Phase-responsive angular tracking device

An apparatus for generating phase modulated angular positional signals in digital form. A phase tracking loop receives a phase modulated signal from the rotor of a resolver whose stator windings are excited in quadrature. The phase output of the resolver is proportional to the angular displacement of the rotor. Signals for exciting the stator windings of the resolver are applied in phase quadrature to a phase detector to develop an analog error signal when combined with the rotor output signal. The analog phase error signal provides an output indicative of the angular displacement of the rotor. The error signal is applied to a voltage controlled oscillator, converted to digital form, and combined with the excitation signals in a closed loop to force the error signal to a null, whereupon the indicated digital output angle is in coincidence with the angular displacement of the rotor shaft.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates generally to angular measuring systems, and more 
particularly to a phase-analog detector for providing a digital readout 
indicative of the angular displacement of a rotary inductive sensor. 
2. Description of the Prior Art 
Accurate measurement of angular displacement is currently required in many 
military, aerospace, satellite, radar and fire control systems, where the 
electrical output signals are required to drive numerical readout 
displays, provide servo loop feedback signals, and generate computer input 
data. Among the methods which have found wide application for precise 
angular measurements are optical encoders, which, for example, may have a 
pattern impressed upon a disk which is used in conjunction with a light 
source and a sensor to provide a digital output that is generated when the 
disk is rotated. Very high resolutions and accuracies are available, but 
such devices are prohibitively expensive and lack sufficient ruggedness in 
many applications. 
A second approach is the use of a resolver, which is a rotating transformer 
which provides output analog voltages that are uniquely related to the 
input shaft angle. Such a resolver is comprised of two orthogonal stator 
windings and a rotor which is coupled to the input shaft. It provides an 
absolute indication of position from 0.degree. to 360.degree. of rotation. 
Two or more resolvers, each yielding data over a unique but limited range, 
may have their outputs combined in a multi-resolver configuration to yield 
an absolute indication of greater resolution through 360.degree. of 
rotation. A resolver is a robust mechanical device that can be exposed to 
extreme environments without damage or loss of accuracy. As a transformer 
device, it provides signal isolation and a common-mode rejection to 
electrical interference. Since it is an analog device, only four wires are 
necessary for angular data transmission. 
Transducers are also available which operate on the principles of inductive 
or capacitive coupling between conductive patterns bonded to a rigid 
substrate. Since, as in the resolver, there are no contacting elements 
except for slip rings, they provide high reliability and maintain original 
accuracy indefinitely. One such device is the INDUCTOSYN.RTM. position 
transducer. These transducers are available in both linear and rotary form 
for a wide range of applications. The term "resolver" is defined herein to 
include conventional resolvers, inductive and capacitive transducers, and 
similar devices. 
Two methods have been used with a resolver to obtain output voltages 
proportional to the shaft angle. In the first method, an alternating 
current is applied to excite the rotor winding and outputs are taken from 
the two stator windings. Since the stator windings are orthogonally 
disposed, the output signal amplitudes are related by the trigonometric 
sine and cosine of the angular shaft displacement. Both stator output 
signals will have the same phase as the original excitation signal, while 
their amplitudes are modulated respectively by the sine and cosine 
functions as the shaft rotates. The ratio of the output amplitudes may 
then be compared to provide an output signal which provides a high degree 
of noise immunity. By applying the resultant signal to an amplitude 
tracking loop, the output may be made to follow automatically the input up 
to a specified maximum tracking rate. In this application the device is 
called a tracking converter. 
In some systems, however, it is desired to produce a phase-modulated signal 
because it may conveniently be utilized for both rate and position control 
in a phase-locked loop. Thus the second method applies two signals in 
phase quadrature to the respective stator windings. The voltage induced in 
the rotor when the shaft is displaced angularly has a constant amplitude 
and frequency, but a phase varying with shaft angle. Thus, when the rotor 
windings are aligned with the first stator winding, the rotor output 
signal will be at 0.degree. phase shift, while when the rotor windings 
align with the second stator winding, the output will be at a maximum of 
90.degree. phase shift. At angles between 0.degree. and 90.degree., the 
phase of the output signal varies substantially linearly with the angle of 
displacement. As the rotor rotates through 360.degree., the phase of the 
output rotor signal also varies from 0.degree. to 360.degree. and back to 
0.degree.. 
One technique for converting the phase-modulated signals into digital 
position data is known as the phase counting scheme, and is based on the 
direct measurement of phase angle by means of gating a counter with the 
phase-modulated position signal. Thus, a zero-crossing detector provides 
an output corresponding to an applied sinosoidal excitation signal and 
also to the zero-crossing of the rotor signal. The time interval between 
the two zero crossings is used to gate a pulse generator, which is applied 
to a counter to provide a digital readout. Because the phase output is 
sampled, and produces only one position measurement per excitation cycle, 
a low excitation frequency, such as 400 Hz, as used by many standard 
resolvers, results in a measurement delay as long as 2.5 ms. Moreover, 
since this reading also takes time to process, a delay of as much as 3.75 
ms may result. This is not acceptable for many high-bandwidth position 
control servo loops, since these delay variations are a destabilizing 
influence on the control loop. Further since only one measurement is made 
per excitation cycle, the resolution of the converter is limited by the 
frequency of the excitation signal, and the accuracy is limited by the 
accuracy of the zero-crossing detector. 
The present invention provides improved performance by utilizing the 
stability obtained in state of the art frequency synthesizers to generate 
highly accurate and stable frequency independent phase-tracking signals to 
provide a digital output corresponding to the angle of rotation of a 
resolver. It provides an apparatus for measuring angular displacement by 
continuously tracking the input signal and applying the phase modulated 
output derived from the rotor of a resolver whose stator windings are 
excited in quadrature to a phase tracking loop, and provides a digitized 
output. It affords high accuracy with minimal measurement delays. 
Measurement accuracy is independent of excitation frequency and less 
sensitive to incoherent noise sources. 
SUMMARY OF THE INVENTION 
The present invention provides an apparatus for generating a digital signal 
proportional to an angular displacement of a shaft. In a preferred 
embodiment, first and second signals in phase quadrature relationship are 
applied to excite a transducer coupled to the shaft. A third signal 
providing a phase difference proportional to an angular displacement of 
the shaft is generated by the transducer. The first, second, and third 
signals are combined to provide a difference signal, wherein the 
difference signal is indicative of an error between the angular 
displacement and a digital indication thereof. The difference signal is 
then applied in a closed loop to the first and second signals, whereby the 
difference signal is urged to a null value. When the difference signal has 
reached a null value, the digital indication corresponds to the angular 
displacement of the sensor rotor.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to FIG. 1, resolver 10 is comprised of stator windings 12 and 
14 and a rotor 16. The rotor 16 is shown displaced at an angle .theta. 
from a reference axis 18. An oscillator 20 generates sine and cosine 
waveforms which are used to excite the respective stator windings. A first 
excitation signal E.sub.o sin .omega..sub.o t is applied to excite a first 
stator winding 12. A second excitation signal, E.sub.o cos .omega..sub.o t 
is applied to winding 14 in quadrature to the signal applied to winding 
12. FIG. 4 shows the phase relationship of the waveforms applied to the 
respective windings. These waveforms are applied at an angular frequency 
.omega..sub.0 consistent with the type of sensor. Typically, resolvers 
operate in a frequency range up to 400 Hz, while inductive and capacitive 
sensors may operate from 2.5 KHz to as high as 100 KHz. Since the resolver 
acts as a transformer, the winding ratio may be represented by the 
coupling coefficient K. The coupling coefficient K is modulated by the 
mechanical displacement of the rotor and the resulting output signal 22 is 
a constant amplitude signal that undergoes a continuous phase shift of 
360.degree. for each complete rotation of the rotor. The phase-shifted 
signal is then converted to digital form by a phase tracking loop in a 
manner to be described. It will be clear to one skilled in the art that 
the resolver output may be coupled through slip rings or a rotary 
transformer to allow 360.degree. rotation of the rotor. Similarly, an 
amplifier may be applied to the rotor output to improve the 
signal-to-noise ratio when the output must be transmitted over an 
appreciable distance. 
The rotor output 22 is applied to one input of a phase detector 24. Phase 
detector 24 is also supplied with a second input signal on line 56 
proportional to a digital output angle .phi. generated by the signal on 
line 26. The value of the input angle .theta. is combined with the signal 
on line 56 proportional to digital output angle .phi. to generate an error 
signal on line 58 which is applied via VCO 64 to counter 28. When the 
difference between the input angle .theta. and the feedback angle .phi. is 
zero, then the digital output angle generated by the up/down counter 28 is 
equal to the resolver input angle .theta.. To generate the difference 
signal, E.sub.o cos (.omega.bt+.phi.) on line 56, certain trigonometric 
functions must be performed by the system. Thus, sine multiplier 30 
receives a sine signal on line 32 from oscillator 20. Counter 28 provides 
a digital output signal representative of the digital output angle .phi. 
on line 34 to the sine digital-to-analog converter 36. The analog sine 
output thereof is coupled on line 38 to a second input of sine multiplier 
30. The product E.sub.o sin .omega..sub.o t sin .phi. of multiplier 30 
appears on line 40 as one input to summing junction 42. In a similar 
manner, a quadrature signal E.sub.o cos .omega..sub.o t on line 44 
generated by oscillator 20 is applied to cosine multiplier 46. Counter 28 
furnishes a signal representative of the digital output angle .phi. on 
line 48 to cosine digital to analog converter 50. The analog output of 
converter 50 is then couple on line 52 to cosine multiplier 46. The output 
E.sub.o cos .omega..sub.o t cos .phi. thereof is applied on line 54 to a 
second input of junction 42. The difference of the signals applied to 
summing junction 42 appears on line 56, where it is seen to be a function 
of the digital output angle .phi. and is applied to phase detector 24. 
Phase detector 24 effectively multiplies the two inputs on lines 22 and 56 
to generate a product that has a first term proportional to the excitation 
frequency and a second term proportional to the difference between the 
angular displacement of the rotor and the indicated digital output angle. 
The difference output on line 58 is passed through a filter 60 which 
removes the excitation frequency and also acts an an integrator. The 
output of filter 60, which is a function of the sine of the difference 
angle, is numerically equal to the difference angle for small angles. 
Thus, the difference signal is an analog representation of the error 
between the rotor input angle .theta. and the digital output angle .phi.. 
This signal is applied to a conventional voltage controlled oscillator 
(VCO) 64. VCO 64 generates an output frequency proportional to the 
magnitude of the error signal on line 66 and an up/down command on line 68 
in accordance with the polarity of the error signal on line 62. Counter 28 
receives the signals on lines 66 and 68 to generate a corresponding binary 
output representative of the digital output angle .phi.. In a conventional 
manner, the angle stored in counter 28 drives the error signal on line 56 
in closed loop fashion until the error signal is urged to zero, whereupon 
the digital output angle .phi. is equal to the analog input angle .theta. 
of the rotor. 
The two-phase oscillator 20 may be generated in a variety of conventional 
manners. For example, the quadrature signals may be generated from the 
primary signal by means of a 90.degree. phase shift circuit. 
Alternatively, two square-wave oscillators may be appropriately 
synchronized and the outputs filtered to provide a sine wave. Sine 
multiplier 30 and cosine multiplier 46 are available as conventional 
integrated circuit elements, such as Analog Devices part number AD534L. 
Analog Devices part number DAC71, a 16-bit D/A converter, in combination 
with Analog Devices part number AD639, an analog to sin/cos converter, is 
suitable for sine DAC 36 and cosine DAC 50. Alternatively, elements 30, 
46, 36, and 50 are available in the form of a dual sin/cos multiplying D/A 
converter, such as Natel part number HDSC2036. 
Up/down counter 28 may be any suitable integrated circuit, such as Texas 
Instruments part number SN54AS867. The voltage controlled oscillator 64 
may be comprised of a VCO, part number AD650, as manufactured by Analog 
Devices, to provide the frequency output on line 66, and a zero-crossing 
detector, which may be a comparator, such as National Semiconductor part 
number LM319, or a conventional operational amplifier, such as National 
Semiconductor part number LF155, configured as a voltage comparator, 
referenced to ground potential, to provide the up/down control signal. 
Details of one configuration of the phase detector 24 are shown in FIG. 2. 
A first input signal E.sub.o cos (.omega..sub.o t+.phi.) applied to input 
202 is coupled on line 204 to an operational amplifier 206 configured as 
an inverting amplifier. Resistors R1 and R2 determine the gain of the 
amplifier. The output of amplifier 206 is coupled to a first input 208 of 
an analog switch 210; such as Harris part number HI 1-0305-2. Signal 202 
is further coupled on line 212 to a second input 214 of analog switch 210. 
Switch 210 is activated by a zero-crossing detector 216 when energized by 
a signal E.sub.o K (sin .omega..sub.o t+.theta.) applied at input 218. The 
output of detector 216 is either a logic high or logic low, in accordance 
with the voltage level of the applied signal at input 218, which activates 
switch 210 accordingly between inputs 208 and 214. The output of switch 
210 is applied on line 219 to low-pass filter 220. Filter 220 acts to 
attenuate the high frequency components resulting from the switching 
action of switch 210. Resistor R3 and capacitor C1 may be chosen in a 
conventional manner, and adapted to the excitation frequency. The output 
of filter 220 is a dc voltage proportional to the sine of the phase 
difference of the signals applied to the two input terminals of the phase 
detector as shown in FIG. 4. A further operational amplifier 224 is used 
to invert the signal input applied on line 222 and restore the output on 
line 226 to the original phase relationship. For small angles, the sine of 
the angle is approximately equal to the value of the angle. Thus, the 
output on line 226 is an analog value proportional to the phase difference 
of the input signals as the control loop approaches a null error 
condition. 
Resolver-to-digital converters are commercially available in the form of 
hybrid circuits using integrated circuit chips. Suitable devices include 
series TACH-12, as manufactured by Control Sciences Incorporated of 
Chatsworth, CA and part number IRDC 1732, manufactured by Analog Devices. 
Referring now to FIG. 3, filter 60 will be described. Filter 60 performs 
three primary functions in the phase tracking loop. Firstly, it removes 
any remaining undesirable high frequency components from the output of the 
phase detector. Secondly, it integrates the phase difference signal in 
such a way as to drive the error in the output angle .phi. to zero; and 
thirdly, it is designed to "tailor" the performance of the phase tracking 
loop. Thus, it will affect the tracking loop bandwidth (i.e., how fast the 
loop will respond to changes in its input), the amount of overshoot which 
will occur for a step change in input, the damping ratio (a measure of how 
quickly the overshoot and ringing due to input changes decay), and the 
stability of the loop. Preferably, the block takes the form of an 
integrator/lead combination, with a transfer function given by: 
##EQU1## 
the frequency response of which will have an asymptotic approximation as 
shown in the figure. This transfer function can be implemented with 
standard operational amplifiers, capacitors, and resistors. 
FIG. 4 shows waveforms typical of the invention as described above, 
including the stator excitation signals 32 and 44, the rotor output signal 
22, and the output signal 58 of the zero crossing detector. In operation, 
the two stator signals E.sub.o sin .omega..sub.o t and E.sub.o cos 
.omega..sub.o t are each amplitude modulated by the coupling coefficient K 
of the rotor angle .theta. and summed into the rotor. The rotor output is 
then 
EQU E.sub.o k sin (.omega..sub.o t+.theta.) (2) 
As shown in FIG. 1, the phase tracking loop operates by summing the two 
orthogonal excitation signals and the rotor signal and generates a digital 
number representing the displacement angle .theta.. The oscillator 
quadrature signals on lines 32 and 44 are multiplied by the sine and 
cosine, respectively, of the current digital output angle .theta.. This 
yields a signal 
EQU E.sub.o sin (W.sub.o t) sin (.phi.) (3) 
and a second signal 
EQU E.sub.o cos (.omega..sub.o t) cos (.phi.) (4) 
which are subtracted, yielding the carrier frequency phase modulated by the 
current output angle .phi.: 
EQU E.sub.o cos (.omega..sub.o t+.phi.) (5) 
This signal, on line 56, is applied to phase detector 24 and compared with 
the rotor output 1/2E.sub.o.sup.2 K[sin (2.omega..sub.o 
t+.phi.+.theta.)+sin (.theta.-.phi.)] on line 22. The phase detector 
effectively multiplies these two inputs to generate its output. Thus, the 
output is 
##EQU2## 
The first term is at a frequency twice that of the excitation frequency, 
and will be filtered out by filter 60. The signal remaining is 
EQU (1/2)E.sub.o.sup.2 K sin (.theta.-.phi.) (8) 
This signal is frequency compensated (in order to yield optimum loop 
behavior), and then drives VCO 64 to provide a pulse count to counter 28 
until .phi., the angle held in the counter, drives the phase difference 
signal (8) to zero. When this occurs, .phi., the digital output angle, 
will be equal to .theta., the analog input angle, and the VCO control loop 
will be satisfied. 
While the invention has been described in its preferred embodiment, it is 
to be understood that the words which have been used are words of 
description rather than limitation and that changes may be made within the 
purview of the appended claims without departing from the true scope and 
spirit of the invention in its broader aspects.