GB2471458A

GB2471458A - An angle to PWM converter for a resolver, using a single high frequency reference sine wave

Info

Publication number: GB2471458A
Application number: GB0911185A
Authority: GB
Inventors: Mohieddine Benammar; Lazhar Ben-Brahim; Kamel Besbes
Original assignee: Qatar University
Current assignee: Qatar University
Priority date: 2009-06-29
Filing date: 2009-06-29
Publication date: 2011-01-05
Also published as: GB0911185D0

Abstract

A sinusoidal reference waveform from generator 30 is input to a comparison block 101 which also receives amplitude-demodulated sine and cosine values from a transducer 20 such as a resolver. A flip-flop 102 is set by comparator C2 when the reference signal passes positively through zero and is reset by comparator C1 when the reference sinusoid equals the sine value from transducer 20. The output of the flip-flop is a PWM signal with duty ratio proportional to the angle. The comparator C3, responsive to the cosine value, allows the circuit to output PWM signals encoded for angles between 90 and 270 degrees. The range of the sine and cosine values is adjusted to match the range of the reference sinusoid, so that the angle measurement is independent of the amplitude of the reference waveform, which may be the transducer excitation signal. To improve resolution where the sine value is near its maximum or minimum a PWM signal derived from a comparison of the cosine value with the reference signal may be selected, instead of the sine-derived PWM signal, when the angle lies between 45-135 or 225-315 degrees (figures 4-8).

Description

AN APPARATUS FOR THE DETERMINATION OF THE ANGLE

FROM ITS SINE/COSINE VALUES

NON-PATENT REFERENCES

1. Catalog of Admotec "Understanding Resolvers and Resolver-to-Digital Conversion" http://www.adrnotec.coni"1T02.pdf, 1998 2. M. Benammar, L. Ben Brahim & Mohd A. Alhamadi, "A Novel Resolver-to-360 Degree Linearized converter", IEEE Sensors Journal, Vol 4, 2004, pp 96-101.

3. M. Benammar, L. Ben Brahim, Mohd A. Aiharnadi, & M. El-Naimi, "A novel method for estimating the angle from analog co-sinusoidal quadrature signals," Sensors and Actuators A, Vo1A 142, 2008, pp 225-23 1.

PATENT REFERENCES

1. Resolver To 360 degrees Linear Analog Converter And Method W000/33466-8-6-2000 2. Apparatus For The Determination Of The Angle From Sine/Cosine Transducers GB244790 1 A-0 1-10-2008

AN APPARATUS FOR THE DETERMINATION OF THE ANGLE FROM ITS

SINE/COSINE VALUES The present invention relates to a converter apparatus for determining an unknown angle O from its sine and cosine values: sin(G) and cos(G). It is about new scheme which can be applied to sinusoidal quadrature encoders, resolvers, or to any other source generating quadrature sinusoidal signals. The new method of conversion makes use of a separately generated constant-frequency sinusoidal signal as reference against which the amplitudes of the transducer signals A xsin(O) and A xcos(O) are compared, resulting in digital pulses with rising and falling fronts. The time differences between fronts are used in an arrangement that enables the determination of the input angle, 0. In the case of transducers which require sinusoidal excitation signal for their operation (such as resolvers), the same excitation signal may be used as reference in the proposed scheme (patent reference 1, patent reference 2). This offers an additional advantage as the determination of the angle will be immune to fluctuations of amplitude of the excitation (and reference) signal. The scheme of the invention greatly simplifies the derivation of the angle without compromising precision of the conversion process.

BACKGROUND OF THE INVENTION

Various transducers, such as resolvers and sinusoidal encoders, generate electrical signals in the form of the sine and the cosine of the angular position of their shaft. The present invention relates to an open-loop converter circuit that may be used with these transducers in order to determine the angle from their sinusoidal output signals. The new converter incorporates fixed frequency sinusoidal signal, against which the amplitude of the input sine and cosine signals are compared for the purpose of determining the angle.

The pulses resulting from these comparisons are used in a time measurement arrangement to deduce the unknown input angle. This converter is suitable for all transducers generating sine and cosine signals. However the technique is particularly useful for transducers requiring excitation with sinusoidal signals; in this case this necessary element for operating the transducer may be used simultaneously by the converter. For this reason, the analysis given below refers to a converter used with a resolver. The resolver is basically a rotaly transformer (non-patent literature 1), usually with a rotating armature and two stationary windings which are placed at right angles to one another.

The winding of the rotor is supplied with a high-frequency sinusoidal carrier signal, VRS(t)= A sin(wt) (1) where A and w are the peak amplitude and angular frequency respectively (their magnitudes are typically bY and 8000it rad/s). The resolver operates as a rotating transformer, and provided that the rotating angular velocity dO/dt of the rotor is much lower than the angular frequency of VRS(t), the two stator windings of the resolver generate modulated signals given by: [V (t, 0) = aA sin(0) x sin(t) (7) LVc (t, 0) = wi cos(0) x sin(wt) where 0 is the angular position of the shaft of the resolver and a is the transformation ratio (constant) between rotor and stator windings. Note that the resolver is usually driven at low speeds in positioning applications, and therefore its outputs are closely described by (2). By simple demodulation of the stator signals, the carrier may be removed, resulting in sine and cosine signals. The maximum amplitude of these signals may be made equal to that of VRS(t) through an appropriate amplification stage. The obtained signals after demodulation are denoted: Vç(0)Axsin(0) (3) Lvc(0) Axcos(0) The present invention relates to an open-loop converter circuit that may be used with these transducers in order to determine the angle 0 from (3) and (1).

CONVENTIONAL OPEN-LOOP METHODS

In addition to closed-loop methods (i.e., Phase Locked Loop (PLL) or Tracking converters), various open-loop converters providing linear outputs have been described for the measurement of Oby appropriate processing of Asin(0) and Axcos(O).

Conventional open loop techniques based upon the tangent/cotangent of the shaft angle have been used (non-patent literature 1). Tn these schemes, the absolute values of the sine and cosine signals are determined. By appropriate processing the smaller of the two values is divided by the greater, providing either the tangent or cotangent of the unknown angle. The estimated value °e of the input angle Ois then, either computed numerically or determined from the highly non-linear tangent using a look-up-table.

Other open-loop methods include also an approach based upon the linearization of the difference between the absolute values of the sine and cosine signals (non-patent reference 2). Another open-loop method for determining the angle from sine and cosine signals was based on a scheme generating multiple phase-shifted sinusoids (PSS) from the transducer signals (non patent reference 3). A suitable arrangement enables the use of the pseudo-linear segments of the PSS, alternating around zero crossings, in order to determine the angle continuously and linearly without the need for processors or look-up

tables.

A recently reported method (patent reference 2) is based on the use of two constant frequency quadrature reference signals (Axsin(wt) and Axcos(wt)) against which the transducer signals Axsin(O) and Axcos(O) are compared. A third saw tooth reference signal W(wt) is also generated from Axsin(wt) using additional circuitry. The instants at which the amplitudes of the quadrature reference signals are equal to their respective amplitudes of the transducer signals are used to trigger a sample and hold device that provides a sample from P(wt). The analog output from the sample and hold is proportional to the unknown angle 0. The arrangement used in this scheme is complicated and requires three synchronized reference signals. The circuitry used for controlling the sample and hold is also complicated. The new converter proposed in the present invention avoids these drawbacks by using only a single reference signal Axsin(wt); in case the converter is used for a resolver, the same signal used for its excitation may be used as reference for the converter. Additionally, the present invention requires few components for its implementation and provides an output readily in a digital form. Finally, the precision of the prior converter of patent reference 2 relies heavily on the linearity of the sawtooth reference signal kP(ot). This is not the case in the present invention.

SUMMARY OF THE INVENTION

The present invention relates to an apparatus for converting the input signals Axsin(O) and Axcos(O) into signals representative of the position 0. It is about a new scheme which can be applied to a transducer such as quadratue encoder or resolver devices. Unlike most conventional converters, the new apparatus is based on a feed forward technique that is simple to implement and requires only low cost hardware. The present apparatus makes use of separately generated high-frequency sinusoidal reference signal A xsin(@t) in order to extract the angle 0 from Axsin(O) and Axcos(9) signals. The scheme of the invention simplifies the derivation of the angle without using expensive non-linear components.

Fig. 1 is the simplified block diagram of the converter described in the present invention.

The converter (10) produces an output signal that is linearly proportional to the shaft angle of the transducer (20) over 360 degrees. A fixed-frequency generator (30) produces a sinusoidal signal used as reference by the converter. For effective operation and precision of the present invention, the frequency of the reference signal must be at least an order of magnitude higher than the maximum rate of change of 0. The converter (10) is made up of a set of comparators (101) and a time measurement unit (102).

The basic idea of the proposed converter (10) is detailed in Fig.2, and shown to make use of the input sine signal (Axsin(8)) only. The maximum amplitudes of the reference signal and input (e.g., transducer) signals are made equal. The comparator Cl in (101) used to compare the instantaneous amplitudes ofAxsin(0) and Axsin(wt) produces a pulse whose rising and falling edges occur at wtj= 0 and Wt2=lt-O in each period of the reference signal. The comparator C2 in (101), used to detect the zero crossing of the reference signal, gives a pulse whose rising edge occurs at wt0= 0. It is clear that the time difference (t1-t0) is proportional to the unknown angle 0. The measurement unit (102) is intended to measure this time difference; one way to measure this is to use an RS flip flop that produces a pulse width proportional to the unknown angle. The estimated value of the angle from this time difference is given by: OeS =2ir'<(ti to)/T.

I is the period of the reference signal (T= 2ir/w). This can be considered constant or can be measured by the same timer used to measure (t1-t0). In the latter case the measurement of the angle is independent of the frequency of the reference signal. For resolver application, the measurement of the angle is robust to fluctuations in the maximum amplitude (A) of the excitation (and reference) signal, as any change in this amplitude results in an equivalent change in the transducer signals. The net of effect of this is that the positions of the fronts of the pulses, and the measurement of 0 is independent of A. Now because of the symmetry of the sine function, an ambiguity will be observed between angles of values 0 and ir-O. This ambiguity can easily be eliminated by modifying (101) by including a comparator C3 that determines the sign of the second transducer signal Axcos(O) as shown in Fig. 3. In this modification that takes into consideration the sign of the sine signal, the rising edge of the stop count signal will always occur at the correct angle.

A drawback of the basic idea described in Fig. 3 is that sensitivity around the angle values of ir/2 and 3ir/2 is poor. The reason for this is that when Axsin(O) is around its peak values, the result of the comparison of its amplitude to that of Axsin(wt) is unreliable. This could lead to loss of precision of measurement of the angle in these regions. The solution to this is to further modify (101) so that it takes this into account.

One way to do this is to rely on the accurate comparison of the amplitudes of the alternating pseudo-linear segments of both Axsin(9) and Axcos(O) (i.e., bold segments in Fig. 4), and to avoid unreliable triggering that may result by using the highly non-linear peaks of the sinusoids. A possible way to best use the pseudo-linear sections of the transducer signals is to modify (101) and (102) and realize a converter employing both sine and cosine values of the unknown angle to generate two outputs °eS and OeC as shown in Fig, 5: °eS results from using Axsin(O) and Axsin(ut) and °eC from Axcos(O) and Axsin(wt). Of course, because of phase shift, the pulse width generated from comparison ofAxcos(O) and Axsin(wt) will be proportional to ir/2+O. The validated output is selected according to the quadrant of input angle as shown in Fig. 4. In this final design, three signals C, F and G are produced by (101) and used by the time measurement unit (102) to produce the independent measures OeS and °eC of the unknown angle. This is ensured by two counters in (102).

The converter may be implemented using hardware only or may be partly programmed into a processor as the signals used by the counting devices are readily in digital form.

Figure 6 depicts the input and output waveforms of converter for various values of the input angle.

A different and simpler embodiment of the described invention is shown in Fig.7. In this second embodiment, (101) is simplified by dispensing with comparator C3 and the two exclusive or gates required in the first implementation given in Fig. 5. The inputs to the time measurement unit (102) are also changed. The measurement of the input angle may be based on the measurement of the width of the pulses Ats and At obtained by comparing the amplitude ofAxsin(O) to that of Axsin(wt) and the amplitude ofAxcos(O) to that of Axsin(ot). Analysis based on simple trigonometry leads to the expressions relating the outputs of the converter to the estimated measures OeS and °eC as summarized in Table 1 for the four quadrants of input angle 0. Figure 8 depicts the input and output waveforms Ats and At of the second implementation of the converter for the input angle 0 values of 30°, 100° and 200°. Sample computation Of OeS and °eC arc also shown.

Table 1: Parameters of the second implementation of the proposed open-loop converter method [0,m/2] [ir/2,ir] [ir,3ir/2] [3m/2,2ir] [0,2ir] Pulse-width of (ir-20)/w (20-ir)/w (20-ir)/w (5ir-20)/w 9eS = 2 + (Wt5 X E) StateofE 0 1 1 0 Pulse-width of 201w 201w (4ir-20)/w (4ir-20)/w AAt ______ 0eC = + (2it -ü.Lltc) X B StateofB 0 0 1 1

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 shows a simplified diagram of the proposed converter with a single reference signal Figure 2 shows the basic idea behind the proposed open-loop converter method Figure 3 shows an improved version of the basic idea for unambiguous measurement of the angle Figure 4 shows the validation of measurement results that ensures use high precision due to usage of the pseudo-linear segments of input signals shown in heavy line Figure 5 shows a first implementation of the proposed open-loop converter method Figure 6 shows an example of input/outputs and reference signal for the first implementation of the proposed converter Figure 7 shows a second implementation of the proposed open-loop converter method Figure 8 shows an example of input/outputs and reference signal for the second implementation of the proposed converter

Claims

AN APPARATUS FOR THE DETERMINATION OF THE ANGLEFROM ITS SINE/COSINE VALUESCLMMS1. A converter for determining in a feed-forward manner an angle 0 from slowly varying Axsin(G) and Axcos(G) input signals, using only one relatively high frequency analog sinewave generator (Axsin(oit)), where 0) is the angular frequency of the sine signal and t is time. The converter comprises a feed-forward angle computation scheme that produces an angle °e as an estimate of the angle 0 using A xsin( , Ax cos( 8 and A xsin(ot) signals.
2. A converter as in claim 1, wherein the high frequency Axsin(iot) signal is a reference signal generated by an external generator. The low frequency trigonometric input signals Axsin(9j and Axcos(e can be response signals received from an external device in response to a mechanical rotation angle 0.
3. A converter as in claim 1, where the angle computation from transducers employing an excitation signal (such as resolvers) is unaffected by fluctuations in the amplitude and frequency of the reference and excitation signal.
4. A converter as in claim 1, wherein the angle computation scheme comprises: * A comparator that detects the zero crossing ofAxsin(ot), * A set of comparators which compare the value of Axsin(G) to the instantaneous amplitude ofAxsin(iot) and the value ofAxcos(G) to the instantaneous amplitude ofAxsin(iot) and generate pulse signals used for determining and * A time measurement circuit controlled by the outputs of the comparators to produce two independent measures of 0 in a form of time.* A validation mechanism that selects the most accurate measure of 0 depending on its range where either Axsin(Gj or Axcos(G is most linear.