Permanent magnet synchronous motor current loop control method based on predictive nonlinear active disturbance rejection

Abstract

The application belongs to the technical field of motor drive control, and discloses a permanent magnet synchronous motor current loop control method based on a predictive nonlinear active disturbance rejection, which comprises the following steps: step 1, establishing a permanent magnet synchronous motor control system model considering time delay; step 2, establishing a current loop extended state observer with time delay compensation; and step 3, designing a nonlinear current feedback control law based on finite time convergence. The application establishes a discrete domain extended model for the current loop of the permanent magnet synchronous motor, and proposes a high-performance nonlinear active disturbance rejection current control method for the permanent magnet synchronous motor. The high-frequency response current controller designed by the application is composed of a predictive extended state observer and a nonlinear current feedback control law, and can solve the problem that the frequency response of the permanent magnet synchronous motor drive is limited due to the digital delay in the motor digital control system and the low-pass filter delay in the current feedback channel, and improve the anti-disturbance performance when the motor parameters change.

Description

Technical Field

[0001] This invention belongs to the field of motor drive control technology, and particularly relates to a current loop control method for permanent magnet synchronous motors based on predictive nonlinear active disturbance rejection. Background Technology

[0002] Permanent magnet synchronous motors are widely used in aerospace servo systems, electric vehicles, robots, and other fields. Their control performance largely determines the efficiency of robots on assembly lines, the technical specifications of aerospace servo motors, and the machining accuracy of CNC machine tools. Whether it is to achieve high-performance position control or speed control of permanent magnet synchronous motors, it is based on high-frequency response current loop control. However, high-frequency response current control is affected by the following factors: (1) In aerospace, electric vehicle and other application scenarios, the motor drive working environment has relatively harsh conditions such as high and low temperatures, strong vibration, and salt spray, which causes changes in parameters such as motor resistance, inductance and permanent magnet flux linkage, thereby causing a decrease in the performance of the controller based on the accurate motor model and parameter design; (2) Permanent magnet synchronous motor control algorithms are usually implemented using digital microprocessors, and there is a time delay in the execution and output update of the algorithm in the discrete domain; (3) After current sampling, a low-pass filter is usually set to filter out high-frequency noise, but the low-pass filter causes the current feedback channel to lag, and the current signal sent to the controller has a time delay due to measurement compared with the actual motor current. Therefore, parameter perturbation and time delay in permanent magnet synchronous motor drive systems are key factors that limit the improvement of current loop bandwidth. Summary of the Invention

[0003] The purpose of this invention is to provide a current loop control method for permanent magnet synchronous motors based on predictive nonlinear active disturbance rejection, so as to solve the above-mentioned technical problems.

[0004] To solve the above-mentioned technical problems, the specific technical solution of the permanent magnet synchronous motor current loop control method based on predictive nonlinear active disturbance rejection of the present invention is as follows:

[0005] A current loop control method for permanent magnet synchronous motors based on predictive nonlinear active disturbance rejection includes the following steps:

[0006] Step 1: Establish a permanent magnet synchronous motor control system model that takes time delay into account;

[0007] Step 2: Establish a time-delay compensated current loop expansion state observer; the current loop expansion state observer uses the d-axis voltage u d q-axis voltage u q d-axis current i d q-axis current i q Electric angular velocity ω e As input, the outputs are the delayed-compensated current estimate and disturbance estimate;

[0008] Step 3: Design a nonlinear current feedback control law based on finite-time convergence. The input variables of the nonlinear current feedback control law are the two output variables of the predictive extended state observer and the current command value. The output of the control law is the d-axis voltage u. d and q-axis voltage u q .

[0009] Furthermore, the permanent magnet synchronous motor in step 1 includes a surface-mounted permanent magnet synchronous motor, an internal permanent magnet synchronous motor, a trapezoidal wave permanent magnet synchronous motor, or an external rotor permanent magnet synchronous motor.

[0010] Furthermore, the permanent magnet synchronous motor control system model considering time delay in step 1 includes digital control one-step update delay and current measurement filtering delay.

[0011] Furthermore, step 1 includes the following specific steps:

[0012] The mathematical model of the permanent magnet synchronous motor in the dq rotating coordinate system is shown in equation (1):

[0013]

[0014] Where u d and u q It is the voltage in the dq coordinate system, R is the motor resistance, and i d and i q These are the d-axis and q-axis currents, L d and L q These are the d-axis and q-axis inductances, ω e It is the electric angular velocity, ψ r It is a permanent magnet flux linkage, d d (t) and d q (t) represents the total disturbance along the d-axis and q-axis, respectively;

[0015] Using the Euler method to discretize formula (1), and considering the one-step delay in the execution process of the digital controller, the discrete domain mathematical model of the permanent magnet synchronous motor with a one-step update time delay is established as follows:

[0016]

[0017] Where i d (k+1) and i q (k+1) represents the d-axis current and q-axis current at time k+1, i 1d (k+1) and i 1q (k+1) represents the d-axis current and q-axis current after a one-beat delay;

[0018] The measured current passes through a low-pass filter.

[0019]

[0020] Where T i i is the time constant of a first-order low-pass filter. df (k+1) and i qf (k+1) represents the d-axis current and q-axis current after passing through the low-pass filter at time k+1.

[0021] Furthermore, step 2 includes the following specific steps:

[0022] First, a current estimator is established based on known model information and measured current, as shown below:

[0023]

[0024] Where T s For discretized periods;

[0025] Considering the inherent one-step digital control time delay in the current loop control system, and combining the current value estimated by the state observer expressed by formula (4), the discrete domain estimate after the one-step delay is obtained.

[0026]

[0027] in and Predict the current after a one-beat delay;

[0028] Considering the influence of low-pass filters on the d-axis and q-axis current feedback channels, the above estimates are then passed through a low-pass filter again to obtain the low-pass filtered current estimates. and

[0029]

[0030] Where T i To measure the time constant of a current low-pass filter;

[0031] Subtracting the current estimate considering the control system time delay and low-pass filter delay from the current estimate estimated by the known model (4), formula (6) yields the current hysteresis error information:

[0032]

[0033] Measuring current i d (k) and i q (k) The expression after the low-pass filter is:

[0034]

[0035] Where i df (k) and iqf (k) represents the d-axis and q-axis current values ​​after low-pass filtering at time k, i df (k-1) and i qf (k-1) represents the d-axis and q-axis current values ​​after low-pass filtering at time k-1;

[0036] The final predicted current after digital control one-step delay and current measurement low-pass filter delay compensation is:

[0037]

[0038] In the formula, and This is the predicted current value after time delay compensation;

[0039] Current prediction value after delay compensation and The extended state observer is designed as follows:

[0040]

[0041] In the formula, l1 and l2 are the gains of the extended state observer.

[0042] Furthermore, the low-pass filter in step 2 includes a first-order low-pass filter, a second-order low-pass filter, a higher-order finite impulse response low-pass filter, and a higher-order infinite impulse response low-pass filter.

[0043] Furthermore, step 3 includes the following specific steps:

[0044] A nonlinear switching function falN is proposed, as shown in equation (11).

[0045]

[0046] In the formula, e is the input to the function falN; sign(·) is the sign function; α N1 α N2 δ N1 δ N2 It is an adjustable parameter.

[0047] And satisfy α N1 >1, 0<α N2 <1,δ N1 ≥1, δ N2 ≤1;

[0048] The current nonlinear feedback control law with finite-time convergence based on the falN function is designed as follows:

[0049]

[0050] Among them, k1, k2, α1, α2, δ1, and δ2 are adjustable parameters, and satisfy α1>1, 0<α2<1, δ1≥1, and δ2≤1.

[0051] The current loop control method for permanent magnet synchronous motors based on predictive nonlinear active disturbance rejection of the present invention has the following advantages: The present invention proposes a current control method for permanent magnet synchronous motors based on predictive nonlinear active disturbance rejection. The main approach is to establish a discrete-domain delay mathematical model for the permanent magnet synchronous motor, and to specifically design a time delay compensation strategy to address the inherent one-step delay of digital control and the low-pass filter delay of the current measurement channel. An extended state observer with integrated prediction mechanism is proposed to realize high-frequency response current control of the permanent magnet synchronous motor and improve the anti-motor parameter perturbation capability of the control system.

[0052] Compared with existing technologies, the advantages of this method are:

[0053] (1) In-depth analysis of the limiting factors for improving the current ring frequency response of permanent magnet synchronous motor, and establishment of a discrete domain motor model considering the delay of one-step digital control and the delay of current feedback low-pass filtering.

[0054] (2) To address the problem of limited frequency response of the current loop, the time delay effect is extracted based on known model information, and the prediction mechanism is integrated for compensation to reduce the impact of time delay on the frequency response of closed-loop control.

[0055] (3) To address the issue of reduced current control performance due to unmodeled dynamics and parameter perturbations in permanent magnet synchronous motors, an extended state observer and a nonlinear finite-time convergent feedback control law were designed to compensate for the total disturbance in the motor drive current loop in real time, thereby improving the anti-disturbance performance of the motor current loop. Attached Figure Description

[0056] Figure 1 This is a control block diagram for a high-frequency response permanent magnet synchronous motor.

[0057] Figure 2 The simulation results of the step response of the active disturbance rejection control current without time delay compensation are shown in the figure.

[0058] Figure 3 The figure shows the simulation results of the predictive active disturbance rejection control current step response with time delay compensation.

[0059] Figure 4 The figure shows the simulation results of predicted active disturbance rejection control when the resistance R is twice the nominal value.

[0060] Figure 5 Simulation waveform of a motor subjected to a sudden load;

[0061] Figure 6 This is a detailed waveform diagram of the q-axis current during a sudden load application to the motor. Detailed Implementation

[0062] To better understand the purpose, structure, and function of this invention, the following detailed description of a current loop control method for permanent magnet synchronous motors based on predictive nonlinear active disturbance rejection, in conjunction with the accompanying drawings, is provided.

[0063] like Figure 1 As shown, the current loop control method for permanent magnet synchronous motors based on predictive nonlinear active disturbance rejection of the present invention includes the following steps:

[0064] Step 1: Establish a permanent magnet synchronous motor control system model that takes into account time delay.

[0065] Permanent magnet synchronous motors include surface-mounted permanent magnet synchronous motors, built-in permanent magnet synchronous motors, trapezoidal wave permanent magnet synchronous motors, or external rotor permanent magnet synchronous motors. The mathematical model of a permanent magnet synchronous motor in a rotating coordinate system is shown in equation (1):

[0066]

[0067] Where u d and u q It is the voltage in the dq coordinate system, R is the motor resistance, and i d and i q These are the d-axis and q-axis currents, L d and L q These are the d-axis and q-axis inductances, ω e It is the electric angular velocity, ψ r It is a permanent magnet flux linkage, d d (t) and d q (t) represents the total disturbance along the d-axis and q-axis, respectively.

[0068] By discretizing formula (1) using the Euler method and considering the one-step delay in the execution process of the digital controller, the discrete domain mathematical model of the permanent magnet synchronous motor with a one-step update time delay can be established as follows:

[0069]

[0070] Where i d (k+1) and i q (k+1) represents the d-axis current and q-axis current at time k+1, i 1d (k+1) and i 1q (k+1) represents the d-axis current and q-axis current after a one-beat delay.

[0071] The measured current passes through a low-pass filter.

[0072]

[0073] Where T ii is the time constant of a first-order low-pass filter. df (k+1) and i qf (k+1) represents the d-axis current and q-axis current after passing through the low-pass filter at time k+1.

[0074] Step 2: Establish a time-delay compensated current loop expansion state observer.

[0075] First, a current estimator is established based on known model information and measured current, as shown below:

[0076]

[0077] Where T s For discretized periods.

[0078] Considering the inherent one-step digital control time delay in the current loop control system, and combining the current value estimated by the state observer expressed by formula (4), the discrete domain estimate after the one-step delay is obtained.

[0079]

[0080] in and Predict the current after a one-beat delay.

[0081] Further considering the influence of low-pass filters on the d-axis and q-axis current feedback channels, the above estimates are then passed through a low-pass filter to obtain the low-pass filtered current estimates. and

[0082]

[0083] Where T i This is to measure the time constant of a current low-pass filter.

[0084] To compensate for the time delay, it is necessary to extract the current hysteresis information caused by the time delay. The current estimate based on the known model (Equation 4) is subtracted from the current estimate considering the control system time delay and low-pass filter delay (Equation 6) to obtain the current hysteresis error information:

[0085]

[0086] Measuring current i d (k) and i q (k) The expression after the low-pass filter is:

[0087]

[0088] Where i df (k) and i qf(k) represents the d-axis and q-axis current values ​​after low-pass filtering at time k, i df (k-1) and i qf (k-1) represents the d-axis and q-axis current values ​​after low-pass filtering at time k-1. Low-pass filters include first-order low-pass filters, second-order low-pass filters, higher-order finite impulse response low-pass filters, and higher-order infinite impulse response low-pass filters.

[0089] The final predicted current after digital control one-step delay and current measurement low-pass filter delay compensation is:

[0090]

[0091] In the formula, and This is the predicted current value after time delay compensation.

[0092] Current prediction value after delay compensation and The extended state observer is designed as follows:

[0093]

[0094] In the formula, l1 and l2 are the gains of the extended state observer.

[0095] Step 3: Design a nonlinear current feedback control law based on finite-time convergence, the principle of which is as follows:

[0096] To achieve rapid convergence of current control error, a nonlinear switching function falN is proposed, as shown in equation (11). The proposed falN function also possesses the characteristics of a smooth function (α). N1 >1) and non-smooth functions (α) N2 The advantage of <1) is that the absolute value of the error is less than δ. N2 When the function is linear, it avoids oscillations caused by the sign function in steady state.

[0097]

[0098] In the formula, e is the input to the function falN; sign(·) is the sign function; α N1 α N2 δ N1 δ N2 It is an adjustable parameter and satisfies α N1 >1, 0<α N2 <1,δ N1 ≥1, δ N2 ≤1.

[0099] The current nonlinear feedback control law with finite-time convergence based on the falN function is designed as follows:

[0100]

[0101] Among them, k1, k2, α1, α2, δ1, and δ2 are adjustable parameters, and satisfy α1>1, 0<α2<1, δ1≥1, and δ2≤1.

[0102] The advantages of the designed feedback control law are: when the current command changes abruptly, the current error is large, the equivalent gain of the falN function is large, the current error is quickly reduced, and high dynamic current fast tracking is achieved; when the current error is small, the finite-time convergence characteristic of the falN function is used to quickly converge the current error to the allowable attraction domain.

[0103] The specific parameters of the permanent magnet synchronous motor used in this embodiment of the invention are shown in Table 1, and the control system framework is as follows. Figure 1 As shown.

[0104] Table 1 Parameters of Permanent Magnet Synchronous Motor

[0105]

[0106] The specific steps included in the embodiment are as follows:

[0107] Step 1: Based on equation (4), establish a current estimator based on known model information and measured current:

[0108]

[0109] Based on formulas (5) and (6), the predicted current value considering the one-time update delay and low-pass filtering is obtained:

[0110]

[0111] According to formula (8), the current i is measured. d (k) and i q (k) The expression after the low-pass filter is:

[0112]

[0113] According to formula (9), the final predicted current after digital control one-step delay and current measurement low-pass filter delay compensation is:

[0114]

[0115] Step 2: Based on formula (10), establish the extended state observer as follows:

[0116]

[0117] Where, l1=2ω o , For the extended state observer parameters, ω in this embodiment o =4000.

[0118] Step 3: According to formula (12), design the current nonlinear feedback control law based on the falN function with finite-time convergence as follows:

[0119]

[0120] The above current control method was simulated and verified. Figure 1 The current command channel is switched to gear 1, with no speed closed loop, and the current command is directly given. The simulation results of the active disturbance rejection control current step response with a given q-axis current of 10A and no time delay compensation are as follows: Figure 2 As shown, the feedback current i q Overshoot of 2A occurred, and current oscillations were observed during the adjustment process. At 0.02s, the q-axis current setpoint decreased from 10A to 0A, also exhibiting oscillations; at this time, the d-axis fluctuation range was -0.02A to 0.02A. The simulation results of the predictive active disturbance rejection control current step response with time delay compensation are as follows: Figure 3 As shown, at startup, the q-axis current has almost no overshoot, and at 0.02s, the q-axis current setpoint drops to 0A, with no further overshoot. Furthermore, the d-axis current fluctuation is less than when the time delay is not compensated. This is because the time delay in the system is compensated, increasing the phase margin of the closed-loop system and eliminating oscillations. Figure 4 The figure shown is a simulation result of the predicted active disturbance rejection control when the resistance R is twice the nominal value, which shows good resistance to parameter disturbances.

[0121] To further test the method of this invention, the current loop was used as the inner loop of a dual closed-loop speed control system for speed control. The simulation results are as follows: Figure 5 As shown. Given a rotational speed of 100 rad / s, a sudden load of 20 N·m is applied at 0.3 s. Given a torque T... eref Increase, motor feedback torque T e It can track a given torque very well, and the speed only drops by 4 rad / s before quickly recovering to 100 rad / s. The highly dynamic current control performance ensures excellent closed-loop characteristics of motor speed. Figure 6 This displays the detailed waveform of the q-axis current during a sudden load application to the motor, and the current i after low-pass filtering. qf Lagging actual current i q The observed current value proposed in this invention Able to accurately predict actual current i q The time delay was reduced, verifying the effectiveness of the method of the present invention.

[0122] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for current loop control of a permanent magnet synchronous motor based on predictive nonlinear active disturbance rejection, characterized in that, Comprising the following steps: Step 1: establishing a permanent magnet synchronous motor control system model considering time delay; Step 2: Establish a time delay compensated current loop extended state observer; the current loop extended state observer uses d-axis voltage u d , q-axis voltage u q , d-axis current i d , q-axis current i q , electrical angular velocity ω e as input, output time delay compensated current estimation value and disturbance estimation value; First, establish a current estimator based on known model information and measured current, as follows: where R is the motor resistance, L d and L q are the d-axis and q-axis inductances, ω e is the electrical angular velocity, ψ r is the permanent magnet flux linkage, T s is the discretization period; Considering the inherent one-tick digital control time delay existing in the current loop control system, combined with the state observer estimated current value expressed by formula (4), the one-tick delayed discrete domain estimated value is wherein and is the one-beat delayed prediction current; Considering the influence of low-pass filters on the d-axis and q-axis current feedback channels, the above-mentioned estimated values are further subjected to low-pass filters to obtain low-pass filtered current estimated values and where T i is the time constant of the measurement current low pass filter; Subtract the current estimation value considering the control system time delay and low-pass filter delay, formula (6), from the current estimation formula (4) based on known model to obtain the current lag error information as: The measured current i d (k) and i q (k) after low-pass filtering where i df (k) and i qf (k) are the low-pass filtered d-axis and q-axis current values at time k, i df (k-1) and i qf (k-1) are the low-pass filtered d-axis and q-axis current values at time k-1. The final predicted current after compensation of digital control one-tick delay and current measurement low-pass filter delay is In the formula, and is the predicted current value after time delay compensation; Based on the delay-compensated current prediction value and The extended state observer is designed as follows: Where l1 and l2 are extended state observer gains; Step 3: Design a nonlinear current feedback control law based on finite-time convergence, the input variables of which are the two output variables of the predictive extended state observer and the current command value, the output of which is the d-axis voltage u d and the q-axis voltage u q .

2. The method of claim 1, wherein the predictive nonlinear active-disturbance-rejection-based current loop control method for permanent magnet synchronous motor is characterized by, The permanent magnet synchronous motor of step 1 includes a surface-mounted permanent magnet synchronous motor, an interior permanent magnet synchronous motor, a trapezoidal wave permanent magnet synchronous motor, and an external rotor permanent magnet synchronous motor.

3. The method of claim 1, wherein the method is characterized by: The permanent magnet synchronous motor control system model considering time delay of step 1 includes digital control one-tick update delay and current measurement filter delay.

4. The method of claim 1, wherein the method is characterized by: Step 1 includes the following specific steps: The mathematical model of the permanent magnet synchronous motor in the dq rotating coordinate system is shown in formula (1): where u d and u q are the voltages in dq frame, R is the motor resistance, i d and i q are the d and q axis currents, L d and L q are the d and q axis inductances, ω e is the electrical angular speed, ψ r is the permanent magnet flux linkage, d d (t) and d q (t) are the total disturbances for the d and q axis respectively; Discretize formula (1) using the Euler method, and then consider the one-tick delay in the digital controller execution process to establish a permanent magnet synchronous motor discrete domain mathematical model with one-tick update time delay as follows: where i d (k+1) and i q (k+1) are the d-axis current and q-axis current at the k+1 time, i 1d (k+1) and i 1q (k+1) are the d-axis current and q-axis current after one beat delay. The measured current passes through a low-pass filter as where T i is the time constant of the first order low pass filter, i df (k+1) and i qf (k+1) are the d-axis and q-axis currents after passing through the low pass filter at the k+1 time instant.

5. The method of claim 1, wherein the method is characterized by: The low-pass filter of step 2 includes a first-order low-pass filter, a second-order low-pass filter, a high-order finite impulse response low-pass filter, or a high-order infinite impulse response low-pass filter.

6. The method of claim 1, wherein the method is characterized by: Step 3 includes the following specific steps: A nonlinear switching function falN is proposed, as shown in formula (11), where e is the input of the function falN; sign(·) is the sign function; a N1 , a N2 , d N1 , d N2 are adjustable parameters, and satisfies a N1 >1, 0 < a N2 <1, δ N1 ≥1, δ N2 ≤1; Based on the falN function, a current nonlinear feedback control law with finite time convergence is designed as follows: Where k1, k2, α1, α2, δ1, and δ2 are adjustable parameters, and satisfy α1>1, 0<α2<1, δ1≥1, and δ2≤1.

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