GB2447901A

GB2447901A - Means for determining an utilizing an open loop arrangement

Info

Publication number: GB2447901A
Application number: GB0705763A
Authority: GB
Inventors: Lazhar Ben-Brahim; Mohieddine Benammar; Mohd A Alhamadi; Nasser A Al-Emadi; Mohamed Al-Hitmi
Original assignee: Qatar University
Current assignee: Qatar University
Priority date: 2007-03-26
Filing date: 2007-03-26
Publication date: 2008-10-01
Anticipated expiration: 2027-03-26
Also published as: GB2447901B; GB0705763D0

Abstract

The present invention relates to converter means utilizing an open loop arrangement for converting the sine/cosine transducer signals into a measure of the input angle without using look-up tables. The converter comprises a phase shifter 40 that produces a cos( l t) signal from a generated 30 sin( l t) signal, a sawtooth generator that produces a d ( l t) signal from the generated sin( l t) signal: and a feed-forward arrangement producing an angle R e as an estimate of the angle R using sin( R ), cos( R ), sin( l t), cos( l t) and d ( l t) signals.

Description

APPARATUS FOR THE DETERMINATION OF THE ANGLE

FROM SINE/COSINE TRANSDUCERS

NON-PATENT REFERENCES

I. Catalog of Admotec "Understanding Resolvers and Resolver-to-Digital Conversion" http://www.admotec.comiTTO2.pdf, 1998 2. M. Benammar, L. Ben Brahim & Mohd A. Aihamadi, "A Novel Resolver-to- 360 Degree Linearized Converter", IEEE Sensors Journal, Vol 4, No 1, Feb 2004, pp 96-101.

3. M. Benammar, L. Ben Brahim, Mohd A. Aihamadi, & M. El-Naimi, "Accurate Interface for Resolvers and Sinusoidal Encoders," Proc. Eurosensors XX Conference, Goteborg, Sweden, I 7-20 Sept. 2006. CD Rom ISBN 91-63 1-9281-0 & ISBN 978-91-63 1-9281-4.

PATENT REFERENCES

1. Resolver To 360 degrees Linear Analog Converter And Method 2. Resolver/Digital Converter And Control Apparatus using the sameUSO28O57O-12-3-2005

BACKGROUND OF THE INVENTION

Various transducers, such as resolvers and sinusoidal encoders, generate electrical signals in the form of the sine (i.e., sin(O)) and the cosine (i.e., cos(9)) of the mechanical angle (i.e., 0) 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.

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 9 by appropriate processing of sin(9) and cos(8) transducer signals.

Conventional open loop techniques based upon the tangent/cotangent of the shaft angle have been used (non-patent literature l&2). In 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 ofthe unknown angle. The estimated value 9e of the input angle 0 is 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.

SUMMARY OF THE INVENTION

The present invention relates to an apparatus, preferably in the form of an analog arcsine converter, for converting the sin(9) and cos(0) input signals into analog or digital 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 does not use a look-up table for its implementation. The present apparatus makes use of separately generated high-frequency sinusoidal signal in order to extract the angle 9 from sin(0) and cos(0) signals. The scheme of the invention simplifies the derivation of the angle without using expensive non-linear components.

Fig.l is the 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 separately-generated signal must be at least an order of magnitude higher than the maximum rate of change of the input signals sin(0) and cos(0). The 90 phase shifter (40) produces a cos(ot) from the sin(wt) signal generated by (30). If a quadrature oscillator is used instead of the sinewave generator (30), both sine and cosine are readily available and a phase shifter is not needed. A saw-toothed waveform P(t) proportional to wt is derived using converter (50) having sin(wt) as its input. These signals (cos(ot), sin(cot), and P(ot)) serve as the equivalent of an analog look-up-table for the converter.

By comparing the amplitudes of sin(0) and cos(9) signals coming from the transducer, a quadrant determination circuit (101) distinguishes the four quadrants of the input angle by outputting four binary outputs (Q' through Q4) as shown in Fig. I and Fig. 2. These binary signals differentiate between the quadrants (-45 =0 =45 ), (45 =O =l35 ), (135 =O =225 ), and (225 = =315 ). A possible implementation of the quadrant determination circuit (101) is shown in Fig. 3. This circuit is composed of some operational amplifiers and logic gates. The transducer signals sin(e) and cos(8) are also compared in the block (103) to their respective reference signals sin(ot) and cos(ut). The results of the comparison are output as Cs and Cc signals. A possible implementation of (103) is shown in Fig. 4. The trigger circuit (102) receives the four binary data (Q through Q4) and the outputs Cs and Cc of the comparators (103) to generate a control signal TSH(t,9) in order to trigger the sample & Hold device (104).

This device (104) outputs the value of'1'(cot) when sin(O)=sin(ot) and cos(0)cos(cot), thus providing a measure e of the input angle 0 (Oe = 0 = P(ot) at the sampling time) As depicted in Fig.4, this solution ensures that the triggering of the sample and hold relies on the accurate comparison of the amplitude of the pseudo-linear segments of sin(0) and cos(0) (i.e., bold segments in Fig. 2), and avoids unreliable triggering that may result by using the highly non-linear peaks of the sinusoids. Evidently since at the time of triggering sin(O)=sin(U)t) and cos(O)=cos(ot), the pseudo-linear segments of sin(0) and cos(O) correspond to pseudo-linear segments of sin(wt) and cos(0t) respectively. As a result, the angle B is extracted without look-up table or processor and with a good precision and linearity due to the adequate triggering of circuit (102).

A possible implementation of (102) requiring only basic logic gates is shown in Fig. 5. The triggering circuit (I 02) of Fig. 5 guarantees a higher precision of the present converter as it is selecting the pseudo-linear segment of the trigonometric function for the calculation of the estimation angle. For this task, the triggering circuit (102) performs the following Boolean operation: T11(1,&') = (Q1.C)(Q2.C)(Q3.C) (Q4 C.) For instance, Q allows the selection of the triggering for the quadrant (-45 =O =45 ) using the sin(0) signal since it is more linear than the cos(O) signal as illustrated in Fig. 2. On the other hand Q2 allows the selection of the triggering for the quadrant (45 =0 =135 ) using the cos(O) since it is more linear than the sin(O) as illustrated in Fig. 2.

Fig. 6 shows waveforms of the input angle made to change in an arbitrary fashion, the reference signals sin(ot), cos(wt) and P(ot), and the transducer signals sin(O) and cos(O). This Figure depicts waveforms showing the triggering technique used in this invention. The accurate triggering relies on the validation of one of the two comparisons of the amplitude of sin(O) to that of sin(t) and the amplitude of cos(9) to that of cos(ot) depending on the states of the four binary data (Qi through Q4). This ensures that triggering of the Sample & Hold device (I 04) occurs, alternately, on the linear segments of sin(0), cos(0), sin(ot) and cos(ot) as illustrated in the zoomed part of Fig. 6. Note that the triggering occurs at the falling edge of l'5H(t,O).

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. I shows the details of the converter according to the preferred embodiment Fig. 2 shows the inputs/output of quadrant determination circuit(lOI) portion of the converter circuit of Fig. I. The pseudo-linear segments of input signals are shown in heavy line Fig. 3 shows an implementation of quadrant determination circuit (lOl)portion of the converter circuit of Fig. I Fig. 4 shows an implementation of(l03) portion of the converter circuit of Fig. 1 Fig. S shows an implementation of the Triggering circuit (102) portion of the converter circuit of Fig. I Fig. 6 shows an example of input/outputs and reference signals of the converter circuit of Fig. 1; the zoomed part shows the used triggering technique

Claims

1. A converter for determining in a feed-forward manner an angle 0 from low frequency sin(O) and cos(0) input signals, using a relatively high frequency analog sinewave generator (sin(ot)), where w is the angular frequency of the sine signal and t is time, the converter comprising: A phase shifter that produces a cos(t) signal from the generated sin(0t) signal; a sawtooth generator that produces a (Ot) signal from the generated sin(o)t) signal; and a feed-forward angle computation scheme that produces an angle 0e as an estimate of the angle 0 using sin(9), cos(0), sin(wt), cos(wt) and P(wt) signals.

2. A converter as in claim 1, wherein: The high frequency sin(U)t) signal is a reference signal generated by an external generator, and the low frequency trigonometric input signals sin(0) and cos(0) can be response signals received from an external device in response to a mechanical rotation angle 0.

3. A converter as in claim 1, wherein the saw-tooth generator that comprises: An integrator that integrates a constant and is reset by the zero crossing of Sin(cit) to give a linear sawtooth signal P(cct) proportional to cit.

4. A converter as in claim I, wherein the angle computation scheme comprises: * A quadrant determination circuit which generates four binary signals (Qj, Q2, Q, Q) to differentiate between quadrant#l (-45 =0 =45 ), quadrant2 (45 =0 = 135 ), quadrant#3 (1 35 =0 =225 ), and quadrant4 (225 =9 =3 I 50) respectively.

* A set of comparators which compare the amplitudes of sin(0) to sin(ot) and cos(O) to cos(cot) and generate signals C5 and Cc; and A circuit that, depending on the (Q, Q2, Q, Q4 and the comparators outputs (Cs, Cc), generates a triggering signal TSH(t,O) to sample and hold the value of 4(ot) and guarantees that triggering relies on the accurate comparison of the amplitudes of the trigonometric signals when they are most linear.

5. A converter as in claim 4, wherein the quadrant determination circuit comprises: Two comparators and a summer of the trigonometric input signals and a few logic gates to output the quadrant identification binary signals (Q, Q2, Q, Q) to differentiate between the quadrant#1 (-45 =8 =45 ), quadrant#2 (45 =9 =l35 ), quadrantI3 (l35 =O =225 ), and quadrant#4 (225 =e =315 ) respectively.

6. A converter as in claim 4, wherein the comparators circuit comprises: Two comparators to compare the amplitude of sin(e) to that of sin(0t) and the amplitude of cos(O) to that of cos(cot) signals to output two binary signals C5 and Cc, respectively.

7. A converter as in claim 4, wherein the triggering circuit comprises: Logic gates which process the binary signals (Qi, Q2, Q, Q) coming from the quadrant determination circuit and the Cs, C signals to produce triggering signal T5H(t,O) for the sample and hold circuit. This ensures that the triggering occurs during the linear segments of all trigonometric signals. This increases the precision of the calculation of 9 by avoiding the non-linear flat segments of the trigonometric signals.