A dead-time compensation method for permanent magnet synchronous motor based on KF-ESO

Abstract

The application provides a KF-ESO-based dead-time compensation method for a permanent magnet synchronous motor, comprising the following steps: step S1, acquiring error voltage generated by dead-time effect of the permanent magnet synchronous motor in real time; step S2, establishing a mathematical model of the permanent magnet synchronous motor, and decoupling the mathematical model to obtain a current value; step S3, weakening noise of the current value through a Kalman filter to obtain a state variable of an extended state observer; step S4, observing the filtered current estimation value and total disturbance through the extended state observer, and compensating the estimated total disturbance value to the control system as a dead-time compensation value; and step S5, obtaining a system control amount through PI adjustment. The application can compensate the dead-time voltage on line, dynamically adjust the size of the dead-time voltage compensation, and enhance the stability of the system.

Description

Technical Field

[0001] This invention relates to the field of motor dead zone compensation technology, and in particular to a method for dead zone compensation of permanent magnet synchronous motors based on KF-ESO. Background Technology

[0002] Permanent magnet synchronous motors are primarily driven by inverter circuits. However, in the same bridge arm circuit, to prevent short circuits caused by simultaneous conduction of the upper and lower bridge arms, dead time needs to be added to the drive signals of both arms. Furthermore, due to the non-ideal characteristics of switching equipment, such as the switching delay of power devices and the on-state voltage drop, voltage distortion exists between the reference voltage and the actual voltage, known as the dead time effect. The dead time effect distorts the current waveform, affecting motor performance, and is more pronounced at low speeds, causing significant torque ripple. Therefore, effective compensation for the dead time effect is necessary.

[0003] Existing dead-zone compensation methods for permanent magnet synchronous motors mainly include traditional dead-zone compensation methods, such as current feedback compensation and dead-zone vector compensation; or compensation through modern control methods, such as fuzzy adaptive control and disturbance observers. Traditional dead-zone compensation methods rely on the determination of current polarity, but due to complex operating conditions, they are prone to miscompensation. Summary of the Invention

[0004] To address the shortcomings of the aforementioned related technologies, this invention proposes a dead-zone compensation method for permanent magnet synchronous motors based on KF-ESO, which can dynamically adjust the magnitude of dead-zone voltage compensation and enhance system stability.

[0005] To address the aforementioned technical problems, this invention provides a method for dead-time compensation of permanent magnet synchronous motors based on KF-ESO, comprising the following steps:

[0006] Step S1: Real-time acquisition of the error voltage generated by the dead zone effect of the permanent magnet synchronous motor;

[0007] Step S2: Establish a mathematical model of the permanent magnet synchronous motor and decouple the mathematical model to obtain the current value;

[0008] Step S3: Reduce noise in the current value using a Kalman filter to obtain the state variables of the extended state observer;

[0009] Step S4: Observe the filtered current estimate and total disturbance through the extended state observer, and use the estimated total disturbance value as the dead zone compensation value to compensate the control system.

[0010] Step S5: Obtain the system control quantity through PI adjustment.

[0011] Preferably, step S1 specifically includes the following sub-steps:

[0012] Using the equivalent dead time T dead The formula is:

[0013] T dead =T d +T on -T off …(1)

[0014] In the above formula, T d For dead time, T on T is the turn-on delay time for power devices. off This refers to the power device turn-off delay time.

[0015] Error voltage U caused by equivalent dead time e The formula is:

[0016]

[0017] In the above formula, U dc U is the DC bus voltage. sw For the on-state voltage drop of power devices, U D T is the forward voltage drop of the diode. s The time of one switching cycle;

[0018] Based on the polarity of the three-phase currents, the average error voltage of the three phases can be obtained as follows:

[0019]

[0020] In the above formula, the direction of power flow from the power device to the motor is defined as the positive direction, denoted as i. k >0, otherwise i k <0;

[0021] The error voltage on the three-phase coordinate system is transformed to the dq coordinate system for calculation:

[0022]

[0023] In the above formula, θ is the rotor angle.

[0024] Preferably, step S2 specifically includes the following sub-steps:

[0025] Based on the establishment of an ideal PMSM mathematical model in the dp coordinate system;

[0026]

[0027] Among them, i d i qU represents the d-axis and q-axis currents. d U q R represents the d-axis and q-axis voltages. S L is the stator resistance. d L q Let ψ be the inductance along the d and q axes. f For permanent magnet flux linkage, w e The electric rotation speed;

[0028] In the ideal PMSM mathematical model, based on the coupling relationship between the d-axis and q-axis currents, feedforward compensation control is applied to the PI control of the current loop to decouple the d-axis and q-axis.

[0029] Obtain the coupling compensation voltage u d 'and u q Its formula is as follows (6):

[0030]

[0031] The current equation after feedforward compensation is in the form of formula (7):

[0032]

[0033] Considering the error voltage ΔU caused by dead time ed and ΔU eq The equation in the form of (8), i d 'and i q 'This is the actual current value after adding the dead-time error voltage:'

[0034]

[0035] Add dead-time compensation voltage U com_d and U com_q Then, ideally, ΔU ed =U com_d ΔU eq =U com_q , will U com_d and U com_q Compensating into formula (8) yields current formula (9):

[0036]

[0037] Preferably, step S3 specifically includes the following sub-steps:

[0038] Establish the system's state equations and debug the system based on these equations.

[0039] A mathematical model of the Kalman filter is established based on the state equation of the system.

[0040] The discrete state-space equation and predicted state variables are obtained based on the mathematical model of the Kalman filter.

[0041] The prediction state error covariance matrix is ​​obtained based on the predicted state variables;

[0042] Kalman gain and state variable updates are performed based on the predicted state error covariance matrix.

[0043] The state error covariance matrix is ​​updated based on the Kalman gain update and the state variable update.

[0044] By continuously iterating, a value that approximates the true value can be obtained.

[0045] The estimated values ​​of the d-axis and q-axis currents of the Kalman filter are used as the state variables of the extended state observer.

[0046] Preferably, step S4 specifically includes the following sub-steps:

[0047] Based on the first-order state equation of the current loop, a first-order linear active disturbance rejection controller is set.

[0048] The disturbances present in the system are estimated based on the extended state observer, wherein the error voltage caused by the dead zone of the system and the unknown disturbances are regarded as the total disturbances;

[0049] Establish an ESO model;

[0050] The ESO model is discretized to obtain the observed values ​​and the perturbation observed values;

[0051] After passing through the state observer, the observed total disturbance is used as the compensation value of the error voltage and then added to the current formula to obtain the compensation value.

[0052] Preferably, step S5 specifically includes the following sub-steps:

[0053] The expression for the PI controller is:

[0054] Calculate the d-axis and q-axis voltages:

[0055] In the above formula, u d1 To calculate the d-axis voltage after dead-time compensation, u q1 To calculate the q-axis voltage after dead-time compensation, k p1 and k p2 The proportional gain for the d-axis and q-axis PI controllers are k and k, respectively. i1 and k i2 These are the integral coefficients of the d-axis and q-axis PI controllers, respectively.

[0056] Compared with related technologies, this invention acquires the error voltage caused by the dead-zone effect of a permanent magnet synchronous motor in real time; establishes a mathematical model of the permanent magnet synchronous motor and decouples the mathematical model to obtain the current value; reduces noise in the current value using a Kalman filter to obtain the state variables of an extended state observer; observes the filtered current estimate and total disturbance using the extended state observer, and uses the estimated total disturbance value as a dead-zone compensation value to compensate the control system; finally, the system control quantity is obtained through PI regulation. By calculating the error voltage caused by the dead-zone effect in real time and decoupling the established current model, the impact of coupling on the system can be reduced, enhancing the system's stability. Further weakening current noise and disturbances using a Kalman filter improves the accuracy of current polarity determination and reduces the impact of current clamping. Observing the filtered current estimate and total disturbance using an extended state observer, and then using the estimated total disturbance as dead-zone compensation in the control system, enhances compensation accuracy, eliminates the effects of dead-zone, and improves control system stability. The KF-ESO composite control method, compared to traditional ESO observation methods, effectively suppresses noise interference and exhibits superior convergence. This method enables online dead-zone voltage compensation, dynamically adjusting the magnitude of the compensation based on a fixed error voltage. Attached Figure Description

[0057] The present invention will now be described in detail with reference to the accompanying drawings. The above and other aspects of the present invention will become clearer and more readily understood through the detailed description following the accompanying drawings. In the drawings:

[0058] Figure 1 This is a flowchart of the dead-zone compensation method for permanent magnet synchronous motors based on KF-ESO according to the present invention;

[0059] Figure 2 This is the overall control diagram for step S5 of the KF-ESO-based dead-zone compensation method for permanent magnet synchronous motors of the present invention. Detailed Implementation

[0060] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0061] The specific embodiments / examples described herein are specific implementations of the present invention, used to illustrate the concept of the invention, and are illustrative and exemplary, and should not be construed as limiting the implementation methods or scope of the present invention. In addition to the embodiments described herein, those skilled in the art can employ other obvious technical solutions based on the content disclosed in the claims and specification of this application. These technical solutions include those that make any obvious substitutions and modifications to the embodiments described herein, all of which are within the protection scope of the present invention.

[0062] Example 1

[0063] Please see the appendix Figure 1 As shown, this invention provides a dead-time compensation method for permanent magnet synchronous motors based on KF-ESO, comprising the following steps:

[0064] Step S1: Real-time acquisition of the error voltage generated by the dead zone effect of the permanent magnet synchronous motor.

[0065] Step S2: Establish a mathematical model of the permanent magnet synchronous motor and decouple the mathematical model to obtain the current value. Decoupling the established current model reduces the impact of coupling on the system.

[0066] Step S3: Reduce the noise of the current value using a Kalman filter to obtain the state variables of the extended state observer. Reducing system noise using a Kalman filter can improve the accuracy of current polarity determination.

[0067] Step S4: The filtered current estimate and total disturbance are observed using the extended state observer. The estimated total disturbance value is then used as the dead-zone compensation value and applied back to the control system. Observing the filtered current estimate and total disturbance using the extended state observer and applying the estimated total disturbance value as the dead-zone compensation value to the control system helps improve the accuracy of the compensation.

[0068] Step S5: The system control quantity is obtained through PI regulation. This enables online compensation of dead-zone voltage, dynamically adjusting the magnitude of the dead-zone voltage compensation based on a fixed error voltage.

[0069] Specifically, the error voltage caused by the dead-zone effect of the permanent magnet synchronous motor is acquired in real time; a mathematical model of the permanent magnet synchronous motor is established and decoupled to obtain the current value; noise reduction of the current value is achieved using a Kalman filter to obtain the state variables of the extended state observer; the filtered current estimate and total disturbance are observed through the extended state observer, and the estimated total disturbance value is used as the dead-zone compensation value to compensate the control system; the system control quantity is obtained after PI regulation. By calculating the error voltage caused by the dead-zone effect in real time and decoupling the established current model, the impact of coupling on the system can be reduced, enhancing the system stability. Further weakening current noise and disturbances using a Kalman filter improves the accuracy of current polarity determination and reduces the impact of current clamping. Observing the filtered current estimate and total disturbance using an extended state observer, and then using the estimated total disturbance as dead-zone compensation in the control system, enhances compensation accuracy, eliminates the effects of dead-zone, and improves control system stability. The KF-ESO composite control method, compared to traditional ESO observation methods, effectively suppresses noise interference and exhibits superior convergence. This method enables online dead-zone voltage compensation, dynamically adjusting the magnitude of the compensation based on a fixed error voltage.

[0070] In this embodiment, step S1 specifically includes the following sub-steps:

[0071] Using the equivalent dead time T dead The formula is:

[0072] T dead =T d +T on -T off …(1)

[0073] In the above formula, T d For dead time, T on T is the turn-on delay time for power devices. off This refers to the power device turn-off delay time.

[0074] Error voltage U caused by equivalent dead time e The formula is:

[0075]

[0076] In the above formula, U dc U is the DC bus voltage. sw For the on-state voltage drop of power devices, U D T is the forward voltage drop of the diode. s The time of one switching cycle;

[0077] Based on the polarity of the three-phase currents, the average error voltage of the three phases can be obtained as follows:

[0078]

[0079] In the above formula, the direction of power flow from the power device to the motor is defined as the positive direction, denoted as i. k >0, otherwise i k <0;

[0080] The error voltage on the three-phase coordinate system is transformed to the dq coordinate system for calculation:

[0081]

[0082] In the above formula, θ is the rotor angle.

[0083] In this embodiment, step S2 specifically includes the following sub-steps:

[0084] Based on the establishment of an ideal PMSM mathematical model in the dp coordinate system;

[0085]

[0086] Among them, i d i q U represents the d-axis and q-axis currents. d U q R represents the d-axis and q-axis voltages. S L is the stator resistance. d L q Let ψ be the inductance along the d and q axes. f For permanent magnet flux linkage, w e The electric rotation speed;

[0087] In the ideal PMSM mathematical model, based on the coupling relationship between the d-axis and q-axis currents, feedforward compensation control is applied to the PI control of the current loop to decouple the d-axis and q-axis.

[0088] Obtain the coupling compensation voltage u d 'and u q Its formula is as follows (6):

[0089]

[0090] The current equation after feedforward compensation is in the form of formula (7):

[0091]

[0092] Considering the error voltage ΔU caused by dead time ed and ΔU eqThe equation in the form of (8), i d 'and i q 'This is the actual current value after adding the dead-time error voltage:'

[0093]

[0094] Add dead-time compensation voltage U com_d and U com_q Then, ideally, ΔU ed =U com_d ΔU eq =U com_q , will U com_d and U com_q Compensating into formula (8) yields current formula (9):

[0095]

[0096] In this embodiment, step S3 specifically includes the following sub-steps:

[0097] Establish the system's state equations and debug the system based on these equations. The system's state equations are formed as follows:

[0098]

[0099] In the above formula, V represents the system's measurement noise.

[0100] V is a measurement noise that follows a zero-mean Gaussian distribution, with a covariance matrix of R. It is the disturbance estimation error. It is an estimate of the disturbance. The covariance matrix is ​​Q d Q d R can be debugged according to the system.

[0101]

[0102] Cov(V)=E(VV T ) = R.

[0103] A mathematical model of the Kalman filter is established based on the state equation of the system.

[0104] Based on the mathematical model of the Kalman filter, the discrete state-space equation and the predicted state variables are obtained; the above formula (12) is written as the discrete state-space equation:

[0105]

[0106] "~" represents the predicted value, the predicted state variable:

[0107]

[0108] The prediction state error covariance matrix is ​​obtained based on the predicted state variables;

[0109]

[0110] Kalman gain and state variable updates are performed based on the predicted state error covariance matrix; where, Kalman gain update:

[0111]

[0112]

[0113] State variable update:

[0114] The state error covariance matrix is ​​updated based on the Kalman gain update and the state variable update.

[0115]

[0116] By continuously iterating, a value that approximates the true value can be obtained.

[0117] The estimated values ​​of the d-axis and q-axis currents obtained through the Kalman filter are used as the state variables of the extended state observer. The posterior estimate from the previous iteration is used as the prior estimate for the next iteration, and the true value is approximated through continuous iteration. x(k-1) obtained through the Kalman filter, i.e. For current i d ′ and i q The estimated value of ′ is used as the state variable of the extended state observer.

[0118] In this embodiment, step S4 specifically includes the following sub-steps:

[0119] Based on the first-order state equation of the current loop, a first-order linear active disturbance rejection controller is set.

[0120] The disturbances present in the system are estimated based on the extended state observer, wherein the error voltage caused by the system's dead zone and the unknown disturbances are considered as the total disturbance; denoted as f. u This yields the following formula:

[0121]

[0122] in, for The first variable, i d The estimated value of ′. fd This is an unknown disturbance.

[0123] Establishing an ESO model:

[0124] The ESO model is discretized to obtain the observed values ​​and the disturbance observed values; wherein, the discretization of the ESO model yields:

[0125] Z1 is Z2 is the observed value of the disturbance, h is the sampling time, w0 is the bandwidth of the state observer, β1 = 2w0, β2 = w0 2 .

[0126] After passing through the state observer, the observed total disturbance is used as the compensation value of the error voltage and then added to the current formula to obtain the compensation value.

[0127] After passing through the state observer, the total disturbance observed is used as the compensation value of the error voltage to compensate for the current formula (9); where U com_d =z2.

[0128] For formula (9)U com_q The perturbation observations yielded U com_d The steps are the same, so they will not be repeated here.

[0129] In this embodiment, as Figure 2 As shown, step S5 specifically includes the following sub-steps:

[0130] The expression for the PI controller is:

[0131] Calculate the d-axis and q-axis voltages:

[0132] In the above formula, u d1 To calculate the d-axis voltage after dead-time compensation, u q1 To calculate the q-axis voltage after dead-time compensation, k p1 and k p2 The proportional gain for the d-axis and q-axis PI controllers are k and k, respectively. i1 and k i2 These are the integral coefficients of the d-axis and q-axis PI controllers, respectively.

[0133] Specifically, by inputting the d-axis and q-axis currents to the PI controller, which performs Park transformation, the output is fed to SVPWM. The SVPWM algorithm controls the power switch output current waveform of the three-phase power inverter to approximate a sine wave, reducing motor torque pulses, making the rotating magnetic field closer to a circle, and improving the utilization rate of the DC bus voltage, thus facilitating digital motor control. By acquiring the motor current and the angle identified by the rotor sensor, the required input current value and rotor angle are processed through Park transformation. The resulting d-axis and q-axis currents are then fed back to the PI controller to achieve cyclic control.

[0134] The technical effects of this invention are as follows:

[0135] (1) By calculating the error voltage caused by the dead zone effect in real time and decoupling the established current model, the influence of coupling on the system can be reduced, and the stability of the system can be enhanced. Furthermore, by using a Kalman filter to weaken the noise and disturbance of the current, the accuracy of current polarity determination can be improved, and the influence of current clamping can be reduced.

[0136] (2) By observing the filtered current estimate and total disturbance through the extended state observer, the estimated total disturbance value is used as the dead zone compensation value and then compensated into the control system. This helps to improve the accuracy of compensation, eliminate the influence of the dead zone effect, and improve the stability of the control system.

[0137] (3) The KF-ESO composite control method, compared with the traditional ESO observation method, can effectively suppress noise interference and has a better convergence effect. This method can perform online compensation of dead zone voltage, and dynamically adjust the magnitude of dead zone voltage compensation based on the compensation of a fixed error voltage.

[0138] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any alterations, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for dead-zone compensation of a permanent magnet synchronous motor based on KF-ESO, characterized in that, Includes the following steps: Step S1: Real-time acquisition of the error voltage generated by the dead zone effect of the permanent magnet synchronous motor; Step S2: Establish a mathematical model of the permanent magnet synchronous motor and decouple the mathematical model to obtain the current value; Step S3: Reduce noise in the current value using a Kalman filter to obtain the state variables of the extended state observer; Step S4: Observe the filtered current estimate and total disturbance through the extended state observer, and use the estimated total disturbance value as the dead zone compensation value to compensate the control system. Step S5: Obtain the system control quantity through PI adjustment; Step S1 specifically includes the following sub-steps: Equivalent dead time The formula is: …（1） In the above formula, T d Dead time, For the turn-on delay time of power devices This refers to the power device turn-off delay time. Error voltage caused by equivalent dead time The formula is: …（2） In the above formula, U dc This is the DC bus voltage. U sw For power device on-state voltage drop, U D This is the forward voltage drop of the diode. T s The time of one switching cycle; Based on the polarity of the three-phase currents, the average error voltage of the three phases can be obtained as follows: …（3） In the above formula, i a Indicates a three-phase motor a Phase stator current, i b Indicates a three-phase motor b Phase stator current, i c Indicates a three-phase motor c The stator current is defined as the direction in which the power devices flow towards the motor, and is denoted as […]. ,on the contrary ; The error voltage on the three-phase coordinate system is transformed to the dq coordinate system via coordinate transformation: …（4） In the above formula, For the rotor angle, Δ U ed Δ U eq These represent the d-axis error voltage and q-axis error voltage generated by the dead zone effect in the dq coordinate system, respectively.

2. The dead-time compensation method for permanent magnet synchronous motors based on KF-ESO as described in claim 1, characterized in that, Step S2 specifically includes the following sub-steps: An ideal mathematical model of a permanent magnet synchronous motor is established in the dq coordinate system; …(5) in, , For the d-axis and q-axis currents, , For the d-axis and q-axis voltages, For stator resistance, , For d-axis and q-axis inductance, It is a permanent magnet flux linkage. The electric rotation speed; In the ideal mathematical model of the permanent magnet synchronous motor, based on the coupling relationship between the d-axis and q-axis currents, feedforward compensation control is applied to the PI control of the current loop to decouple the d-axis and q-axis. Obtaining coupling compensation voltage and Its formula is as follows (6): …（6） The current equation after feedforward compensation is in the form of formula (7): …（7） Considering the error voltage caused by dead time and The equation form after (8) and The actual current value after adding the dead-time error voltage: …（8） Add dead-time compensation voltage and Then, ideally, , ,Will and Compensating to formula (8) yields current formula (9): …（9）。 3. The dead-time compensation method for permanent magnet synchronous motors based on KF-ESO as described in claim 1, characterized in that, Step S3 specifically includes the following sub-steps: Establish the system's state equations and debug the system based on these equations. A mathematical model of the Kalman filter is established based on the state equation of the system. The discrete state-space equation and predicted state variables are obtained based on the mathematical model of the Kalman filter. The prediction state error covariance matrix is ​​obtained based on the predicted state variables; Kalman gain and state variable updates are performed based on the predicted state error covariance matrix. The state error covariance matrix is ​​updated based on the Kalman gain update and the state variable update. By continuously iterating, a value that approximates the true value can be obtained. The estimated values ​​of the d-axis and q-axis currents of the Kalman filter are used as the state variables of the extended state observer.

4. The dead-time compensation method for permanent magnet synchronous motors based on KF-ESO as described in claim 2, characterized in that, Step S4 specifically includes the following sub-steps: Based on the first-order state equation of the current loop, a first-order linear active disturbance rejection controller is set. The disturbances present in the system are estimated based on the extended state observer, wherein the error voltage caused by the dead zone of the system and the unknown disturbances are regarded as the total disturbances; Establish an extended state observer model; The extended state observer model is discretized to obtain the observed values ​​and the perturbation observed values; After observation by the extended state observer, the total disturbance observed is used as the compensation value of the error voltage and then added to the current formula to obtain the compensation value.

5. The dead-time compensation method for permanent magnet synchronous motors based on KF-ESO as described in claim 4, characterized in that, Step S5 specifically includes the following sub-steps: The expression for the PI controller is: …(10); Calculate the d-axis and q-axis voltages: …（11）； In the above formula, The d-axis voltage after dead-time compensation. The q-axis voltage after dead-time compensation. k p The proportional gain of the PI controller. k i The integral coefficient of the PI controller; and These are the proportional coefficients of the PI controllers for the d-axis and q-axis, respectively. and These are the integral coefficients of the PI controller for the d-axis and q-axis, respectively. This is the coupling compensation voltage along the d-axis. is the coupling compensation voltage along the q-axis, and s is the Laplace operator.

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