the unknown disturbance, and the estimated error convergence time satisfies:

[0194]

[0195] The above-mentioned fixed convergence time calculation method is explained using the d-axis as an example.

[0196] Substituting the sliding mode control law (15) into the derivative of the sliding mode surface, we get:

[0197]

[0198] Therefore, the first term of formula (16) is satisfied, and the non-periodic interference caused by parameter mismatch and voltage error between reference voltage and actual voltage can be regarded as slow time-varying disturbance, that is, Therefore, the second term of formula (16) can be further expressed as:

[0199]

[0200] make but Formula (19) can be rewritten as:

[0201]

[0202] Where, Solving formula (20), the upper bound of the convergence time can be estimated as:

[0203]

[0204] The stability of the superhelical controller with a fixed-time adaptive law is demonstrated below based on Lyapunov stability theory:

[0205] Construct a quadratic Lyapunov function of the following form:

[0206]

[0207] Take a positive definite matrix Then V is continuous positive definite, and dividing s d = 0 and is differentiable everywhere.

[0208] Since the time derivative of η

[0209] in, Assume that at any time This condition is met in permanent magnet synchronous motor systems.

[0210] Then, by solving the derivative of the quadratic Lyapunov function (22), we can obtain:

[0211]

[0212] In the formula, C=1 0.

[0213] make When the values ​​of α and β satisfy:

[0214] α>2,

[0215] Q is positive definite symmetric, so The above formula shows that the system current tracking error formula (13) can converge to zero under the control law formula (15).

[0216] In order to better illustrate the purpose and advantages of the present invention, the present invention is further described below with reference to the accompanying drawings.

[0217] Figure 7 This is the structural block diagram of the permanent magnet synchronous motor speed servo system based on the cascade sliding mode resonant controller.

[0218] The system consists of a permanent magnet synchronous motor, a three-phase inverter, space voltage vector pulse width modulation (SVPWM), a position sensor, a PI controller for the velocity loop, a cascaded sliding mode resonant controller (current controller), and a coordinate transformation module. The velocity loop uses a PI controller to generate the q-axis current setpoint, while the current loop uses a cascaded sliding mode resonant controller to generate the control voltage. The SVPWM control strategy is used to switch the power components of the three-phase inverter, ultimately driving the permanent magnet synchronous motor.

[0219] First, in order to evaluate the impact of inverter nonlinearity on the permanent magnet synchronous motor system, the current loop and speed loop are both traditional proportional integral controllers, and the IGBT conduction voltage drop U CE is 1.9V and the freewheeling diode voltage drop U F Under the condition of 2.5V, Figure 8 The total harmonic distortion (THD) of the phase current under different motor speeds and different inverter dead time is given. Figure 9 shows the total harmonic distortion (THD) of the phase current under different motor speeds and different inverter dead time. CE =1.9V, U F =2.5V, t d=5μs) without applying inverter nonlinearity, a Fourier analysis of the motor phase current, and a comparison of the output torque waveforms. Specifically, Figure 9(a) shows the motor phase current, a Fourier analysis of the phase current, and a waveform of the output torque without applying inverter nonlinearity under the simulation of the present invention at a motor speed of 100r / min; Figure 9(b) shows the motor phase current, a Fourier analysis of the phase current, and a waveform of the output torque under the simulation of the present invention at a motor speed of 100r / min with inverter nonlinearity applied. The results show that inverter nonlinearity seriously affects the smoothness of the permanent magnet synchronous motor phase current and output torque, and the longer the inverter dead time and the lower the motor operating speed, the more obvious the impact of inverter nonlinearity. This also demonstrates the accuracy of the model established in step 1.

[0220] To evaluate the proposed algorithm, a comparative simulation experiment was conducted. PI and PIR controllers were used for comparison with the proposed control algorithm. To ensure fairness, the speed loop used a PI controller with identical parameters.

[0221] Figure 10 、 11 12 are the dq axis current responses, three-phase current responses and Fourier analysis diagrams of the three-phase currents of PI, PIR and the algorithm of the present invention to the step signal respectively; Figure 13 From left to right, the results of PI, PIR and the algorithm of the present invention on the sinusoidal signal are shown in the figure. The q-axis current response diagram. Figure 10-12 It can be seen that the PI, PIR, and the algorithm of the present invention took 0.0295, 0.0255, and 0.0068 seconds to track the reference current, respectively. At the same time, the algorithm of the present invention has the smallest fluctuation range of 0.0134A in steady state, which is smaller than 0.023A of PI and 0.0176A of PIR. The total harmonic distortion rate of the phase current is the smallest, and the amplitude of the harmonics of the specific order caused by the nonlinearity of the inverter is greatly attenuated. And from Figure 13 It can be clearly seen that the proposed algorithm has the best ability among the three algorithms when tracking the sinusoidal reference.

[0222] Figure 14 The result diagram of the proposed fixed-time adaptive law estimation is shown in the figure. It can be seen from the figure that the adaptive law can quickly and accurately predict the unknown disturbance D q Make an estimate.

[0223] To further illustrate the robustness of the proposed technique to parameter mismatch, Figure 15 The q-axis current response of the proposed algorithm is shown for a motor with a speed of 100 rpm and a PIR current loop under varying motor parameters. The figure shows that the proposed method achieves shorter current amplitude changes and shorter recovery times than the traditional proportional-integral-resonance method when faced with varying motor parameters.

[0224] The above experimental results show that the permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance of the present invention can not only effectively reduce the influence of the nonlinearity of the inverter of the permanent magnet synchronous motor drive system, but also has good dynamic response capability and robustness to parameter changes.

[0225] Example 3

[0226] A storage medium stores a program file capable of implementing any one of the above-mentioned permanent magnet synchronous motor current loop control methods based on cascade sliding mode resonance.

[0227] Example 4

[0228] A processor is used to run a program, wherein when the program is run, any one of the above-mentioned permanent magnet synchronous motor current loop control methods based on cascade sliding mode resonance is executed.

[0229] The serial numbers of the above embodiments of the present invention are for description only and do not represent the advantages or disadvantages of the embodiments.

[0230] In the above embodiments of the present invention, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0231] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the system embodiments described above are only exemplary. For example, the division of units can be a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.

[0232] Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple units. Some or all of the units may be selected to achieve the purpose of the present embodiment according to actual needs.

[0233] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0234] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server or network device, etc.) to execute all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk, etc. Various media that can store program codes.

[0235] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance, characterized in that: The following steps are involved: S101: constructing a mathematical model of a permanent magnet synchronous motor, wherein the mathematical model of the permanent magnet synchronous motor takes into account the nonlinear effect of the inverter during construction; Among them, considering the influence of inverter nonlinearity and parameter mismatch, the state equation of PMSM is modeled as: In the formula, i d 、i q They represent the d and q axis currents of the permanent magnet synchronous motor respectively; u d is the d-axis voltage, u q is the q-axis voltage; R, L and ψf They represent the stator resistance, inductance and permanent magnet flux linkage of the permanent magnet synchronous motor respectively; d ddc and d qdc They represent the non-periodic interference of d and q axes caused by the voltage error between the reference voltage and the actual voltage and the parameter mismatch; d dac and d qac They represent the harmonic interference caused by the inverter respectively; ω e represents the resonant frequency; S102: constructing a cascade sliding mode resonance controller, wherein the cascade sliding mode resonance controller designs a super spiral sliding mode control law based on a high-order sliding mode theory during construction; The super-helical sliding mode control law based on the high-order sliding mode theory is designed as follows: In the formula, α>0, β>0, sig y (x)=|x| y sgn(x), y is a real number; E d and E q Denotes a known disturbance; D d and D q represents the unknown disturbance, D d =-d ddc / L,D q =-d qdc / L; define sliding surface s d =e d ,s q =e q ; and D d and D q The estimated value of u d is the d-axis voltage, u q is the q-axis voltage; e d is the d-axis current tracking error, e q is the q-axis current tracking error; S103: designing a fixed-time adaptive estimation law in the cascade sliding mode resonant controller to estimate unknown disturbances; In order to observe and compensate for the unknown disturbance of parameter mismatch, an adaptive law based on fixed-time convergence theory is proposed. The adaptive law is as follows: In the formula, e dd and e dq are the estimated errors of unknown disturbances in dq axis, m, n, p and q are all positive odd numbers and satisfy m>n, p<q; Formula (16) is used to estimate the unknown disturbance, and the estimated error convergence time satisfies:

2. The permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance according to claim 1 is characterized in that: The factors affecting the inverter nonlinearity include: the inverter dead time, device delay time and the voltage drop of the power device tube.

3. The permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance according to claim 2 is characterized in that: The device turn-on delay and turn-off delay are much smaller than the dead time of motor control; when the motor is running in steady state, the motor phase current is sinusoidal.

4. The permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance according to claim 3 is characterized in that: The non-periodic disturbance caused by parameter mismatch and voltage error between reference voltage and actual voltage will be suppressed by the super-helical controller.

5. The permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance according to claim 4 is characterized in that: The non-periodic interference caused by parameter mismatch and voltage error between reference voltage and actual voltage is a slow time-varying disturbance.

6. The permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance according to claim 1, characterized in that: The method further comprises the steps of: S104: Based on Lyapunov stability theory, the stability of the superhelical controller with fixed-time adaptive law is proved.

7. A permanent magnet synchronous motor current loop control device based on cascade sliding mode resonance, characterized in that: A permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance as described in any one of claims 1 to 6 is adopted; the control device comprises: A model building unit, used for building a mathematical model of a permanent magnet synchronous motor, wherein the mathematical model of the permanent magnet synchronous motor takes into account the nonlinear effect of the inverter during construction; A controller construction unit, used for constructing a cascade sliding mode resonance controller, wherein the cascade sliding mode resonance controller designs a super-helical sliding mode control law based on a high-order sliding mode theory during construction; The estimation unit is used to design a fixed-time adaptive estimation law in the cascade sliding mode resonant controller to estimate unknown disturbances.

8. The permanent magnet synchronous motor current loop control device based on cascade sliding mode resonance according to claim 7, characterized in that: The device also includes: Proof unit for proving the stability of the superhelical controller with fixed-time adaptive law based on Lyapunov stability theory.

9. A storage medium, characterized in that: The storage medium stores a program file capable of implementing the permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance as described in any one of claims 1 to 6.

10. A processor, characterized in that: The processor is used to run a program, wherein the program, when running, executes the permanent magnet synchronous motor current loop control method based on cascade sliding mode resonance as described in any one of claims 1 to 6.

Images