Stepping motors a guide to theory and practice pdf

The transistor must be rated according to the peak current it is conducting, which is a disadvantage in stepping motor drives, where the ratio of peak to rms current may be high in voltage-controlled circuits.

Switching can occur at high frequencies without excessive losses. Because of internal charge storage, switching speeds are restricted. SENSEFETs incorporate a current mirror terminal, which allows the channel current to be monitored without the need for power-consuming current sensing resistors. Under these conditions the full dc supply voltage is applied across the series combination of phase winding and forcing resistance, since the voltage drop across the saturated transistor is small typically 0.

The build-up of phase current to its rated value would be too slow for satisfactory operation of the motor at high speeds. By adding the forcing resistance, with a proportional increase in supply voltage, the phase electrical time constant can be reduced, enabling operation over a wider speed range. The function of the forcing resistance is given more detailed consideration in Chapter 5. If the base drive of the switching transistor was suddenly removed a large induced voltage would appear between the transistor collector and emitter, causing permanent damage to the drive circuit.

This possibil- ity is avoided by providing an alternative current path — known as the freewheeling circuit — for the phase current. If the phase current is established at its rated value then the maximum voltage Vce max across the switching transistor occurs in the instant after the transistor switch is opened. The rated phase current is 2 A.

Design a simple unipolar drive circuit to give electrical time constants of 2 ms at phase turn-on and 1 ms at turn-off. In this case the resistances are equal, so half the stored energy 0. The analysis of power losses at higher speeds becomes more involved, because the phase current at turn-off is itself a function of operating speed. The switching device must tolerate a maximum off-state voltage given by eqn 2.

The transistors are switched in pairs according to the current polarity required. For positive excitation of the phase winding, transistors T1 and T4 are turned on, so that the current path is from the supply, through transistor T1 to the phase winding and forcing resistance, then through transistor T4 back to the supply. In the opposite case the transistors T2 and T3 are turned on so that the current direction in the phase winding is reversed.

For this reason the phase control signals to these upper base drives are often transmitted via a stage of optical isolation. A bridge of four diodes, connected in reverse parallel with the switching tran- sistors, provides the path for freewheeling currents. In the illustration of Fig. The freewheeling path includes the dc supply and therefore some of the energy stored in the phase winding induc- tance at turn-off is returned to the supply.

Freewheeling currents in the bipolar drive decay more rapidly than in the unipolar drive, because they are opposed by the dc supply voltage. Therefore it is not necessary to include additional freewheeling resistance in the bipolar bridge drive.

At turn-off, estimate the time taken for the phase current to fall to zero and the proportion of the stored inductive energy returned to the supply.

The additional volume does, of course, increase the manufacturing costs but for small sizes of hybrid motor the winding cost is outweighed by the resultant reduction in drive costs. Drive circuits 21 2. Find the winding current time variation at switch-on if the opposite phase winding carries a current of a zero and b rated, but winding excitation removed. Differentiating eqn 2. The current waveforms are shown in Fig.

Chapter 3 Accurate load positioning: static torque characteristics 3. External load torques, perhaps caused by friction, give rise to a small error in position when the motor is stationary. The motor must develop enough torque to balance the load torque and the rotor is therefore displaced by a small angle from the expected step position. The maximum allowable positional error under static conditions often dictates the choice of motor, so this chapter deals with the relationship between the static position error and the parameters of the motor, drive and load.

An alternative method of minimising static error is to connect the motor to the load by a gear or, if linear load positioning is required, by a leadscrew, so the effects of these mechanical connections are also investigated. At the step position the appropriate sets of rotor and stator teeth are completely aligned see Chapter 1 and no torque is produced by the motor. If the rotor is slightly displaced from the step position a force is developed between the stator and rotor teeth Harris et al.

For larger displacements the rotor and stator teeth become aligned at a distance which is a multiple of the rotor tooth pitch from the required step position see Fig. Prediction of the characteristic from the internal geometry of the motor is a complex electromagnetic problem e.

Ertan et al. However it is important to note the relationship between static torque and phase current when the rotor is displaced from the step position. In the absence of magnetic saturation it can be shown that the torque produced is proportional to phase current 2 in a variable-reluctance motor and linearly proportional to the phase current in a hybrid motor.

Strictly speaking the peak static torque is a function of phase current, but it is often quoted as a single value corresponding to the rated phase current. The maximum torque which the motor can produce, and therefore the maximum load which can be applied under static conditions, is equal to the peak static torque. If the load exceeds the peak static torque then the motor cannot hold the load at the position demanded by the phase excitation. With a load torque of 0. Eqn 3.

Remembering that the step length of a motor is inversely proportional to the number of rotor teeth Chapter 1 , we see that a short step-length motor gives a smaller static position error than an equally loaded motor with the same peak static torque but longer step length.

In Fig. The effective stiffness must then be chosen according to the expected amplitude of the rotor displacement, as shown in Fig. Variable-reluctance and hybrid motors are discussed separately in the following sections.

There is a mutual displacement between the characteristics corresponding to one step length, so, for example, the equilibrium position for phase A excited is one step length away from the equilibrium position for phase B excited. Conversely, if the excitation is changed from A to C the torque is initially negative, moving the rotor in the negative direction to the phase C equilibrium. The effect of exciting two phases at any time is illustrated in Fig.

Comparing Figs 3. One further variation is to operate the motor with alternate one- and two-phase-on excitation, i. For simplicity in deriving the analytical results sinusoidal approximations to the characteristics have been used, but nevertheless the general conclusions are valid in most cases. For single-stack variable-reluctance stepping motors the direct summation is not strictly valid, since the mutual induc- tance between phases contributes an additional torque component.

This situation is illustrated in Fig. It can be shown generally that the maximum peak static torque is produced in a multi-phase stepping motor when half of the phases are excited Acarnley et al. If each phase is excited in turn four steps are executed while the rotor moves one tooth pitch. The effect of exciting a pair of phases together is shown in Fig. Although the torque produced can often be improved by exciting several phases, it must be remembered that more power is required to excite the extra phases.

If two phases of the hybrid motor are excited the power supply must be doubled in capacity, but the torque produced is improved by a factor of only 1. This can be an important consideration in applications where the power available to drive the motor is limited. Imbalance between phases can reduce step accuracy when multi-phase excitation is used, and this effect has been investigated by Singh et al.

During one cycle of excitation the current in one phase passes twice through each level and the rotor moves one tooth pitch. However, the mini-step positions are critically dependent on the currents in each of the phase windings and any error in current level is translated directly into a position error. As mini-steps can be made much shorter than full-steps a typical reduction is 20 mini-steps per full-step the positional resolution of the stepping motor is improved.

Stepping motors operated with full-step drives are prone to mechanical resonance see Section 4. The major disadvantage of the mini-step drive is the cost of implementation due to the need for partial excitation of the motor windings at many current levels, using a chopper drive circuit see Section 5.

A schematic diagram of a system incorporating a simple gear train is shown in Fig. As far as static operation is concerned, therefore, there is a considerable advantage in using a high gear ratio to link the motor and load, since the effective load torque at the motor is reduced and the allowable static position error increases compared to the situation where the motor and load are directly connected. In this case the static position error is 0. From eqn 3. Conversely with a low gear ratio the effective load inertia is high and the motor accelerates slowly, but has to reach a relatively low stepping rate to move the load at a satisfactory speed.

Backlash in the gear can degrade the performance of the system; positional accuracy is reduced and resonance problems see Chapter 4 are worsened Ward and Lawrenson, However the range of linear stepping motors is restricted and many linear loads are driven from a rotary stepping motor by a leadscrew, which may be an integral part of the motor, as in Fig. In the system shown schematically in Fig. As far as the dynamic situation is concerned, however, there is a close parallel between the use of a small screw pitch and the high gear-down ratio discussed in the previous section.

For a small screw pitch the effective inertia of the load is reduced and the motor can accelerate rapidly, but must attain a high stepping rate to compensate for the small increments of linear movement produced by each motor step. For simplicity in this analysis the leadscrew has been assumed ideal, i. In this case the motor would be able to drive a load torque of 0.

However, for a load torque of 0. Section 4. The phase current cannot be maintained at its rated value and therefore the torque produced by the motor is reduced. With this condition of high inertia the pull-out torque is equal to the maximum average torque which can be produced by the motor. During the excitation of each phase the motor produces equal positive and negative torques, so there is no net torque production.

The system is in stable equilibrium because a small increase in the load torque retards the rotor, so the excitation changes occur at slightly smaller rotor positions. During excitation of each phase the motor then produces more positive than negative torque and in the new steady state the average motor torque again balances the load torque.

Now consider the effect of applying a load torque equal to the pull-out value, so that the motor has to produce the maximum available torque. The rotor is retarded by the load torque, so that the motor produces a positive torque throughout each excitation period, as shown in Fig.

The equilibrium position for the excited phase is never attained because more torque can be produced by switching to the next phase as the step position is approached. There is a part of each step during which the motor torque is less than the load torque, so that the system decelerates. In the middle of each step the motor torque is near its maximum value, which is greater than the load torque, and the system accelerates.

With pull-out load torque applied the system is in unstable equilibrium, since any small increase in load retards the rotor, causing a reduction in motor torque. Having established the rotor positions at which switching must occur to maximise the torque, it is possible to deduce the pull-out torque. The dependence of peak static torque on excitation scheme is highlighted in Section 3. Referring again to Fig. A timing diagram for this phase switching is shown in Fig.

Motors with even numbers of phases must have half of the phases excited at any time. The maximum pull-out torque can be calculated for an n-phase motor with a peak static torque of TP K when one phase is excited. Aside from the sharp dips, which are discussed in the next section, there is a gradual decline in pull-out torque to 0. The cause of this effect is the oscillation in rotor velocity shown in Figs 4.

For a system with a relatively low inertia this assumption may not be true and the rotor can stop whenever the load exceeds the motor torque. For motors with a large number of phases the torque reduction at low speeds is less pronounced.

With a four-phase motor excited one-phase-on, however, the pull-out torque for low inertia is 0. As the number of phases increases the reduction factor tends towards unity and the system inertia has less effect on the low-speed pull-out torque.

The reduction in pull-out torque occurs when the stepping rate is less than the natural frequency of mechanical oscillations for the system, which can be determined from the results of Section 4. The response of the system to each excitation change — known as the single-step response — is generally very oscillatory Russell and Pickup, ; a typical response is shown in Fig.

In applications requiring frequent accurate positioning this poorly damped response can be a great disadvan- tage. For example, if a stepping motor is used to drive a printer carriage then the system must come to rest for the printing of each letter. The operating speed of the printer is limited by the time taken for the system to settle to within the required accuracy at each letter position.

In practice there is a small amount of viscous friction present in the system so that 2 steps position rotor overshoot final 1 step position initial position settling time time rise time Figure 4. Friction effects in an electromechanical system are generally undesirable, since they lead to wear in the moving parts, and are variable, because they are a function of this wear.

The designer attempts to reduce friction as far as possible, so most stepping motor systems have very little inherent damping and consequently a poorly damped single-step response.

One consequence of the highly oscillatory single-step response is the existence of resonance effects at stepping rates up to the natural frequency of rotor oscillation. Figure 4. The rotor quickly settles into a uniform response to each step. As a result of this initial velocity the response to the second step is more oscillatory; the rotor swings still further from the equilibrium position. The rotor oscillations increase in amplitude as successive steps are executed until the rotor lags or leads the demanded step position by more than half a rotor tooth pitch.

Once this oscillation amplitude is exceeded the motor torque causes the rotor to move towards an alternative step position which is a complete rotor tooth pitch from the expected position see Fig. The correspondence between rotor position and the number of excitation changes is now lost and the subsequent rotor movement is erratic. Note that motors with a large number of phases have an advantage here, since a step length is a small proportion of the rotor tooth pitch eqn 1.

The location of these dips can be predicted if the natural frequency is known either from eqn 4. Resonance is likely to occur if, at the end of the excitation interval, the rotor is in advance of the equilibrium position and has a positive velocity. These regions are indicated in Fig. The additional complication of damping-dependent oscillation frequency is included in the analysis by Lawrenson and Kingham For applications requiring repeated fast positioning over a single step, it is possible to utilise the high overshoot of the system.

The contrast between this response and the effect of changing directly from single-phase excitation of A to B is shown in Fig. Unfortunately the timing of the excitation changes in this intermediate half-step control is quite critical and is heavily dependent on load conditions Miura and Taniguchi, It is therefore restricted in application to situations where the load is constant, or to closed-loop position control systems see Section 7.

The resonant tendencies of a stepping motor system can be reduced by introducing more damping and therefore limiting the amplitude of oscillation in the single-step response.

There are two important techniques for improving the damping, using either mechanical or electrical methods, and these are discussed in the following sections. However, the use of straightforward viscous friction is undesirable because the operation of the motor at high speeds is severely limited by the friction torque. A solution to this problem is the viscously coupled inertia damper VCID , sometimes known as the Lanchester damper.

This device gives a viscous friction torque for rapid speed changes, such as occur in the single-step response, but does not interfere with operation at constant speeds. Externally the damper appears as a cylindrical inertial load which can be clamped to the motor shaft so the damper housing rotates at the same speed as the motor. When relative motion occurs between the damper components there is a mutual drag torque. Dampers are carefully designed so that this linear relationship is preserved over a wide range of speed difference.

From eqn 4. A well designed damper can produce a considerable improvement in the single- step response. If the inherent friction torque of the system can be neglected the equation for the rotor position relative to equilibrium, eqn 4.

Substituting for TD from eqn 4. One problem here is to establish a suitable criterion to judge the quality of a single-step response. Faced with this problem, Lawrenson and Kingham chose to min- imise the integral-of-absolute-error IAE , which corresponds to minimising the area shown in Fig.

However, the damper does have the effect of increasing the rise time of the response, because the available motor torque has to accelerate both the load and damper inertias towards the step position. The penalty to be paid for the use of a VCID is that the system is slower to accelerate. Even if the viscous coupling is low so that the damper housing and rotor operate almost independently the system inertia is increased by the housing inertia and the acceleration is correspondingly reduced.

With a high value of kD the damper housing and rotor are closely coupled, so the effective system inertia is increased by both the housing and damper rotor inertia. Now consider the situation when two phases are excited.

It is these induced voltages which are used to extract energy from the mechanical system and provide electromagnetic damping. A rigorous analysis of the mechanisms involved in electromagnetic damping has been undertaken by Hughes and Lawrenson , who demonstrated that the single- step response is third-order when the electrical circuit is taken into account. With two-phases-on excitation, damping occurs because the induced voltages produce additional ac components of phase current, which are superimposed on the steady dc phase current.

These ac current components give extra power losses in the phase resistance when the rotor is oscillating, so mechanical energy is extracted from the system to supply this extra power. If the phase resistance is set too high the ac current component is low and the power losses i 2 r are small.

Conversely if the phase resistance is below the optimum value the ac current is high, but there is very little resistance in which the current can dissipate power. Typical values of k are in the range 0. A similar result to eqn 4. Although the optimum phase resistance can be calculated, in practice it is a fairly simple matter to determine the optimum experimentally. The single-step response can be examined over a range of forcing resistance values with appropriate changes of supply voltage to maintain constant phase current until a suitable response is obtained.

The discussion has centred on the two-phase hybrid motor, but electromag- netic damping can be produced in all types of motor, provided more than one phase is excited when the rotor is settling to the equilibrium position. In some cases the elec- tromagnetic damping effect can be enhanced by introducing a dc bias to all phases of the motor Tal and Konecny, In addition, Jones and Finch have shown that the single-step response can be optimised by allowing the phase winding currents to change gradually.

In the next chapter it is shown that the system requires a large forcing resistance to operate at the highest speeds and in most cases the total phase resistance is then much greater than the optimum for electromagnetic damping. The system designer is therefore left to make a compromise choice of forcing resistance according to the application.

Chapter 5 High-speed operation 5. If the load torque is 0. However, for a load 1. Clearly the designer of the system with a load torque of 1 Nm would like to know what parameters of the motor and drive need to be changed so that a pull-out torque of 1 Nm is available at steps per second.

A quantitative treatment of these effects for both hybrid and variable-reluctance motors is presented in this chapter. Typical phase current waveforms for one-phase-on unipolar excitation of a three-phase variable-reluctance motor are shown in Fig.

At the lowest operating speeds Fig. For stepping rates where the phase is only excited for a time similar to the winding time constant, however, the waveform Fig. At very high operating speeds the voltage induced in the phase windings by the rotor motion must be considered.

The effect of these induced voltages can be seen in the high-speed waveform of Fig. Even while the phase is switched on it is possible for the current to be reduced by the induced voltage, which is at its maximum positive value when the phase is excited.

Similarly when the phase is turned off the decay of current can be temporarily reversed as the induced voltage passes through its maximum negative value. In most stepping motor systems the winding time constant is much less than the period of rotor oscillations about each equilibrium position. It is, of course, possible to take account of the speed variations Pickup and Tipping, , but this is an unnecessary complication in the evaluation of pull-out torque.

Hybrid and variable-reluctance motors receive separate treatment because there are fundamental differences in the analysis of the two types.

A hybrid motor has two phase windings, which are mounted on separate stator poles Chapter 1 and therefore the phase circuit model must include the resistance and inductance of each winding.

The phase circuit model shown in Fig. The complete model must also take account of the voltages induced in the phase winding by rotor motion. Details of the induced voltage are not usually supplied by the stepping motor manufacturer, but fortunately the voltage can be measured experimentally.

If the motor under test has its windings open-circuit and is driven by another motor Fig. The hybrid stepping motor has two phases, which are excited by positive or negative currents. A complete excitation cycle consists of four steps, corresponding to excitation of each phase by each current polarity. This angle accounts for the lag of the rotor behind the phase equilibrium position as the load on the motor increases.

The voltage applied to each phase circuit is a dc supply which can be switched on or off in the positive or negative sense. This switched supply introduces a non-linearity, which can be eliminated by considering only the fundamental components of voltage and current. In Section 5.

As the induced voltage is essentially sinusoidal only the sinusoidal component of phase current at the same frequency is required for the torque calculations. Substituting from eqn 5. This component needs to be calculated according to the excitation scheme being used. Substituting the fundamental voltage and current components into eqn 5. In the phasor diagram the applied phase voltage is equal to the vector sum of the induced voltage and the voltage drops across the resistance and inductance.

It must be emphasised that this phasor diagram applies only to the fundamental current component and that the complete phase current waveform contains many other higher frequency components, which do not contribute to the torque produced by the motor.

The mechanical output power per phase is the product of the phase current and the induced voltage. The expres- sion eA iA can only produce a constant term if both eA and iA have equal frequencies and, since eA has only a fundamental component, it is the corresponding component of iA which is required. From eqn 5. When the pull-out load is applied, the load angle is such that the expression for torque is maximised.

By inspection of eqn 5. These two alternatives can be investigated by setting the pull-out torque expression 5. The maximum stepping rate corresponding to eqn 5.

In choosing a motor for high speed operation a low value of kH is desirable, as the denominator in the expression for maximum operating frequency is then minimised. The second factor shows that at the highest speeds the pull-out torque is inversely proportional to the supply frequency and that, as before, a large total phase resistance improves the high speed performance. Finally we see that the constant kH is important: a motor with low kH has more torque at high speeds.

If electromagnetic damping of the single-step response is required, however, the results of Section 4. This analysis assumes that the voltage waveform applied to the phase circuit is independent of speed, but with a bridge drive circuit this may not be true. For two-phases-on excitation of the hybrid motor each phase is excited continuously by either positive or negative voltages.

When operating at low speed the freewheeling time of the phase currents is short compared to the total excitation time and for most of the cycle the phase current is carried by the switching transistors. At high speeds the freewheeling time is relatively long but the effective phase voltage is unchanged, even though the bridge diodes are conducting for a substantial part of the cycle. With one-phase-on excitation, however, there are times in the excitation cycle when the phase voltage is zero.

During these freewheeling intervals the effective phase voltage is equal to the dc supply voltage. Therefore with one-phase-on operation of the hybrid motor the fun- damental component of the phase voltage increases with speed and consequently the pull-out torque at high speeds is greater than that predicted by eqn 5.

During deceleration the motor produces negative braking torque, which [from eqn 5. The solution to this problem is in two parts.

The pull-out torque and maximum stepping rate can then be found from eqn 5. For a hybrid stepping motor with p rotor teeth the step length is given by eqn 1. The pull-out torque at low speeds can be expressed in terms of the peak static torque using the methods described in Section 4. For two-phases-on excitation of the hybrid motor the peak static torque is 1. The variation of phase inductance is approximately sinusoidal with a wavelength equal to the rotor tooth pitch, as shown in Fig.

Substituting from eqns 5. If the mechanical output power is to be found by evaluating the product of phase current and motional voltage, it appears that a large number of harmonics will need to be considered.

By neglecting the harmonics of current an error is introduced into the analysis, but the next Section shows how this error can be cor- rected by evaluating the pull-out torque at low speeds.

There is a broad similarity between the equation linking the fundamental voltage and current compo- nents in the variable-reluctance motor, eqn 5. The phasor diagram representation of eqn 5. This phasor diagram is similar to Fig. In the preceding section it has been shown that these harmonics can contribute to the mechanical output power, because harmon- ics of current lead to harmonics of motional voltage.

It is assumed that the correction factor is independent of speed and therefore it can be evaluated quite simply for the rectangular current waveforms typical of low-speed operation. The magnitude of this contribution can be calculated for any excitation scheme by expressing the current components in terms of the rated winding current using a Fourier analysis of the waveform.

This process is illustrated in Fig. The total torque, when all current components are considered, can be found by evaluating eqn 5. The average torque per phase can then be found by averaging the instantaneous torque over one cycle. This method can be repeated for each excitation scheme to give an exact expression for the pull-out torque in terms of phase current and inductance. In Table 5. Table 5. With the half-stepping excitation scheme, for example, the pull-out torque is predicted precisely from the dc and fundamental current components.

If one-phase-on excitation is used, however, the pull-out torque obtained from the dc and fundamental components must be multiplied by 1. However, in Chapter 3 we have already seen that the peak static torque of a three-phase motor is the same for one- and two-phases-on and this result therefore extends to the pull-out torque at low speeds. Having established the torque correction factors for the common excitation schemes of a three-phase motor and illustrated the method by which the factor may be found for motors with larger numbers of phases, we can now consider how the pull-out torque produced by the dc and fundamental current components varies with stepping rate.

By analogy to the hybrid motor the expression for pull-out torque in a variable-reluctance motor can be found directly. Writing eqn 5. The hybrid motor has two phases, so the pull-out torque per phase is half of the value indicated in eqn 5. The variable-reluctance motor has n phases, so the pull-out torque per phase must be multiplied by n, with the overall result shown in eqn 5.

An expression for the maximum operating speed of the variable-reluctance motor follows from eqn 5. The corresponding maximum stepping rate can be found from eqn 5.

Eqns 5. For a three-phase motor the voltage component ratio for each excitation scheme is shown in Table 5. By operating the motor with one-phase-on excitation the speed range is consid- erably improved compared to two-phases-on operation, for which the value of kv is doubled.

In eqn 5. Finally the relevant torque correction factor is found from Table 5. For the one- phase-on excitation scheme the correction factor is 1. As the phase resistance can be controlled by changing the forcing resistance, it is possible to operate stepping motors at very high speeds using the simple drive circuits described in Chapter 2 with a large forcing resistance.

However, the supply voltage must also be increased to maintain the phase current at its rated value when the motor is stationary, and consequently a large dc power supply is needed. For small motors this may be a perfectly satisfactory method of obtaining a wide speed range, because the size of power supply is unimportant.

With larger motors, however, the power supply may have to have a capacity of several kilowatts if the system is to operate over a satisfactory speed range.

In these circumstances it is worth reconsidering the design of the drive circuit. A large supply voltage and phase resistance are only required when the motor is operating at high speeds. An alternative viewpoint is obtained from the circuit model for the phase windings.

For both types of motor the circuit model Fig. Increases in applied voltage must be accompanied by proportional increases in phase resistance if the winding current is to be limited to its rated value when the motor is stationary. At the highest speeds the phase current is low, so the voltage drop across the series resistance is small and the applied voltage balances the induced voltage. A high voltage is used when the phase current is to be turned on or off, while a lower voltage maintains the current at its rated value during continuous excitation.

The circuit diagram for one phase of a unipolar bilevel drive is shown in Fig. There is no series resistance to limit the current, which therefore starts to rise towards a value which is many times the rated winding current. Rapid decay of the current is assured, because the high supply voltage VH is included in this freewheeling path. A typical current waveform for one excitation interval is illustrated in Fig. Substituting in eqn 5. One disadvantage of the bilevel drive in this form is that it is unable to counteract the motional voltage and this voltage has been neglected in the analysis of drive circuit performance.

If the phase excitation signal is present, the base drive for transistor T2 is controlled by the voltage vc dropped across the small resistance Rc by the winding current.

At the beginning of the excitation interval the transistor T1 is switched on and the base drive to T2 is enabled. As the phase current is initially zero there is no voltage across vc and the transistor T2 is switched on.

The full supply voltage is therefore applied to the phase winding, as shown in the timing diagram, Fig. The phase current rises rapidly until it slightly exceeds its rated value I. This current path has a small resistance and no opposing voltage, so the decay of current is relatively slow. The full supply voltage is applied to the winding and the current is rapidly boosted to slightly above rated.

At the end of the excitation interval both transistors are switched off and the winding current freewheels via diodes D1 and D2. The current is now opposed by the supply voltage and is rapidly forced to zero. The chopper drive incorporates more sophisticated control circuitry, e.

If these levels are not well separated, the transistor T2 switches on and off at a very high frequency, causing interference with adjacent equipment and additional iron losses in the motor. However, the chopper drive does have the advantage that the available supply voltage is fully utilised, enabling operation over the widest possible speed range, and the power losses in forcing resistors are eliminated.

Experience has shown that the effects of the instability can be avoided if the system is accelerated briskly through the unstable region. Furthermore the effects are min- imised in heavily loaded open-loop systems with substantial viscous damping and are completely avoided in closed-loop systems. It is fortunate for the stepping motor user that, after varying levels of tortuous analysis, all of these studies have agreed on some surprisingly simple results.

The most important of these results is that the instability occurs close to those stepping rates where the angular frequency of the phase winding excitation is equal to the phase resistance R divided by the phase winding inductance L. Chapter 6 Open-loop control 6. When this task of selection is completed, the designer must consider how the motor and drive are to be controlled and interfaced to the remainder of the system.

The aim of the following chapters, therefore, is to show that system performance can be maximised and costs minimised by correct choice of control scheme and interfacing technique. The open-loop control schemes discussed in this chapter have the merits of simplicity and consequent low cost. A block diagram for a typical open-loop con- trol system is shown in Fig.

Although the system illustrated receives its phase control signals from a microprocessor a number of alternatives are presented later in this chapter. Whatever the signal source, the designer needs to know what restrictions are imposed on the timing of the control signals by the parameters of the drive, motor and load. Some of these restrictions stem from the steady-state performance e.

If the system has a high inertia, for example, the maximum drive microprocessor circuit motor load torque timed phase phase control signals currents Figure 6. In an open-loop control scheme there is no feedback of load position to the con- troller and therefore it is imperative that the motor responds correctly to each excitation change. If the excitation changes are made too quickly the motor is unable to move the rotor to the new demanded position and consequently there is a permanent error in the actual load position compared to the position expected by the controller.

The timing of phase control signals for optimum open-loop performance is reasonably straightforward if the load parameters are substantially constant with time. The excitation sequence generator produces the phase control signals and is triggered by step command pulses from a constant frequency clock. This clock can be turned on by the START signal, causing the motor to run at a stepping rate equal to the clock frequency, and turned off by the STOP signal, in which case the motor is halted.

Initially the target direction is sent to the excitation sequence generator, which then produces phase control signals to turn the motor in the appropriate direction. The target position is loaded into a downcounter, which keeps a tally of the steps commanded. Clock pulses are fed to both the phase sequence generator and the downcounter. Changes in phase excitation are therefore made at the constant clock frequency, and the instantaneous position of the motor relative to the target is recorded in the downcounter.

When the load reaches the target the downcounter contents are zero and this zero count is used to generate the clock STOP signal. In a simple constant frequency system, however, the clock must be set at the lower of the two rates to ensure reliable starting and stopping.

When the motor is accelerating from rest the stepping rates are low; the period of each phase excitation interval is much longer than the electrical time constant of the phase circuit. These characteristics are displaced from each other by the step length, as shown in Fig. If the calculated starting rate does coincide with a resonant rate the designer can either elect to use a lower frequency clock or try to reduce the resonance with additional damping.

More sophisticated methods of open-loop control enable the system to approach its pull-out rate and there- fore the dependence of motor torque on stepping rate must be taken into account. Variations of load and friction torques with speed can also be taken into account. Typical pull-out torque and load torque characteristics are shown in Fig. In this case a linear speed scale must be used and therefore the shape of the characteristic is rather different from those illustrated in Chapters 4 and 5, where a logarithmic speed scale has been used.

At a stepping rate f the pull-out torque is denoted by T f and the load torque by TL f. If the motor is to accelerate as quickly as possible the maximum pull-out torque must be developed at all speeds.

Figure 6. The time, t1 , taken to reach stepping rate f1 can then be found from eqn 6. The variation of pull-out torque with speed can be approximated by the straight lines shown dotted in Fig.

From eqn 6. When the system is decelerating the motor must produce a negative torque and therefore each phase must be switched on after the rotor has passed the phase equi- librium position. Alternatively deceleration can be initiated by extending a phase excitation time until the rotor moves forward of the equilibrium position and the motor produces neg- ative torque. At the end of this time the rotor has moved forward to a position where the motor is producing negative torque.

The transition to deceleration is slower than for the excitation jump method, because the motor torque only changes sign in response to a rotor movement, rather than an excitation change, but the complication of decrementing the step count is avoided. For example, an exponential ramp may be required for optimum acceleration, but its implementation is expensive and so the designer may compromise with a linear ramp, which is available at very low cost.

With open-loop control even lightly loaded motors can rarely operate at speeds of more than 10 steps per second. Therefore the microprocessor need only issue a step command every 0. As the program time needed to produce each step command is likely to be much less than 0. Control is then returned to the main program.

Execution of the main program continues until the next clock interrupt, which returns the processor to the motor control routine at ENTER.

The times between step commands are therefore proportional to the constant clock period and the look-up table values. Deceleration commences with a long delay number 25 , which allows time for the rotor to swing past the equilibrium position into a position where the motor is producing the negative torque required for deceleration. Only four steps are required to decelerate the motor, as the load torque contributes to the decelerating torque.

Additional steps can be pro- duced by expanding the look-up table to include more high-speed short-delay values. Open-loop control However, if the target is less than 14 steps from the original position the appropriate number of look-up table entries can be deleted, starting with the short-delay values. The look-up table entries can be calculated, using the methods described in Sec- tion 6.

Alternatively the table values can be found experimentally. How is the clock interrupt rate determined? Suppose the delay number stored in the look-up table is m for the maximum stepping rate of steps per second.

The clock rate is then m Hz, because there are m clock cycles per step command. At a clock frequency of 9. The number of motors which can be controlled is limited by the requirement that step commands may have to be issued to all motors between successive clock interrupts. Therefore no more than three motors can be controlled by a single microprocessor. MIDI-based controller of electrical drives. The purpose of this paper is to provide a cost effective … Expand.

A closed-loop stepper motor drive based on EtherCAT. With the advent of increased industrial the automation and microprocessor applications, the interest in digital motion control systems has also expanded. Hybrid Stepper Motors are widely used in … Expand. Spontaneous speed reversals in stepper motors. Physics, Computer Science. Experimental data shows that permanent magnet stepper motors can spontaneously reverse their direction of rotation when controlled in full step, open-loop mode.

The paper shows that the reversal of … Expand. Two hybrid stepper motor models. ICIA The … Expand. View 1 excerpt.

Stepping motors and their microprocessor controls. Richly illustrated, this book covers all aspects of stepping motors including basic theory; principles of design, construction, and application; torque production mechanism; dynamic characteristics; … Expand. Unifying approach to the static torque of stepping-motor structures. Important stepping-motor structures are compared and their logical relationship to a basic doubly-salient machine is demonstrated. This leads to a single expression for holding torque, applicable to … Expand.

View 2 excerpts, references background. Simplified approach to the dynamic modelling of variable-reluctance stepping motors. The paper establishes a simplified theoretical model for variable-reluctance stepping motor systems, based on linearisation of the motor's dynamic torque-producing characteristics about an arbitrary … Expand.

A circuital method for the prediction of pull-out torque characteristics of hybrid stepping motors. Optimal controlcn of a voltage-driven stepping motor.

The single-step optimal control of a voltage-driven variable-reluctance stepping motor, with an inertia load, is considered. A solution for the optimal control policy is achieved by a conjugate … Expand. An analytical study of dynamic instability in hybrid permanent-magnet stepping motors is described, the principal features of which can be applied, more generally, to a wide range of … Expand. Analysis of single-step damping in a multistack variable reluctance stepping motor.

An analytical method is developed for calculating the single step dynamic torque characteristics and rotor position response of a multistator, variable reluctance stepping motor. Representation of … Expand. Improved method of controlling stepping motor switching angle.