Discrete domain adaptive extended state observer and construction method and control method thereof

Abstract

The application discloses a discrete domain self-adaptive extended state observer and a construction method and a control method thereof. In view of the problems of the discretization error caused by the approximate discretization of the continuous domain observer under a low carrier ratio, the decrease of back electromotive force observation accuracy, and the fact that the back electromotive force estimation is easily affected by the direct current bias. The observer reconstructs the double-path correction gain by directly configuring the zero-pole in the discrete domain: the z-domain direct current zero point is introduced in the back electromotive force state correction gain, which effectively suppresses the direct current bias of the estimated back electromotive force; the conjugate complex pole corresponding to the operating fundamental frequency of the motor is introduced in the current state correction gain, so that the passband center frequency of the back electromotive force estimation channel is adaptively matched with the motor speed. After gain adjustment, the channel has the unit gain and zero phase lag characteristics at the fundamental frequency, forming a band-pass filtering effect with an adaptive center frequency. The application can improve the back electromotive force observation accuracy, the rotor position estimation accuracy and the system stability under a low carrier ratio.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control, and particularly relates to a discrete domain adaptive extended state observer and its construction and control methods. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in new energy vehicles, rail transportation, aerospace, and industrial servo applications due to their advantages such as high efficiency, high power density, and fast dynamic response. High-performance control requires accurate rotor position and speed information. Traditional mechanical position sensors increase cost, size, and wiring complexity, and reduce system reliability in extreme environments such as high temperature, high speed, and strong vibration. Therefore, sensorless control has become an important research direction.

[0003] Existing sensorless control methods mainly include high-frequency signal injection and model-based methods. High-frequency signal injection is suitable for the zero-speed and low-speed range, but requires additional high-frequency signal injection, which can easily introduce losses, noise, and torque ripple. The fundamental frequency model method utilizes motor voltage, current, and parameter information to estimate the back electromotive force or flux linkage through an observer, thereby obtaining the rotor position and speed, and is suitable for the medium- and high-speed range. Commonly used observers include sliding mode observers, model reference adaptive observers, extended Kalman filters, full-order observers, and extended state observers. Among them, the extended state observer can convert back electromotive force, parameter uncertainties, and unmodeled disturbances into extended state estimates.

[0004] However, as motor drive systems develop towards higher speeds and greater power, the inverter switching frequency is difficult to increase due to limitations in power device switching losses and heat dissipation capacity. When the motor fundamental frequency increases or the carrier frequency is limited, the system enters a low carrier ratio operating condition. Under this condition, the change in the motor electrical angle within a sampling period is not negligible, and changes in back EMF, sample-and-hold characteristics, and digital control delays will significantly affect the observer performance. If a continuous domain observer is still used for approximate discretization via Euler's method or bilinear transform, discretization errors and phase errors are easily generated, which may even lead to distortion of back EMF estimation or system instability.

[0005] Furthermore, traditional extended state observers typically approximate the back EMF or total disturbance as constant over a single sampling period. However, at low carrier ratios, the complex vector of the back EMF rotates with the motor's electrical angular velocity. Ignoring this rotational characteristic leads to amplitude attenuation, phase lag, and dynamic errors in the estimated back EMF. Traditional linear extended state observers often exhibit low-pass characteristics in their estimation channels, making it difficult to simultaneously achieve zero amplitude attenuation, zero phase lag, and DC bias suppression at the fundamental frequency. These shortcomings severely limit the accuracy and stability of sensorless control at low carrier ratios. Summary of the Invention

[0006] The purpose of this invention is to provide a discrete-domain adaptive extended state observer and its construction and control methods, which solve the problems in existing sensorless control technology for permanent magnet synchronous motors. Traditional extended state observers in the continuous domain, when implemented with approximate discretization, are difficult to adapt to low carrier ratio conditions and cannot accurately describe the rotational variation characteristics of the back EMF within the sampling period. This results in discretization errors, amplitude attenuation, and phase lag in the back EMF estimation. Simultaneously, traditional linear extended state observers exhibit significant low-pass characteristics, making it difficult to simultaneously achieve accurate estimation of the fundamental back EMF, DC bias suppression, and non-target frequency disturbance suppression, thereby increasing the rotor position estimation error.

[0007] This invention provides the following technical solution:

[0008] Firstly, a discrete-domain adaptive extended state observer is provided for sensorless control of permanent magnet synchronous motors under low carrier ratio conditions, including: The current error generation unit is used to subtract the estimated current from the measured current to obtain the current observation error. The dual-path correction unit is used to adjust the current observation error by using the current state correction gain and the back EMF state correction gain respectively, and outputs the current state correction signal and the back EMF state correction signal. The current state closed-loop unit is used to combine the current estimated current, measured voltage, current estimated back EMF and current state correction signal to update the estimated current at the next moment, and then feed it back to the current error generation unit after a delay. The back EMF state closed-loop unit is used to combine the current estimated back EMF, the back EMF expansion state discrete rotation factor, and the back EMF state correction signal to update the estimated back EMF at the next moment, and then feed it back to the current state closed-loop unit after a delay. Wherein, the current state correction gain and the back electromotive force state correction gain are adaptive gains obtained through discrete domain zero-pole configuration: The back EMF state correction gain is configured to enable the back EMF estimation channel. z Domain transfer functions have z DC frequency zero point in the domain; The current state correction gain is configured to enable the back EMF estimation channel. z The domain transfer function has a frequency corresponding to the fundamental frequency of the motor. z Domain conjugate complex poles.

[0009] Secondly, the present invention provides a method for constructing a discrete-domain adaptive extended state observer, for constructing the aforementioned discrete-domain adaptive extended state observer, the method comprising: In the αβ axis coordinate system, the back electromotive force of the permanent magnet synchronous motor is taken as the disturbance to be observed, and a continuous domain complex vector mathematical model of the permanent magnet synchronous motor is established. Within a single sampling period, the stator voltage and back electromotive force are maintained in segments, and the differential equations of the continuous domain complex vector mathematical model are solved to obtain the discrete model of the permanent magnet synchronous motor. The back EMF of the permanent magnet synchronous motor is used as the extended state variable. Based on the characteristic that the complex vector of the back EMF rotates with the electric angular velocity of the motor, the extended state equation of the back EMF is established. The linear differential equation of the extended state equation of the back EMF is solved in a single sampling period to obtain the discrete expression of the extended state of the back EMF. Based on the discrete model of permanent magnet synchronous motor and the discrete expression of back EMF extended state, an extended state observer with a dual-state closed loop structure is constructed in the discrete domain, and the z-domain transfer function of the back EMF estimation channel is derived. Channel estimation based on back electromotive force z The domain transfer function is used to reconstruct the current state correction gain and the back EMF state correction gain through discrete domain zero-pole configuration, respectively; where the back EMF state correction gain is... z Introducing a zero at the DC frequency point in the domain, the current state correction gain is at... z By introducing conjugate complex poles corresponding to the fundamental frequency of motor operation into the domain, and ensuring that the back EMF estimation channel satisfies unity gain and zero phase lag at the fundamental frequency of the motor, a center frequency adaptive bandpass filter characteristic is formed, thus completing the construction of the discrete domain adaptive extended state observer.

[0010] In one implementation, the continuous-domain complex vector mathematical model of the permanent magnet synchronous motor is as follows: , In the formula, For differential operators, Represents time, and for shaft current, and for shaft voltage, and for Shaft back electromotive force, and These are the coefficients of the continuous-domain complex vector mathematical model of the permanent magnet synchronous motor. For stator resistance, and These are the d-axis inductance and the q-axis inductance, respectively. This is an estimated value for the motor speed. for Axial current complex vector, for Axial voltage complex vector for Axial back electromotive force complex vector.

[0011] In one implementation, in the first Within each sampling period, if the voltage is considered as a zero-order hold signal, then the voltage and back electromotive force are expressed as: , , In the formula, , For sampling sequence number, The sampling period is For the first Each sampling time Axial voltage complex vector For the first Each sampling time The back electromotive force of the axis is a complex vector. This refers to the motor speed; The discrete model of the permanent magnet synchronous motor is as follows: , In the formula, , The first , Each sampling time Axial current complex vector, , , These represent the current state transition coefficient, voltage input discrete coefficient, and back EMF input discrete coefficient in the discrete model of the permanent magnet synchronous motor; where... , In the formula, This represents the base of the natural logarithm. This is an intermediate coefficient related to the salient pole characteristics of the motor. This is an intermediate coefficient related to the stator resistance attenuation characteristics. and These are the transitional combination coefficients in the discretization derivation process.

[0012] In one implementation, the discrete expression for the back electromotive force expansion state is: , In the formula, For the first Each sampling time The back electromotive force of the axis is a complex vector. The imaginary unit, This represents the differential component of the disturbance caused by the amplitude change.

[0013] In one implementation, the extended state observer of the dual-state closed-loop structure is: , In the formula, and The first The and the first Each sampling time Axis estimation of stator current complex vector, and The first The and the first Each sampling time Axial estimation of back electromotive force complex vector, For the first Sampling time Axis current observation error For current state correction gain, This is the gain for back electromotive force state correction. The discrete rotation factor for the back electromotive force expansion state; Based on the expression of the extended state observer of the two-state closed-loop structure, the z-domain transfer function of the back EMF estimation channel is derived. for: , In the formula, z for z Domain complex variables, for z The transformed back electromotive force for z The estimated back electromotive force after transformation.

[0014] In one embodiment, the method further includes: constructing a target transfer function with bandpass filtering characteristics to enable the z-domain transfer function of the back EMF estimation channel to have bandpass filtering characteristics that can suppress the DC bias in the estimated back EMF. for: , In the formula, This is the gain of the discrete-domain extended state observer.

[0015] In one implementation, the expressions for the gain of the discrete-domain extended state observer, the current state correction gain, and the back electromotive force state correction gain are as follows: .

[0016] Thirdly, the present invention provides a sensorless control method for a permanent magnet synchronous motor with a low carrier ratio, the method comprising: Obtain permanent magnet synchronous motor Shaft voltage and current signals; permanent magnet synchronous motor The shaft voltage and current signals are used as inputs, and the back electromotive force vector of the motor is obtained through the discrete domain adaptive extended state observer mentioned above. The motor speed and position signals are estimated using a phase-locked loop based on the motor's back electromotive force vector; The motor speed and position signals are input to the motor closed-loop control system to achieve sensorless closed-loop control of the permanent magnet synchronous motor.

[0017] Fourthly, the present invention provides a sensorless control device for a permanent magnet synchronous motor with a low carrier ratio, the device comprising: The acquisition module is used to acquire information about permanent magnet synchronous motors. Shaft voltage and current signals; The aforementioned discrete-domain adaptive extended state observer is used to monitor permanent magnet synchronous motors. The back electromotive force vector of the motor is obtained by taking the shaft voltage and current signals as inputs. The motor speed and position signal estimation module is used to estimate the motor speed and position signals based on the back electromotive force vector of the motor using a phase-locked loop; The motor speed and position signal transmission module is used to input the motor speed and position signals to the motor closed-loop control system to realize sensorless closed-loop control of the permanent magnet synchronous motor.

[0018] Beneficial effects of this invention:

[0019] (1) Based on the precise discrete model of permanent magnet synchronous motor, the present invention directly constructs an extended state observer in the discrete domain and considers the characteristic of the back EMF rotating with the electric angular velocity of the motor during the sampling period. The extended state equation of the back EMF is precisely discretized, avoiding the discretization error and pole offset problem generated when the traditional continuous domain observer is implemented by approximate discretization. This improves the back EMF estimation accuracy and observer stability under low carrier ratio.

[0020] (2) The present invention designs the observer correction gain by configuring the zero poles in the z domain, so that the back EMF estimation channel has bandpass characteristics, can obtain the estimated back EMF without amplitude attenuation and phase lag at the fundamental frequency, and suppress DC bias.

[0021] (3) This invention introduces a conjugate complex pole corresponding to the fundamental frequency of the motor in the current state correction gain, so that the passband center frequency of the back EMF estimation channel adaptively matches the motor speed. After gain adjustment, the channel has unity gain and zero phase lag characteristics at the fundamental frequency, forming a bandpass filtering effect with adaptive center frequency. This invention can improve the back EMF observation accuracy, rotor position estimation accuracy and system stability under low carrier ratio. Attached Figure Description

[0022] The accompanying drawings, as part of this invention, are provided to further illustrate the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation thereof. Clearly, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0023] Figure 1 This is a schematic diagram of the structure of a discrete domain adaptive extended state observer provided in an embodiment of the present invention;

[0024] Figure 2 This is a flowchart of a method for constructing a discrete-domain adaptive extended state observer provided in one embodiment of the present invention;

[0025] Figure 3 This is a flowchart of a sensorless control method for a permanent magnet synchronous motor with a low carrier ratio provided in one embodiment of the present invention;

[0026] Figure 4 This is a Bode plot of a discrete-domain adaptive extended state observer provided in one embodiment of the present invention at different motor operating frequencies;

[0027] Figure 5 This is a schematic diagram showing the relative error of the current state transition coefficient between the mathematical model of a permanent magnet synchronous motor approximated by the forward Euler method provided in one embodiment of the present invention and the discrete model of the permanent magnet synchronous motor of the present invention.

[0028] Figure 6 This is a schematic diagram showing the distribution of closed-loop poles of a discrete-domain adaptive extended state observer within the unit circle in the z-domain, according to an embodiment of the present invention.

[0029] Figure 7 This is a schematic diagram of the permanent magnet synchronous motor control system provided in one embodiment of the present invention;

[0030] Figure 8 This presents experimental comparison results of the actual rotational speed, estimated rotational speed, and position estimation error of a permanent magnet synchronous motor under acceleration conditions, as provided in one embodiment of the present invention; wherein, Figure 8 (a) shows the experimental results of the traditional linear extended state observer. Figure 8 (b) shows the experimental results of the adaptive complex coefficient extended state observer. Figure 8 (c) shows the experimental results of the discrete-domain adaptive extended state observer;

[0031] Figure 9 This presents experimental comparison results of estimating position error under a 2A DC disturbance injected along the α-axis, as provided in one embodiment of the present invention; wherein, Figure 9 (a) shows the experimental results of the traditional linear extended state observer. Figure 9 (b) shows the experimental results of the complex coefficient adaptive extended state observer; Figure 9 (c) shows the experimental results of the discrete-domain adaptive extended state observer.

[0032] It should be noted that these accompanying drawings and textual descriptions are not intended to limit the scope of the invention in any way, but rather to illustrate the concept of the invention to those skilled in the art by referring to specific embodiments. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0034] An embodiment of the present invention illustrates a discrete-domain adaptive extended state observer applied to sensorless control of a permanent magnet synchronous motor under low carrier ratio. The observer includes a current error generation unit, a dual-path correction unit, a current state closed-loop unit, and a back-EMF state closed-loop unit. The current error generation unit is used to subtract the estimated current from the measured current to obtain the current observation error. The dual-path correction unit is used to adjust the current observation error using the current state correction gain and the back-EMF state correction gain respectively, outputting a current state correction signal and a back-EMF state correction signal. The current state closed-loop unit is used to combine... The current estimated current, measured voltage, current estimated back EMF, and current state correction signal are used to update the estimated current for the next time step, and after a delay, the result is fed back to the current error generation unit. The back EMF state closed-loop unit combines the current estimated back EMF, the back EMF expansion state discrete rotation factor, and the back EMF state correction signal to update the estimated back EMF for the next time step, and after a delay, the result is fed back to the current state closed-loop unit. The current state correction gain and the back EMF state correction gain are adaptive gains obtained through discrete domain zero-pole configuration. The back EMF state correction gain is configured to make the back EMF estimation channel... z Domain transfer functions have z The DC frequency zero point is located in the domain; the current state correction gain is configured to enable the back EMF estimation channel. z The domain transfer function has a frequency corresponding to the fundamental frequency of the motor. z Domain conjugate complex poles.

[0035] In this embodiment, the estimated current, the measured current, and the estimated back electromotive force are all two-phase stationary. The complex vector corresponding to the coordinate system. (Refer to...) Figure 1 As shown, the signal connection relationships and working principles of each unit are as follows: The current error generation unit is used to generate the current error of the first unit. Each sampling time Axis estimation of stator current complex vector With the Each sampling time Axial current complex vector By taking the difference, we can calculate the first... Each sampling time Axis current observation error This current observation error serves as the common feedback quantity for the two state correction branches of the observer. The dual-path correction unit receives the first... Each sampling time Axis current observation error and respectively via current state correction gain and back EMF state correction gain Adjustments are made. After adjustment, two correction signals are output: one is the current state correction signal input to the current state closed-loop unit; the other is the back EMF state correction signal input to the back EMF state closed-loop unit. The back EMF state correction gain is specified. By configuration, a zero is introduced at the DC frequency point in the z-domain (z=1) to effectively suppress the DC bias component in the estimated back electromotive force; current state correction gain. By configuring the system, a conjugate complex pole corresponding to the motor's fundamental operating frequency is introduced in the z-domain, enabling the passband center frequency of the back EMF estimation channel to adaptively match the motor's operating frequency; through the... and Gain adjustment ensures that the back EMF estimation channel satisfies the unity gain and zero phase lag condition at the motor fundamental frequency, and effectively suppresses the DC bias component in the estimated back EMF, thus enabling the observer to exhibit the desired bandpass filtering characteristics that are adaptive to the center frequency. The current-state closed-loop unit, with the first... Each sampling time Axis estimation of stator current complex vector , No. Each sampling time Axial voltage complex vector , No. Each sampling time Axial estimation of back electromotive force complex vector And the current state correction signal from the dual-path correction unit, according to the current state transition coefficient. Voltage input dispersion coefficient Back EMF input dispersion coefficient Perform weighted operations to calculate the result. The motor of time Axis estimation of stator current complex vector And after a delay step. After processing, the error is fed back to the current error generation unit, forming a current closed loop. The back EMF state closed loop unit, with the first... Each sampling time Axial estimation of back electromotive force complex vector Back EMF expansion state discrete rotation factor And the back EMF state correction signal from the dual-path correction unit, the first... Each sampling time Axial estimation of back electromotive force complex vector The updated next-moment estimate of the back electromotive force is obtained after a one-step delay. Delay one sampling period Then, it splits into two paths: one path serves as the output of the entire discrete-domain adaptive extended state observer, i.e., the first path... Each sampling time Axial estimation of back electromotive force complex vector One path provides the rotor position and speed for subsequent phase-locked loop calculations; the other path feeds back to the current state closed-loop unit to update the current state, forming a back EMF closed loop. Both the current state correction gain and the back EMF state correction gain are based on the back EMF estimation channel. z The domain transfer function is obtained through discrete-domain pole-zero placement. The back electromotive force state correction gain is... z A zero is introduced at the DC frequency point in the domain to suppress the DC bias component of the estimated back EMF; the current state correction gain is... z The domain introduces a conjugate complex pole corresponding to the motor's operating fundamental frequency, enabling the passband center frequency of the back EMF estimation channel to adaptively match the motor's operating frequency. The two work together to ensure that the back EMF estimation channel satisfies unity gain and zero phase lag at the motor's fundamental frequency, forming a center frequency adaptive bandpass filter characteristic.

[0036] This discrete-domain adaptive extended state observer is based on the precise discrete model of a permanent magnet synchronous motor in a two-phase stationary coordinate system. It uses the back electromotive force (EMF) as the extended state variable and, based on the characteristic that the complex vector of the back EMF rotates with the electric angular velocity of the motor, precisely discretizes the extended state equation of the back EMF. On this basis, the extended state observer is directly constructed in the discrete domain, and its operation is further refined by... z The zero-pole configuration of the domain is used to design the observer correction gain, so that the observer has bandpass filtering characteristics.

[0037] One embodiment of the present invention proposes a method for constructing a discrete-domain adaptive extended state observer, which is used to build a discrete-domain adaptive extended state observer, with reference to... Figure 2 As shown, the construction method includes:

[0038] Step S100: In In the axial coordinate system, the back electromotive force of the permanent magnet synchronous motor is taken as the disturbance to be observed, and a complex vector mathematical model of the permanent magnet synchronous motor in the continuous domain is established.

[0039] The continuous domain complex vector mathematical model of a permanent magnet synchronous motor is as follows:

[0040]

[0041] In the formula, For differential operators, Represents time, and for shaft current, and for shaft voltage, and for Shaft back electromotive force, and These are the coefficients of the continuous-domain complex vector mathematical model of the permanent magnet synchronous motor. For stator resistance, and These are the d-axis inductance and the q-axis inductance, respectively. This is an estimated value for the motor speed. for Axial current complex vector, for Axial voltage complex vector for Axial back electromotive force complex vector.

[0042] After sorting, we can obtain:

[0043] .

[0044] Step S110: Within a single sampling period, the stator voltage and back electromotive force are maintained in segments, and the differential equations of the continuous domain complex vector mathematical model are solved to obtain the discrete model of the permanent magnet synchronous motor.

[0045] In the Within each sampling period, if the voltage is considered as a zero-order hold signal, then the voltage and back electromotive force can be expressed as:

[0046]

[0047]

[0048] in, , For sampling sequence number, The sampling period is For the first Each sampling time Axial voltage complex vector For the first Each sampling time The back electromotive force of the axis is a complex vector. This represents the motor speed.

[0049] Furthermore, by solving the linear differential equations of the continuous domain complex vector mathematical model of the permanent magnet synchronous motor within the sampling period, the discrete model of the permanent magnet synchronous motor is obtained as follows:

[0050]

[0051] In the formula, , The first , Each sampling time Axial current complex vector, for Moment Axial voltage complex vector For the first Each sampling time The back electromotive force of the axis is a complex vector. , , These are the current state transition coefficient, voltage input discrete coefficient, and back EMF input discrete coefficient in the discrete model of the permanent magnet synchronous motor, respectively.

[0052] in,

[0053]

[0054] In the formula, This represents the base of the natural logarithm. This is an intermediate coefficient related to the salient pole characteristics of the motor. This is an intermediate coefficient related to the stator resistance attenuation characteristics. and These are the transitional combination coefficients in the discretization derivation process.

[0055] Step S120: The back EMF of the permanent magnet synchronous motor is used as the extended state variable. Based on the characteristic that the complex vector of the back EMF rotates with the electric angular velocity of the motor, the extended state equation of the back EMF is established. The extended state equation of the back EMF is solved by linear differential equation within a single sampling period to obtain the discrete expression of the extended state of the back EMF.

[0056] The complex vector of back electromotive force can be expressed as:

[0057]

[0058] In the formula, The magnitude of the back electromotive force. It is the phase of the back electromotive force and satisfies , This represents the motor speed.

[0059] The derivative of the complex vector of back electromotive force with respect to time is:

[0060]

[0061] In the formula, This indicates taking the derivative with respect to time. This represents the differential component of the disturbance caused by the amplitude change.

[0062] Furthermore, by solving the linear differential equation of the back EMF expansion state equation within the sampling period, the discrete expression of the back EMF expansion state can be obtained as follows:

[0063]

[0064] In the formula, For the first Each sampling time The back electromotive force of the axis is a complex vector. The imaginary unit, This represents the differential component of the disturbance caused by the amplitude change.

[0065] When a permanent magnet synchronous motor is operating in steady state or quasi-steady state, the amplitude of the back electromotive force changes relatively little, satisfying the following:

[0066]

[0067] That is, N(t)≈0, then the discrete expression for the back electromotive force expansion state simplifies to:

[0068]

[0069] in, It is the discrete rotation factor for the back electromotive force expansion state.

[0070] Step S130: Based on the discrete model of the permanent magnet synchronous motor and the discrete expression of the back EMF extended state, construct the extended state observer with a dual-state closed loop structure in the discrete domain, and derive the z-domain transfer function of the back EMF estimation channel.

[0071] Furthermore, the extended state observer for the two-state closed-loop structure is:

[0072]

[0073] In the formula, and The first The and the first Each sampling time Axis estimation of stator current complex vector, and The first The and the first Each sampling time Axial estimation of back electromotive force complex vector, For the first Each sampling time Axis current observation error For current state correction gain, This is the gain for back electromotive force state correction. It is the discrete rotation factor for the back electromotive force expansion state.

[0074] Based on the expression of the extended state observer of the two-state closed-loop structure, the z-domain transfer function of the back EMF estimation channel is derived. for:

[0075]

[0076] In the formula, z for z Domain complex variables, for z Transformed Shaft back electromotive force, for z Transformed The back electromotive force is estimated by the axis.

[0077] Furthermore, in order to ensure that the z-domain transfer function of the back EMF estimation channel has bandpass filtering characteristics, and to suppress...

[0078] To estimate the DC bias in the back electromotive force, construct the target transfer function of the bandpass filter characteristics. for:

[0079]

[0080] In the formula, This is the gain of the discrete-domain extended state observer.

[0081] Step S140: Estimating the channel based on back electromotive force z The domain transfer function is used to reconstruct the current state correction gain and the back EMF state correction gain through discrete domain zero-pole configuration, respectively; where the back EMF state correction gain is... z Introducing a zero at the DC frequency point in the domain, the current state correction gain is at... z By introducing conjugate complex poles corresponding to the fundamental frequency of motor operation into the domain, and ensuring that the back EMF estimation channel satisfies unity gain and zero phase lag at the fundamental frequency of the motor, a center frequency adaptive bandpass filter characteristic is formed, thus completing the construction of the discrete domain adaptive extended state observer.

[0082] By making It can be obtained .

[0083] It has bandpass filtering characteristics that can suppress DC bias in the estimation of back EMF, and the center frequency adapts to the motor operating frequency.

[0084] right Design it to meet the following requirements:

[0085]

[0086] in, Estimate the motor speed.

[0087] Will and Substitution From the denominator, we can obtain... Characteristic polynomial for:

[0088]

[0089] Configure the closed-loop poles as follows:

[0090]

[0091] So The characteristic polynomial can be expressed as:

[0092]

[0093] United The equality constraints are achieved by configuring the DC zero and conjugate complex poles and matching the z-domain transfer function of the back EMF estimation channel. With preset bandpass transfer function The characteristic polynomial coefficients are used to obtain expressions for the gain, current state correction gain, and back EMF state correction gain of the discrete domain extended state observer.

[0094] Furthermore, the expressions for the gain of the discrete-domain extended state observer, the current state correction gain, and the back EMF state correction gain are as follows:

[0095] .

[0096] Reference Figure 3 This disclosure provides a sensorless control method for a permanent magnet synchronous motor with a low carrier ratio, which specifically includes the following steps:

[0097] Step S200: Obtain the permanent magnet synchronous motor Shaft voltage and current signals;

[0098] Step S210: Install the permanent magnet synchronous motor The shaft voltage and current signals are used as inputs, and the back electromotive force vector of the motor is obtained through a discrete domain adaptive extended state observer.

[0099] Step S220: Use a phase-locked loop to estimate the motor speed and position signals based on the motor's back electromotive force vector;

[0100] Step S230: Input the motor speed and position signals to the motor closed-loop control system to realize sensorless closed-loop control of the permanent magnet synchronous motor.

[0101] In one alternative implementation, after obtaining the motor speed, the control method further includes: using a low-pass filter to smooth the estimated speed in order to suppress high-frequency noise.

[0102] Traditional continuous-domain linear extended state observers typically exhibit low-pass filtering characteristics in their back-EMF estimation channels, making it difficult to accurately track the sinusoidal back-EMF. This leads to amplitude attenuation and phase lag at the motor's fundamental frequency, and makes it challenging to suppress the DC bias of the back-EMF caused by current sampling errors. Furthermore, the approximate discretization method struggles to adapt to low carrier ratio conditions, further increasing discretization and rotor position estimation errors. The proposed discrete-domain adaptive extended state observer, however, is built directly in the discrete domain based on an accurate discretization model. It precisely discretizes the extended state equation of the back-EMF and, through z-domain zero-pole configuration, makes the back-EMF estimation channel bandpass-like. This enables the acquisition of back-EMF estimates without amplitude attenuation or phase lag at the fundamental frequency, while suppressing the DC bias in the back-EMF and improving the accuracy of sensorless control at low carrier ratios.

[0103] To verify the ability of the discrete-domain adaptive extended state observer to suppress DC bias and adapt to frequency. Figure 4 Bode plots of a discrete-domain adaptive extended state observer at different motor operating frequencies are shown. Figure 4 It can be concluded that the discrete-domain adaptive extended state observer can obtain the estimated back electromotive force without phase lag at the motor operating frequency and has the ability to suppress DC bias.

[0104] Figure 5 This diagram illustrates the relative error of the current state transition coefficients between the discrete mathematical model of the permanent magnet synchronous motor (PMSM) approximated using the forward Euler method and the discrete model of the PMSM of this invention. In the diagram,

[0105]

[0106] in, and These are the values ​​in the first row and first column of the current state transition coefficient matrix in the mathematical model of a permanent magnet synchronous motor approximated by the forward Euler method, respectively; and These are the values ​​in the first row and first column of the current state transition coefficient matrix and the values ​​in the first row and second column of the current state transition coefficient matrix in the discrete model of the permanent magnet synchronous motor of the present invention, respectively. and The mathematical models of permanent magnet synchronous motors approximated by the forward Euler method are respectively represented in the following ways: and In the discrete model of the permanent magnet synchronous motor of this invention and The absolute value of the relative error between them.

[0107] like Figure 5 As shown, the carrier ratio decreases with increasing speed. and As the carrier ratio increases, the accuracy of the Euler discrete model decreases significantly under such high-speed and low-carrier-ratio conditions. This leads to an increase in the back EMF estimation error, resulting in an unacceptable position estimation error.

[0108] like Figure 6 As shown, when the motor operating frequency increases from 0 rad / s to 500π rad / s, the poles of the transfer function of the discrete-domain adaptive extended state observer are always located inside the unit circle, indicating that the discrete-domain adaptive extended state observer remains stable throughout the entire speed range.

[0109] The following is an embodiment of the present invention based on a sensorless control device for a permanent magnet synchronous motor under low carrier ratio, which can be used to execute an embodiment of the present invention based on a sensorless control method for a permanent magnet synchronous motor under low carrier ratio. For details not disclosed in the embodiment of the present invention based on a sensorless control device for a permanent magnet synchronous motor under low carrier ratio, please refer to the embodiment of the present invention based on a sensorless control method for a permanent magnet synchronous motor under low carrier ratio.

[0110] An exemplary embodiment of the present invention provides a sensorless control device for a permanent magnet synchronous motor with a low carrier ratio, the device comprising:

[0111] The acquisition module is used to acquire information about permanent magnet synchronous motors. Shaft voltage and current signals;

[0112] Discrete-domain adaptive extended state observer for permanent magnet synchronous motors The back electromotive force vector of the motor is obtained by taking the shaft voltage and current signals as inputs.

[0113] The motor speed and position signal estimation module is used to estimate the motor speed and position signals based on the back electromotive force vector of the motor using a phase-locked loop;

[0114] The motor speed and position signal transmission module is used to input the motor speed and position signals to the motor closed-loop control system to realize sensorless closed-loop control of the permanent magnet synchronous motor.

[0115] It should be noted that the description of the discrete-domain adaptive extended state observer is the same or similar to the description above, and will not be repeated here.

[0116] Reference Figure 7 As shown, the system includes a sensorless control device for a permanent magnet synchronous motor under low carrier ratio. The specific working process of the system is as follows: the estimated motor speed is... and motor speed setpoint The difference is calculated to obtain the speed difference value; this speed difference value is then input into the speed PI controller to obtain... Shaft current The three-phase current of the permanent magnet synchronous motor is obtained through current sampling. The three-phase current is first obtained by Clark transformation. shaft current Then, after Park transformation, we get Shaft current feedback value ;Will Shaft current and current feedback value The difference is calculated by subtracting the values; this current difference is then input to a current PI controller to obtain the final output. Shaft reference voltage ;Will Shaft reference voltage After coordinate transformation, we obtain shaft voltage ;Will shaft voltage Input to the SVPWM modulation module output duty cycle signal The duty cycle signal is input to the DC bus side voltage. The inverter controls the on / off state of the inverter, and simultaneously acquires the data from the acquisition module. A discrete-domain adaptive extended state observer with shaft current and voltage inputs is obtained. Axis estimation of back electromotive force and ;Will The estimated back electromotive force of the shaft is input to the phase-locked loop to obtain the estimated rotor position. And motor speed estimate The estimated rotational speed is filtered out by a low-pass filter to remove high-order harmonics and then used as the next rotational speed feedback to control the permanent magnet synchronous motor.

[0117] In an alternative embodiment, the device further includes a filter module for using a low-pass filter to smooth the estimated rotational speed in order to suppress high-frequency noise introduced by the derivative.

[0118] It should be noted that the above embodiments of the sensorless control device for a permanent magnet synchronous motor with a low carrier ratio, when executing the sensorless control method for a permanent magnet synchronous motor with a low carrier ratio, are only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above.

[0119] The beneficial effects of this invention were verified using a simulation model built in MATLAB / Simulink. The parameters of the permanent magnet synchronous motor used were: rated speed 3000 rpm, rated frequency 250 Hz, d-axis inductance 4.7 mH, q-axis inductance 6.7 mH, stator resistance 0.93 Ω, permanent magnet flux linkage 0.053 Wb, number of pole pairs 5, and both sampling frequency and switching frequency 2.5 kHz.

[0120] Figure 8 This presents experimental comparisons of the actual speed, estimated speed, and position estimation error of a permanent magnet synchronous motor under acceleration conditions, with the speed increasing from 1000 rpm to 2000 rpm and then to 3000 rpm. Figure 8 (a) and Figure 8 As shown in (b), the maximum position estimation error of both the traditional linear extended state observer and the complex coefficient adaptive extended state observer increases with increasing rotational speed throughout the dynamic process, with maximum position estimation errors of 93.6 degrees and 24.7 degrees, respectively. Figure 8 As shown in (c), after adopting the discrete domain adaptive extended state observer, the rotor position error does not increase with the increase of motor speed. The maximum position estimation error is limited to 0.67 degrees throughout the dynamic process, indicating that the discrete domain adaptive extended state observer can effectively improve the dynamic response capability of sensorless control and suppress the position estimation error generated in the dynamic process.

[0121] Figure 9 The experimental comparison results are used to estimate the position error under a 2A DC disturbance injected into the α-axis current. Figure 9 In Figure (a), the experimental results of the traditional linear extended state observer are shown. After the DC disturbance is injected, the speed and the estimated rotor position error fluctuate significantly. The maximum speed fluctuation is 2.74 rpm, and the steady-state rotor position estimation error is 1.43 degrees, indicating that the traditional linear extended state observer cannot suppress the DC disturbance error in the current. Figure 9(b) shows the experimental results of the complex coefficient adaptive extended state observer. After the DC disturbance was injected, the speed and the estimated rotor position error did not fluctuate significantly. The maximum speed fluctuation was 0.92 rpm, and the steady-state rotor position estimation error was 0.3 degrees. This indicates that the complex coefficient adaptive extended state observer can effectively suppress the DC disturbance error in the current. Figure 9 (c) shows the experimental results of the discrete-domain adaptive extended state observer. After the DC disturbance is injected, the speed and the estimated rotor position error do not fluctuate significantly. The maximum speed fluctuation is 1.2 rpm, and the steady-state rotor position estimation error is 0.95 degrees. This indicates that the discrete-domain adaptive extended state observer can suppress the DC bias of the estimated back EMF caused by the DC bias of the current sampling, thereby improving the accuracy of rotor position estimation.

[0122] The experimental results above show that the sensorless control method for permanent magnet synchronous motors of the present invention can effectively reduce the back EMF estimation error caused by approximate discretization and the low-pass filtering characteristics of traditional linear extended state observers under low carrier ratio conditions. It achieves back EMF estimation without amplitude attenuation and phase lag at the fundamental frequency and suppresses DC bias in the back EMF, thereby reducing rotor position estimation error and improving the accuracy and stability of sensorless control.

[0123] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0124] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A discrete-domain adaptive extended state observer, applied to sensorless control of permanent magnet synchronous motors under low carrier ratio, characterized in that, include: The current error generation unit is used to subtract the estimated current from the measured current to obtain the current observation error. The dual-path correction unit is used to adjust the current observation error by using the current state correction gain and the back EMF state correction gain respectively, and outputs the current state correction signal and the back EMF state correction signal. The current state closed-loop unit is used to combine the current estimated current, measured voltage, current estimated back EMF and current state correction signal to update the estimated current at the next moment, and then feed it back to the current error generation unit after a delay. The back EMF state closed-loop unit is used to combine the current estimated back EMF, the back EMF expansion state discrete rotation factor, and the back EMF state correction signal to update the estimated back EMF at the next moment, and then feed it back to the current state closed-loop unit after a delay. The discrete-domain adaptive extended state observer is constructed using the following method: exist In the axial coordinate system, the back electromotive force of the permanent magnet synchronous motor is taken as the disturbance to be observed, and a complex vector mathematical model of the permanent magnet synchronous motor in the continuous domain is established. Within a single sampling period, the stator voltage and back electromotive force are maintained in segments, and the differential equations of the continuous domain complex vector mathematical model are solved to obtain the discrete model of the permanent magnet synchronous motor. The back EMF of the permanent magnet synchronous motor is used as the extended state variable. Based on the characteristic that the complex vector of the back EMF rotates with the electric angular velocity of the motor, the extended state equation of the back EMF is established. The linear differential equation of the extended state equation of the back EMF is solved in a single sampling period to obtain the discrete expression of the extended state of the back EMF. Based on the discrete model of the permanent magnet synchronous motor and the discrete expression of the back EMF extended state, a dual-state closed-loop extended state observer is constructed in the discrete domain, and the back EMF estimation channel is derived. z Domain transfer function; The extended state observer of the dual-state closed-loop structure is: ， In the formula, and The first The and the first Each sampling time Axis estimation of stator current complex vector, and The first The and the first Each sampling time Axial estimation of back electromotive force complex vector, For the first Each sampling time Axial voltage complex vector For the first Each sampling time Axis current observation error For current state correction gain, This is the gain for back electromotive force state correction. The discrete rotation factor for the back electromotive force expansion state; , , These are the current state transition coefficient, voltage input discrete coefficient, and back EMF input discrete coefficient in the discrete model of the permanent magnet synchronous motor, respectively. for Each sampling time Axial current complex vector; Based on the expression of the extended state observer of the two-state closed-loop structure, the z-domain transfer function of the back EMF estimation channel is derived. for: ， In the formula, z for z Domain complex variables, for z Transformed Shaft back electromotive force, for z Transformed Axial estimation of back electromotive force; Channel estimation based on back electromotive force z The domain transfer function is used to reconstruct the current state correction gain and the back EMF state correction gain through discrete domain zero-pole configuration, respectively; where the back EMF state correction gain is... z Introducing a zero at the DC frequency point in the domain, the current state correction gain is at... z The domain introduces the conjugate complex poles corresponding to the fundamental frequency of the motor operation, and makes the back EMF estimation channel satisfy unity gain and zero phase lag at the fundamental frequency of the motor, forming the center frequency adaptive bandpass filter characteristic, thus completing the construction of the discrete domain adaptive extended state observer. To ensure that the z-domain transfer function of the back EMF estimation channel possesses bandpass filtering characteristics, a target transfer function with bandpass filtering characteristics is constructed. for: ， In the formula, The gain of the discrete-domain extended state observer; The expressions for the gain, current state correction gain, and back EMF state correction gain of the discrete-domain extended state observer are as follows: ， In the formula, The sampling period is This is an estimated value for the motor speed. It is the imaginary unit.

2. The discrete-domain adaptive extended state observer according to claim 1, characterized in that, The continuous domain complex vector mathematical model of a permanent magnet synchronous motor is as follows: ， In the formula, For differential operators, Represents time, and for shaft current, and for shaft voltage, and for Shaft back electromotive force, and These are the coefficients of the continuous-domain complex vector mathematical model of the permanent magnet synchronous motor. For stator resistance, and These are the d-axis inductance and the q-axis inductance, respectively. It is a complex vector of current. for Axial voltage complex vector for Axial back electromotive force complex vector.

3. The discrete-domain adaptive extended state observer according to claim 2, characterized in that, In the Within each sampling period, if the voltage is considered as a zero-order hold signal, then the voltage and back electromotive force are expressed as: ， ， In the formula, , For sampling sequence number, For the first Each sampling time Axial voltage complex vector For the first Each sampling time The back electromotive force of the axis is a complex vector. This refers to the motor speed; The discrete model of the permanent magnet synchronous motor is as follows: ， In the formula, For the first Each sampling time The axis current complex vector, where, ， In the formula, This represents the base of the natural logarithm. This is an intermediate coefficient related to the salient pole characteristics of the motor. This is an intermediate coefficient related to the stator resistance attenuation characteristics. and These are the transitional combination coefficients in the discretization derivation process.

4. The discrete-domain adaptive extended state observer according to claim 3, characterized in that, The discrete expression for the back electromotive force expansion state is: ， In the formula, For the first Each sampling time The back electromotive force of the axis is a complex vector. This represents the differential component of the disturbance caused by the amplitude change.

5. A sensorless control method for a permanent magnet synchronous motor with a low carrier ratio, characterized in that, The method includes: Obtain permanent magnet synchronous motor Shaft voltage and current signals; permanent magnet synchronous motor The shaft voltage and current signals are used as inputs, and the back electromotive force vector of the motor is obtained through the discrete domain adaptive extended state observer as described in claim 1. The motor speed and position signals are estimated using a phase-locked loop based on the motor's back electromotive force vector; The motor speed and position signals are input to the motor closed-loop control system to achieve sensorless closed-loop control of the permanent magnet synchronous motor.

6. A sensorless control device for a permanent magnet synchronous motor with a low carrier ratio, characterized in that, The device includes: The acquisition module is used to acquire information about permanent magnet synchronous motors. Shaft voltage and current signals; The discrete-domain adaptive extended state observer of claim 1 is used to observe the permanent magnet synchronous motor. The back electromotive force vector of the motor is obtained by taking the shaft voltage and current signals as inputs. The motor speed and position signal estimation module is used to estimate the motor speed and position signals based on the back electromotive force vector of the motor using a phase-locked loop; The motor speed and position signal transmission module is used to input the motor speed and position signals to the motor closed-loop control system to realize sensorless closed-loop control of the permanent magnet synchronous motor.

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