阅读说明：本技术 利用pwm引起的伪像对交流电动机进行无传感器pwm控制的变速驱动器 (Variable speed drive for sensorless PWM control of an AC motor using PWM induced artifacts ) 是由 P.库姆斯 D.苏罗普 P.马丁 P.鲁肯 于 2020-09-25 设计创作，主要内容包括：一种用于基于控制律控制电动机(300)的变速驱动器(200),包括用于向电动机(300)输送驱动电压(u-(pwm))的输出端(210)、驱动电压产生功率逆变器(220)、驱动控制器(230)和用于测量由电动机(300)吸收的驱动电流的电流传感器(240),驱动控制器(230)包括PWM发生器(232)、控制律模块(234)和用于估计电动机(300)的状态变量的状态变量估计器(236)。(A variable speed drive (200) for controlling an electric motor (300) based on a control law, comprising means for controlling the electric motor(300) Supply drive voltage (u) pwm ) The drive control system comprises an output (210) of the motor, a drive voltage generating power inverter (220), a drive controller (230) and a current sensor (240) for measuring a drive current absorbed by the motor (300), the drive controller (230) comprising a PWM generator (232), a control law module (234) and a state variable estimator (236) for estimating a state variable of the motor (300).)

1. A variable speed drive (200) for closed loop control of operation of an AC motor (300) based on a given control law, the variable speed drive (200) comprising:

-output terminals (210) for delivering a controlled alternating drive voltage (u) to a controlled AC motor (300)_pwm)；

-a solid state power inverter (220) for generating a drive voltage (u)_pwm)；

-a drive controller (230) for controlling the power inverter (220) to generate a drive voltage; and

-a drive current sensing means (240) for measuring the instantaneous intensity of the drive current absorbed by the controlled AC motor (300) and using the resulting measurement as a drive current intensity signal (i)_s) Is provided to a drive controller (230),

wherein the drive controller (230) comprises:

-a pulse width modulation generator (232);

-a control law module (234) storing a given control law; and

-a state variable estimation module (236) for estimating an instantaneous value of at least one state variable (z) of the controlled AC motor (300),

wherein the control law module (234) is adapted to calculate a target voltage signal (u) based on the stored control laws and the state variable estimation value (z) provided by the estimation module (236)_s) And outputs the calculated target voltage signal to a pulse width modulation generator (232),

wherein the pulse width modulation generator (232) is adapted to:

-approximating the received target voltage signal (u) with a pulse width modulated inverter control signal (M)_s)；

-controlling the operation of the power inverter (220) using the inverter control signal (M) so as to obtain the drive voltage (u)_pwm)；

-based on the inverter control signal (M) and the target voltage signal (u)_s) To calculate a state variable estimation support signal(s)₁) (ii) a And

-estimating a support signal(s) from the calculated state variables₁) Output to a state variable estimation module (236), an

Wherein the state variable estimation module (236) is adapted to:

-estimating a support signal(s) based on the received state variables₁) And a drive current strength signal (i) provided by the drive current sensing means (240)_s) To estimate instantaneous values of state variables (z) of the AC motor (300); and

-outputting the obtained state variable estimate (z) to the control law module (234).

2. The variable speed drive (200) of claim 1, wherein the pulse width modulation generator (232) is adapted to calculate a state variable estimation support signal(s) based on a pulse width modulation intrinsic disturbance signal₁) Said pulse width modulated natural disturbance signal being generated by subtracting a target voltage signal (u) from an inverter control signal (M)_s) And then obtaining the product.

3. The variable speed drive (200) of claim 2, wherein the pulse width modulation generator (232) is adapted to calculate a state variable estimation support signal(s) by integrating the disturbance signal to obtain a primitive of the disturbance signal₁)。

4. The variable speed drive (200) according to any of the preceding claims, wherein the variable speed drive is adapted to perform closed loop control of the AC motor (300) in dependence of a single feedback, i.e. the drive current strength signal (i) provided by the drive current sensing means_s)。

5. The variable speed drive (200) according to any of the preceding claims, wherein the variable speed drive is adapted to control the operation of the AC motor (300) without injecting a dedicated detection signal to the drive voltage (u)_pwm) In (1).

6. The variable speed drive (200) of any of the preceding claims, wherein the drive controller (230) further comprises an analog-to-digital converter (238), the analog-to-digital converter (238) being configured to drive the current intensity signal (i)_s) The state variable estimate module (236) converts it to a digital signal before input to it.

7. The variable speed drive (200) according to any of the preceding claims, wherein the state variable estimation module (236) is adapted to estimate a support signal(s) based on the received state variable₁) And a drive current strength signal (i) provided by said drive current sensing means_s) An instantaneous value of the rotor position of the motor (300) is estimated.

8. The variable speed drive (200) of any of the preceding claims, wherein the pulse width modulation generator (232) is adapted to apply a three-phase pulse width modulation with a single carrier to generate the inverter control signal (M).

9. The variable speed drive (200) of any of claims 1-7 wherein the pulse width modulation generator (232) is adapted to apply three-phase pulse width modulation with interleaved carriers to generate the inverter control signal (M).

10. An electric drive assembly (100) comprising a synchronous reluctance motor (300) and a variable speed drive (200) according to any of the preceding claims for controlling the synchronous reluctance motor.

11. An electric drive assembly (100) comprising a permanent magnet synchronous motor (300) and a variable speed drive (200) according to any of the preceding claims for controlling the permanent magnet synchronous motor.

12. A method of controlling operation of an AC electric motor (300) in a closed loop based on a given control law, the method comprising the steps of:

a) measuring the instantaneous intensity (i) of the drive current absorbed by the controlled AC motor (300)_s)；

b) Using measured drive current intensity (i)_s) To estimate instantaneous values of state variables (z) of the AC motor (300);

c) calculating a target voltage signal (u) based on a given control law and an estimated state variable (z)_s)；

d) Approximating a calculated target voltage signal (u) with a pulse width modulated inverter control signal (M)_s)；

e) Based on the inverter control signal (M) and the target voltage signal (u)_s) To calculate a state variable estimation support signal(s)₁)；

f) Generating a controlled alternating drive voltage (u) by voltage inversion using an inverter control signal (M)_pwm) (ii) a And

g) the generated driving voltage (u)_pwm) To a controlled AC motor (300);

wherein the state variable estimation according to step b) depends on the state variable estimation support signal(s) calculated in step e) as an additional input₁) And the drive current intensity (i) measured in step a)_s)。

Technical Field

The present disclosure relates generally to the field of motor control. More specifically, it relates to Variable Speed Drives (VSDs) for controlling the operation of Alternating Current (AC) motors. The emphasis is a VSD that relies on Pulse-Width Modulation (PWM) to continuously control the speed of a controlled AC motor.

VSDs are commonly used as industrial drives in plants, facilities, HVAC systems, and the like, for controlling the position, speed, and/or torque of, for example, a motor dedicated to a particular task, such as operation of a fan or lifting of a load.

Background

To perform closed loop control of an AC motor, a VSD needs to have real-time information about the operating state of the AC motor. This information can be, for example, the instantaneous angular position and/or angular speed of the motor rotor.

The VSD can obtain this information from dedicated sensors disposed on the motor and monitoring the operating state of the motor. However, mounting such sensors to the motor adds complexity and size to the overall drive assembly. The required sensors and sensor wiring also increase the price and reduce reliability.

This is why so-called "sensorless" VSDs are becoming more and more popular. In these sensorless VSDs, the operating state of the motor is estimated based on measurements of the drive current of the motor. No additional external sensors are used. To improve the estimation, especially when the motor is operating at low speed, it is a standard procedure to inject an external high frequency probe signal into the drive voltage of the motor.

The article "Adding virtual measurements by signal information" published in the discourse (pages 999 and beyond) of the Pascal Combes et al, 2016 U.S. conference of control conceptualizes and summarizes the signal injection technique for sensorless control of motors at low speeds.

Signal injection is an effective method, but it comes at a cost: the ripple (ripple) it generates may actually generate unpleasant acoustic noise and give rise to unmodeled dynamics. In particular, in the case of very common motors fed by a PWM inverter, the frequency of the injected detection signal may not be as high as desired in order not to interfere with PWM (in general, in industrial drives with a PWM frequency of 4kHz, it cannot exceed 500 Hz).

Wang et al, article "a novel approach for sensorless control of PM machines down to zero speed with signal information or specific PWM technique" (IEEE electric and electronic institute of electrical and electronic products, volume 19, 6 th, 11 months 2004, page 1601 and beyond) proposes to measure the phase current ripple caused by conventional PWM to derive the rotor position and speed of a PWM controlled motor. However, this method is based on measurement of the current derivative, which requires a dedicated current sensor and is sensitive to noise.

Disclosure of Invention

In view of the above, it is an object of the present disclosure to provide a PWM-based variable speed drive with improved sensorless AC motor control without signal injection.

According to the present disclosure, this object is achieved with a variable speed drive for closed loop control of operation of an AC motor based on a given control law, the variable speed drive comprising:

-output terminals for delivering a controlled alternating current drive voltage to a controlled AC motor;

-a solid state power inverter for generating a drive voltage;

-a drive controller for controlling the power inverter to generate a drive voltage; and

-drive current sensing means for measuring the momentary strength of the drive current absorbed (take up) by the controlled AC motor and providing the resulting measurement as a drive current strength signal to the drive controller,

wherein the drive controller includes:

-a pulse width modulation generator;

-a control law module storing a given control law; and

a state variable estimation module for estimating an instantaneous value of at least one state variable of the controlled AC motor,

wherein the control law module is adapted to calculate a target voltage signal based on the stored control laws and the state variable estimation values provided by the estimation module, and to output the calculated target voltage signal to the pulse width modulation generator,

wherein the pulse width modulation generator is adapted to:

-approximating the received target voltage signal with a pulse width modulated inverter control signal;

-controlling the operation of the power inverter using the inverter control signal, thereby obtaining a drive voltage;

-calculating a state variable estimation support signal based on a deviation between the inverter control signal and the target voltage signal; and

-outputting the calculated state variable estimation support signal to a state variable estimation module, and

wherein the state variable estimation module is adapted to:

-estimating an instantaneous value of a state variable of the AC motor based on the received state variable estimation support signal and the drive current strength signal provided by the drive current sensing device; and

-outputting the obtained state variable estimation values to the control law module.

By modifying the PWM generator to calculate the estimation support signal based on PWM and by providing the estimation support signal to the state variable estimator, the state variable estimator has its complementary information available to improve its state variable estimation.

Alternatively, the variable speed drive according to the present disclosure may have the following features, alone or in combination with other features:

-the pulse width modulation generator is adapted to calculate the state variable estimation support signal based on a pulse width modulated intrinsic disturbance signal obtained by subtracting the target voltage signal from the inverter control signal;

-the pulse width modulation generator is adapted to calculate the state variable estimation support signal by integrating the disturbance signal to obtain a primitive (primary) of the disturbance signal;

the variable speed drive is adapted to perform a closed loop control of the AC motor in dependence of a single feedback, i.e. the drive current strength signal provided by the drive current sensing means;

-the variable speed drive is adapted to control operation of the AC motor without injecting a dedicated probing signal into the drive voltage;

the drive controller further comprises an analog-to-digital converter for converting the drive current strength signal into a digital signal before inputting it to the state variable estimation module;

-the state variable estimation module is adapted to estimate an instantaneous value of the rotor position of the electric motor based on the received state variable estimation support signal and the drive current strength signal provided by the drive current sensing means;

-the pulse width modulation generator is adapted to apply a three-phase pulse width modulation with a single carrier for generating the inverter control signal;

-the pulse width modulation generator is adapted to apply three-phase pulse width modulation with interleaved carriers to generate the inverter control signal.

According to another aspect, the present disclosure also relates to an electric drive assembly comprising a synchronous reluctance motor or a permanent magnet synchronous motor and a variable speed drive as described above for controlling the motor.

According to yet another aspect, the present disclosure also relates to a method of controlling operation of an AC motor in a closed loop based on a given control law, the method comprising the steps of:

a) measuring the instantaneous intensity of the drive current absorbed by the controlled AC motor;

b) estimating instantaneous values of state variables of the AC motor using the measured drive current intensities;

c) calculating a target voltage signal based on a given control law and an estimated state variable;

d) approximating the calculated target voltage signal with a pulse width modulated inverter control signal;

e) calculating a state variable estimation support signal based on a deviation between the inverter control signal and the target voltage signal;

f) generating a controlled ac drive voltage using an inverter control signal by voltage inversion; and

g) delivering the generated drive voltage to a controlled AC motor;

wherein the state variable estimation according to step b) depends on the state variable estimation support signal calculated in step e) as an additional input and on the drive current strength measured in step a).

Drawings

Other features, details and advantages will be apparent from the following detailed description and the accompanying drawings, in which:

FIG. 1 is a block diagram of an electric drive assembly of the present disclosure having a variable speed drive and an AC motor.

FIG. 2 is a block diagram illustrating signal flow and processing in the electric drive assembly of FIG. 1.

FIG. 3 is a block diagram illustrating a comparison of u with c to generate u according to an embodiment of the disclosure_pwmU, c and u in PWM process of (1)_pwmSchematic representation of (a).

Fig. 4 is a diagram illustrating s for u-0, 0.2, 0.4 according to an embodiment of the present disclosure₀(u,. above) and s₁(u, ·) (middle) and W (below).

FIG. 5 is a diagram illustrating a state x utilizing an ideal control law and utilizing an actual control law according to an embodiment of the present disclosure₁、x₂And x₃Schematic representation of (a).

FIG. 6 is a block diagram illustrating a control input u and its modulation u corresponding to the case of FIG. 5, according to an embodiment of the present disclosure_pwmA full view (above) and an enlarged view (below).

Fig. 7 is a schematic diagram showing a full view (above) and an enlarged view (below) of the measurement output y corresponding to the case of fig. 5, according to an embodiment of the present disclosure.

Fig. 8 is a schematic diagram showing a full view (top) and an enlarged view (bottom) of the measurement output y with and without noise for testing according to an embodiment of the present disclosure.

FIG. 9 is a block diagram illustrating a situation in the presence of noise according to an embodiment of the present disclosurex₁Andschematic representation of (a).

FIG. 10 is a block diagram illustrating a comparison of u with c to generate u according to an embodiment of the disclosure_pwmU, c and u in PWM process of (1)_pwmSchematic representation of (a).

Fig. 11 is a diagram illustrating s for u-0, 0.2, 0.4 according to an embodiment of the present disclosure₀(u,. above) and s₁(u, ·) (middle) and W (below).

Fig. 12 is a flowchart illustrating single carrier PWM in a case where rank is 2 (upper, without degradation) and in a case where rank is 1 (lower, with degradation) according to an embodiment of the present disclosureSchematic diagram of an example of the shape of (simulation data).

Fig. 13 shows a schematic diagram of the principle of three-phase PWM with interleaved carriers, wherein the three interleaved carriers are identified with thinner solid, dashed and dotted lines, respectively (top), the same reference is identified with a thick solid line (top), which produces different PWM signals corresponding to the three interleaved carriers, identified with thinner solid, dashed and dotted lines (bottom), according to an embodiment of the disclosure.

FIG. 14 is a block diagram illustrating for interleaved PWM according to an embodiment of the present disclosureSchematic of examples of (simulated data) shapes, more or less seenAppearing as two orthogonal signals.

FIG. 15 is a graph illustrating results obtained by simulating cos 2 θ (above) and sin 2 θ (below) through a reconstruction process according to an embodiment of the disclosure(above) andschematic of (below).

FIG. 16 is a diagram illustrating results obtained by simulating θ (in radians) through a reconstruction process according to an embodiment of the disclosure, including θ and its reconstruction resultsAnd the difference between the twoCurve (lower).

FIG. 17 is a block diagram illustrating an embodiment of the present disclosureIs 2 (upper, without degradation) and when the rank is 1 (lower, with degradation), the ripple envelope of single carrier PWM under substantially the same conditions as in fig. 12Schematic representation of (experimental data).

FIG. 18 is a graph illustrating measured current according to an embodiment of the disclosureAnd a filtered measurement currentSchematic representation of (experimental data).

FIG. 19 is a graph showing a pair of cos 2 θ (top) according to an embodiment of the present disclosureAnd sin 2 theta (lower) results(above) and(bottom) (experimental data).

Fig. 20 is a diagram illustrating a result (experimental data) obtained by reconstructing θ (in radians) according to an embodiment of the present disclosure, including θ and a reconstruction result thereofAnd the difference between the twoCurve (lower).

FIG. 21 is a block diagram illustrating a saliency matrix being reconstructed according to an embodiment of the present disclosureSchematic representation of results obtained from performing simulations, including significance matrixEach component s of₁₁、s₁₂、s₂₁、s₂₂And corresponding reconstructed resultsCurve (c) of (d).

Fig. 22 is a diagram showing a result (in the case where a carrier is shifted) obtained by simulating a rotor position θ through a reconstruction process according to an embodiment of the present disclosure, including θ and an estimated value thereofAnd the difference between the twoCurve (lower).

Detailed Description

I. Exemplary arrangement of a variable speed drive according to the present disclosure

Fig. 1 is a schematic diagram of an electric drive assembly 100 according to the present disclosure. Electric drive assembly 100 includes a variable speed drive (or VSD)200 and an AC motor 300.

The electric drive assembly 100 may be used in various industrial environments. For example, it may drive a fan of a Heating Ventilation and Air Conditioning (HVAC) system. As another example, it may also be used to drive a water pump of a sewage plant. The skilled person can envision many other industrial applications.

Preferably, AC motor 300 is a synchronous motor, such as a permanent magnet synchronous motor (or PMSM), or a synchronous reluctance motor (or SynRM).

The purpose of variable speed drive 200 is to control the proper operation of motor 300. Due to the variable speed drive 200, the motor 300 can operate at the correct speed at the correct time, depending on the application. Variable speed drive 200 may also allow control of the torque output of motor 300 to its load.

Variable speed drive 200 controls motor 300 in a closed loop. This means that during control of the motor, the variable speed drive 200 is constantly receiving feedback on the instantaneous state of the motor 300. Variable speed drive 200 regulates its control of motor 300 based on a given control law. The details of the control law depend on the type of application of the motor 300.

Referring to fig. 1, variable speed drive 200 includes output terminals 210, solid state power inverter 220, drive controller 230, and drive current sensing device or current sensor 240.

The variable speed drive 200 is electrically connected to the motor 300 via its output terminal 210. Power output 210 delivers a controlled AC drive voltage u to AC motor 300_pwm. Drive voltage u_pwmIs a modulated signal whose amplitude is determined by the DC voltage Vbus applied to the power inverter 220. Drive voltage u_pwmDepends on the switching frequency of power inverter 220. ModulationDrive voltage u_pwmAn ideal sinusoidal drive voltage is simulated, the amplitude and frequency of which determine the operation of the motor 300.

The power inverter 220 generates the drive voltage u by chopping (chopping up) the DC voltage by means of the solid-state switches T1, T2_pwm。

The skilled person will note that the diagram of fig. 1 shows a single phase control. This is for simplicity only. Typically, the motor 300 will be a three-phase motor. In this case, the power inverter 220 generates a driving voltage for each of the three phases of the motor.

The current sensor 240 of the VSD 200 measures the instantaneous intensity of the drive current drawn by the motor 300. The current sensor 240 takes the measurement result thereof as a drive current intensity signal i_sIs provided to the drive controller 230.

According to the present disclosure, the motor control performed by the VSD 200 is so-called "sensorless" control. This means that the control feedback is completely dependent on the current measurement provided by the current sensor 240. No external sensors (such as shaft encoders) are mounted on the motor 300 to provide feedback to the VSD 200 regarding the state of the motor.

Drive controller 230 controls power inverter 220 to generate drive voltage u_pwm. This is done based on the inverter control signal M provided to the power inverter 220 by the drive controller 230.

The drive controller 230 may be implemented as a microcontroller or a Field Programmable Gate Array (FPGA).

In accordance with the present disclosure, the drive controller 230 includes a pulse width modulation (or PWM) generator 232, a control law module 234 that stores a given control law, a state variable estimation module 236, and an analog-to-digital converter (or ADC) 238.

The control law module 234 is adapted to be based on the stored control laws and the state variable estimate z provided by the estimation module 236₀To z_nTo calculate a target voltage signal u_sAnd the calculated target voltage signal u_sTo the PWM generator 232.

Target voltage signal u_sThe representation must be applied to electric driveThe stator windings of the machine 300 are wound to obtain an analog voltage of a desired speed or torque from the motor 300.

Since the variable speed drive 200 relies on pulse width modulation, the target voltage signal u_sNot directly applied to the motor 300. Instead, it is fed to the PWM generator 232 to be approximated by a pulse width modulated inverter control signal M, which in turn is used to control the power inverter 220.

The pwm generator 232 may apply three-phase pwm with single carrier to generate the inverter control signal M (i.e., the target voltage signal u)_sApproximate of (d).

Alternatively, the PWM generator may also apply three-phase pulse width modulation with interleaved carriers to generate the inverter control signal M.

The PWM generator 232 may of course use other PWM schemes to generate the inverter control signal M.

According to the present disclosure, the PWM generator 232 has a characteristic that it is based on the inverter control signal M and the target voltage signal u_sTo calculate a state variable estimation support signal s₁And estimating the calculated state variable by a support signal s₁Output to the state variable estimation module 236.

The state variable estimation module or estimator 236 is based on a drive current strength signal i provided by a drive current sensor 240_sTo estimate instantaneous values of one or more state variables of AC motor 300.

As shown in fig. 1 and 2, the estimator 236 may estimate several state variables z₀To z_n. These state variables may for example correspond to the rotor position of the motor, the angular velocity of the motor rotor, etc.

According to the present disclosure, estimator 236 also uses the estimation support signal s₁To estimate the state variable z₀To z_nA value of at least one of.

Estimator 236 provides state variable estimate z to control law module 234₀To z_n. Control law module 234 uses these estimates in a stored control law to determine a target voltage signalNumber u_s。

As shown, drive controller 230 may also include an analog-to-digital converter 238. The purpose of the ADC 238 is to convert the analog current signal i provided by the current sensor 240 into an analog current signal_sInto a digital signal that can be processed by the estimator 236.

Fig. 2 illustrates signal flow between different components of the electric drive assembly 100 of fig. 1. PWM generator 232 receives the target voltage signal u from control law module 234_s. Using pulse width modulation, which approximates the target voltage signal u by means of the inverter control signal M (u, t/epsilon)_s. The inverter control signal M is fed to the power inverter 220. Based on the control signal M, the inverter 220 supplies a drive voltage u to the motor 300_pwm. The current in the motor stator windings is measured and digitized in the ADC 238 using the current sensor 240. The digitized current signal is then fed to an estimator 236. The estimator 236 also receives an estimation support signal s from the PWM generator 232₁(u, t/ε). The estimator 236 provides different motor state variables z based on the received input₀To z_nAn estimate of (d).

An important aspect of the present disclosure is an enhanced PWM generator 232 that generates not only the inverter control signal M, but also the state variable estimation support signal s₁. By estimating the supporting signal s₁The estimation module 236 may derive the current signal i from_sTo extract supplemental information to improve state variable estimation.

PWM generator 232 is based on pulse width modulation intrinsic disturbance signal s₀To calculate a state variable estimation support signal s₁. In fact, the present disclosure relies on the recognition that the inverter control signal M generated by the PWM generator 232 can be modeled as a target voltage signal u_sAnd a disturbance signal s₀And (3) superposition. In practice, the inverter control signal M is a series of rectangular voltage pulses of different widths, which on average correspond to the desired target voltage signal u_s. In other words, the inverter control signal M may be considered as a desired target voltage signal u with the voltage "ripple" added thereto_s. Such ripple or PWM disturbances in the voltageA disturbance in the stator flux of the machine 300 is generated, which in turn generates a measured current i_sTo generate a disturbance.

The present disclosure takes advantage of this unintended side effect of pulse width modulation. The ripple/artifact caused by the pulse width modulation in the measured current is used for state variable estimation. This improves the estimate and thus the control of the motor 300.

Pulse width modulated disturbance signal s₀(i.e. ripple) measurement may be obtained by subtracting the target voltage signal u from the inverter control signal M_sTo obtain the final product. Target voltage signal u_sAnd the inverter control signal M may then be integrated to obtain the disturbance signal s₀S of₁。

These calculations, i.e., subtraction and integration, are performed by the PWM generator 232. As shown, PWM generator 232 will output result s₁Is provided to the estimator 236.

It can be seen mathematically (see the remainder of this disclosure) that the primitive s₁Is a useful input to estimator 236 for determining instantaneous values of state variables of motor 300, such as rotor position theta.

The variable speed drive of the present disclosure is particularly useful for control of synchronous motors at low speeds. By properly using the excitation provided by the pulse width modulation itself, the variable speed drive of the present disclosure has the same advantages as a conventional variable speed drive that relies on an external excitation signal without the disadvantages of increased acoustic noise and potential interference with the pulse width modulation.

In the variable speed drive of the present disclosure, the standard pulse width modulation need not be modified.

Further, the estimation by the estimation module 236 requires only current measurements from standard current sensors. There is no need to make current measurements at extremely precise times, which are prone to measurement errors and are highly impractical in industrial drives.

Furthermore, the variable speed drive of the present disclosure also does not require a dedicated sensor capable of measuring the current derivative, as other known solutions do.

The teachings of the present disclosure may also be applied to the control of other types of actuators. For example, one may think of controlling the operation of an electromagnet in a magnetic bearing, or the operation of a solenoid valve of a hydraulic or pneumatic cylinder.

Mathematical derivation of an exemplary estimator for sensorless motor control

Control system taking into account modeling by evolutionary equations

y_a＝h(z) (1)

Where z is the internal state vector of the system, u is the control input vector, y_aIs a measurement vector. In some practical applications (particularly electromechanical devices fed by PWM inverters), the control input is not applied directly, but by fast periodic modulation, which produces only a mean value of u. Thus, the actual system is

y＝h(x)

Where x is the state vector of the system perturbed by the modulator and y is the corresponding measurement. E > 0 is a known very small number,is periodic by 1 (1-period) with respect to its second argument and has a mean value u, i.e.Andthe system can be clearly written as

y＝h(x)

Wherein, byDefined s₀Is periodic by 1 with respect to its second argument and has a zero mean, s₀(v，σ)＝s₀(v, σ +1) andin other words, consider a generalized class of signal injection, where the signal s is detected₀Generated by the modulation process itself; note s₀Depending on u, this poses several difficulties.

Due to mathematical analysis based on the theory of second order averaging, it can be shown that the measurement signal y can be written as

Wherein, byDefined s₁Is s₀Zero mean primitive, u is considered a parameter; "actual measurement result" y_aAnd "virtual measurement results"Can be interpreted as the output of an "ideal" system without modulation (1), i.e.

y_a＝h(z) (2)

Note that the square matrixAre generally reversible (see below) "Multiphase PWM "), so we have y_v＝h′(z)g(z)。

The general object of the invention is to extract from the measurement signal y that can be used in a control system_aAnd y_vAn estimate of (d). All that then seems to be the control of an "ideal" system without modulation (1) with a feedback law (feedback law) that depends not only on the "actual measurements" (2) but also on the "virtual measurements" (3). Then, the problem is simpler due to the supplementary information (3); in particular, in the case of a sensorless controlled motor at a low speed, the supplementary information is important in the design of the control law since it gives the rotor position. The invention mainly consists of two parts:

1) enhanced modulator not only generating a modulated signalAnd also produces s₀Zero mean primitive s₁；

2) EstimatorAnduse thereof s₁Not only extracting y from the measurement signal y_aAlso extract y_v。

One possible implementation of the estimator is

Which is related to the desired signal by

Note that these estimators are periodic low-pass filters with FIR (finite impulse response); many variations are possible that rely on different periodic low-pass FIR filters.

Pulse Width Modulation (PWM)

Generating an analog physical power signal is extremely impractical because a large amount of power must be consumed in the amplifier. Pulse Width Modulation (PWM) solves this problem by using transistors in saturation mode. In practice, the transistor is more efficient to use when in saturation than when in its linear range. The desired value is achieved in the form of an average value by adjusting the width of the pulse (hence the name of the technique).

The simplest way to implement a PWM modulator is to couple the analog signal u to the on-u_maxAnd u_maxThe triangular carrier c oscillating in between is compared as follows:

wherein

This is the natural sampling PWM illustrated in fig. 10, where the carrier is printed in "horizontal lines", the analog signal is printed in "dashed short lines", and the PWM signal is printed in "dotted dot lines".

One of the disadvantages of naturally sampled PWM is that the pulses are asymmetric. To solve this problem, the analog signal may be first sampled to obtain u [ k ] ═ u (kt), and then PWM modulation is applied to the sampled signal, as shown in fig. 11, where the analog signal is a solid line and the sampled analog signal is a dashed short line. With this PWM scheme, it can be checked

u_PWMCan be rewritten intoIn the form of (1), wherein

Which is a fast varying periodic signal with zero mean depending on the control.

Multiphase PWM

When controlling a poly-phase electrical device, the analog reference n > 1 must be modulated.

In this case, s₁It will be a vector with n rows,is an n x n matrix.

Traditionally, for ease of implementation, the n modulators use the same carrier. In this case, when two of the references are equal, this control scheme results in s₁Of the two equal components, which means thatWill be irreversible, meaning that all the information in h' (z) g (z) is not obtained. In addition, when the two components are close to each other,the adjustment will be poor, which complicates the signal processing.

In order to obtain more information and improveThe adjustment of (2) may use a different carrier for each reference. In thatIn this case, s₁Are always independent. Thus, a matrixIs always reversible and well regulated.

Use of sensorless control of unsaturated synchronous reluctance motors (SynRM)

Using Clarke transformation matrix

And rotating

The model of a synchronous reluctance motor (SynRM) is given by

The state of the system is phi_SDQ(vector of stator flux in field orientation DQ coordinate system (frame)) and θ (angular position of rotor). Vector u of stator voltages in physical abc coordinate system_SabcIs a control input and the rotor speed omega is a disturbance input that must be obtained to achieve proper control of the SynRM. When using "sensorless" control, the only measurement available is the vector iota of the stator current in the physical abc coordinate system_Sabc. The parameter of the model is the stator resistance R_sAnd an inductance matrix

Since PWM is used, the voltage can be written as

On a time scale σ: rewrite the system for t/e to obtain

This is like the standard form of averaging. Applying an averaging process, it can be shown that PWM perturbations in the voltage produce perturbations in the stator flux, which becomeWhereinIs thatWhich is zero mean in the PWM method. The flux disturbance in turn generates a disturbance in the measurement current, which becomes

Undisturbed variable follows the original model

Thanks to the proposed estimator, providedIs reversible (see "multiphase PWM" above), can be derived from iota_SabcMiddle recoveryAndthis allows operation according toComputingAnd can use the original control lawTaking θ, as can be done with HF implantation, does not require additional perturbation.

1. Adding virtual measurement results (Dilshad Surroop) by PWM-induced signal injection^1，2、Pascal Combes²、Philippe Martin¹And Pierre Rouchon¹)

Abstract-it is shown that for PWM operated devices, signal injection without an external probe signal can be benefited by appropriate use of the excitation provided by the PWM itself. As in the general signal injection framework conceptualized in [1], additional "virtual measurements" can be provided for control laws, but without the practical drawbacks caused by external signals.

I. Introduction theory

Signal injection is a control technique that involves adding a rapidly varying probing signal to the control input. This excitation produces very little ripple in the measurement, which, if decoded properly, contains useful information. [2] This idea is introduced in [3] for controlling the motor at low speed using only the measurement result of the current. This was later conceptualized in [1] as a way of generating "virtual measurements" that can be used to control the system, particularly to overcome observability degradation. Signal injection is a very efficient method, see for example the application of this method to electromechanical devices in [4], [5], but this is at a cost: the ripple it generates may actually generate unpleasant acoustic noise and give rise to unmodeled dynamics, especially in the very common case of devices fed by Pulse Width Modulation (PWM) inverters; in practice, the frequency of the probing signal may not be as high as desired in order not to interfere with PWM (typically, in industrial drives with 4kHz-PWM frequency, the frequency of the probing signal cannot exceed 500 Hz).

The purpose here is to show that for PWM operated devices, by appropriate use of the excitation provided by the PWM itself, it is possible to benefit from signal injection without an external probe signal, as used in [6 ]. More precisely, consider a single input single output system

y＝h(x)， (1b)

Where u is the control input and y is the measurement output. Sections 1-II first show that when controlled by PWM plus (impress), the dynamics can be written as

Wherein s is₀With a period of 1 and zero mean in the second argument, i.e. for all u, s₀(u，σ+1)＝s₀(u, σ) andε is the PWM period, so it is assumed to be small. Unlike the usual signal injection, the detection signal s is generated by a modulation process₀Now not only on the time but also on the control input u. This makes the situation more complicated, in particular because s₀May be discontinuous in both of its arguments. However, it is shown in sections 1-III that [1]The second order averaging analysis of (a) can be extended to this case. In the same manner, in sections 1 to IV, [1] is indicated]May be adapted to provide in addition to the actual measurement y_a：＝H₀(x) The method comprises the following steps So-called virtual measurement results other than h (x)

y_υ：＝H₁(x)：＝εh′(x)g(x)，

This additional signal would likely simplify the design of the control law, as shown in the numerical example of sections 1-V.

Finally, some definitions used throughout are listed; s represents a function of two variables, which in the second argument is periodic by T, i.e. S (ν, σ + T) is S (ν, σ) for all v:

the mean of S in the second argument is (with one variable) a functionIf S is constantly zero, S has a zero mean in the second argument

If S has a zero mean in the second argument, its zero mean in the second argument is originally defined as follows

Note that S₁In the second argument is the periodIs T because S has a zero mean in the second argument.

The moving average value M (k) of k is determined by

·A uniform "large O" symbol representing the analysis, i.e., for epsilon small enough, if | f (z, epsilon) | ≦ K ε^pThen, thenWhere K > 0 is independent of z and ε.

PWM induced signal injection

When the control input u in (4) is applied by a PWM process with a period ε, the resulting dynamic behavior is recorded as

Wherein the content of the first and second substances,in the second argument is period 1 and mean u; is given belowThe detailed expression of (a). Is provided with(3) Apparently takes the form of (2) wherein s₀In the second argument the period is 1 and zero mean.

Period of epsilon and range of [ -u ]_m，u_m]Is obtained by comparing the input signal u with a saw-tooth carrier of period epsilon defined by

Function with period of 1Package is toNormalized time ofIf u changes slowly enough, it will be in timeCrosses carrier c exactly once on each rising and falling ramp, so that

Thus, the PWM encoded signal is given by

FIG. 3 shows signals u, c and u_pwm. Function(s)

This is clearly periodic 1 with respect to its second argument and has a mean value u, thus fully describing the PWM process, since

Finally, the resulting zero-mean detection signal is

And the zero mean primitive in the second argument is

Note 1: because of s₀But only piecewise continuous, one may expect the problem of defining a "solution" for (2). However, as described above, if the input u (t) to the PWM encoder changes slowly enough, its outputThere will be exactly two breaks in each PWM period. Therefore, tremor (chattering) is excluded, which is sufficient to ensure the existence and uniqueness of the solution of (2), see [7 ]]Without the need for more general Filipov theory [8]. Of course, assume (without loss of generality in practice) that f, g, and h in (1) are sufficiently smooth.

Note that s₁C, continuous and segmented in both its arguments¹. Regularity in the second argument is expected since s₁(u,. is) s₀(u, ·) original; on the other hand, regularity in the first argument is derived from s₀In particular forms thereof.

Average and PWM induced injection

Section 1-III-A outlines the overall approach and states the main theorem 1, which is demonstrated in section 1-III-B, which is somewhat technical. In fact, proofs can be skipped without losing mainlines; so to say, if s₀Lipschitz, in the first argument, proved to be essentially a pass through [1]]The "standard" second order average of (a), which involves more computation.

A. Main results

Assuming that a suitable control law has been designed

Wherein the content of the first and second substances,for the system

By "suitable" is meant that the resulting closed loop system

Has the required stable performance of index. Has already been usedThe notation of the variables was changed to easily distinguish the following solution of (4) and solution of (7). Of course, this describes an unrealistic situation:

PWM is not considered

The control law is not implementable, since it uses not only the actual outputBut also using virtual outputs that are not available a priori

Now define (depending on)) Function(s)

Wherein s is₁Is s₀Zero mean primitive in the second independent variable, taking into account the control law

The resulting closed loop system including PWM is noted

Although PWM is now considered, the control law (6) still seems to contain an unknown term. However, it is achievable as will be seen from the results below.

Theorem 1: let (x), (t), η (t)) be from (x)₀，η₀) The solution of (7) at the beginning, defining u (t): α (η (t), H (x (t)), t) and y (t): h (x (t)); is provided withIs a slave (x)₀-εg(x₀)s₁(u(0)，0)，η₀) Solution of (4) from the beginning, definitionThen, for all t ≧ 0,

the practical meaning of the theorem is as follows. Since the solution (x (t), η (t))) is a piecewise C¹Derived by Taylor expansion using (8a) - (8b)In the same way, since s₁C, also segmented¹To obtain

Thus, it is possible to reverse (8a) - (8b) to obtain

Using it in (5) and then obtaining

On the other hand, as will be seen in sections 1-IV, due to (8c), an estimate can be generatedThis means the dynamic (3) of the PWM feedback acted on by the feedback that can be implemented

Behaves exactly as the "ideal" closed loop system (4) except for the presence of small ripple (described by (8a) - (8 b)).

Note 2: note that according to Note 1, (8c) ofAndcan be smoothed as desired (regularity is inherited only from f, g, h, α, a); on the other hand, in the case of a liquid,only continuous and segmented C¹. However, this is sufficient to confirm all taylor expansions performed in the article.

B. Proof of theorem 1

Due to s₀Lack of regularity, must return to chapter [9, 2]]The basis of the second-order averaging theory presented in (with slow time dependence [9, section 3.3]]). Two special definitions are first introduced.

Definition 1: if λ > 0 is present, such that the following equation is satisfied for a sufficiently small ε, the functionThe variation is slow on the average value and,

wherein p, q are continuous and q is bounded; a and T > 0 are arbitrary constants. Note that ifIn the first variable, Lipschitz, it is slowly changing on average. The meaning of this definition is that it consists of s₀And (4) meeting the requirement.

Definition 2: if K > 0 is present, so that for all σ ≧ 0,the average value of the function phi isObviously, if φ isIt has an average value of

Proof of theorem 1 follows the same procedure as [9, chapter 2], but with weaker assumptions. First on a fast time scale σ: rewriting (7) as t/epsilon

Wherein, X: is ═ x, η) and

note that F is periodic 1 in the second argument. Also considered are so-called averaging systems

Wherein the content of the first and second substances,is the mean of F in the second argument.

Defining an approximate identity transform

Wherein the content of the first and second substances,and is

Inverting (13) to obtain

By introduction 1, the transformation will place (11) into

Phi is periodic and zero-mean in the second argument, slowly varying on average, and the average of phi is

Starting from the same initial conditions by way of example 2, the solutions of (12) and (15) areAndsatisfy the requirement of

As a result, from X₀Solution X (σ) of (11) from the beginning and from X₀-εW(X₀0, 0) starting solution of (12)ByTaken together, this is exactly (8a) - (8 b). (8a) was inserted into y ═ h (x) and taylor expansion was performed to obtain (8 c).

Note 3: if s is₀Is differentiable in the first variable, then φ will be Lipschitz and φ will be in (15)Thus [ 9)]The average theory of (2) will apply directly.

Note 4: subsequently, for simplicity, the estimation is only demonstrated on the time scale 1/εAnd [1, appendix]Is exactly the same, a continuation to infinity results from the exponential stability of (4).

In the same way, lemma 2 was shown to have no slow temporal correlation, as in section [9, 3.3], the generalization is obvious.

Introduction 1: the transformation (13) puts (11) in (15), where Φ is periodic and zero-mean in the second argument and varies slowly over the mean, and the mean of Φ is

And (3) proving that: to determineIs calculated as two different methodsdX/d σ of the function of (c). On the one hand, X is replaced by a transformation (13) of X in the closed-loop system (11), and on the other hand, the transformation (13) is differentiated with respect to sigma.

First of all asOf a function ofExactly as in (10), in useReplacement ofAnd in the case of replacement of (9) by (14), it follows

Thus, by Taylor expansion

Wherein, K_αIs bounded. s₀The lack of regularity of (a) hinders further taylor expansion; nevertheless, it is still possible to write

Finally, the (13) is inserted (11) and subjected to Taylor expansion, which, after a tedious but simple calculation, yields

The following notations have been introduced

Now, time differentiation is performed on (13), (13) is noted as

This is achieved

Because of the fact thatNow assume thatSatisfy the requirement of

Wherein the content of the first and second substances,and yet to be calculated. Inserting (18) into (17),

next, (19) and (16) are made equal and Ψ is satisfied

This gives the expression of phi and phi in (15),

wherein

The last step is to check if Φ and Φ satisfy the lemma assumption. Because of the fact thatAndperiodic and zero mean in the second argument and slowly varying on the average, as does Φ. Have yet to be demonstrated on averageBecause of the fact thatThe variation is slow on the average value and,

wherein λ is₀Is greater than 0. G is composed of a constant c_gBy definition, it is meant

In a similar manner to that described above,from c₁₁Definition, Ψ₁Satisfy the requirement of

Adding the two inequalities to obtain

This concludes the proof.

2, leading: is provided withAndrespectively, the solutions of (12) and (15) starting from 0 of the same initial condition. Then, for all σ ≧ 0

And (3) proving that: let E (σ): x (σ) -X (σ). Then the process of the first step is carried out,

since F is a constant of λ_FThe Lipschitz (R) of (1),

on the other hand, by lemma 3, there is c₁So that

Finally, since the average value of phi isSo there is c₂So that

The sum of these estimates yields

||E(σ)||≤ελ_F∫₀ ^σ||E(s)||ds+c₁ε²+c₂ε³σ

Then, by the theory of Gronwall [9, theory 1.3.3]

This means that

The following lemma is the lemma of Besjes [9, lemma 2.8.2]In thatNo longer Lipschitz but only as a spread over slow changes in the mean.

And 3, introduction: suppose thatIn the second argument, the period is T and zero mean, bounded, and varies slowly over the mean. Suppose thatThe solution X (σ) of (c) is defined for 0 ≦ σ ≦ L/ε. Presence of c₁> 0 such that

And (3) proving that: according to the method of [9], the interval [0, T ] is divided into m sub-intervals [0, T ], [ T ], [ m-1 ] T, mT ] and a remainder [ mT, T ]. By splitting the integrals over these intervals, write as

Wherein each integral in the first summation is zero, becauseIs periodic and has a zero mean. Due to the fact thatIs bounded by the followingWith the remainder also being constant c₂> 0. In addition to this

Where q is continuous and bounded. By assuming that λ > 0 exists such that for 0 ≦ i ≦ m,

thus, by summing the previous estimates,

where T is not less than mT but not more than L/ε, so m λ T ε + c₂≤λL+c₂(ii) a This concludes the proof.

Demodulation of

According to (8c), the measurement signal y can be written as

Wherein the signal u fed to the PWM encoder is known. The following results show that y can be estimated from y_aAnd y_vFor the control law described in section 1-III-a.

Theorem 2: consider an estimator defined byAnd

wherein the content of the first and second substances,is a moving average operator, andis thatMean in the second argument (see end of section 1-I). Then, the user can use the device to perform the operation,

review by constructionThus (21b) is essentially a first order estimate; note also that when u (t) does not exceed the range of the PWM encoder,is always non-zero.

And (3) proving that: taylor expansion y_a、y_v、u、s₁To obtain

In the second equation, useThen y_aMoving average of

For theSimilar calculation results

Because of s₁In the second argument the period is 1 and zero mean. Summing (22) and (23), and finally finding

As a result, after another Taylor expansion

This is the desired estimate (21 a).

On the other hand, (21a) means

Continue to calculate, regarding M (k)_υ) It has found

Is divided byA desired estimate is obtained (21 b).

Example of V. numerical value

Illustrating the interest of this approach in

y＝x₂+x₁x₃，

Where d is an unknown perturbation; u will pass at a frequency of 1kHz (i.e.. epsilon. -. 10)^-3) And the range is [ -20, 20]Is applied. The goal is to control x with a response time of a few seconds₁While suppressing the disturbance d. It is desirable to operate near the equilibrium point forAnd d^eqConstant hasIn the form of (1). Note that observability degrades at these points, which makes the design of the control laws less straightforward.

However, the PWM-induced signal injection makes available a virtual measurement as follows

Whereby a suitable control law can be easily designed even without actually inputting y_a＝x₂+x₁x₃. The system is now completely linear, using a classical controller-observer, with disturbance estimation to ensure the implicit integration effect. Thus, the observer is given by

And the controller is given by

The gains were chosen to place the observer eigenvalues at (-1.19, -0.73, -0.49 ± 0.57i) and the controller eigenvalues at (-6.59, -3.30 ± 5.71 i). According to dual loop transfer recovery (dual loop transfer recovery), the observer is slower than the controller, thus ensuring reasonable robustness. Is provided with Obviously, the controller-observer is noted as

Finally, this ideal control law is implemented as

Wherein the content of the first and second substances,is a PWM function described in sections 1-II, andare obtained by the demodulation process of sections 1-IV.

The test scenario is as follows: when t is 0, the system starts from a static state at the origin; starting from t-2, apply a perturbation d-0.25 to the system; when t is 14, for referenceA filtering unit step is applied. In FIG. 5, the ideal control law (24), i.e. without PWM and assuming y_vIt is known that, in comparison with the real control law (25): (25) is excellent and it is almost impossible to distinguish about x₁And x₂Because of the corresponding ripple through (8a) is onlyAt x₃A ripple can be seen, wherein the ripple isCorresponding control signals u and u_pwmShown in fig. 6, and the corresponding measurement output is shown in fig. 7.

To investigate the sensitivity to measurement noise, adding band-limited white noise (power density 1 × 10) to y was performed^-9Sampling time of 1 × 10^-5) The same test as in (c). Although the ripple in the measured output is hidden in noise (see fig. 8), the virtual output is correctly demodulated and the control law (25) still performs well.

Conclusion

A method is proposed to take advantage of the benefits of signal injection in PWM fed systems without the need for external probing signals. For simplicity, it is limited to single-input single-output systems, but considering multiple-input multiple-output systems has no inherent difficulty. In addition to this, while classical PWM has been focused on, the method can be easily extended to any modulation process, such as multi-level PWM; in fact, the only requirement is s₀And s₁Satisfying the regularity assumption discussed in note 1.

2. Sensorless rotor position estimation by PWM induced signal injection (Dilshad Surroop)^1，2、Pascal Combes²、Philippe Martin¹And Pierre Rouchon¹)

Abstract-one shows how the rotor position of a PWM controlled PMSM can be recovered from the measured current by appropriate use of the excitation provided by the PWM itself. This provides the benefits of signal injection, particularly the ability to operate even at low speeds, without the disadvantages of external probing signals. The relevance of the method is illustrated by simulation and experimental results.

Indexing terminology-sensorless control, PMSM, signal injection, PWM induced ripple.

Term list

PWM pulse width modulation

x^dqVector (x) in dq coordinate system^d，x^q)^T

x^αβVector (x) in α β coordinate system^α，，x^β)^T

x^abcVector (x) in abc coordinate system^a，x^b，x^c)^T

R_sStator resistor

Rotation matrix of angle π/2:

moment of inertia of J

number of n pole pairs (pole pair)

Speed of omega rotor

T_lLoad torque

θ，Actual rotor position, estimated rotor position

φ_mPermanent magnetic flux

L_d，Ld-axis and q-axis inductances

C Clarke transformation:

rotation matrix for angle θ:

epsilon PWM period

u_mPW amplitude

S (theta) significance matrix (saliency matrix)

The "large O" symbol analyzed: for C independent of z and epsilon,meaning that k (z, ε) | ≦ C ε.

I. Introduction theory

Sensorless control of AC motors in the low speed range is a challenging task. In fact, from the current measurements, the observability of the system degrades at rest, which limits the performance of any basic model-based control law at low speeds.

One method that is now widely used to overcome this problem is the so-called signal injection technique. This technique is to superimpose a signal for accelerating the speed change on the control law. This injection, if properly decoded, will produce a ripple on the current measurements that carries rotor position information. However, introducing a rapidly varying signal increases acoustic noise and may induce mechanical resonance. For systems controlled by Pulse Width Modulation (PWM), the injection frequency is also inherently limited by the modulation frequency. That is, an inverter-friendly waveform can also be injected to produce the same effect as the so-called "notification" method in [10], [11 ]. For a PWM fed Permanent Magnet Synchronous Motor (PMSM), the oscillating nature of the input can be seen as a generalized rectangular injection on three input voltages, which provides the benefits of signal injection, particularly the ability to operate even at low speeds, without the disadvantages of external probe signals.

It is shown on the basis of the quantitative analysis developed in [12] how the rotor position of the PWM controlled PMSM can be recovered from the measured current by appropriate use of the excitation provided by the PWM itself. No modification of the PWM stage is required, nor is the high frequency signal injected as in [6 ].

Section 2 is arranged as follows: the effect of PWM on current measurement according to the method of [12] is described in section 2.II, with a slight generalization to the multiple-input multiple-output framework. In section 2.III, it is demonstrated how rotor position is recovered for two PWM schemes, standard single carrier PWM and interleaved PWM. The relevance of this approach is illustrated in section 2.IV by numerical values and experimental results.

Virtual measurement results caused by PWM

Considering the state space model of PMSM in dq coordinate system

Wherein the content of the first and second substances,is the stator flux linkage, ω is the rotor speed, θ is the rotor position,is the current of the stator and is,is the stator voltage, T_lIs the load torque; r_sJ and n are constant parameters (meaning see notation nomenclature). For simplicity, no magnetic saturation is assumed, i.e. linear current-flux relationship

Wherein phi is_mIs a permanent magnetic flux; for a detailed discussion of magnetic saturation in the context of signal injection, see [4]]. The input is a voltage according to the following relationship

In industrial drives, the actual applied voltage is not directlyBut rather its PWM encodedThe PWM period is epsilon. The function M describing PWM is periodic by 1 and has an average value of 1 in the second argumentNamely, it isAnd isThe expression of which is given in section 2. III. Is provided with Thus, the applied voltage is denoted as

Wherein the content of the first and second substances,in the second argument is periodic 1 and zero mean;it can be seen as a rectangular detection signal caused by PWM, which produces ripple but has no other effect. Finally, as we are concerned with sensorless control, the only measurement is the currentOr equivalentlyBecause of the fact that

[12] And [1] accurate quantitative analysis of signal injection was developed. These results are somewhat generalized to the multiple-input multiple-output case, and the effect of PWM induced signal injection can be analyzed in the following way by means of second order averaging. Consider a system

y＝h(x)，

Where u is the control input, ε is the (assumed small) PWM period, s₀Cycle 1 in the second argument, with zero mean in the second argument; then, a so-called virtual measurement result of order epsilon accuracy can be extracted from the actual measurement result y

I.e. the estimate can be calculated by a suitable filtering process

Matrix capable of on-line calculationIs defined as follows

Wherein s is₁Is s₀Zero mean primitive in the second argument, i.e.

s₁(υ，τ)：＝∫₀ ¹s₀(υ，σ)dσ-∫₀ ¹∫₀ ^τs₀(υ，σ)dσdτ

Measurement ofIs an excitation signalRipple induced on the output y; although small, it contains valuable information when properly processed.

For a belt with outputPMSM (26) - (28) of (1), certain algebra are obtained

Wherein

And isIn [4]]The so-called saliency matrix introduced in (a),

if the motor has sufficient geometric significance, i.e. if L_dAnd L_qSufficiently different, then rotor position θ can be varied from y_vAs described in section 2. III. When the geometric significance is small, information about θ is usually still present when considering magnetic saturation, see [4]]。

Extracting theta from the virtual measurement results

From y_vThe extracted rotor position θ depends on a 2 × 3 matrixIs determined. The structure of this matrix depends on the details of the PWM employed, and therefore the rank of this matrix also depends on the details of the PWM employed. After reviewing the basis of single-phase PWM, two cases were studied: standard three-phase PWM with single carrier and three-phase PWM with interleaved carriers.

Before that, it was notedHaving the same rank as the 2 x 2 matrix

Wherein the content of the first and second substances,in practice, the amount of the liquid to be used,

this means thatAndhave the same singular values and therefore the same rank. Therefore, considerRather than the raw virtual measurement y_vWithout losing information.

A. Single phase PWM

In a period of epsilon and in a range of [ -u [ ]_m，u_m]In the "natural" PWM of (1), the input signal u is compared with a triangular carrier with a period of epsilon

Function with period of 1Package is toNormalized time ofIf u changes slowly enough, it will be in timeCrosses carrier c exactly once on each rising and falling ramp, so that

Thus, the PWM encoded signal is given by

FIG. 10 shows signals u, c and u_pwm. Function(s)

It is clear that the second argument with respect thereto is periodic by 1 and has a mean value u, thus fully describing the PWM process, since

Then the resulting zero-mean detection signal is

And its zero mean primitive in the second argument is

Signal s₀、s₁And w are shown in figure 11. Note that by construction s₀(±u_m，σ)＝s₁(±u_mσ) is 0, so there is no ripple at the PWM limit, and thus no information is available.

B. Three-phase PWM with single carrier

In three-phase PWM with a single carrier,each component ofComparing with the same carrier wave to obtain

Wherein s is₀And s₁As in single phase PWM. This is the most common PWM in industrial drivers because it is easy to implement. Note that if it happens to happenAre equal, e.g.Then

This in turn means thatRank of 1 (its determinant vanishes); it can be shown that this is the only case that leads to a rank of 1. If it is notAll 3 components are equal, thenIs 0 (i.e., all its entries are zero); this is a quite special case where exclusion is made. If not, then,is 2 (i.e., it is invertible). Fig. 12 shows the case where the rank is 2 (upper) and the case where the rank is 1An example of the shape of (a), wherein,

since the case of rank 1 occurs very often, it must be passed for the slaveAnd extracting theta for processing. Due to the fact thatThis can be done by a linear least squares method. Is provided with

And isCan be combined withIs rewritten as

The least squares solution of this (coherent) overdetermined linear system is

Estimated values of cos 2 theta and sin 2 thetaUsing the same formula, using the estimated formula instead of the actual y_ijTo obtain

Thus, there are

Finally, an estimated value of θ is obtained by the following equation

Wherein the content of the first and second substances,is the number of turns.

C. Three-phase PWM with interleaved carriers

At the cost of more complex implementations, the result is that PWM schemes with (regularly) interleaved carriers offer several benefits over single carrier PWM. In the case of this embodiment, the process is,is compared with a shifted version of the same triangular carrier (0 for a-axis shift, 1/3 for b-axis shift, 2/3 for c-axis shift), resulting in

Fig. 13 shows the principle of this scheme. Figure 14 shows that the signal looks more or less like two orthogonal signalsExamples of the shape of (c).

Now, even whenAre equal to each other,it also remains reversible (except, of course, at the PWM limit) because each component has a different PWM pattern due to the interleaving. Thus, the significance matrix can be recovered by the following equationAll four entries of

Note that becauseThe rotor angle theta can be calculated from the matrix entries by the following equation

Wherein the content of the first and second substances,is the number of turns. Estimated value of thetaThus can be determined byItem ofIs calculated to obtain

Without knowing the magnetic parameter L_dAnd L_qThis is indeed a practical feature.

Simulation and experimental results

The demodulation process was simulated and experimentally tested. All values and tests tested using a fairly significant PMSM with the parameters listed in table I. The PWM frequency is 4 kHz.

TABLE I nominal parameters

The test scenario is as follows: starting from a stationary state at t-0 seconds, the motor remains there for 0.5 seconds, then follows a speed ramp (electrical) from 0 to 5Hz, and finally remains at 5Hz starting from t-8.5 seconds; it withstands a constant load torque of about 40% of the rated torque during the entire experiment. Since section 2 only relates to the estimation of the rotor angle θ, the control law of the drive motor is allowed to use the measured angle. In addition to this, data cannot be processed in real time, and thus data is recorded and processed off-line.

A. Single carrier PWM.

Fig. 15 and 16 show results obtained by simulating cos 2 θ, sin 2 θ and θ through the reconstruction process of section 2-III-B. The agreement between the estimated value and the actual value is very good.

Fig. 19 and 20 show the corresponding results with respect to the experimental data. The agreement between the estimated value and the actual situation is still very satisfactory, although of course not as good as the simulation. The effect of magnetic saturation may be a cause of partial differences.

FIG. 17 shows a schematic view of a display deviceWhen rank is 2 (upper) and when rank is 1, ripple envelopes under substantially the same conditions as those of fig. 12A close-up view of whereinThey illustrate that they can be used for demodulation despite experimental signal distortions.

Finally, important differences between the simulated data and the experimental data are indicated. In the experimental measurements, periodic spikes in the current measurements were noted, see fig. 18; this is due to the discharge of parasitic capacitances in the inverter transistors each time a PWM commutation occurs. Since the demodulation process of [12] and [1] may be hampered, the measurement current is first preprocessed by a zero-phase (non-causal) moving average with a short window length of 0.01 epsilon. An improved demodulation process that does not require pre-filtering is currently being investigated.

B. Interleaved PWM (analog)

FIGS. 21 and 22 show the reconstruction process through section 2-III-C on the significance matrixAnd the results obtained by performing a simulation on θ. The agreement between the estimated value and the actual value is very good. The reconstruction is not considered to require knowledge of the magnetic parameters.

Conclusion V

Section 2 proposes an analysis method to extract the rotor position of a PWM-fed PSMM using signal injection provided by the PWM itself. Experimental and simulated results illustrate the effectiveness of this technique. Further work includes demodulation strategies that do not require pre-filtering of the measured current and are suitable for real-time processing. The final goal is of course to be able to use the estimated rotor position in the feedback loop.

The present disclosure also relates to the following subject matter:

clause 1: a method for controlling an actuator includes providing a control signal for the actuator, and modulating the control signal by a modulation signal.

Clause 2: the method of clause 1, further comprising: determining a zero-mean primitive of the modulated control signal, obtaining a measurement signal from the actuator, obtaining a virtual measurement result by demodulating the measurement signal based on the zero-mean primitive of the modulated control signal, adapting the control signal in response to the obtained virtual measurement result.

Clause 3: the method of clause 1 or 2, wherein the modulation signal comprises pulse width modulation.

Clause 4: the method of any of clauses 1-3, wherein the actuator is an electric motor.

Clause 5: a control system for controlling an actuator, comprising a control module for generating a control signal, a PWM module for generating a modulated control signal and a zero-mean primitive of the modulated control signal by pulse width modulation, a measurement unit for obtaining a measurement signal from the actuator, and an estimator module for obtaining a virtual measurement result by demodulating the measurement signal based on the zero-mean primitive of the modulated control signal, wherein the control module is arranged for adapting the control signal based on feedback in the form of the obtained virtual measurement result.

Clause 6: the system of clause 5, wherein the modulated signal comprises pulse width modulation.

Clause 7: the system of clause 5 or 6, wherein the actuator is an electric motor.

The present disclosure is not limited to the specific embodiments described herein, which are intended as examples only. The present invention encompasses every alternative that may occur to those skilled in the art upon reading the present disclosure.

Reference to the literature

[1]P.Combes，A.K.Jebai，F.Malrait，P.Martin，and P.Rouchon，“Adding virtual measurements by signal injection，”in American Control Conference，2016，pp.999-1005.

[2]P.Jansen and R.Lorenz，“Transducerless position and velocity estimation in induction and salient AC machines，”IEEE Trans.Industry Applications，vol.31，pp.240-247，1995.

[3]M.Corley and R.Lorenz，“Rotor position and velocity estimation for a salient-pole permanent magnet synchronous machine at standstill and high speeds.”IEEE Trans.Industry Applications，vol.34，pp.784-789，1998.

[4]A.K.Jebai，F.Malrait，P.Marin，and P.Rouchon，“Sensorless position estimation and control of permanent-magnet synchronous motors using a saturation model，”International Journal of Control，vol.89，no.3，pp.535-549，2016.

[5]B.Yi，R.Ortega，and W.Zhang，“Relaxing the conditions for parameter estimation-based observers of nonlinear systems via signal injection，”Systems and Control Letters，vol.111，pp.18-26，2018.

[6]C.Wang and L.Xu，“A novel approach for sensorless control of PM machines down to zero speed without signal inj ection or special PWM technique，”IEEE Transactions onPower Electronics，vol.19，no.6，pp.1601-1607，2004.

[7]B.Lehman and R.M.Bass，“Extensions of averaging theory for power electronic systems，”IEEE Transactions on Power Electronics，vol.11，no.4，pp.542-553，July 1996.

[8]A.Filippov，Differential equations with discontinuous righthand sides.Control systems，ser.Mathematics and its Applications.Kluwer，1988.

[9]J.Sanders，F.Verhulst，and J.Murdock，Averaging methods in nonlinear dynamical systems，2nd ed.Springer，2005.

[10]E.Robeischl and M.Schroedl，“Optimized inform measurement sequence for sensorless pm synchronous motor drives with respect to minimum current distortion，”IEEE Transactions on Industry Applications，vol.40，no.2，2004.

[11]M.Schroedl，“Sensorless control of ac machines at low speed and standstill based on the″inform″method，”in IAS’96.Conference Record of the 1996 IEEE Industry Applications Conference Thirty-First IAS Annual Meeting，vol.1，1996，pp.270-277 vol.1.

[12]D.Surroop，P.Combes，P.Martin，and P.Rouchon，“Adding virtual measurements by pwm-induced signal injection，”in 2020 American Control Conference(ACC)，2020，pp.2692-2698.