CN107659224A - The device and method of rotary transformer axes-angle conversion based on square wave excitation signal - Google Patents
The device and method of rotary transformer axes-angle conversion based on square wave excitation signal Download PDFInfo
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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
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
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Abstract
The invention discloses a kind of device for being used to realize rotary transformer axes-angle conversion, mainly including dsp chip, peripheral circuit is connected between dsp chip and rotary transformer transformer, peripheral circuit includes amplifying circuit, two-way demodulator circuit and two-way modulate circuit；Wherein, demodulator circuit is mainly made up of analog multiplier chip.The step of realizing rotary transformer axes-angle conversion method using the present invention includes：The generation of square wave excitation signal, the waveform of square wave excitation signal function output voltage signal after rotary transformer, rotary transformer output voltage signal is demodulated using the method that pumping signal is multiplied with modulating wave, so as to obtain continuous, smooth solution harmonic waveform, fixed frequency Sampling is avoided；Then, it is using modulate circuit that the range-adjusting for solving harmonic is extremely consistent with sampling request；Rotor-position is accurately calculated using arctan function after sampling, improves the control performance of motor.
Description
Technical Field
The invention belongs to the field of motor control, and particularly relates to a shaft angle conversion method for realizing rotor position measurement by using a rotary transformer.
Background
The permanent magnet synchronous motor has the advantages of simple structure, reliable operation, good speed regulation performance and the like, and is widely applied to the fields of aerospace, numerical control machine tools and the like. In a drive system of a motor, it is important to obtain accurate rotor position information. The accuracy of the rotor position is related to the control performance of the motor drive system. The rotary transformer has been widely used in the field of position detection due to its advantages of strong anti-interference capability, convenient and reliable installation, etc.
Although the output signal of the resolver contains rotor position information, the analog output signal of the resolver must be converted by shaft angle conversion to a signal representing the rotor position. The shaft angle conversion process mainly comprises the generation of excitation, the demodulation of an output signal and the calculation of a rotor position. When the excitation signal is applied to the resolver, the output winding of the resolver generates an output signal that varies with the rotation angle of the rotor. And demodulating the output signal to obtain a demodulation wave in direct proportion to the sine and cosine values of the rotor position, and finally calculating the rotor position through the demodulation wave.
Currently, sine and cosine signals are mostly adopted as excitation signals of the rotary transformer, and the signals are mainly generated by an oscillating circuit or a DSP. The DSP generation method, which is generally used to generate sine and cosine excitation signals by filtering a PWM waveform, is simple to implement compared to an oscillation circuit, but the use of a filter circuit causes a delay between the PWM waveform and an output signal of a resolver. Demodulation is typically achieved using peak sampling techniques and oversampling techniques for the output signal of the resolver. The peak value sampling is to sample the output signal of the rotary transformer when the excitation voltage reaches the peak value, thereby realizing demodulation. The method is simple to implement, but the output signal of the rotary transformer needs to be sampled when the excitation signal reaches the peak value, and the sampling frequency is consistent with the excitation frequency, so that the accuracy of the position of the rotor is limited. The oversampling technology samples the output signal of the rotary transformer through the sampling frequency which is multiple times of the excitation frequency, and the sampling value is filtered through the band-pass filter, so that the bandwidth of the output signal is reduced, and the precision of the sampling value is improved. Demodulation is achieved by taking one sample out of a plurality of samples in each excitation period. The oversampling method improves the precision of the sampling value, but the filter can bring about the delay problem; in the extraction process in the method, the sampling rate is reduced to be consistent with the excitation frequency, so that the same problem exists in oversampling and peak value sampling, namely the improvement of the rotor position detection precision is limited by the fixed sampling rate. Since the excitation frequency of the rotary transformer is usually 1 to 10kHz, the actual sampling rate corresponding to the two sampling methods is also 1 to 10kHz. For a resolver with a low excitation frequency, the rotor position value calculated from the sampled values will produce a large quantization error at high speed.
The existing shaft angle conversion method of the rotary transformer still has some problems, and the excitation signal generated by the PWM waveform through a filter circuit has the problem of time delay; demodulation is realized by means of a sampling technology, the technology needs to sample at a fixed point of an output signal of the rotary transformer, and the requirement on the accuracy of a sampling point is high; the sampling frequency is consistent with the excitation frequency, so that the sampling precision of a demodulation signal is limited, and the calculation of the rotor position can bring obvious quantization errors when the motor is at a high speed, so that the accuracy of the final rotor position detection is influenced, and the control performance of the motor is influenced.
Disclosure of Invention
The invention aims to solve the technical problem of providing a resolver shaft angle conversion method based on square wave excitation signals for measuring the position of a rotor.
In order to solve the technical problem, the device for realizing the shaft angle conversion of the rotary transformer comprises a DSP chip, wherein a peripheral circuit is connected between the DSP chip and the transformer and comprises an amplifying circuit, two demodulation circuits and two conditioning circuits; the amplifying circuit comprises a first operational amplifier chip and an optocoupler chip, a first resistor is connected between the output end of the first operational amplifier chip and an input cathode, and a second resistor is connected between one GPIO port on the DSP chip and an input anode of the first operational amplifier chip; the anode of the optocoupler chip is connected in parallel with one end of a third resistor and one end of a fourth resistor, the other end of the third resistor is connected with the output end of the operational amplifier chip, and the other end of the fourth resistor is grounded; the output of the optical coupling circuit is connected to an excitation winding of the rotary transformer; the sine output winding and the cosine output winding of the rotary transformer are respectively connected with two demodulation circuits with the same structure, and the outputs of the two demodulation circuits are respectively connected with the inputs of the two conditioning circuits; the demodulation circuit comprises an analog multiplier chip and a second-order RC filter circuit; the conditioning circuit comprises a first voltage following circuit, a second voltage following circuit and an anti-parallel diode, wherein the first voltage following circuit is composed of a second operational amplifier chip, a fifth resistor and a sixth resistor, the fifth resistor is connected between the output end and the input cathode of the second operational amplifier chip, and the sixth resistor is connected between the output of the demodulation circuit and the input anode of the second operational amplifier chip; the second voltage follower circuit has the same structure as the first voltage follower circuit, and a voltage division circuit is connected between the first voltage follower circuit and the second voltage follower circuit; an RC filter circuit is arranged between the output end of the second voltage follower circuit and the anti-parallel diode; the outputs of the two paths of conditioning circuits are respectively connected with two ADC interfaces of the DSP chip.
Further, in the invention, the positive power supply and the negative power supply of the operational amplifier chip are both connected with a filter capacitor. And a positive power supply and a negative power supply of the optocoupler chip are both connected with a filter capacitor.
The invention also provides a rotary transformer shaft angle conversion method based on square wave excitation signals by using the device for realizing rotary transformer shaft angle conversion, which comprises the following steps:
step one, square wave excitation signal u i Generation of (a):
the DSP chip generates a rectangular wave with a duty ratio of 50%, and the rectangular wave signal is amplified in power and amplitude through an amplifying circuit in the peripheral circuit to obtain a square wave excitation signal u i ；
Step two, square wave excitation signal u i The waveform of the output voltage signal after acting on the rotary transformer:
when square wave excitation signal u i Acting on said rotary transformer, the square-wave excitation signal u i Is shown as
In the formula (1), U m Is the amplitude of the square wave excitation signal, T is the period of the square wave signal, and n is a non-negative integer;
the equivalent model of the resolver is:
in the formula (2), u sin ，u cos The output voltage of the sine output winding and the output voltage of the cosine output winding are respectively; l is 1 Is an excitation winding inductance; i.e. i i Is an exciting current; m m The mutual inductance amplitude between the excitation winding and the output winding is shown, and theta is the position of a rotor of the rotary transformer;
substituting formula (1) into formula (1) in formula (2) to obtain exciting current i under square wave excitation shown in formula (3) i Formula (2)
Substituting the formula (3) into the formula 2 of the formula (2) to obtain the output voltage u of the sinusoidal output winding of the square-wave excited lower-rotation transformer sin And (3) substituting the formula (3) into the formula (3) of the formula (2) to obtain the output voltage u of the cosine output winding of the square-wave excited lower rotary transformer cos ：
In formula (4), k = M m /L 1 ω is the angular velocity of rotation of the rotor; the term "ku" on the right side of the No. 1 medium symbol in the formula (4) i sin θ of amplitude A s1 ＝kU m ；
In the same excitation period T, the term on the right side 2 of the medium sign in the formula (1) in the formula (4) is M m i i ω cos θ, where the current i i Is obtained at T/4 within the first period, and T =2 pi/ω e ，ω e At the frequency of the square-wave excitation signal, M m i i The magnitude of ω cos θ is:
due to omega e >>ω，A s1 >>A s2 The formula (4) is simplified as follows
During the positive half-cycle of square-wave excitation u i ＝U m Derived from the formula (6)
The output voltage u of the sinusoidal output winding of the resolver during the positive half-cycle of a square-wave excitation sin And the output voltage u of the cosine output winding cos Proportional to the sine and cosine values of the rotor position, respectively, in a ratio kU m ；
In the negative half-cycle of square-wave excitation u i ＝-U m Derived from formula (6):
the output voltage u of the sinusoidal output winding of the rotary transformer during the negative half-cycle of the square-wave excitation sin And the output voltage u of the cosine output winding cos Proportional to the sine and cosine values of the rotor position, respectively, in a ratio of-kU m ；
Step three, demodulating the output voltage signal of the rotary transformer:
multiplying the output voltage of the rotary transformer by the excitation voltage to obtain:
the formula (7) and the formula (8) are respectively substituted into the formula (9), and the sine demodulation wave u in the whole excitation period s And cosine demodulation wave u c The following were used:
sine-demodulated wave u obtained by equation (10) s And cosine demodulation wave u c Is proportional to the sine and cosine values of the rotor position at any time, the ratio being kU m 2 ；
Step four, utilizing a conditioning circuit to demodulate the sine demodulation wave u s And cosine demodulation wave u c The amplitude of the signal is adjusted to be consistent with the sampling requirement;
fifthly, the conditioned sine demodulation wave u is demodulated through an ADC (analog to digital converter) interface of the DSP chip s And cosine demodulation wave u c Sampling is carried out, the rotor position theta is calculated by using the formula (11), so that the shaft angle conversion of the rotary transformer is realized,
compared with the prior art, the invention has the beneficial effects that:
the invention mainly directly generates the excitation signal through the controller DSP, the generation method is simple, and compared with the method for generating the excitation by PWM in the prior art, the method does not need to arrange a filter circuit at the front end of an amplifying circuit and does not cause the delay of the output signal of the rotary transformer. The invention realizes the demodulation of the output signal by adopting the method of multiplying the excitation signal by the modulation wave, thereby obtaining the continuous and smooth waveform of the demodulation wave. Compared with the peak value sampling and oversampling technology in the prior art, the demodulation waveform can be sampled at any time, and the sampling frequency is not limited by the excitation frequency any more. For the rotary transformer with the same excitation frequency, the accuracy of the rotor position measurement can be improved by increasing the sampling frequency and reducing the quantization error of the rotor position in the shaft angle conversion method under square wave excitation.
Drawings
FIG. 1 is a general implementation diagram of a shaft angle conversion method under square wave excitation;
FIG. 2a is a block diagram of a resolver;
FIG. 2b is an equivalent diagram of the excitation winding and the output winding of the resolver;
FIG. 3 is a waveform diagram of a resolver output signal under square wave excitation;
FIG. 4 is a hardware layout of a peripheral circuit;
Detailed Description
The following describes the square wave excitation signal-based axis angle conversion method according to the present invention in detail with reference to the following embodiments and the accompanying drawings.
As shown in fig. 1, the apparatus for implementing the shaft angle conversion of the rotary transformer provided by the present invention includes a DSP chip, and a peripheral circuit is connected between the DSP chip and the transformer, and the peripheral circuit includes an amplifying circuit, two demodulation circuits, and two conditioning circuits.
As shown in fig. 4, the amplifying circuit includes a first operational amplifier chip and an optocoupler chip, a first resistor is connected between an output end of the first operational amplifier chip and an input negative electrode, and a second resistor is connected between one GPIO port on the DSP chip and an input positive electrode of the first operational amplifier chip; the anode of the optocoupler chip is connected with one end of a third resistor and one end of a fourth resistor in parallel, the other end of the third resistor is connected with the output end of the operational amplifier chip, and the other end of the fourth resistor is grounded; the output of the optocoupler circuit is connected to the excitation winding R1R2 of the resolver, as shown in fig. 1. The DSP chip is of a TMS320F28335 model, the operational amplifier chip in the amplifying circuit in the figure 4 is TL082, and the optical coupler chip is P346.
As shown in fig. 1, the sine output winding S2S4 and the cosine output winding S1S3 of the resolver are respectively connected to two demodulation circuits having the same structure. As shown in fig. 4, the demodulation circuit includes an analog multiplier chip and a second-order RC filter circuit, the output signal of the winding is respectively used as one input of the multiplier chip in the two demodulation circuits, and the other input is an excitation signal. The outputs of the two demodulation circuits are respectively connected with the inputs of the two conditioning circuits. The model of the analog multiplier of the demodulation circuit in the invention shown in FIG. 4 is AD633.
As shown in fig. 4, the conditioning circuit includes a first voltage follower circuit, a second voltage follower circuit, and an anti-parallel diode, where the first voltage follower circuit is composed of a second operational amplifier chip, a fifth resistor, and a sixth resistor, the fifth resistor is connected between the output end and the input cathode of the second operational amplifier chip, and the sixth resistor is connected between the output of the demodulation circuit and the input anode of the second operational amplifier chip; the second voltage follower circuit has the same structure as the first voltage follower circuit, and a voltage division circuit is connected between the first voltage follower circuit and the second voltage follower circuit; an RC filter circuit is arranged between the output end of the second voltage follower circuit and the anti-parallel diode; the outputs of the two conditioning circuits are respectively connected with two ADC interfaces of the DSP chip, as shown in FIG. 1. In the invention, the model of the operational amplifier chip of the demodulation circuit shown in FIG. 4 is LF353.
In order to filter the power clutter, the positive power supply and the negative power supply of the operational amplifier chip are both connected with a filter capacitor. And a positive power supply and a negative power supply of the optocoupler chip are both connected with a filter capacitor.
The invention provides a rotary transformer shaft angle conversion method based on square wave excitation signals, which utilizes the device for realizing the rotary transformer shaft angle conversion and comprises the following steps:
step one, square wave excitation signal u i Generation of (a):
the DSP chip generates a rectangular wave with a duty ratio of 50%, and the rectangular wave signal is amplified in power and amplitude by an amplifying circuit in a peripheral circuit to obtain a square wave excitation signal u i (ii) a The input end of the amplifying circuit is a rectangular wave with the amplitude range of 0-1 generated by the DSP, and the output end is an alternating current square wave excitation signal u with the amplitude range of +/-10V i 。
Step two, square wave excitation signal u i Waveform of the output voltage signal after acting on the resolver:
the resolver is a device for detecting the position of a rotor by the electromagnetic induction principle, and the basic structure of the resolver is composed of a stator and a rotor, wherein the structure of the reluctance type resolver is shown in figure 2a, the rotor of the resolver is not provided with a winding, and an excitation winding R1R2, a sine output winding S2S4 and a cosine output winding S1S3 are wound on the stator. When the excitation winding R1R2 is energized with a high-frequency alternating voltage u i When neglecting the effects of winding resistance, leakage impedance and core saturation, an output voltage u associated with the rotor position θ is generated across the output windings S2S4 and S1S3 sin And u cos 。
Fig. 2b is an equivalent model of the excitation winding R1R2 and the output windings S2S4 and S1S3. In the figure i i Is an exciting current; i.e. i sin ，i cos The sine and cosine output winding currents are respectively; l is 1 ，L 2 Respectively an excitation winding and an output winding inductor; m s ，M c Which are the mutual inductances between the excitation winding and the sine and cosine output windings, respectively.
Input voltage u in equivalent model of resolver i And an output voltage u sin ，u cos Has a relationship of
When square wave excitation signal u i Acting on the rotary transformer, the square-wave excitation signal u i Is shown as
In the formula (1), U m Is the amplitude of the square wave excitation signal, T is the period of the square wave signal, and n is a non-negative number.
The working principle of the reluctance type rotary transformer is as follows: when the rotor rotates at an electrical angular velocity omega, mutual inductance M between the excitation winding and the sine and cosine output windings is caused s 、M c In a regular sine and cosine relationship, has M s ＝M m sinωt，M c ＝M m cos ω t. In the formula, M m Is the mutual inductance amplitude. Assuming that in the equivalent model of the rotary transformer, the output winding is open-circuited and outputs a current i sin ＝0，i cos And =0. Then:
substituting formula (1) into formula (1) in formula (2) to obtain exciting current i under square wave excitation shown in formula (3) i Formula (2)
Substituting the formula (3) into the formula 2 of the formula (2) to obtain the output voltage u of the sinusoidal output winding of the square-wave excited lower-rotation transformer sin Substituting the formula (3) into the formula (3) of the formula (2) to obtain the output voltage u of the cosine output winding of the square-wave excited downward rotation transformer cos ：
In formula (4), k = M m /L 1 In the formula (4), the term on the right side 1 of the number 1 in the formula 1 is ku i sin θ of amplitude A s1 ＝kU m ；
In the same excitation period T, the term on the right side 2 of the medium sign in the formula (1) in the formula (4) is M m i i ω cos θ, where the current i i Is obtained at T/4 within the first period, and T =2 pi/ω e ，ω e At the frequency of the square-wave excitation signal, M m i i The magnitude of ω cos θ is:
due to omega e >&At gt, omega, A s1 >>A s2 The formula (4) is simplified as follows
During the positive half-cycle of square-wave excitation u i ＝U m Derived from the formula (6)
Output voltage u of sinusoidal output winding of rotary transformer during positive half-cycle of square wave excitation sin And the output voltage u of the cosine output winding cos Proportional to the sine and cosine values of the rotor position, respectively, in a ratio kU m ；
In the negative half-cycle of square-wave excitation u i ＝-U m Derived from formula (6):
output of the sinusoidal output winding of the resolver during the negative half-cycle of the square wave excitationVoltage u sin And the output voltage u of the cosine output winding cos Proportional to the sine and cosine values of the rotor position, respectively, in a ratio of-kU m ；
Thus, a square-wave excitation u is obtained i Corresponding to sine value output signal u of rotary transformer sin And cosine output signal u cos Is shown in fig. 3.
Step three, demodulating the output voltage signal of the rotary transformer:
as can be seen from FIG. 3, the sinusoidal output signal u sin And cosine output signal u cos Is an amplitude modulated quadrature signal. The envelope of this signal contains the rotor position information. In the figure, u i During the positive half period, the output signal u sin And u cos Are respectively kU m sin theta and kU m cos theta, the output signal at the moment represents the sine and cosine values of the rotor position; at u i Output signal u during the negative half period sin And u cos Are each-kU m sin theta and-kU m cos θ, the output signal at this time represents the inverse of the rotor position sine and cosine values. Therefore u i The output signal of the rotary transformer corresponding to the positive half period is the required demodulation wave u i The negative half cycle corresponds to a reverse demodulation wave of the output signal of the resolver.
Therefore, in order to obtain a complete demodulation wave in the whole period, the sign of the output voltage in the positive half period of the square wave excitation signal needs to be ensured to be unchanged, and the sign of the output voltage in the negative half period of the square wave excitation signal needs to be opposite. The invention adopts the method of multiplying the output voltage of the rotary transformer by the excitation voltage to unify the signs of the demodulation waves to obtain the demodulation wave u s And u c ：
The formula (7) and the formula (8) are respectively substituted into the formula (9), and the sine demodulation wave u in the whole excitation period s And cosine demodulation wave u c The following were used:
sine-demodulated wave u obtained by equation (10) s And cosine demodulation wave u c Is proportional to the sine and cosine values of the rotor position at any time, the ratio being kU m 2 ；
The resolver output waveform is changed from (1) to (2) in fig. 1 by the demodulation circuit.
Step four, utilizing a conditioning circuit to demodulate the sine demodulation wave u s And cosine demodulation wave u c The amplitude of the sampling signal is adjusted to be consistent with the sampling requirement; the conditioning circuit converts the amplitude of the input signal from +/-3V to 0-3V, and the waveform is converted from (2) to (3) in the graph 1.
The demodulation wave obtained by the shaft angle conversion method (as shown in (2) and (3) in fig. 1) is a continuous and smooth sine curve and cosine curve, so that when an ADC module performs sampling, the demodulation wave can be sampled at any time, and the sampling frequency does not need to be consistent with the excitation frequency, thereby solving the problems of fixed point sampling and fixed frequency sampling.
Fifthly, the conditioned sine demodulation wave u is demodulated through an ADC (analog to digital converter) interface of the DSP chip s And cosine demodulation wave u c Sampling is carried out, and the ADC obtains a demodulation wave u s And u c The sampling waveform of (1) is as shown in 1(4); the rotor position theta is calculated by the formula (11), and the rotor position waveform is shown as 1(5), so that the shaft angle conversion of the rotary transformer is realized,
as shown in (4) of fig. 1, the sampling waveform of the demodulation wave is stepped due to the presence of the sampling interval, and thus the calculated value of the rotor position has a quantization error. Since the sampling frequency in the shaft angle conversion method of the present invention is not limited by the excitation frequency, when the sampling frequency is increased, the demodulation wave u in equation (13) s And u c Sample value update rate ofThe quantization error of the rotor position caused by the sampling interval is improved, so that the detection of the rotor position is more accurate.
While the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are illustrative only and not restrictive, and various modifications which do not depart from the spirit of the present invention and which are intended to be covered by the claims of the present invention may be made by those skilled in the art.
Claims (4)
1. A device for realizing the shaft angle conversion of a rotary transformer comprises a DSP chip, wherein a peripheral circuit is connected between the DSP chip and the transformer and comprises an amplifying circuit, two demodulation circuits and two conditioning circuits; it is characterized in that the preparation method is characterized in that,
the amplifying circuit comprises a first operational amplifier chip and an optocoupler chip, a first resistor is connected between the output end of the first operational amplifier chip and an input cathode, and a second resistor is connected between one GPIO port on the DSP chip and an input anode of the first operational amplifier chip; the anode of the optocoupler chip is connected in parallel with one end of a third resistor and one end of a fourth resistor, the other end of the third resistor is connected with the output end of the operational amplifier chip, and the other end of the fourth resistor is grounded; the output of the optical coupling circuit is connected to an excitation winding of the rotary transformer;
the sine output winding and the cosine output winding of the rotary transformer are respectively connected with two demodulation circuits with the same structure, and the outputs of the two demodulation circuits are respectively connected with the inputs of the two conditioning circuits;
the demodulation circuit comprises an analog multiplier chip and a second-order RC filter circuit;
the conditioning circuit comprises a first voltage following circuit, a second voltage following circuit and an anti-parallel diode, wherein the first voltage following circuit is composed of a second operational amplifier chip, a fifth resistor and a sixth resistor, the fifth resistor is connected between the output end and the input cathode of the second operational amplifier chip, and the sixth resistor is connected between the output of the demodulation circuit and the input anode of the second operational amplifier chip; the second voltage follower circuit has the same structure as the first voltage follower circuit, and a voltage division circuit is connected between the first voltage follower circuit and the second voltage follower circuit; an RC filter circuit is arranged between the output end of the second voltage follower circuit and the anti-parallel diode;
the outputs of the two paths of conditioning circuits are respectively connected with two ADC interfaces of the DSP chip.
2. The device for realizing the axial angle conversion of the rotary transformer as claimed in claim 1, wherein the positive power supply and the negative power supply of the operational amplifier chip are both connected with a filter capacitor.
3. The device for realizing axial angle conversion of the rotary transformer according to claim 1, wherein a positive power supply and a negative power supply of the optical coupling chip are both connected with a filter capacitor.
4. A method for converting the axial angle of a rotary transformer based on a square wave excitation signal, characterized by using the apparatus for converting the axial angle of a rotary transformer as claimed in any of claims 1 to 3, and comprising the steps of:
step one, square wave excitation signal u i Generation of (a):
the DSP chip generates a rectangular wave with a duty ratio of 50%, and the rectangular wave signal is amplified in power and amplitude by an amplifying circuit in the peripheral circuit to obtain a square wave excitation signal u i ；
Step two, square wave excitation signal u i The waveform of the output voltage signal after acting on the rotary transformer is as follows:
when square wave excitation signal u i Acting on said rotary transformer, the square-wave excitation signal u i Is shown as
In the formula (1), U m Is the amplitude of the square wave excitation signal, T is the period of the square wave signal, and n is a non-negative integer;
the equivalent model of the resolver is:
in the formula (2), u sin ，u cos The output voltage of the sine output winding and the output voltage of the cosine output winding are respectively; l is 1 Is an excitation winding inductance; i all right angle i Is an exciting current; m m The mutual inductance amplitude between the excitation winding and the output winding is shown, and theta is the position of a rotor of the rotary transformer;
substituting formula (1) into formula (1) in formula (2) to obtain exciting current i under square wave excitation shown in formula (3) i Formula (2)
Substituting the formula (3) into the formula 2 of the formula (2) to obtain the output voltage u of the sinusoidal output winding of the square-wave excited lower-rotation transformer sin And (3) substituting the formula (3) into the formula (3) of the formula (2) to obtain the output voltage u of the cosine output winding of the square-wave excited lower rotary transformer cos ：
In formula (4), k = M m /L 1 ω is the angular velocity of rotation of the rotor; the term "ku" on the right side of the No. 1 medium symbol in the formula (4) i sin θ of amplitude A s1 ＝kU m ；
In the same excitation period T, the term on the right side 2 of the medium sign in the formula (1) in the formula (4) is M m i i ω cos θ, where the current i i Is obtained at T/4 within the first period, and T =2 pi/ω e ，ω e At the frequency of the square-wave excitation signal, M m i i The magnitude of ω cos θ is:
due to omega e >>ω，A s1 >>A s2 The formula (4) is simplified as follows
During the positive half-cycle of square-wave excitation u i ＝U m Derived from the formula (6)
The output voltage u of the sinusoidal output winding of the rotary transformer during the positive half-cycle of a square-wave excitation sin And the output voltage u of the cosine output winding cos Proportional to the sine and cosine values of the rotor position, respectively, in kU m ；
In the negative half-cycle of square-wave excitation u i ＝-U m Derived from formula (6):
the output voltage u of the sinusoidal output winding of the rotary transformer during the negative half-cycle of the square-wave excitation sin And the output voltage u of the cosine output winding cos Proportional to the sine and cosine values of the rotor position, respectively, in a ratio of-kU m ；
Step three, demodulating the output voltage signal of the rotary transformer:
multiplying the output voltage of the rotary transformer by the excitation voltage to obtain:
the formula (7) and the formula (8) are respectively substituted into the formula (9), and the sine demodulation wave u in the whole excitation period s And cosine demodulation wave u c The following were used:
sine-demodulated wave u obtained by equation (10) s And cosine demodulation wave u c Is proportional to the sine and cosine values of the rotor position at any time, the ratio being kU m 2 ；
Step four, utilizing a conditioning circuit to demodulate the sine demodulation wave u s And cosine demodulation wave u c The amplitude of the signal is adjusted to be consistent with the sampling requirement;
fifthly, the conditioned sine demodulation wave u is demodulated through an ADC (analog to digital converter) interface of the DSP chip s And cosine demodulation wave u c Sampling is carried out, the rotor position theta is calculated by using the formula (11), so that the shaft angle conversion of the rotary transformer is realized,
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| CN201710715983.0A Active CN107659224B (en) | 2017-08-18 | 2017-08-18 | Device and method for converting axial angle of rotary transformer based on square wave excitation signal |
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