A robust, deadbeat-free predictive current control method

Abstract

This invention discloses a highly robust deadbeat-free predictive current control method, applicable to the current control of dual three-phase permanent magnet motor drive systems, belonging to the field of permanent magnet motor control technology. The main steps of this invention are: reconstructing the motor mathematical model using a space vector decoupling matrix and Park transformation, to obtain... dqxy The invention presents the following: motor voltage equations under the shaft; a linear extended state observer is designed; a reference value for the output voltage vector is obtained by combining deadbeat predictive current control; the time delay in the digital control system is calculated and the angle delay is compensated; a closed-loop Smith predictor is designed to compensate for the time delay, thus achieving highly robust deadbeat predictive current control for the dual three-phase permanent magnet motor. The current loop design in this invention is independent of motor parameters and exhibits strong robustness to parameter variations. By introducing a closed-loop Smith predictor, this invention can effectively compensate for large system delays and achieve high-precision current tracking at low switching frequencies.

Description

Technical Field

[0001] This invention belongs to the field of high-performance permanent magnet synchronous motor control technology, specifically relating to a highly robust deadbeat predictive current control method. Background Technology

[0002] Dual three-phase permanent magnet synchronous motors have received widespread attention in recent years due to their excellent speed regulation performance, outstanding torque output, and enhanced fault-tolerant control capabilities. Furthermore, multiphase drive systems offer advantages such as high control flexibility, low current stress, and small DC bus current ripple, making dual three-phase permanent magnet synchronous motors particularly suitable for applications with high reliability requirements, such as aerospace propulsion and electric transportation.

[0003] In high-power applications, dual three-phase permanent magnet synchronous motors typically need to operate at low switching frequencies to minimize switching losses and meet thermal constraints. However, low switching frequencies increase modulation and control delays, thus jeopardizing system stability.

[0004] In actual operation, factors such as changes in motor parameters, nonlinearity of the inverter, and fluctuations in back EMF will introduce disturbances into the control system, thereby causing steady-state fluctuations in the controller and leading to a decline in dynamic performance.

[0005] When multiphase permanent magnet synchronous motors operate at low switching frequencies, reasonable compensation for delay, enhancement of anti-interference capability, and improvement of system stability are urgent problems to be solved. Summary of the Invention

[0006] To address this, the present invention provides a highly robust deadbeat predictive current control method. This method improves system robustness by extending the state observer to resolve motor parameter mismatch issues, and enhances system stability by introducing a closed-loop Smith predictor based on an error correction compensator to compensate for delays and resolve the large delay problem at low switching frequencies.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] This invention provides a highly robust deadbeat-free predictive current control method, which specifically includes the following steps:

[0009] 1) The mathematical model of the dual three-phase permanent magnet motor is reconstructed by using the space vector decoupling matrix and Park transformation, and the motor voltage equation in the dqxy rotating coordinate system is obtained;

[0010] 2) Establish a first-order hyperlocal model for the dq-axis current and design a linear extended state observer to estimate the dq-axis current value and equivalent disturbance value in real time;

[0011] 3) Based on the disturbance value estimated by the linear expansion state observer in step 2, and combined with the dq-axis current reference vector of the next sampling period, solve for the dq-axis voltage vector reference value of the current control period;

[0012] 4) Calculate the delay in the digital control system and compensate for the angle delay;

[0013] 5) Design a closed-loop Smith predictor based on an error correction compensator to predict the dq axis current of a dual three-phase permanent magnet motor, thereby achieving highly robust deadbeat predictive current control of the dual three-phase permanent magnet motor.

[0014] The beneficial effects of this invention are:

[0015] This invention discloses a highly robust deadbeat predictive current control method and system. By designing an extended state observer to estimate system disturbances and applying it to the deadbeat predictive current control system, the use of motor parameters is avoided, eliminating dependence on motor models and improving the system's disturbance rejection and robustness. A closed-loop Smith predictor based on an error correction compensator is introduced into the current regulator to compensate for delays, ensuring the operational stability of the multiphase permanent magnet motor at low switching frequencies. Attached Figure Description

[0016] Figure 1 This is a flowchart of the highly robust deadbeat predictive current control method of the present invention.

[0017] Figure 2 This is the topology diagram of the drive circuit for a dual three-phase permanent magnet synchronous motor.

[0018] Figure 3 Steady-state experimental results of the traditional deadbeat predictive current control method under the condition that all motor parameters are matched.

[0019] Figure 4 The steady-state experimental results of the method of the present invention are given that all motor parameters are matched.

[0020] Figure 5 Motor parameters mismatch (10R) s , 10ψ f 3L s The steady-state experimental results of the traditional deadbeat predictive current control method under the condition of ).

[0021] Figure 6 Motor parameters mismatch (10R) s , 10ψ f 3L s The steady-state experimental results of the method of the present invention under the condition of (). Detailed Implementation

[0022] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0023] like Figure 1 As shown, a highly robust deadbeat predictive current control method is described, and the implementation process of the method is as follows:

[0024] Step 1: Reconstruct the mathematical model of the dual three-phase permanent magnet motor using the space vector decoupling matrix and Park transformation to obtain the motor voltage equation in the dqxy rotating coordinate system.

[0025] Specifically, in this invention, the q-axis current reference value is obtained from the PI controller of the outer speed loop, the d-axis current reference value is 0, and the x-axis and y-axis current reference values ​​are both 0. Both the x-axis and y-axis currents are controlled by PI controllers. However, this is only for implementing this invention and is not limited to this method.

[0026] Then, the mathematical model of the motor is reconstructed using the space vector decoupling matrix and Park transformation as follows:

[0027] By using space vector decoupling transformation, the motor variables are mapped to three orthogonal subspaces, namely the fundamental wave. Subspace, harmonic xy subspace and zero order Subspace. The expression for the space vector decoupling transformation matrix is:

[0028]

[0029] Because the two neutral points of a dual three-phase permanent magnet synchronous motor are isolated, therefore in There is no zero-sequence current component in the subspace. The Park transformation from a stationary reference frame to a synchronously rotating reference frame dq is expressed as:

[0030]

[0031] in Let be the rotor's electrical angular position. The voltage equation for the dual three-phase permanent magnet synchronous motor in the dqxy rotating coordinate system is:

[0032]

[0033] in, For stator resistance, It is a permanent magnet flux linkage. Let be the electric angular velocity, and u, i, and L represent the stator voltage, stator current, and stator inductance, respectively. The subscripts d / q and x / y denote the components in the dq and xy subspaces, respectively. and It includes the higher harmonic back electromotive force components in the xy subspace and the harmonic interference voltage components caused by the inverter nonlinearity.

[0034] Step 2: Establish a first-order hyperlocal model for the dq-axis current and design a linear extended state observer to estimate the dq-axis current value and equivalent disturbance value in real time.

[0035] This invention will use the dq axis current and dq axis equivalent perturbation Together, they are used as state variables of the dual three-phase permanent magnet synchronous motor system. A preset gain coefficient is introduced to describe the first-order hyperlocal relationship between the dq axis current of the dual three-phase permanent magnet synchronous motor and the control input, thereby obtaining a first-order hyperlocal model.

[0036] The first-order hyperlocal model of the dq axis of a dual three-phase permanent magnet synchronous motor is represented by complex vectors:

[0037]

[0038] in, For dq axis perturbation This refers to the gain coefficient of the design.

[0039] Current term and disturbance terms Treating the current as a system state variable and incorporating the current estimation error, a linearly extended state observer is designed. This invention uses the difference between the estimated and actual measured values ​​of the dq-axis current of a dual three-phase permanent magnet synchronous motor as the estimation error, and uses the dq-axis current estimate and the dq-axis disturbance estimate as the observer states. Specifically, the linearly extended state observer is as follows:

[0040]

[0041] in, , for , The estimated value, , This is the error feedback gain of the ESO.

[0042] actual value of disturbance to disturbance estimate s-domain transfer function:

[0043]

[0044] To ensure the system's stability, all roots of the characteristic equation should have negative real parts, such that both roots of the characteristic equation lie in the... Location:

[0045]

[0046] get , for:

[0047]

[0048] in, The bandwidth of the ESO to be designed determines its stability and dynamic performance. To achieve fast response, the bandwidth of the ESO should be increased while ensuring system stability. , The value of affects the distribution of the closed-loop poles of the system, thus affecting the stability of the ESO. Therefore, a reasonable value must be selected. , Ensure system stability and that the controller achieves good control performance.

[0049] In order to design in the z domain The dq-axis current and disturbance state are discretized. The difference between the actual dq-axis current value and the estimated dq-axis current value in the current sampling period is used as the estimation error. This estimation error is applied to the current estimate and disturbance estimate through the first error feedback gain and the second error feedback gain, respectively, to obtain the current estimate and disturbance estimate for the next sampling period, thus forming a discrete-time linear extended state observer. The dq-axis current vector is composed of d-axis current components and q-axis current components, the dq-axis voltage vector is composed of d-axis voltage components and q-axis voltage components, and the disturbance estimation vector is composed of d-axis disturbance estimation components and q-axis disturbance estimation components.

[0050] Specifically, the predicted current and disturbance are discretized as follows:

[0051]

[0052] Where k represents the kth sampling period, , , .

[0053] Based on the discrete model, the transfer relationship from the actual value of the dq-axis current to the estimated value of the dq-axis current is derived. Specifically, from the actual current value... To current estimate z-domain transfer function:

[0054]

[0055] Its characteristic equation is:

[0056]

[0057] Solving for the extreme point:

[0058]

[0059] Calculated :

[0060]

[0061] By choosing the appropriate Make the pole Within the unit circle in the z-plane. If Too small ( Approaching level 1), the system's dynamic response speed will slow down, the system's transition process (such as rise time, peak time, and settling time) will become longer, and the system's dynamic performance will deteriorate. If Too large ( When the input signal is close to zero, the system becomes more sensitive to high-frequency noise, which affects its robustness. The system reacts too drastically to changes in the input signal, potentially causing unnecessary vibrations or disturbances. Therefore, this invention is designed... It exhibits good dynamic response while maintaining system stability.

[0062] Step 3: Based on the disturbance value estimated by the linear expansion state observer in Step 2, and combined with the dq-axis current reference vector of the next sampling period, solve for the dq-axis voltage vector reference value of the current control period.

[0063] In a specific embodiment of the present invention, step 3 is as follows:

[0064] The first-order hyperlocal model is discretized using a first-order forward difference method to establish the relationship between the dq-axis voltage vector at the current sampling time, the dq-axis current vector at the current and next sampling times, and the equivalent disturbance. The equivalent disturbance term cannot be obtained directly and is replaced by the disturbance estimate given by the disturbance observer.

[0065] Assuming the system's dq-axis current can reach the pre-defined reference current vector in the next sampling period, the reference value of the dq-axis voltage vector for the current sampling period is obtained according to the discrete relationship: the difference between the reference current vector for the next sampling period and the current actual current vector is normalized according to the sampling period, then the disturbance estimate is subtracted, and multiplied by the reciprocal of a pre-set gain coefficient. The result is output as the reference value of the dq-axis voltage vector. The dq-axis current reference vector for the next sampling period is output by the speed loop and is used to characterize the target current value that the inner current loop needs to track in the next moment.

[0066] Step 3 can be explained using the following formula: The first-order hyperlocal complex vector model of the dq axis of the dual three-phase permanent magnet synchronous motor is discretized using the first-order forward difference as follows:

[0067]

[0068] Among them, due to Since it cannot be obtained directly, it is used The estimated value Instead. Assume the system at time k+1 Reaching the reference value Then the reference value of the output voltage vector is expressed as:

[0069]

[0070] in, This is the output of the speed loop, representing the current reference value that needs to be tracked at the next moment.

[0071] Step 4: Calculate the delay in the digital control system and compensate for the angle delay.

[0072] In a specific embodiment of the present invention, step 4 specifically includes:

[0073] Digital control system There is a one-cycle control delay and a half-cycle modulation delay in the subplane. After equating the delay to the dq coordinate system, the delay element in the dq subplane can be considered as... Including both time delay and angle delay, the digital control delay can be approximately expressed using a first-order Taylor formula:

[0074]

[0075] in, To delay, , The sampling frequency. This is the voltage reference vector.

[0076] Due to the delay process The presence of a fixed angle delay reduces the phase margin of the system. To minimize its impact on current control performance, an angle delay compensation circuit is connected in series in the voltage reference vector generation channel to perform angle delay compensation.

[0077] Expressed as a formula, the angle delay compensation stage Represented as:

[0078]

[0079] First, the delay element is discretized in the dq coordinate system, which is equivalent to a pure delay of one sampling period and a phase lag determined by the electric angular velocity and the sampling period. Correspondingly, the angle delay compensation element is equivalent to a phase lead element corresponding to the electric angular velocity and the sampling period in the discrete domain.

[0080] The delay element in the dq subplane can be discretized as follows:

[0081]

[0082] Accordingly, the angle delay compensation stage can be discretized as follows:

[0083]

[0084] The present invention further calculates the uncompensated dq-axis voltage vector reference value based on the dq-axis current reference vector of the next sampling period, the actual value of the dq-axis current of the current sampling period, and the disturbance estimate; then, the voltage vector reference value is rotated around the electric angular velocity direction by a compensation angle to obtain the final dq-axis voltage vector reference value used for modulation; the compensation angle is equal to the product of the motor electric angular velocity and the equivalent delay time, wherein the equivalent delay time is 1.5 times the sampling period; the dq-axis voltage vector reference value is the voltage reference quantity output by the inner current loop.

[0085] Specifically, an angle delay compensation process is adopted. To compensate for the angle delay in a digital control system, the reference value of the output voltage vector can be rewritten as:

[0086]

[0087] in , It is the reference value for the current loop output voltage vector.

[0088] Step 5: Design a closed-loop Smith predictor based on an error correction compensator to compensate for time delays and predict the dq axis current of the dual three-phase permanent magnet motor, thereby achieving highly robust deadbeat predictive current control of the dual three-phase permanent magnet motor.

[0089] In a specific embodiment of the present invention, step 5 is as follows:

[0090] The Smith predictor is used to compensate for time delays. The basic idea of ​​the Smith predictor is to introduce a compensation element in parallel with the controller. This compensation element first estimates the dynamic response of the system based on the input signal, and then applies compensation in the feedback path, enabling the current regulator to take into account the time delay and take feedforward action, thereby reducing the adverse effects of time delay.

[0091] Traditional delay compensation strategies based on Smith predictors replace sampled values ​​with predicted current values ​​in the feedback channel. In this case, the predicted current can track the reference value without steady-state error. However, if there is a deviation between the predicted current and the actual sampled value, a tracking error will inevitably occur between the actual value and the reference value.

[0092] Since traditional Smith predictors are open-loop structures, they cannot correct current prediction deviations. Therefore, this invention proposes a closed-loop Smith predictor based on an error correction compensator. In the k-th sampling period, the Smith predictor uses the dq-axis voltage command of the current sampling period, the voltage correction amount given by the error compensation circuit, and the current dq-axis current value to calculate the predicted dq-axis current value for the (k+1)-th sampling period based on a discretized motor mathematical model. Then, the predicted currents of two adjacent sampling periods are differentially processed to obtain a current increment signal. This current increment signal is added to the current actual dq-axis current to form a closed-loop predicted current, which is then used as the input to the current controller. The error correction compensator uses the actual dq-axis current of the dual three-phase permanent magnet motor as the reference input and the closed-loop predicted current of the previous sampling period as the feedback input. It calculates the deviation between the two and processes the deviation through the integral controller to generate a voltage correction amount. The voltage correction amount is injected into the voltage input channel of the Smith predictor to correct the current prediction result of the next sampling period, thereby achieving zero steady-state error tracking of the given dq-axis reference current.

[0093] Specifically, the discretized implementation of the closed-loop Smith predictor based on the error correction compensator is as follows:

[0094]

[0095] Obtained from the closed-loop Smith predictor Value and actual current value When added together, the sum is... It is fed into the current controller for regulation.

[0096] The error compensator proposed in this invention uses the actual current value As a reference input, to predict the current value As feedback input, the deviation between these two values ​​is processed by the integral controller to generate a voltage correction value, which is then input into the above equation to correct the predicted current value. This design forms a closed-loop structure, thereby achieving control over the reference current. Zero steady-state error tracking.

[0097] like Figure 2The diagram shows the drive circuit topology of a dual three-phase permanent magnet synchronous motor. The dual three-phase permanent magnet synchronous motor of this invention adopts a dual-Y structure, with a 30° phase difference between the two three-phase windings. Based on the motor's dual three-phase configuration, the inverter consists of two parallel three-phase bridges, each employing a two-level topology. The inverter has a total of six phases, with each bridge arm composed of two IGBT or MOSFET switching devices. Table 1 shows the parameters of the dual three-phase permanent magnet synchronous motor and controller used in the experiment.

[0098] Table 1: Parameters of Dual Three-Phase Permanent Magnet Synchronous Motors and Controllers

[0099]

[0100] The following comparison uses the method of this invention and conventional methods, such as... Figure 3 and Figure 4 As shown, when the controller parameters and motor parameters are matched, the current tracking performance and current ripple performance of the traditional deadbeat predictive current control method are similar to those of the method proposed in this invention. Figure 5 and Figure 6 As shown, when the controller parameters and motor parameters do not match (10R) s , 10ψ f 3L s In situations where traditional deadbeat predictive current control methods fail to track the given value on the q-axis, the current tracking performance of the proposed method is similar to previous methods, exhibiting good current tracking effect and current ripple performance. It can be seen that the proposed method enhances the system's disturbance rejection capability by adding an observer, avoiding steady-state errors caused by parameter mismatch. Furthermore, the proposed method effectively compensates for the large system delay by introducing a closed-loop Smith predictor based on an error correction compensator, achieving high-precision current tracking at low switching frequencies.

[0101] In summary, the method proposed in this invention, by designing an extended state observer, avoids the use of motor parameters, thereby improving the robustness and disturbance rejection of the system; by compensating for the inherent large delay in the digital control system, it ensures the stable and efficient operation of the permanent magnet motor at low switching frequencies; and the current controller algorithm parameter tuning is simple and effective. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention.

Claims

1. A highly robust, deadbeat-free predictive current control method for stator current control of a dual three-phase permanent magnet motor, characterized in that, The method is applicable to low-switching-frequency inverter drive applications, where low switching frequency refers to the inverter's switching frequency being in the range of 1kHz to 3kHz; the method includes the following steps: 1) The mathematical model of the dual three-phase permanent magnet motor is reconstructed by using the space vector decoupling matrix and Park transformation, and the motor voltage equation in the dqxy rotating coordinate system is obtained; 2) Establish a first-order hyperlocal model for the dq-axis current and design a linear extended state observer to estimate the dq-axis current value and equivalent disturbance value in real time; 3) Based on the disturbance value estimated by the linear expansion state observer in step 2, and combined with the dq-axis current reference vector of the next sampling period, solve for the dq-axis voltage vector reference value of the current control period; 4) Calculate the delay in the digital control system and compensate for the angle delay; 5) Design a closed-loop Smith predictor based on an error correction compensator to predict the dq axis current of a dual three-phase permanent magnet motor, thereby achieving highly robust deadbeat predictive current control of the dual three-phase permanent magnet motor. Step 5) includes: In the kth sampling period, the Smith predictor uses the dq-axis voltage command of the current sampling period, the voltage correction given by the error compensation circuit, and the current dq-axis current value to calculate the predicted value of the dq-axis current in the (k+1)th sampling period based on the discretized motor mathematical model; then, the predicted current of two adjacent sampling periods is differentially processed to obtain the current increment signal, and the current increment signal is added to the current actual dq-axis current to form a closed-loop predicted current, and the closed-loop predicted current is used as the input of the current controller; The error correction compensator uses the actual dq-axis current of the dual three-phase permanent magnet motor as the reference input and the closed-loop predicted current of the previous sampling period as the feedback input. It calculates the deviation between the two and processes the deviation through the integral controller to generate a voltage correction amount. The voltage correction amount is injected into the voltage input channel of the Smith predictor to correct the current prediction result of the next sampling period, thereby achieving zero steady-state error tracking of the given dq-axis reference current. The discretized implementation of the closed-loop Smith predictor based on the error correction compensator is as follows: ； Obtained from the closed-loop Smith predictor Value and actual current value When added together, the sum is... The data is fed into a current controller for adjustment, where k represents the k-th sampling period. ω is the electric angular velocity.

2. The highly robust deadbeat predictive current control method according to claim 1, characterized in that, Step 2) establishing a first-order hyperlocal model includes: dq axis current and dq axis equivalent perturbation Together, they are used as state variables of the dual three-phase permanent magnet synchronous motor system. A preset gain coefficient is introduced to describe the first-order hyperlocal relationship between the dq-axis current of the dual three-phase permanent magnet synchronous motor and the control input, thus obtaining a first-order hyperlocal model.

3. The highly robust deadbeat predictive current control method according to claim 2, characterized in that, Step 2) The design of the linearly extended state observer includes: The difference between the estimated value and the actual measured value of the dq axis current of the dual three-phase permanent magnet synchronous motor is used as the estimation error. The estimated dq axis current and the estimated dq axis disturbance are used as the observer state. The observer makes state prediction based on the current estimate and disturbance estimate of the previous sampling period, and adds a feedback term proportional to the estimation error to the prediction result, thereby realizing real-time estimation of the dq axis current state and disturbance state at the same time.

4. The highly robust deadbeat predictive current control method according to claim 3, characterized in that, Step 2) also involves designing the parameters of the linearly extended state observer, including the following steps: dq axis equivalent perturbation Actual value to disturbance estimate The s-domain transfer function is expressed as: ； in, The first error feedback gain of the observer ESO, It is the second error feedback gain of the observer ESO. For the Laplace operator, The bandwidth of the ESO to be designed.

5. The highly robust deadbeat predictive current control method according to claim 4, characterized in that, The ESO bandwidth The design method is as follows: First, the dq-axis current and disturbance state are discretized. The difference between the actual value of the dq-axis current and the estimated value of the dq-axis current in the current sampling period is used as the estimation error. This estimation error is applied to the current estimate and the disturbance estimate through the first error feedback gain and the second error feedback gain, respectively, to obtain the current estimate and the disturbance estimate for the next sampling period, thus forming a discrete-time linear extended state observer. The transitivity from the actual value of the dq-axis current to its estimated value is derived. The denominator of this transitivity corresponds to a second-order characteristic polynomial. By finding the roots of this second-order characteristic polynomial, the two poles are selected as the same real poles. Furthermore, it is required that the pole lies within the unit circle in the z-plane to ensure the stability of the extended state observer; based on the correspondence between the pole location and the observer bandwidth, the following is calculated: This determines the observer bandwidth; by selecting the observer bandwidth, the poles are made more suitable for the observation. Take the position corresponding to 0.

5.

6. The highly robust deadbeat predictive current control method according to claim 1, characterized in that, Step 3) includes: The first-order hyperlocal model is discretized using a first-order forward difference method to establish the relationship between the dq-axis voltage vector at the current sampling time, the dq-axis current vector at the current and next sampling times, and the equivalent disturbance; wherein, the equivalent disturbance is replaced by the disturbance estimate given by the observer. The difference between the reference current vector of the next sampling period and the current actual current vector is normalized according to the sampling period, then the disturbance estimate is subtracted, and multiplied by the reciprocal of the pre-set gain coefficient. The result is used as the reference value of the dq axis voltage vector. The dq axis current reference vector of the next sampling period is output by the speed loop and is used to characterize the target current value that the inner current loop needs to track at the next moment.

7. The highly robust deadbeat predictive current control method according to claim 1, characterized in that, Step 4) includes: The digital control system has a one-cycle control delay and a half-cycle modulation delay in the αβ coordinate system. After converting the delay to the dq coordinate system, it is assumed that the delay element includes both time delay and angle delay. An angle delay compensation element is set to compensate for the angle delay, including: After discretizing the delay element in the dq coordinate system, it is equivalent to a pure delay of one sampling period and a phase lag determined by the electric angular velocity and the sampling period. Correspondingly, the angle delay compensation element is equivalent to a phase lead element corresponding to the electric angular velocity and the sampling period in the discrete domain. The uncompensated dq-axis voltage vector reference value is calculated based on the dq-axis current reference vector of the next sampling period, the actual dq-axis current value of the current sampling period, and the disturbance estimate. Subsequently, this voltage vector reference value is rotated around the direction of the electric angular velocity by a compensation angle to obtain the final dq-axis voltage vector reference value used for modulation. The compensation angle is equal to the product of the motor's electric angular velocity and the equivalent delay time, where the equivalent delay time is 1.5 times the sampling period. The dq-axis voltage vector reference value is the voltage reference value output by the inner current loop.

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