ELECTRONICS & POWER OCTOBER 1978 747

High-speed operationof stepping motorsb y A . H u g h e s , B.Sc, Ph.D., C.Eng., M.I.E.E.

Stepping rates as high as 20 000 steps/second are now not unusual instepping-motor systems. To achieve suchhigh rates, the drive circuits must be moresophisticated than for single stepping, andmany different techniques are in use. Byusing these techniques, even relativelypoor motors, most of them designed asstatic devices, can be forced to run fast byproviding sufficient power in the drive cir-cuits. The need for this 'sledgehammer'approach can, however, be reduced if boththe motor and its drive are designed spec-ifically for high-speed running

The principal advantage of the stepping motor overother forms of position control is that it is anopen-loop device. The output shaft rotates througha definite angle (step) every time a step commandpulse is delivered to the drive circuit. Hence,providing the permissible mechanical load on theshaft is not exceeded, the total angle turned throughby the rotor is always equal to the number of inputpulses times the step angle.

The step angle is a property of the motor, andcommonly available angles range from 0-45° to 90°;motors with 1 -8°/step (200 steps a revolution) arevery common, especially in machine-tool appli-cations. Motors generally have between three andsix sets of windings (phases) on the stator. and theseare switched sequentially from a d.c. supply. Whenone phase is switched off, and another is switchedon, the toothed rotor, which in some cases includesa permanent magnet, moves to a new alignmentposition, torque being provided by the magneticalignment forces between stator and rotor teeth.1

The rotor remains held in the new position untilexcitation is switched to the next phase.

A typical single-step response is shown in Fig. la.It is similar to that of a 2nd-order position servo,with settling times typically in the range 25-150 ms.The relatively poor damping is often an embarr-assment,2 though at the same time the low dampingfactor allows the motor to run fast (see later).

If further step commands are received before therotor has come to rest, the response may be asshown in Fig. \b. The motor is still 'stepping', eventhough it never comes to rest between steps. Whenthe stepping rate is increased further, however, thesituation shown in Fig. k is reached. This is theslewing mode. The rotor velocity is essentiallyconstant, and equal to the step angle times thenumber of pulses per second.

Austin Hughes is a lecturer with the Department ofElectrical & Electronic Engineering, University ofLeeds, Leeds LS2 9JT, England.

Very high stepping rates can be achieved whenthe motor is slewing. For example, 1-8° step motorsare now frequently driven at 20 000 steps/s, giving ashaft speed of 6000 rev/min. Position integrity ismaintained at these high stepping rates (as indeed itmust be for open-loop position control to beachieved), but, to reach them, the stepping fre-quency must be ramped up and down from themuch lower rate (perhaps 200 steps/s) at which themotor can be started and stopped without losingsteps.

For the motor to be useful, it must, of course, notonly run, but also be able to produce output torquethroughout its speed range. In common with all but

Hybrid stepper motor used in automatic test equipment for testing a.c.contractors. The equipment was designed by, and is used by, Cutler-HammerEuropa Ltd. [Photo: Courtesy of Evershed & Vkjnoles Ltd. ]

0013-5127/78/0564-0747 $1 -50/0v IEE: 1978

l Rotor-position/time responsesa Single stepb Stow steppingc Slewing

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748 ELECTRONICS & POWER OCTOBER 1978the very smallest* electromechanical devices, how-ever, there are problems in operating steppers atthese high exitation frequencies. The principaldrawback is the relatively long time constant of thewindings. For example, each phase of a 4-phasemotor may have a winding time-constant of 5 ms.At 20 000 steps/s, it is being switched on and offevery 0-2 ms. If only rated voltage is applied (i.e.the voltage needed to produce rated direct current),hardly any current will be established before thephase is again turned off, and the available torquewill be very small.

In practice, high speeds are only possible at all ifthe drive circuit has sufficient 'overvoltage' to forcesignificant current at high stepping rates, and con-sequently the usefulness of a given motor iri theslewing range is largely determined by its drivecircuit. This dependence of motor performance onits drive is a constant source of difficulty with users,who can easily be misled into expecting more fromtheir motor than its drive can provide. A furthersource of difficulty centres on the motors them-selves. These are usually specified by their 'static'torque, i.e. the maximum torque that the motor canexert when the rotor is stationary. It often happensthat apparently similar motors give quite differentperformance at high stepping rates, even with iden-tical drives. And unless a particular motor is ope-rated from a particular drive, for which the man-ufacturer can provide performance data, there isalways uncertainty as to whether the package willmeet its specifications.

Drive circuits and torque characteristicsThe simplest and cheapest drive circuit is shown

in Fig. 2a. Each phase has a sitigie switchingtransistor and freewheel diode (through which thecurrent decays after switch off); and the direct voltageVi is just sufficient to give rated current in thewinding. This type of drive is adequate for manysingle-stepping applications and for continuousstepping provided the interval between steps is notmuch less than the winding time constant. But withtime constants of typically 5 ms, its useful range islimited to perhaps 200 steps/s, which representsonly 60 rev/min on a 200 step motor. At higherstepping rates, the phase currents will be so smallthat very little torque will be developed. The fall off•The majority of stepping motors can comfortably be Held in thehand. At the extremes, however, are mottirs of 3 mm diameter foruse in watches, and of 20 cm diameter with outputs of from 750 to1500 W for use in machine tools

in torque as the stepping rate is increased is shownin Fig. 3a. At very low stepping rates, the torqueavailable is roughly equal to the static torque, but,as can be seen, this falls off very quickly withincreasing speed, when the simplest drive is used.

Torque/speed curves are almost always presentedas single-line curves, as in Fig. 3. This sometimesgives the erroneous impression that the motor pro-duces a unique torque at a given stepping rate. Infact, the area below the curve and bounded by theaxes defines the region in which the motor can beoperated, and the ordinate of the curve indicatesthe maximum steady torque the motor can developat a particular (steady) speed. If the load torqueexceeds this value - known as the pull-out torque -the motor loses synchronism and stops. If thishappens, the vital one-to-one correspondence bet-ween the number of command pulses and thenumber of steps taken is lost: the step counterblithely continues to accumulate command pulses,but the motor and load are stationary. Although notalways catastrophic, this situation is not usuallyacceptable, and it indicates the importance to thesystem designer of the torque/pulse-rate curve. Hemust be sure there is always sufficent torque avail-able for all foreesable loads and speeds, t

The most common method for increasing thetorque available at higher speeds is by the additionof resistance - invariably known as forcing resis-tance - in series with each phase winding, thesupply voltage being raised to maintain the ratedcurrent and thereby to preserve the full static torque(Fig. 2). The extra resistance (typically from 2 to 20times the motor resistance) decreases the effectivetime constant, so that current can be establishedmore rapidly and the motor can operate to a higherstepping rate. It provides an approximation to a'constant-current' drive (see below).

Broadly, increasing the total phase circuit resis-tance by a factor of, say, five causes a givenhigh-speed pull-out torque to be available at fivetimes the original stepping rate, as shown in Fig 3b.The much improved performance is only obtainedat the expense of an increased power supply rating(five times rated voltage in the example above),however, and the overall efficiency is poor, par-ticularly at low speeds, where most (about 80%) ofthe power is wasted as heat in the resistors.

t In practice, there are always 'dips' in the torque/speed curves atvarious frequencies, owing to resonances and instability; but forthe sake of simplicity, they are ignored in this discussion

motorwinding

2 Improvements to basic drive circuit a for one phase by addition of forcing resistance b and bypasscapacitor c. Voltage V« is larger than Vi to give the same direct current

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Although the extra resistance is always referredto as forcing resistance, this description is not reallyaccurate, and 'limiting resistance' would be a betterterm. This is because the increased voltage isresponsible for the faster rise of current, not theresistance. The function of the resistance is to limitthe steady current to the safe (rated) value for themotor, when it is single-stepping or stationary.When the stepping rate is high enough for thecurrent not to reach its final value, the resistanceserves no useful purpose: it simply consumes power,and, because of the IR drop across it, decreases thevoltage available at the motor. And if the resistancecould be short circuited at high stepping rates, whenit is not needed for current-limiting, the motor's per-formance would be improved.

Bypassing of the forcing resistance at high step-ping rates can be achieved using capacitors inparallel with the resistors (Fig. 2c). For unipolardrives, in which the current always flows in thesame direction through the winding, relatively cheapelectrolytic capacitors can be used, and substantialimprovements in output torque can be obtained. InFig. 3c, for example, by adding 500 yxF capacitors inparallel with each resistor, approximately twice asmuch torque is available over the speed range500-100 pulses/s.

The inherently low efficiency of the forcing resis-tance drives is avoided by the use of a bilevel drive.Two supply voltages are needed. A high voltage isapplied at the start and finish of the excitationperiod, to provide rapid buildup and decay ofcurrent, and a lower (rated) voltage is used tomaintain the current during the 'on' period. Thetransition from high to low voltage is made after afixed time interval, or, more reliably, by sensing thephase current and switching over when rated cur-rent is reached.

All the above drives suffer from the disadvantagethat they include no provision for taking account ofthe influence of the motor's motional e.m.f. ('backe.m.f.') on the current. In effect, such drives provideonly 'open-loop' current control. For maximumoutput, particularly at high stepping rates, closed-loop current-control schemes are used.

Constant-current drivesTo obtain maximum pull-out torque over the

widest possible speed range, full current must beheld during each 'on' period. This is achieved byproviding closed-loop control of winding current,and two systems are widely used.

ELECTRONICS & POWER OCTOBER 1978In the first, the net motor current is measured,

and the supply voltage is controlled to keep thecurrent constant. As the stepping rate is increased,the supply voltage rises to compensate for theeffects of the winding time constant and themotional e.m.f. An upper limit is finally reachedwhen the supply voltage is at its maximum value,and torque then falls with stepping rate.

The variable voltage is obtained from the mainsvia a phase-controlled rectifier and smoothingcapacitors. Because of the relatively slow responsetime of the supply voltage, the rate at which thestepping frequency is changed must be limited. Thisis particularly important when changing from highto low stepping rates: if the stepping frequency isdecreased too quickly, the voltage may not be ableto fall quickly enough, and the winding transistorswill consequently be subjected to overcurrents.

The second constant-current drive, used in high-performance systems, which justify the higher cost,is the 'chopper' drive. A fixed high voltage, typically20 times motor voltage, is used to provide a rapidinitial rise of current. When rated current is sensed,the voltage is switched off, and the current decaysto a level (typically 90% of rated current), beforethe high voltage is reapplied. This 'chopping' pro-cess continues until the end of the 'on' period. Asthe stepping rate is increased, a point is reachedwhen the chopping action ceases: full voltage isapplied throughout the 'on' period, but the currenthas insufficient time to reach rated value. Abovethis speed, there is inevitably a rapid falloff inpull-out torque.

High-speed motorsThe importance of the drive circuit in determining

the high-speed performance has been emphasisedabove, and over the last ten years or so, a greatdeal of effort and progress has been made in thatarea. But no matter how good the drive circuit is, itis the motor that ultimately does the work; and,obviously, the optimum overall performancerequires the 'best' motor and the 'best' drive circuit.

As mentioned earlier, however, motors are usu-ally catalogued, and initially selected, on the basisof their static torque. The task of finding a motorthat has good high-speed torque capability has,hitherto, been something of a hit-and-miss business,with motors of the same static torque and timeconstant having quite different high-speed torque,even when operated under identical drive con-ditions.

749

forcing \ forcing resistanceresistance \and bypass

added \capacitance\added\\\\v\\\\\\\

WOO 2000

3 Pull-out torque curves, showing the improvement to the basic curve a by the addition of five times windingresistance b and bypass capacitance c

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750 ELECTRONICS & POWER OCTOBER 1978

4 Pull-out torque curves for hybrid motors with the same static torqueand time constant but different internal design

The principal reasons for these differences havebecome clearer from some recent work3 aimed atfinding out how motors should be designed toproduce high torque at high stepping rates. Thesestudies extend the very considerable volume ofrecent publications4 that deal with optimising statictorque in stepping motors, and some of the con-clusions can be illustrated by considering the mostnumerous type of motor, the so-called hybridpermanent-magnet (p.m.) type.

In this type of motor, torque is produced by theinteraction of the flux 0 from the permanent magneton the rotor with the current / in the statorwindings. The torque depends on the product 0/,and so a given static torque can be achieved in aninfinite variety of ways. While one motor may havea relatively large magnet, and small stator current(or, strictly, stator m.m.f.), another motor achievesthe same static torque from a smaller magnet but alarger stator m.m.f.

In the analysis of the motors' high-speed torquecapability, it turns out that the torque at a givenstepping rate is governed by a parameter k, which isthe ratio of the magnet flux 0 to the stator windingself flux (which is itself proportional to statorm.m.f.). Hence, for a given static torque, theproduct of two quantities has to be constant; butthe ratio of the same two quantities determineswhat proportion of the static torque will be avail-able at a given speed; or, in other words, theparameter k determines how fast the pull-out torquefalls off with increasing stepping rate, the drivevoltage being constant.

The influence of the parameter k is shown in Fig.4. All the motors have the same static torque, andthe same winding time constant, but achieve thestatic torque in different ways. A critical case occursat k = 1. Motors with k < 1 can, theorectically,produce torque at all stepping rates, whereas, if k >1, there is a definite maximum speed above whichthe motor cannot produce output torque. Appar-ently, the smaller k is, the better the motor'shigh-speed torque.

This suggests that motors with 'weak' magnets(low k) should be best for high-speed running, andthis conclusion is broadly confirmed by tests on

various manufacturers' motors. For a wide range ofmotors, k is found to vary considerably, from as lowas 0-3 to as high as 1 -3. The low-A: motors, althoughbest suited to high-speed running, have inherentlypoorer damping than the high-/: ones. Not sur-prisingly, therefore, there is a conflict between therequirements of fast running and good single-stepdamping, and a compromise generally has to beaccepted.

If high speed is the prime concern, however, itappears from Fig. 4 that the lower k is, the better.In fact, however, this is not so when properaccount is taken of the drive requirements. This isbecause, although Fig. 4 is for motors havingidentical static torques, time constants, and drivevoltage, it disguises the fact that the power .of thedrive is different for each value of k. A motor withlow k has a higher stator current, and therefore ahigher-power (and more expensive) drive; and ittherefore seems only reasonable to expect betterperformance from such a motor. To obtain the'best' combination of drive and motor for fastrunning, it has to be recognised that, broadlyspeaking, the cost of the drive will be proportionalto its power output. Hence the motor must bechosen to give maximum high-speed torque for agiven drive power. On this basis, the optimum valueof k is 0-5. By contrast the optimum value of k,which is arrived at from static design considerations,is approximately 1. Many existing motors havevalues of k close to 1, and are therefore 'good' in astatic sense; but, inevitably, they are also inherentlypoorly suited to high-speed running.

References1 LAWRENSON, P.J.: 'Stepping up to date'. Electron. &Pwr., 1975, 21, pp. 306-3082 HUGHES, A., and LAWRENSON, P.J.: 'Electro-magnetic damping in stepping motors', Proc. IEE, 1975,122,(8), pp.819-8243 HUGHES, A.: 'Parameters governing the dynamic per-formance of permanent magnet stepping motors'. Pro-ceedings of the 6th Incremental Motion Control Systems& Devices Symposium, University of Illinois, 19774 HARRIS, M.R., et. ai: 'Unifying approach to the statictorque of stepping-motor structures', Proc. IEE, 1977,124,(12), pp. 1215-1224

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