Micro Stepping

34.8.6 Micro Stepping

In micro stepping, the regular step angle of the motor is subdi- The drive sequences mentioned in Section 34.8.2 normally vided further by a factor, typically from 10 to 100, by energizing switch rated current through the motor windings. These pro- the windings partially, with combinations of currents ranging duce regular step angles. The half-stepping operation also uses from zero to full rated value in more than one windings simul- rated motor currents. Halving of the step angle is arranged taneously. This does not lead to any sacrifice of the developed mainly through the selection of the windings switched. torque, since the phase currents are so selected that the peak

972 M. F. Rahman et al. of total torque contributed by two partially energized wind-

3. Dissipates no more than the rated power loss (I 2 R) for ings is not lower than the peak detent torque T max obtained in

every combination of winding currents. regular stepping.

The preceding conditions are necessary if the motor is The idea behind micro stepping is readily understood when to retain its static accuracy, maximum torque, and power it is considered that by increasing the current in phase A of a

dissipation characteristics.

two-phase hybrid in 10 equal steps to full value and decreasing The static torque characteristics (Fig. 34.92) of stepper the current in phase B in a similar manner, the motor step size motors are close to, but not exactly, sinusoidal functions of may be divided by a factor of 10. If the closed-loop current angle θ. The required current references for all windings controllers are added to the two drive circuits of Fig. 34.91 of a stepper motor, including the variable-reluctance motor and distinct current references are obtained from a reference of three or more phases, can easily be calculated from the generator, a complete micro stepping drive is realized. data of the T–θ characteristics of the motor for each phase In micro stepping, the two current references must have for various currents and rotor positions. A typical set of T–θ values such that the motor does the following: data for a three-phase variable-reluctance motor is shown in

1. Develops the same T max for every combination of Fig. 34.93. The application of the three conditions mentioned winding currents.

earlier leads to an unique set of current references for each

2. Develops the same torque slope, i.e. dt/dθ at every phase of the motor for each micro step. Figure 34.94 shows micro stepping detent position.

the current references for this motor for micro stepping.

A BF + Winding

Winding

(phase A)

(phase A)

FIGURE 34.92 Drive circuits for one phase of a bifilar-wound motor: (a) bifilar pole windings and (b) drive circuits.

Phase A

Phase B

Phase C

FIGURE 34.93 T–θ characteristics of a three-phase variable-reluctance motor.

34 Motor Drives 973 The fastest acceleration–deceleration profile, a stepper

motor is capable of is largely determined by its pull-out (T–ω) characteristic, which in turn is determined by the motor wind- ing parameters and the drive circuit. An optimized stepping profile to and from the top speed may have a number of segments as indicated in Fig. 34.95. These profiles are easily computed from the pull-out (T–ω) characteristic by integrat- ing the dynamic torque balance equation of the drive. For

a large positioning angle, the entire profile, including some constant-speed running at the top speed, may be used. For short positioning angles, only part of the profile may be tra-

FIGURE 34.94 Micro stepping current references for the VR motor of Fig. 34.93. Stepping rate: 28,800 steps/s., I

versed. In general, a single segment acceleration–deceleration

= 6 A (maximum).

profile is used in commercial stepper motor controllers, so as to avoid a great deal of realtime number crunching by the profile controller.

In multi stepping operation, these micro stepping current The overall stepper motor controller thus consists of the references have to be issued to the current controllers for each blocks depicted in Fig. 34.96.

phase, at a rate determined by the commanded stepping rate. Care has to be taken in designing the phase-current con- trollers so that the actual winding currents match the current references in both single and multi stepping operation up to

34.9 Switched-reluctance Motor Drives

the maximum stepping rate desired. Since the current refer- ences are time varying, high-bandwidth current controllers are

34.9.1 Introduction

normally required to cover the desired speed range. The switched-reluctance (SR) motor is a doubly salient electric machine with salient-poles on both the stator and rotor. The machine is operated by switching current pulses to each stator

34.8.7 Open-loop Acceleration–Deceleration

winding on and off in a continuous switching sequence. The

rotor poles have no excitation. Figure 34.97 shows the physi- As mentioned in Section 34.8.4, many applications require the cal topology of a typical SR motor. The diagram illustrates a

Profiles

stepper motors to be driven far above the stepping rates to and motor with eight salient stator poles (numbered A1 to D2) and from which the motor can start and stop abruptly without six salient rotor poles (numbered 1 to 6). Although many com- losing or gaining any step. This calls for carefully designed binations of the number of stator and rotor poles are possible, acceleration–deceleration profiles that the stepping pulse rate this particular type has found widespread use. must not exceed.

The phase windings on the stator of the SR motor consist The number of steps the motor is to be stepped and its of concentrated windings wrapped around the stator poles.

direction are normally under the control of the motion con- In the conventional arrangement, each stator pole winding is troller. Once this reference is known, a digital timer/counter connected with that of the diametrically opposite pole to form circuit can be used in the controller to progressively adjust

a stator phase. In Fig. 34.97, the connected stator pole pairs the time between the stepping pulses such that a prescribed are indicated by the same prefix letter. acceleration–deceleration profile, as indicated in Fig. 34.95, is

The general principle of operation of the SR motor is the followed. The timer/counter and the pulsing sequence con- same as all types of reluctance machines, i.e. the stator and

troller (the translator) need to be managed in realtime to the rotor poles seek the minimum-reluctance position, so execute the motion-control task at hand.

that the stator excited flux becomes maximum. Hence, when current flows in an SR motor stator phase and produces a magnetic field, the nearest rotor pole will tend to position itself with the direction of the developed magnetic field. This

fmax, ksteps/sec

position, which is termed the aligned position, is reached when the rotor pole center axis is aligned with the stator pole cen-

Stepping ter axis (assuming symmetrical poles). The aligned position rate

also corresponds to the position of minimum reluctance, and hence the position of maximum inductance.

It should be noted that the unaligned position is defined t=0

as the position when the inter-pole axis, or the axis of the FIGURE 34.95 Typical acceleration–deceleration profiles.

Time, t

center of the inter-polar space in the rotor, is aligned with a

974 M. F. Rahman et al.

Stepping pulses

Stepper Controller

FIGURE 34.96 Structure of an open-loop motion controller for a stepper motor.

+V dc i current switched off, and coils B1 and B2 of phase B are now excited, then in a similar fashion the rotor will move so that the poles 2 and 5 are aligned with stator poles B1 and B2. Exciting phases A, B, C, and D in sequence will produce rotor rotation A1 in the counterclockwise direction.

B1 D2 From the preceding discussion, one may see that the switch- ing on and off of excitation current to the motor phases is

6 1 related to the rotor pole positions. This means that some form C1 C2 of position sensor is essential for the effective operation of the 5 2

SR motor. 4 3

B2 D1 34.9.2 Advantages and Disadvantages of A2 Switched-reluctance Motors

The SR motor has a number of inherent advantages that makes it suitable for use in certain variable-speed drive applications.

O Nevertheless, the motor also has some inherent disadvantages i

that must be considered before choosing the motor for a par- FIGURE 34.97 Four-phase SR motor topology.

ticular application. In Table 34.6, the main advantages and disadvantages of the SR motor drive are summarized.

Rotor pole center

axis

34.9.3 Switched-reluctance Motor Variable-speed Drive Applications

Inter-pole axis

The main application for SR motors is in variable-speed drive systems. One application area has been general-purpose indus- trial drives where speed, acceleration, and torque control are desired. SR-motor-based industrial drives provide the advan- tages of a very wide range of operating speeds as well as

FIGURE 34.98 Rotor pole axis positions. TABLE 34.6 Advantages and disadvantages of SR drives Advantages

Disadvantages

stator pole axis. This position corresponds to the position of Low cost motor.

Need for position measurement.

minimum inductance. These rotor axis positions are illustrated Robust motor construction.

Higher torque ripple than other

in Fig. 34.98.

machine types.

To achieve continuous rotation, the stator phase currents Absence of brushes.

Higher noise than other machine types.

are switched on and off in each phase in a sequence according Nonlinear and complex characteristics.

No motor short-circuit fault.

No shoot-through faults.

to the position of the rotor. Consider the motor schematic Ability to operate with faulted illustrated in Fig. 34.97. If coils A1 and A2 of phase A are

phase.

excited and produce a magnetic field in a vertical direction, High torque to inertia ratio. then poles 1 and 4 on the rotor will align themselves with the Unidirectional currents. High efficiency. stator poles of phase A. If the coils of phase A now have their

34 Motor Drives 975 high efficiency and robustness. Other applications of the SR

34.9.4.2 Maximum Speed

drive include automotive applications, where the SR motor has The SR motor is capable of operating at very high speeds advantages of robustness and fault tolerance. The SR motor in because of its robust rotor construction, and in most applica- this application can also be easily controlled for acceleration, tions the maximum speed is limited by the inverter switching steady speed, and regenerative braking.

speed and not limited by the motor itself. The maximum speed The SR motor is also well suited to aerospace applications of the SR motor is itself normally greater than 15,000 rpm for

where the ability to operate under faulted conditions and its

a standard SR motor.

suitability for operation under harsh environments are critical. However, to determine the maximum drive speed, the con- Additionally, the very high-speed capability and high-power troller and motor must be considered together. This is because

density also make these motors well suited in the aerospace the power-electronic device switching speed is directly pro- field. There are also many domestic appliances where cost is of portional to the commutation frequency, which is in turn primary concern. In these products, the SR motor can provide proportional to the motor speed. The maximum switching

a low-cost solution for a brushless fully controllable motor frequency of the power devices must therefore be taken into drive. In addition, the motor can be used in battery-powered account in the SR drive design. applications, where the motor-high efficiency and ability to use

a dc supply are important.

34.9.4.3 Number of Power Devices

In general, the number of switches per phase in SR motor