CN111697874B - Motor stator vibration mode observation method based on nonlinear sliding mode observer - Google Patents
Motor stator vibration mode observation method based on nonlinear sliding mode observer Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
- H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
- H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
- H02N2/12—Constructional details
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
- H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
- H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
- H02N2/14—Drive circuits; Control arrangements or methods
- H02N2/142—Small signal circuits; Means for controlling position or derived quantities, e.g. speed, torque, starting, stopping, reversing
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
- H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
- H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
- H02N2/16—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors using travelling waves, i.e. Rayleigh surface waves
- H02N2/163—Motors with ring stator
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
- H02P23/12—Observer control, e.g. using Luenberger observers or Kalman filters
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
- H02P23/14—Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
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- General Electrical Machinery Utilizing Piezoelectricity, Electrostriction Or Magnetostriction (AREA)
Abstract
The invention discloses a motor stator vibration mode observation method based on a nonlinear sliding mode observer, which is realized by using equipment comprising an FPGA, a Hall current sensor, a voltage division sampling resistor, a high-speed ADC, an H-bridge driving circuit and a traveling wave type rotary ultrasonic motor, wherein the steps are as follows: firstly, controlling a Hall current sensor and a voltage division sampling resistor by using an FPGA, sampling output voltage and current when a traveling wave type rotary ultrasonic motor operates at a sampling frequency of 4MHz, realizing digital-to-analog conversion by using a high-speed ADC, and establishing a first derivative aiming at a vibration modeIs a visual observation of (1): a second step of establishing a first derivative of the vibration mode according to the first stepAnd (3) establishing a vibration mode nonlinear sliding mode observer. The method aims at the traveling wave type rotary ultrasonic motor, can realize accurate observation of the vibration mode of the stator, has certain parameter robustness, and can overcome the problems of difficult implementation and low measurement precision of the existing measurement technology.
Description
Technical Field
The invention relates to the technical field of motor stator vibration mode measurement, in particular to a traveling wave type rotary ultrasonic motor stator vibration mode observation method based on a nonlinear sliding mode observer.
Background
The traveling wave ultrasonic motor (TWUSM) is a miniature motor, has simple structure, small volume and quick response, is not interfered by electromagnetic fields, and is widely applied to occasions with high control precision requirements, such as aerospace, medical fields and the like.
The TWUSM utilizes the inverse piezoelectric effect of piezoelectric materials, and applies two-phase high-frequency excitation voltage to excite a stator to generate vibration traveling wave, so that particles on the surface of the stator move in an elliptical track, and the rotor is driven to rotate through contact friction with the rotor. According to the driving mechanism, the travelling wave generated by the stator is a driving key, and the travelling wave is formed by superposing two-phase vibration modes of the stator, so that the research on the measurement of the vibration modes of the stator is necessary. According to the analysis of the current literature, the measurement of the stator vibration mode mainly depends on modes such as a high-speed camera, a sensor, a transformer bridge circuit and the like, and the measurement modes are not easy to install, expensive in instrument and not beneficial to popularization and use. In summary, current measurement techniques for stator vibration modes are not easily implemented for widespread use.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a motor stator vibration mode observation method based on a nonlinear sliding mode observer. The method aims at the traveling wave type rotary ultrasonic motor, can realize accurate observation of the vibration mode of the stator, has certain parameter robustness, and can overcome the problems of difficult implementation and low measurement precision of the existing measurement technology.
The technical scheme adopted by the invention for solving the technical problems is as follows: the motor stator vibration mode observation method based on the nonlinear sliding mode observer comprises the following steps of FPGA, hall current sensor, voltage division sampling resistor, high-speed ADC, H-bridge driving circuit and traveling wave type rotary ultrasonic motor:
firstly, controlling a Hall current sensor and a voltage division sampling resistor by using an FPGA, sampling output voltage and current during running of a traveling wave type rotary ultrasonic motor at a sampling frequency of 4MHz, and realizing digital-to-analog conversion by using a high-speed ADCChanging and establishing the first derivative of the vibration modeObtaining the first derivative of the vibration mode +.>Is a measurement of the observed value of (2);
a second step of obtaining a first derivative of the vibration mode according to the first stepEstablishing a vibration mode nonlinear sliding mode observer;
thirdly, the stability and the convergence of the vibration mode nonlinear sliding mode observer designed in the second step are proved.
Compared with the prior art, the invention has the beneficial effects that:
1. starting from a TWUSM model, the method of the invention builds a vibration mode first order conduction observer to realize the first order conduction observation of the stator vibration mode.
2. According to the method, the nonlinear sliding mode observer is built to estimate the vibration mode of the stator, so that the TWUSM vibration mode sensorless measurement is realized, and the cost is reduced.
3. The method of the invention overcomes the problem that TWUSM is easily affected by environment to generate parameter uncertainty in theory, and realizes accurate observation.
4. The method of the invention can theoretically overcome the influence caused by the non-measurable nonlinear quantity generated by the complex driving mechanism of the TWUSM and realize accurate observation.
5. The method aims at measuring the vibration mode of the stator, directly reflects the vibration state of the stator, indirectly knows the response state of the rotor, and is beneficial to researching the internal state of the motor.
Drawings
The invention will be further described with reference to the drawings and examples.
FIG. 1 is a schematic diagram of the method of the present invention.
Fig. 2 is a schematic diagram showing the comparison between the observation result of the vibration mode nonlinear sliding mode observer and the simulation reality value in the parameter steady state.
Fig. 3 is a schematic diagram showing the comparison between the observation result of the vibration mode nonlinear sliding mode observer and the simulation reality value in the parameter time-varying state.
Detailed Description
The invention provides a motor stator vibration mode observation method based on a nonlinear sliding mode observer, equipment used for realizing the method comprises an FPGA (Altera cyclone IV series), a Hall current sensor (the model is HCS-LTS 06A), a voltage division sampling resistor, a high-speed ADC (high-speed analog-to-digital converter of ADI company), an H-bridge driving circuit and a traveling wave type rotary ultrasonic motor (short for motor), and the method comprises the following steps:
the first step, utilize FPGA control Hall current sensor, voltage divider sampling resistor, realize sampling to output voltage, electric current when traveling wave type rotary ultrasonic motor is running with 4MHz sampling frequency, realize digital-to-analog conversion through high-speed ADC, and establish the first derivative of vibration modeObtaining the first derivative of the vibration mode +.>Is a measurement of the observed value of (2);
specifically, the output voltage and current of the motor during operation are sampled at a sampling frequency of 4MHz by controlling a Hall current sensor and a voltage dividing sampling resistor through an FPGA, digital-to-analog conversion is realized by utilizing a high-speed ADC and the digital-to-analog conversion is transmitted back to the FPGA, so that two-phase voltage u= [ u ] of the motor is obtained A ,u B ]And a two-phase current i= [ i ] A ,i B ]The method comprises the steps of carrying out a first treatment on the surface of the Wherein A and B respectively represent two phases of the motor, and are the same as below;
the piezoelectric vibrator equation for a known TWUSM is:
wherein R is d ＝diag{R dA ,R dB }、C d ＝diag{C dA ,C dB Dielectric loss resistance and static capacitance of the two-phase piezoelectric vibrator; Θ is the electromechanical coupling coefficient.
Establishing a stator vibration mode first order conduction observer:
according to the piezoelectric vibrator equation (1), A, B two-phase expressions are consistent, and one-phase equation is rewritten into the equation (3) according to the state variable voltage u:
design slip form surfaceFor the observed value of u, designing a stator vibration mode first order derivative observer as follows:
wherein, the equation (4) is taken into the equation (3) to obtain the first derivative of the vibration modeExpressed as:
m and k 1 Is a design parameter.
A second step of obtaining a first derivative of the vibration mode according to the first stepEstablishing a vibration mode nonlinear sliding mode observer;
the first derivative of the vibration mode obtained in the first stepIs used as the first order derivative of the real vibration mode>Two-phase voltage u= [ u ] A ,u B ]And a two-phase current i= [ i ] A ,i B ]TWUSM electromechanical coupling equation:
where m=diag { M sA ,m sB }、D＝diag{d sA ,d sB C=diag { C } sA ,c sB Respectively represent two-phase modal mass, modal damping and modal stiffness, Θ is an electromechanical coupling coefficient, F c Is a modal force.
According to TWUSM electromechanical coupling equation (2), since A, B two-phase expressions are consistent, a single-phase state equation (6) is established, wherein the state variables are takenOutput-> C＝[0 1]And taking into account disturbances in system parameters:
the vibration mode nonlinear sliding mode observer is designed according to the formula (6) and is as follows:
for the observer estimated system state, G is the design matrix.
Thirdly, the stability and the convergence of the vibration mode nonlinear sliding mode observer designed in the second step are proved.
Since the vibration mode nonlinear sliding mode observer is based on the first derivative of the vibration mode obtained in the first stepIs used as the first order derivative of the real vibration mode>And the stability and the convergence of the vibration mode first-order conduction observer are firstly verified.
The first-step designed vibration mode first-order derivative observer is shown as a formula (4), wherein the parameter design requirements are as follows: k (k) 1 >0，0<r<1。
The stability is proved, and a Lyapunov function is set:
its first derivative:
as long as the design parametersCan ensure
Combining Lyapunov functions can obtain
The vibration mode first order derivative observer is not only gradually stable in the global range, but also stable in finite time, and the stable time depends on the initial value s of s 0 ：
Furthermore, the vibration mode nonlinear sliding mode observer designed in the second step is shown in the formula (7):
wherein the matrix G εR 2×1 The method comprises the steps of carrying out a first treatment on the surface of the To meet the requirement of A 0 The =a-GC has a parameter design matrix with stable eigenvalues, and for a certain constant f there are Lyapunov symmetric positive definite matrices P and Q, satisfying:
the control input v of the vibration mode nonlinear sliding mode observer is:
in the method, in the process of the invention,for state deviation, the design parameter ρ is more than or equal to D+η, and η is a positive real number.
According to the above requirements, the following design matrix is obtained:
the stability of the product is proved, and a Lyapunov function is set:
V(e)＝e T Pe (10)
then there are:
the first term, Q, is a semi-positive definite matrix, but satisfies that the term is not constantly zero along any track, so its equilibrium point is the origin. The second term is that ρ is equal to or greater than D+η, η is a positive real number and is necessarily equal to or less than 0, so:
therefore, the vibration mode nonlinear sliding mode observer converges stably and is robust to disturbance of parameters.
And establishing an observer for observing first-order conduction of the vibration mode and a nonlinear sliding mode observer for observing the vibration mode according to the requirements, wherein TWUSM parameters are measured by an admittance circle method.
The vibration mode first-order conduction observer and the vibration mode nonlinear sliding mode observer are realized through an FPGA, the traveling wave type rotary ultrasonic motor is selected as a model TRUM60A, and an H-bridge driving circuit (also called a full-bridge driving circuit) is used in a matched mode.
FIG. 1 is a schematic diagram of the method of the present invention, wherein the apparatus used to implement the method comprises an FPGA (Altera cyclone IV series), a Hall current sensor (model HCS-LTSA), a voltage division sampling resistor, a high-speed ADC, and an H-bridge driving circuit, and TWUSM is TRUM60A; the FPGA is provided with a sampling module (namely, a control Hall current sensor (the model is HCS-LTSA) and a voltage division sampling resistor for realizing sampling), and a vibration mode first-order conduction observer and a vibration mode nonlinear sliding mode observer are built. Sampling output voltage and output current of a motor in operation at a sampling frequency of 4MHz by using a Hall current sensor and a voltage divider resistor through an FPGA, realizing digital-to-analog conversion by using a high-speed ADC (analog-to-digital converter), transmitting the digital-to-analog conversion back to the FPGA, and establishing a vibration mode first-order conduction observer and a vibration mode nonlinear sliding mode observer in the FPGA through software;
the principle of the method of the invention is as follows: the first step, the output voltage u= [ u ] of the motor during operation is realized by using a Hall current sensor and a voltage divider resistor through an FPGA at a sampling frequency of 4MHz A ,u B ]Current i= [ i ] A ,i B ]The real-time sampling of the stator vibration mode is realized by utilizing a high-speed ADC to realize digital-to-analog conversion and transmitting the digital-to-analog conversion back to the FPGA, inputting the digital-to-analog conversion to a vibration mode first-order conduction observer, and realizing the first-order conduction of the stator vibration modeReflecting the actual state of the TWUSM; secondly, inputting voltage quantities obtained by calculation to obtain a first order derivative of a real vibration mode and FPGA sampling to a vibration mode nonlinear sliding mode observer module, and calculating a stator vibration mode observation value according to a designed nonlinear sliding mode observer (7)>Stator vibration mode first order conduction observation value +.>And an observation error value of a first order derivative of the stator vibration mode +.>The observation error value of the first order derivative of the stator vibration mode is fed back to the vibration mode nonlinear sliding mode observer in the form of a switching function v to compensate, so that the observation of the stator vibration mode is realized.
Fig. 2 and 3 show simulation results of a TWUSM vibration mode nonlinear sliding mode observer designed by the invention, and upper solid curves in fig. 2 and 3 are simulation actual values w= [ w ] A ,w B ]The dashed curve is the observed value of the observer outputWhile the observation curve is translated up 0.5 μm for observation. The lower curves in FIGS. 2 and 3 show the relative error of the observed value and the actual value, wherein the solid curve is the relative error e of phase A rA The dashed curve is the relative error e of phase B rB 。
The simulation result shown in fig. 2 shows that the relative error between the output of the vibration mode nonlinear sliding mode observer designed under the parameter steady state and the true value is very small, and accurate tracking can be realized. The simulation result shown in fig. 3 shows that the relative error between the output of the designed vibration mode nonlinear sliding mode observer and the true value is still very small in the parameter time-varying state, and accurate observation can be realized under the parameter disturbance. The vibration mode nonlinear sliding mode observer designed by the invention has the characteristics of high accuracy and strong robustness.
The invention is applicable to the prior art where it is not described.
Claims (6)
1. The motor stator vibration mode observation method based on the nonlinear sliding mode observer comprises the following steps of FPGA, hall current sensor, voltage division sampling resistor, high-speed ADC, H-bridge driving circuit and traveling wave type rotary ultrasonic motor:
the first step, utilize FPGA control Hall current sensor, voltage divider sampling resistor, realize sampling to output voltage, electric current when traveling wave type rotary ultrasonic motor is running with 4MHz sampling frequency, realize digital-to-analog conversion through high-speed ADC, and establish the first derivative of vibration modeObtaining the first derivative of the vibration mode +.>Is a measurement of the observed value of (2);
a second step of obtaining a first derivative of the vibration mode according to the first stepEstablishing a vibration mode nonlinear sliding mode observer;
thirdly, proving the stability and convergence of the vibration mode nonlinear sliding mode observer designed in the second step;
the specific process of the first step is as follows: the output voltage and current of the motor are sampled at the sampling frequency of 4MHz by controlling a Hall current sensor and a voltage dividing sampling resistor through an FPGA, digital-to-analog conversion is realized by utilizing a high-speed ADC and the digital-to-analog conversion is transmitted back to the FPGA, so that the two-phase voltage u= [ u ] of the motor is obtained A ,u B ]And a two-phase current i= [ i ] A ,i B ]The method comprises the steps of carrying out a first treatment on the surface of the Wherein A and B respectively represent two phases of the motor, and are the same as below;
the piezoelectric vibrator equation for a known TWUSM is:
wherein R is d ＝diag{R dA ,R dB }、C d ＝diag{C dA ,C dB Dielectric loss resistance and static capacitance of the two-phase piezoelectric vibrator; Θ is the electromechanical coupling coefficient;
establishing a stator vibration mode first order conduction observer:
according to the piezoelectric vibrator equation (1), A, B two-phase expressions are consistent, and one-phase equation is rewritten into the equation (3) according to the state variable voltage u:
design slip form surface For the observed value of u, designing a stator vibration mode first order derivative observer as follows:
wherein, the equation (4) is taken into the equation (3) to obtain the first derivative of the vibration modeExpressed as:
m and k 1 Is a design parameter; r is a design parameter, 0<r<1。
2. The method for observing the vibration mode of the motor stator based on the nonlinear sliding mode observer according to claim 1, wherein the motor parameters are measured by an admittance circle method.
3. The method for observing the vibration mode of the motor stator based on the nonlinear sliding mode observer according to claim 1, wherein the vibration mode nonlinear sliding mode observer is realized through an FPGA.
4. The method for observing the vibration mode of the motor stator based on the nonlinear sliding mode observer according to claim 1, wherein the model TRUM60A is selected as the traveling wave type rotary ultrasonic motor.
5. The method for observing the vibration mode of the motor stator based on the nonlinear sliding mode observer according to claim 1, wherein the type of the Hall current sensor is HCS-LTS06A.
6. The motor stator vibration mode observation method based on the nonlinear sliding mode observer according to claim 1, wherein the FPGA is Altera cyclone IV series.
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| CN114237045B (en) * | 2021-11-29 | 2022-08-02 | 哈尔滨工业大学 | Sensorless piezoelectric drive closed-loop control method |
| CN114389490B (en) * | 2021-12-10 | 2023-12-15 | 江苏大学 | Permanent magnet synchronous motor rotating speed control method based on fixed time second-order sliding mode technology |
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