IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, VOL. IECI-23, NO. 1, FEBRUARY 1976

Digital Measurement of Angular Velocity for

Instrumentation and Control

COLIN D. DICENZO, SENIOR MEMBER, IEEE, BARNA SZABADOS, MEMBER, IEEE, AND

NARESH K. SINHA, SENIOR MEMBER, IEEE

Abstract-A new approach to digital measurements of angularvelocity for control applications is discussed. An optical transduceris described which provides a pulse rate. The pulse period is meas-ured and the division of time is achieved by either a general purposeor a special purpose processor. Since sampling intervals are small,measurements are available in digital form almost immediately.Other advantages include the capability to measure transientangular velocity characteristics and the accurate measurement ofangular velocity near zero. With modifications the system can betransformed into an accelerometer.

INTRODUCTION

A N accurate measurement of angular velocity andacceleration in digital form is required in many in-

strumentation and control applications. Most of the tech-niques used consist of an application of analog principlesand this results in low resolution and noise contaminationunless filtering is used.More elaborate designs consist of hybrid digital analog

systems. This involves a rectification of the pulses pro-duced by a magnetic or optical transducer giving a trainof pulses with a frequency proportional to the angularvelocity. The use of filtering may alter the informationoutput.

Digital designs for the measurement of angular velocityand acceleration have been suggested [1], [2]. Thesedesigns involve the measurement of angular distanceduring a given time by counting the number of uniformlyspaced signals on a disk. The angular velocity is obtainedby counting the pulses, which is equivalent to an integra-tion over a given interval of time. Filtering is not requiredbut the designs are limited by the angular resolution ofthe transducer and the slow sampling time.The purpose of this paper is to present a new approach

to the digital measurement of angular velocity whichprovides rapid measurement of velocity while retaininggood accuracy and resolution at all speeds, includingthose near zero velocity. Design details are outlined andsupporting experimental results presented.An earlier version of the device [3] was used as a system

Manuscript received August 15, 1975.C. D. diCenzo and N. K. Sinha are with McMaster University,

Hamilton, Ont., Canada.B. Szabados is with the University of New Brunswick, Fredericton,

N.B., Canada.

element in a time-optimal digital position controller [4],[5] using a permanent magnet motor.

DESIGN FEATURES

The digital instrument proposed involves the measuringof time for a given angular displacement and then per-forming the division of time. A biasing speed is added tothe speed to be measured in order to limit the sizes of theregisters required and to reduce the time needed formeasurement.The new instrument therefore has two new design

features. The first is the measurement of the relativespeed between the rotating shaft to be studied and anothershaft rotating in the opposite direction at a constantspeed which will be called -the biasing speed. The other isthe measurement of time between "rotator pulses" pro-duced by a special transducer which sets up a pulse train.The frequency of the pulse train 1/t provides angularvelocity by correct scaling and substraction of the biasingspeed.The inherent properties of the inverse number make this

feature attractive. The presence of the biasing speedsallows zero speed to be detected within a short time. Thereduction of sampling time will be dependent upon thenumber of quantitization intervals per revolution.

If t is the sampling time between two pulses provided bythe optical transducer called "rotator pulses," the relativespeed is proportional to l/t. If fo is the reference speed andfm the speed to be measured, the rotator pulse rate f is

(1)f = fm + foand the desired speed can be obtained

kfrn = - fo

t

where k is a constant determined by the transducerdesign.

OPTICAL TRANSDUCERThe low inertia and frictionless disk, with Nm evenly

spaced contrast engraved, is tightly coupled to the shaftto be studied. It should be noted that Nm does not haveto be very large for good resolution. In fact, the resolutioncan be improved by decreasing Nm, within certain limitsimposed by the speed of the biasing motor. A drum,

(2)

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, FEBRUARY 1976

shaftsevto be- X fconstant

studtod~ ~ ds

Digita lsr nH.having pickup sensors inpProcessor clock

Display |

decimal digital |

Fig. 1. Block diagram of digital instrument.

having pickup sensors in parallel, is coupled to an auxilliarysynchronous motor, rotating at a constant speed in theopposite direction. The drum should have a relativelyhigh inertia to maintain the constant instantaneous speed.A schematic arrangement of the optical transducer isshown in Fig. 1.

ALGORITHMEquation (1) is scaled so that only integral numbers

are used. Capital letters represent the integer correspond-ing to each symbol already defined. Equation (1) thenbecomes

FmT + FoT = K. (3)Since Fo is known, its digital value can be stored as

Fo = E a,j2

Fig. 2. Algorithm block diagram.

If this power of 2 is contained in Fm, K2 is positive andone would store aM-, = 1 and keep K1 = K2 and a one-bitshift towards the right will scan the next power of two.Therefore, the algorithm uses the search for the powers oftwo in a simple sequential way, allowing simple shift andadd procedures. Any digital processor may be used toperform this operation rapidly.

where

or ,1l ,.

A block diagram of the algorithm which can be used in asimple sequential logic design is shown in Fig. 2.Once T has been obtained and shifted N - 1 digits to

the left, T X 2N-1 is obtained. If this factor is included inFo and if aN1 = 1l a parallel binary adder will easilyperform the subtraction

K T X 2N-1

and a one-bit shift right will bring T to the next valueT X 2N-2.When scan of the a's is completed, the algorithm has

performed the subtraction of the constant biasing speedleaving K = K1.Suppose the highest speed the instrument can measure is

Fm-E ai2

wi th

ai = 0 or 1,

and

M> N.

T shifted byM - 1 digits towards the left will representT X 2M-1. The binary adder performs

K2 = K1- T X 2M-1.

DIGITAL PROCESSORThe algorithm shown in Fig. 2 provides a straight-

forward sequential logic and any general purpose digitalprocessor can be used. In the first instrument an economi-cal low cost special-purpose digital processor was designed[6]. This avoided the dedication of a minicomputer tosuch measurements when extensively carried out in thelaboratory.The special-purpose digital processor used is described

in some detail in the referenced paper. Since the intervalbetween the readings of the angular velocity is less thanone millisecond, the average acceleration during the in-terval can be obtained by dividing the change in speed bythe interval. This can be done by either using anotherdigital processor or by using a digital minicomputer.

EXPERIMENTAL RESULTSThe experirmental system described has not been

optimized but it has allowed the authors to test theconcept. The transducer was built with Nm = 50 anda biasing fo = 1800 rpm was selected. A 10 MHz clockwas used as the timing device to the digital processor. Theinstrument itself is used to measure Fo by a disabling stepin the processor while fm = 0. The result is stored and theinstrument is ready for other measurements.With the original digital processor a measurable range

of angular velocity is 0-7800 rpm and the samplinginterval is in the range of 670 to 125 microseconds. The

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DI CENZO et al.: DIGITAL MEASUREMENT OF ANGULAR VELOCITY

total processing time after sampling is completed is 22microseconds but can be shortened if the processor adderis speeded up. The information rate is 1500 samples persecond at zero speed and up to 8000 samples per second at7800 rpm. The resolution of the system is 0.8 radians persecond and the digital processor used introduces an errorof less than 2%.

Experimental results with this tachometer are shownin Figs. 3-5. Fig. 3 shows the samples of the speed-timecharacteristic of the starting of a motor. Existing digitalinstruments would not give such a reasonable shape of thecurve because of their low sampling rates. A slight timedelay due to sampling and processing can be observed.With a slight modification even this delay can be elimi-nated. Suppose that within the very short sampling in-terval tE(tkl,tk), the acceleration remains constant. Hence,the speed processed by the tachometer would representthe average value over the kth sampling interval. If Fkris the tachometer reading, it follows that the correctedvalue can be obtained by the recursive equation

Fkc = 2Fkr - Fkc

starting with Foc = 0. The implementation of this linearaveraging correction is straightforward since, in a binarysystem, multiplication by two is a shift left operation andtraction can be obtained through a binary adder. In theproposed design, since results are sequentially provided,the series binary adder is used and a longer processingtime is not required. The corrected speed-time characteris-tic for this example is shown in Fig. 4. It can be seen thatthe curve obtained is good, and what is more important,the algorithm is self-convergent.Another experiment was the reproduction of a 50 Hz

sine-wave mechanical oscillation on a shaft. The instru-ment performed very well, both in the corrected and theuncorrected modes, as seen in Fig. 5.

CONCLUSIONSThe new digital technique presented allows good record-

ing of high speed characteristics. A resolution of 0.8radians per second over a speed range 0-7800 rpm can beextended with a more expensive implementation. With asimple processor accuracies within 0.2% were obtained.The high rate of information and almost instantaneous

readings, even at zero speed of the instrument, makes itsuitable for transient analysis.The new concept does not require a large quantization

number per revolution thus allowing simple and precisetransducer tooling. The high inertia of the drum and thesynchronous drive maintain a constant speed within 0.1%.The only difficulty has been wobble and misalignment ofthe shafts which has been partially corrected by theparallel pickup sensors used in the design. However, theerror due to the transducer is small and a more carefulchoice of bearings may improve this performance.As indicated the system can be modified to read accelera-

tion without difficulty with the advantages indicated forits use in measuring angular velocity.

Fig. 3. Speed-time characteristics of the starting of a motor andsamples obtained by the instrument.

speed (rd/A)

Fig. 4. Corrected readings for motor starting curve.

speed (rpm)

Fig. 5. Comparison instrument readings using 50 Hz sinusoidalsignal.

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, VOL. IECI-23, NO. 1, FEBRUARY 1976

The instrument can be used as a system element incontrol and instrumentation applications. It has beenused as a vital component of a time-optimal positioncontrol system using a permanent magnet dc motor [4],[5]. The device is very suitable for the study of speed-time transients of rotating devices.

REFERENCES[1] G. Hoffman de Visme, "Digital processing unit for evaluating

angular acceleration," Electronic Engineering, vol. 40, pp. 183-188, 1968.

[2] A Dunworth, "Digital instrumentation for angular velocity and

acceleration," IEEE Trans. Instrum. Meas., vol. IM-18, pp.132-138, 1969.

[3] C. D. diCenzo, N. K. Sinha, and B. Szabados, "Digital tech-niques simplify angular velocity measurements," ElectronicEngineering, vol. 44, pp. 30-32, 1972.

[4] B. Szabados, N. K. Sinha, and C. D. diCenzo, "A time-optimaldigital position controller using a permanent-magnet dc servo-motor," IEEE Trans. Ind. Electron. Contr. Instrum., vol.IECI-19, pp. 74-77, 1972.

[5] , "Practical switching characteristics for minimum-timeposition control using a permanent-magnet motor," IEEETrans. Ind. Electron. Contr. Instrum., vol. IECI-19, pp. 69-73,1972.

[61 B. Szabados, C. D. diCenzo, and N. K. Sinha, "Digital measure-ment of angular velocity," Journal of Physics E: ScientificInstruments, vol. 6, pp. 549-552, 1973.

Digital Computer Simulation of an Adjustable-SpeedInduction Motor Drive with a Cycloconverter-Type

Thyristor-Commutator in the Rotor

AJIT K. CHATTOPADHYAY

Abstract-This paper deals with a digital computer-simulationstudy of a complex drive-system which incorporates a thyristorcycloconverter-type frequency-converter in the rotor circuit of aslip-ring induction motor for speed variation in the subsynchronousas well as the supersynchronous region by secondary voltage controlThe action of the frequency converter is analogous to that of a normalcommutator in the stator-fed ac commutator motor while the circuitbehavior is similar to that of a cycloconverter. A rotor-position de-tector is used to switch the thyristor configuration in a sequentialmanner to generate an output voltage having a predominant slip-frequency component. Simulation involves solution of a set of gener-alized performance equations of an ideal induction machine in anappropriate reference frame under the control conditions imposedby the thyristor-commutator which is simulated using simple logicaland limiting statements. Differential equations are solved by thewell-known Runge-Kutta numerical integration method. Initialsimulation results assuming thyristors as ideal switches and neglect-ing source impedances show very similar characteristics to the casewhen a pure sine-wave slip-frequency voltage is injected to therotor. Rigorous simuIation results include the physical thyristorbehavior, effect of source impedances, overlap, and logical control ofthe circulating currents that may occur. Simulation results arepresented together with the experimental performance of the drive.

NOMENCLATURE

H

Hid8 lia/1oar'lidlnor

Inertia constant, secs.d-q axes stator and rotor currents, p.u.

Voltage regulator ratio.

Manuscript received June 16, 1975; revised August 26, 1975.The author is with the Department of Electrical Engineering,

Indian Institute of Technology, Kharagpur, India.

p8or'r,7'rslsTe, TLV

Var Vbr Vcr

Xm

or4/ds1//q,sy4dr4/qlrs, superscript

= d/dt.Stator and rotor resistance, p.u.Source resistance and inductance.Electromagnetic and load torque, p.u.Peak value of supply voltage, p.u.d-q axes stator and rotor voltages.Rotor phase voltages.Base and rotor electrical angular velocity,rad/sec.Stator and rotor reactance, p.u.Magnetizing reactance, p.u.Phase angle between the injected and in-duced emf in the rotor, degrees.Rotor angular position (w,t), rad.d-q axes flux linkages, p.u.Stator reference frame.

INTRODUCTIONAN adjustable-speed drive system incorporating a

thyristor-cycloconverter-type of frequency-converterin the rotor circuit of a slip-ring induction motor has beendescribed in earlier papers [1], [2]. The presence ofthyristors as switching elements in the drive system in-cluding an induction motor makes the analytical study ofsuch a system quite difficult as it is the dynamic behaviorwhich plays an important role in the system design andperformance. A convenient analytical technique is tosimulate the system either in an analog computer havingparallel logic facilities or a digital computer. A recent

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