Power electronic handbook

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896 M. F. Rahman et al.

When starting, or at a low speed, the current in a winding

is limited only by the very low resistance and, for the machine

above by Ohm’s law, I = E/R would result in more than

2000 amperes.

The most common requirement for a steady current in

the windings is to provide a steady torque. There is always

a back-emf generated in the windings whenever the motor is

rotating, which is proportional to speed and subtracts from

the applied voltage. Thus currents cannot be determined just

by terminal voltage. The winding does however have induc-

tance. Whenever the copper conductors are put in coils in an

iron structure, particularly if there are low reluctance mag-

netic paths with only small airgaps, the creation of quite large

inductances cannot be avoided. These are used to very good

effect.

The nature of inductance is that when a voltage is applied to

an inductor, instantaneous current does not result, rather the

current begins to increase and ramps up in a quite controlled

fashion. If the voltage across the inductor is reversed the cur-

rent does not immediately reverse, rather it ramps down, will

go through zero and reverses if the reversed voltage is left there

long enough. However, if the voltage is alternated by switch-

ing rapidly, as can be done with power electronics, the current

can be controlled to ramp-up and ramp-down either side of

a desired current, staying within any determined tolerance of

that desired current.

Figure 33.63 looks very much like the simple “H” bridge

commutation circuit, but is performing a very different func-

tion. It is controlling the current amplitude to stay within a

desired band. If S1 and S4 are turned on then the current will

begin to increase from left to right in the winding. The current

sensor in the circuit detects when the current reaches a value

of half the hysteresis band of the comparator above the desired

Desired Current (torque),

eg ±5V represents maximum

positive or negative torque.

a′

−

Comparator

with hysteresis, eg

±100 mV

−

PWM logic signal output.

Turns on S1 and S4 if high (current below reference),

or S2 and S3 if low (current above reference)

Current sensor,

voltage output

proportional

to current

FIGURE 33.63 Hysteresis band current control using pulse-width modulation (PWM).

current level and initiates turn-off of S1 and S4 and turn-on

of S2 and S3. (If they were all turned off at once, the inductive

nature of the circuit would produce very high voltages which

would cause arcing in mechanical switches, or breakdown and

failure of semiconductor switches, see later.) The current then

begins to reduce. It reduces a small amount, down to half the

hysteresis band of the comparator below the desired current

level and then the switches reverse again. Thus a desired cur-

rent level is achieved, with an arbitrarily small triangular ripple

superimposed, as shown in Fig. 33.64.

The general process of controlling by switching a voltage

fully on or fully off at high speed is called pulse width mod-

ulation (PWM) and the speciﬁc method of current control

achieved above with PWM, is called hysteresis band current

control (HBCC).

Of course to keep this current ripple small, the switching

may need to be very fast, but with the modern semicon-

ductor switches there is no great problem up to 100 kHz for

small machines and typically above 15 kHz for acoustic noise

reasons, for machines rated up to several hundred kilowatts.

A perceived “drawback” of HBCC is that the switching fre-

quency is determined by the circuit inductance, the width of

hysteresis band, the back-emf, and the applied voltage, ranging

very widely in normal operation. It is not difﬁcult, but it is a

little more complicated, to use a ﬁxed frequency, and a linear

analog of the current error to modify the pulse width of the

PWM signal.

33.6.3.1 Switching Losses

There is a practical limit to how often semiconductor switches

can be operated. At every change of state, if the switch is carry-

ing current as it is opened, then as the voltage rises across the

33 Motor Drives 897

Current

PWM

Logic signal

output

Time

Desired current

Actual current

FIGURE 33.64 Hysteresis band current control and PWM waveforms.

switch and the current through it falls, there is a short pulse

of power dissipated in the switch. Similarly, as the switch is

closed, the voltage will take some time to fall and the current

will take some time to rise, again producing a pulse of power

dissipation. This loss is called switching loss. Fairly obviously

it will represent a power loss proportional to the switching

frequency and so the switching frequency is generally set as

low as it can be without impinging on the effective operation

of the circuit. “Effective operation” might well include criteria

for acoustic noise and levels of vibration.

33.6.3.2 High Efﬁciency Method of Managing the

Switching in the H Bridge

A very common way to control the current with the smallest

number of switching transitions is to combine HBCC with,

for example, alternating only S1 and S2 in Fig. 33.65 leaving

S4 on all the time, on the understanding that there will be a

back-emf in the winding and the current can still be increased

or decreased as desired.

Thus when the motor is rotating and the back-emf is

somewhere between zero and the rail voltage, alternating two

switches rather than four will still allow current control in the

coil, using for example HBCC, exactly as before.

a′

−

+−

Vin

Off

PWM

FIGURE 33.65 H-bridge switching with one switch steadily on and a

back-emf.

This is a very common control scheme and will need some

extra logic to reverse the direction of rotation of the motor, by

either turning S4 off and S3 on continuously, or by swapping

the control signals to the left and right “legs.” For full-servo

operation normal H-bridge switching can be used and the logic

is slightly different, but not signiﬁcantly more complicated.

However, following the discussion above, the switching losses

will be higher.

33.6.3.3 Combining Commutation and PWM Current

Control

The real break-through is that one set of six switches can be

used for both PWM and commutation. That is the clever part

and also the confusing part when one ﬁrst tries to understand

what is going on.

Thus, in a controller there are two control loops. The ﬁrst

is an inner current loop switching at, for example, 15 kHz to

control carefully and exactly the current in two of the coils.

Then at a much lower rate, for example at 50 times per second

at 3000 rpm, the two coils doing the work are changed accord-

ing to Table 33.2, controlled by an outer commutation loop,

using information from the Hall effect shaft position sensors.

A complete controller is shown in the block diagram form

in Fig. 33.66. Various aspects of this block diagram will now

be examined and explained in detail.

33.6.3.3.1 Hardware Details – Semiconductor Switches The

three most likely semiconductor switches for a six step

controller are the bipolar junction transistor (BJT), the

metal-oxide silicon ﬁeld effect transistor (MOSFET) and the

insulated gate bipolar transistor (IGBT). Older controllers

used BJTs, however contemporary controllers tend to use

MOSFETs for lower voltages and powers and IGBTs for higher

voltages and powers. Both of these devices are controlled by a

gate signal and will turn-on when the voltage of the gate above

898 M. F. Rahman et al.

−

G2 G4

Hall effect

shaft

position

sensors

Analog and digital

signal processing

Gate drives G1 to G6

Desired current

(torque) command

Current

sensors

FIGURE 33.66 A complete controller showing the two feedback paths, one for the position sensors and one for the current sensors.

the source or emitter is greater than a threshold, which is typ-

ically about 5 V. Use of about 10 V is common. The devices

are thus off when the gate voltage below the threshold. Sys-

tems typically use zero volts for the off state. The controller of

Fig. 33.66 shows MOSFETs used for the six switches.

The trick is that the voltage at terminal a, also S1’s source, is

either ground or the positive potential of the battery, depend-

ing on which switches are on. Driving S2, S4, and S6 is easy

since the MOSFET sources are all at the potential of the neg-

ative rail and the lower gate drive signals are referred to this

rail.

There is a range of dedicated integrated circuits which can

drive the switches S1, S3, and S5, and which use a “charge

pump” principle to generate the drive signal and the drive

power internally, all related to the MOSFET source potential.

Various approaches to this technical challenge of providing a

ﬂoating gate drive are commonly discussed under the generic

heading of “high side drives.”

For the most sophisticated drives, transformer coupling is

used to provide a tiny power supply especially for the isolated

gate drive and send the control signals either through an opto-

coupler or a separate transformer coupling. The high-side

drive problems here are exactly the same as those encountered

in the traditional buck converter, or in drives for induction

motors and PMSMs.

33.6.3.3.2 Dead Time and Flyback Diodes Two issues have

been mentioned above that must be addressed when using

high-speed electronic switches in inductive circuits.

The ﬁrst, in Section 33.6.2 “Electronic Commutation,” was

that care should be taken to ensure that the upper and lower

switches in the same “leg,” (e.g. S1 and S2) are never turned

on at the same time. If the controller attempts to turn one

off and the other on at the same instant and switch turn-off

is slower than turn-on (as it is with BJTs and IGBTs), then

a short circuit will result for a brief time. The bus capaci-

tor is usually very large to provide ripple current (see later)

and usually of very high quality being fabricated especially for

power-electronic applications, and can easily provide thou-

sands of amperes for a few microseconds, which is enough to

destroy the semiconductor switches.

The second issue, discussed in Section 33.6.3 “Current/

Torque control,” is that one cannot turn-off both switches in

a leg at the same time, even for a few nanoseconds, since the

voltages resulting from attempting to interrupt current in an

inductor will cause avalanche breakdown and failure of the

semiconductors. This sounds like quite a dilemma.

There is actually a very simple and effective solution. At

any transition, the control circuitry ensures that the active

switches are all turned off before any switch is turned on,

usually for a few microseconds. This is known as “dead time”

and its provision is an essential part of most of the dedicated

integrated circuits in use. Then a “ﬂyback”/“freewheel” diode

is put in anti-parallel with each semiconductor switch and this

provides the current path during dead time. These diodes are

shown in Fig. 33.66.

The diode has a little more loss than the switch, since the

diode forward drop is more than the switch drop. This is sig-

niﬁcant in a low voltage controller. However, as stated above,

for a low voltage controller, MOSFETs are the device of choice.

They have a lesser known property, that when gated on, they

can carry current in both directions. Intriguingly the “on” state

resistance is lower in reverse than in the forward direction!

33 Motor Drives 899

PWM

logic signal

output

I up logic

signal

I down logic

signal

Dead time

Time

FIGURE 33.67 Dead time introduced into the PWM logic signal, for switch drive.

Thus for low voltage controllers, when the switch forward drop

represents a signiﬁcant contribution to losses, the MOSFET is

turned on after dead time for both the current directions. Thus

the higher loss in the diode is only for a few microseconds.

It is not difﬁcult to produce from the PWM signal an “I up”

logic signal which is used to cause the current to increase and

an “I down” logic signal used to decrease it, with the timing as

shown in Fig. 33.67. The function can be executed in sequential

logic, or with the simple analog timing circuits.

A. Semiconductor Detail

In MOSFETs and most IGBTs, there is a diode already within

the device; it is unavoidable and results from the fabrication

processes. In modern power semiconductors, this intrinsic

diode is optimized to be a good switching diode. The seri-

ous designer, however, will check the speciﬁcations for reverse

recovery of this diode, since in highly optimized controller

designs, reverse recovery losses in the intrinsic diode can be

signiﬁcant and are very difﬁcult to control. In low voltage

controllers, you can put a Schottky diode in parallel with the

intrinsic body diode. The Schottky diode, with its lower for-

ward voltage drop will tend to take the current and has no

reverse recovery problems, but the current must commutate

to it from the semiconductor die and the inductance of the

connections is critical.

B. The Smoothing Capacitor on the Input to the Controller

This is a substantial capacitor, often very expensive, (it is

shown in Fig. 33.66 as C in) and its design is quite chal-

lenging. The issue of smoothing is quite serious. If there are

high-frequency or sudden current changes in the leads from

the dc supply to the controller, they will radiate electromag-

netic energy. Good design will limit the length of conductors

in which the current is changing rapidly. Thus, a very large

capacitor is placed physically as close to the positive bus of

the switches as possible, aiming to have a steady current in

the longer conductors from the dc supply, up to the capacitor.

When the motor is running at, say, half speed and providing

large torques, a very high level of ripple current is carried by

this capacitor. Kirchhoff’s current law (KCL) must be applied

at node A, as shown in Fig. 33.68. Good capacitors have a rip-

ple current maximum buried away in their speciﬁcation sheet.

It turns out that in general, the size of the capacitor in a given

design has very little to do with how much voltage ripple you

can tolerate at the bus, but rather is determined by the ability

to carry the ripple current without the capacitor heating up

and failing. It has been known that the small electrolytics in

prototype controllers mysteriously explode. On searching, it

is found that they are in parallel with the main capacitor and

quite close to it, so they carry a lot of ripple current, then heat

up and explode!

33.6.4 The Signal Processing for Producing

Switch Drive Signals from Hall Effect

Sensors and Current Sensors

33.6.4.1 Operation of the Hall Sensors

The ﬂux density directly under a magnet pole can be anywhere

from 500 to 800 millitesla with Nd–Fe–B magnets. Hall effect

(HE) sensors with a digital output, called Hall effect switches,

change state at very close to zero ﬂux density. Thus, they will

change state when the north and south pole are equidistant

900 M. F. Rahman et al.

I controller

I capacitor

I supply

Voltage source

To controller switches

FIGURE 33.68 Kirchhoff’s current law at node A.

a′

b′

c′

HE1

HE3

HE2

FIGURE 33.69 Possible Hall effect switch positions in a three-phase

machine.

from them, so that for example, in Fig. 33.69, the switch HE1

is just changing state with the rotor as shown.

In practice, a motor designer needs to consider what magne-

tomotive force comes from the current in the windings which

might result in ﬂux which would trip the HE sensor at a slightly

different time. If you follow all the above logic about six step

switching, you will see that you only need the magnet poles to

have a span of a bit more than 120

◦

. Using 180

◦

magnet poles

can add considerably to the cost, as well as having an impact

on such things as cogging torque. Actual designs often add

extra “sense” magnets to cover 180

◦

just at the circumferential

strip where the HE switches are located, adding minimally to

the magnet mass and ensuring good and accurate triggering.

However, if the switches operate as above, then Table 33.3

will result for the HE switches located as shown in Fig. 33.69.

TABLE 33.3 Hall effect switch outputs for rotor positions as shown, HE

switches placed as in Fig. 33.69

When the center of the rotor

north pole is in this sector

HE1 outputs HE2 outputs HE3 outputs

100

110

111

011

001

000

33 Motor Drives 901

33.6.4.2 Sensing the Current in the Motor Windings

Figure 33.66 shows two current sensors. In the most sophisti-

cated systems, there are two current sensors, one in each of the

two motor phases. The current sensing is done at the winding

and isolated with either an HE sensor in a soft ferromagnetic

magnetic core surrounding the conductor (commercial items

are available), or by using a resistive shunt sensor and some

accurate analog signal isolation/coupling through transformers

or opto-couplers. The isolation is necessary since the poten-

tial at points a, b, and c is either the dc bus voltage or zero,

depending on which switches are on, so that any current mea-

sure such as the small voltage across a shunt is superimposed

on these very large voltage changes. This is a very similar prob-

lem to that for the high side gate drives discussed earlier. The

current in the third winding is determined by the algebraic

application of KCL, given the other two readings.

Simple controllers sometimes avoid the complexities of iso-

lated current measurement and instead measure the current

in the return negative supply, for example from the bottom of

the three lower switches to the bottom of the supply smooth-

ing capacitor. This arrangement senses current when an upper

and a lower switch is on, but not when the current is being

carried in ﬂyback diodes or by two lower switches. While it

is inexpensive, it does not provide fully accurate control. The

system works because the current should be decreasing when

a measure is not available, heading towards zero, so switch or

system failure due to over-current should not occur.

33.6.4.3 Management of Current Sensing

The controller must select the right current to increase or

decrease, dependent on rotor position. The following con-

vention is adopted. Positive current provides torque in the

counterclockwise direction and therefore goes into winding a,

b,orc.

All systems are capable of regeneration, which implies that

negative torque can be commanded (without reversing the

direction of rotation) to make the machine operate as a

generator, developing retarding torque.

Thus for the above sequence of sector determinations, refer-

ring back to Table 33.2, the output of current sensors should

be directed to the current controller as shown in Table 33.4.

The addition and negation required can be carried out

with the standard operational-ampliﬁer circuitry. The three

required analog measures are then fed to a three to one ana-

log multiplexer, gated from the HE switch signals suitably

processed in combinational logic. The resulting single analog

output is fed to the current comparator.

33.6.4.4 Distribution of Control Signals

to the Switches

Given that the dead time is introduced elsewhere in sequential

logic, or with timing circuits, it is a simple matter to develop

TABLE 33.4 Current sensors to use as input to the current

controller, for each of the six rotor position sectors

Hall effect switch outputs

(HE1, HE2, HE3)

Monitor current as read by

100 Negative of (sensor a+ sensor b)

110 Negative of (sensor a+ sensor b)

111 Sensor b

011 Sensor b

001 Sensor a

000 Sensor a

TABLE 33.5 Distribution of control signals to the switches using “High

Efﬁciency Method of Managing the Switching in the H Bridge”

HE states(1,2,3) S1 S2 S3 S4 S5 S6

100 0 0 0 1 I up I down

011 0 1 0 0 I up I down

001 0 1 I up I down 0 0

000 0 0 I up I down 0 1

100 I up I down 0 0 0 1

110 I up I down 0 1 0 0

the combinational logic for directing, or steering, the switching

signals to the right switches. A typical scheme for a speciﬁc

controller is shown in Table 33.5.

It is usual also to include some shutdown logic from ded-

icated protection circuits, for example sensing over-current,

over-bus voltage, under voltage for gate drive and over-

temperature both in the motor and in the controller power

stage. For simplicity, this is not shown in the table.

33.6.5 Summary

What is Discussed in the above

The physical principles of the operation of a PMBDCM have

been discussed which lead to the development of the necessary

parts of a power electronic controller. One speciﬁc type of

current control, hysteresis band current control was explained

in detail, and one speciﬁc type of switch logic pattern was

developed. The exposition has included many of the issues

that can cause difﬁculties for controller designers if they are

not careful.

What is Not Discussed in the above

Many PMBDCMs have more than one pair of poles. The

arguments above can all be extended to higher pole count

machines, by taking any mention of degrees to be electrical

degrees rather than mechanical degrees. The controller dis-

cussed in detail only manages one direction of rotation. It

is an excellent exercise, and straightforward, but not trivial,

to repeat the above steps, preparing the tables for clock-

wise rotation of the simple machine discussed above. Then,

902 M. F. Rahman et al.

following the discussion in the ﬁrst part of Section 33.6.3,

Current/Torque Control about H bridge switching, prepare the

logic tables again for full bidirectional control, using the I up

and I down logic signals exactly as above, but applying them to

both “legs” determined by the rotor position. Only one form

of current sensing was discussed in detail. There are many sim-

pler schemes in use which do not have quite the ﬂexibility and

accuracy of the above, but which can suit certain applications.

Similarly, there are other forms of current control such as

the constant-frequency linear method brieﬂy discussed. Shaft

position sensors take many forms. Adherence to the HE sensor

was for simplicity, and to reinforce the magnetic ﬁeld aspects

of the machine operation.

33.7 Servo Drives

33.7.1 Introduction

Servo drives are motor drives that operate with high dynamic

response. Historically, servo drives have implied motion-

control systems in which sophisticated motor design, drive,

and control techniques have been employed to obtain very

much shorter positioning times than is possible with con-

ventional drive systems. Examples are in machine tool drives,

robotic actuators, computer disk drives, and so on. The power

range for these drives has typically been in the range of a few

kilowatts or less. This range has steadily increased in recent

years as a result of advances in magnetic materials, machine

design, power and signal electronic devices, and sensors.

Apart from the fast positioning times, “high dynamic

response” also means that the drive operates with the follow-

ing:

1. Very smooth torque up to a very low speed,

2. Very high reliability and little maintenance,

3. Immunity from load disturbances.

The last of the foregoing items is brought about by robust

and intelligent control algorithms; the ﬁrst two items are

brought about by innovative and often costly motor and con-

troller designs. As a result of these, the cost of a servo motor

drive is usually much higher than the equivalent power rated

industrial drives.

The distinctions just mentioned may be easily recognized

by noting, for example, that the drives that bring material to

a mill may not require high performance, but the drives that

take part in shaping, milling, or reducing the material should

have high dynamic response in order to increase throughput

and meet the accuracy requirements of the ﬁnal product.

33.7.2 Servo Drive Performance Criteria

The performance of a servo drive can be expressed in terms

of a number or factors such as servo bandwidth, accuracy,

percentage regulation, and stiffness. While servo bandwidth

indicates the ability of the drive to track a moving or cyclic

reference, the percentage regulation and stiffness stipulates the

drive’s static holding performance for speed or position, in the

face of disturbances from the load and in the supply condi-

tions. The servo bandwidth, speciﬁed as a frequency in Hertz

or rad/sec, is often found from the system frequency response

plot, such as the Bode diagram.

The percentage regulation of a speed-controlled system

often refers to the percentage change in speed from no load

to full load. In a type-zero system, this ﬁgure will have a ﬁnite

value. Many systems are type zero, albeit with a high gain so

that the regulation is acceptably low. For such systems, the

regulation is often necessary for operational reasons. In some

applications, zero percentage error is required, which calls for

type 1 or integral type control system.

The servo stiffness is similar to the percentage error men-

tioned earlier, but it applies mainly for the position servo. It

speciﬁes the deﬂection of the load from its reference position,

when full load torque is applied. It is usually the slope of the

deﬂection versus the applied load torque in rad/Nm around

the reference position.

33.7.3 Servo Motors, Shaft Sensors, and

Coupling

Servo drives use motors which allow the desired goals of high

dynamic response to be achieved. The important parameters/

attributes of a servo motor are:

1. High torque-to-inertia ratio,

2. High torque-to-volume ratio,

3. Low inductance of the motor windings,

4. Low cogging torque at low speed,

5. Efﬁcient heat dissipation,

6. Low coefﬁcient of shaft compliance,

7. Direct-coupled, high-resolution, shaft-mounted sensors

for position and speed.

High torque-to-inertia ratio allows fast acceleration or

deceleration of the drive when motion references are changed.

This is often achieved through innovative low-inertia rotor

design and low inductance in the stator winding. One example

of a dc servo motor is the pancake printed armature dc motor

with no iron in the rotor, as indicated in Fig. 33.70. The rotor

is sandwiched between axially mounted stator poles. The com-

mutator is also on the printed armature. Another example is

the disk rotor stepping motor, also without iron in the rotor,

as indicated in Fig. 33.71.

The PM ac synchronous motors with modern high-energy-

density magnets in the rotor, as described in Section 33.6, are

also examples where the motor designer strives to minimize the

rotor inertia. Modern permanent magnets allow the required

airgap ﬂux to be developed with a much reduced volume of

the magnets, consequently reducing the diameter of the rotor.

33 Motor Drives 903

FIGURE 33.70 Pancake armature of a dc servo motor. Courtesy:

Printed Motors Ltd., UK.

FIGURE 33.71 A disk rotor stepping motor with ironless rotor for low

inertia and inductance. Courtesy: Escap Motors.

It is well-known that the moment of inertia of a motor

increases as the fourth power of its outer radius!

Another beneﬁt of the modern permanent-magnet material

is that the motor volume is also reduced. Servo motors often

have to be located in a very conﬁned space, and this reduction

in volume is an important attribute.

The ironless designs mentioned earlier bring other bene-

ﬁts in the form of reduced inductance and cogging torque.

Brushed pancake ironless motors are available with armature

inductance as low as 100 µH.

From Section 33.2.2, the mechanical and electrical time

constants of a brushed dc motor are given by

= mechanical time constant =

and τ

= electrical time constant =

It is well known that for the highest load acceleration, the

load inertia referred to the motor should be equal to the rotor

inertia. Thus, in a matched system, the total inertia the

motor accelerates is twice its own inertia. In other words, the

motor inertia should also be minimized.

For a good servo motor, the ratio between the mechanical

and the electrical time constants is often of the order of ﬁve or

more. This allows the speed and the current-control loops to

be decoupled and noninteracting. The electrical time constant

of a motor determines how quickly the motor current may be

changed and hence how quickly the torque can be changed.

As also mentioned in Section 33.2, drives with a reasonable

dynamic performance should have an inner torque loop. This

torque loop is built around current loops, for the armature for

the brushed dc motor, or for the d- and q-axes currents for

the induction and synchronous motor drives. Having a low

inductance in the winding allows these currents to be followed

dynamically changing current or the torque references with

higher accuracy and bandwidth.

The cogging torque, if appreciable, causes the rotor to have

preferential positions. As a result, the position accuracy of the

motor may suffer. Another problem is the ripple in speed as

the motor is operated at low speed. At high speed, these ripples

due to cogging torque may be ﬁltered out by the motor inertia;

however, the extra loss due to cogging remains. The ironless or

toothless rotor obviously produce very small cogging torque

because of the absence of preferential paths for the airgap ﬂux

to establish through the rotor iron of the brushed dc motor.

The surface-magnet synchronous motor also has this feature.

The interior-magnet motor normally has skewed stator slots

to avoid the production of cogging torque.

Servo motors often operate with frequent start-and-stop

duty, with the fastest allowable acceleration and deceleration

during which the motor current is allowed to reach about

2–3 times the continuously rated current. The increased I

904 M. F. Rahman et al.

loss in such duty must be dissipated. This calls for adequate

cooling measures to be incorporated in the motor housing.

With such operation, it is sometimes possible to excite the

mechanical resonance due to shaft compliance. This is avoided

through proper arrangement of the shaft position/speed sensor

and the coupling between the motor and the sensor. A belt-

driven speed sensor may be acceptable for an industrial drive;

however, for servo applications, a rigid, direct-coupled sensor

mounted as close as possible to the motor armature is prefer-

able. Additionally, the speed sensor is also required to have

negligible noise. Speed signal from analog tachogenerators,

which were used for speed sensing until recently, invariably

needed to be ﬁltered to remove the cyclic ripple/noise that

existed. Such ﬁltering often limits the maximum speed-control

bandwidth of a drive.

33.7.4 The Inner Current/Torque Loop

The inner current loop(s) in a servo motor drive play a

more important role than just limiting the current in case

of overload. These loops operate continuously to regulate

the motor-developed torque so as to meet the load demand,

and for meeting the speed trajectory speciﬁed by the motion

controller. Motor drives of high dynamic response currently

employ PWM current sources. These sources use MOSFET

or IGBT switching devices that allow the modulator to be

operated with a switching frequency between 10 and 25 kHz.

At these frequencies, the inherent switching delay, which is

equivalent to half of the PWM switching period, is made

rather small for the bandwidth of the torque control loop.

The bandwidth of the current control loops closely repre-

sents the bandwidth of the torque control. This is because

the motor-developed torque generally is proportional to these

currents. Servo drives up to a few kilowatts presently have

torque/current control-loop bandwidths in excess of 1 kHz.

For higher power, fast-response drives, such as those used

in the metal-processing industries, thyristor converters have

been used for many years. The switching frequencies of these

converters are rather low, being some multiple of the mains

frequency, according to the converter chosen. Fortunately, the

larger mechanical time constant of the larger power motor

and the nature of the applications have allowed the 300 Hz

(360 Hz in the United States) switch frequency of the three-

phase thyristor bridge converter to be used satisfactorily in

many applications requiring high dynamic response. The

growing availability of faster and higher power IGBT devices

is continually enhancing the dynamic performance of larger

drives.

Fast-response, inner torque control loops have in recent

years been extended to ac induction and synchronous motors.

These motors were hitherto considered only for industrial

drives. The vector methods described in Sections 33.3 and 33.4,

which employ inner quadrature axis current controllers in the

synchronous (for the induction motor) or the rotor (for the

synchronous motor) reference frame, have transformed the

prospects of ac motor drives in servo applications.

Because of the fast dynamic response requirement of servo

drives, the servo motor is nearly always driven with the

maximum torque per ampere (MTPA) characteristic. Field

weakening is normally not used. In other words, ﬁeld con-

trol either directly for a brushed dc motor or a synchronous

motor or indirectly through armature reaction (i.e. through i

current control) for induction or PM ac synchronous motors

is not used for ﬁeld weakening. It is nevertheless used for regu-

lating the ﬁeld at the desired level. Field weakening are mainly

used for drives where the operation at higher than base speed

with constant-power characteristic is desirable.

33.7.5 Sensors for Servo Drives

Servo drives require high-bandwidth current sensors for the

inner torque loop and high-accuracy, noise-free speed and

position sensors for the outer loops. The current sensor is

often a Hall device with an ampliﬁer, which can have band-

widths as high as 100 kHz. The inner current loop both limits

and continuously regulates the motor current in all operating

modes of the drive, including acceleration and deceleration.

About 2–3 times, the continuous rated current of the motor

is tolerated during acceleration and deceleration. This entails

limiting the speed controller output to the level corresponding

to the current sensor output for the limiting values of motor

currents.

The current-sensor output has to be ﬁltered to adequately

remove the switching frequency noise. Otherwise, certain

switching devices in converter may be overloaded. This task

is more important for the thyristor converters for dc drives

for which the switching frequency is rather low. This ﬁlter-

ing of the current-sensor output limits the bandwidth of the

current-control system, i.e. the inner torque-control loop.

Performance of servo-motor drives depends critically on the

noise and accuracy of the speed and position sensors. Synchro-

resolvers with 12 bit or higher digital accuracy were used in

many servo-drive systems until recently. The advent of cheaper

incremental and absolute optical encoders has altered this

situation completely. These digital sensors are actually posi-

tion sensors. The speed information is derived from positions

measured by discrete differentiation. Such differentiation is

not feasible with analog position sensors, because of the noise.

Analog tachogenerators are also avoided for speed servo

systems. This is because of the tachogenerator ripples inherent

in the sensor.

Modern discrete position sensors provide for virtually noise-

free speed and position sensing. This allows very fast dynamic

response to be achieved if the switching frequency of the

converter allows it.

33 Motor Drives 905

33.7.6 Servo Control-loop Design Issues

33.7.6.1 Typical Controllers

33.7.6.1.1 Proportional Controller A proportional con-

troller provides for a straight gain to amplify the error signal.

It has no discriminatory properties. With the input and feed-

resistance values indicated in Fig. 33.72, the total gain of the

controller is (K + 1).

For this controller, v

(

K + 1

)(

−θ

)

(33.79)

FIGURE 33.72 Proportional controller.

33.7.6.1.2 Transient Velocity Feedback Controller It is well-

known that a following error will exist in the preceding system

when a moving or ramp reference is tracked. If a rate feedback,

such as the speed feedback in a position-control system, is used

to damp the system, this error is further increased. To over-

come this following error due to velocity feedback, transient

velocity feedback can be used as indicated in Fig. 33.73.

The speed (velocity) signal is passed through an RC circuit

at the input of the ampliﬁer circuit. An input current occurs

only when the speed signal changes. In the steady state, the

capacitor is fully charged, so that no following error in the

steady state due to the velocity feedback can exist.

In the steady state when the velocities are equal, the output

may lag or lead depending on the relative values of R

and R

It can be shown that in the absence of frictional load torque,

−K

FIGURE 33.73 Transient velocity feedback controller.

as is often the case in servo applications, no following error is

introduced if R

= R

33.7.6.1.3 Integral Controller In the transient-velocity and

error-rate feedback schemes, the following error will exist if

viscous friction and load torque are present. If such loads

are present, the system gain has to be inﬁnity to have a zero

error. Very large gains will make any physical systems unstable,

unless bandwidth limitations exist. One way to employ inﬁnite

gain in the steady state is to use an integrator. This ampliﬁes

the steady-state error until it is eliminated.

Normally, a proportional plus integral (PI) action is used.

A derivative term is normally not used in the control system of

a drive system, since the drive feedback signals are very noisy.

Instead, derivative signals are obtained through sensors such

as tachogenerators. The structure of a PI controller is indicated

in Fig. 33.74.

= K

FIGURE 33.74 Integral controller.

It can be shown that there will be no steady-state error even

in the presence of frictional or other load torque.

Many types of more complex controllers are available,

such as the variable structure controller. Drives with fuzzy

controllers have also been in the marketplace for some years.

The controller circuits just described are usually imple-

mented in analog circuits using operational ampliﬁers. Digital

implementations are also being gradually introduced using the

embedded microcontrollers and digital signal processors.

33.7.6.2 Simpliﬁed Drive Representations

and Control

Consider the block diagram of Fig. 33.75 in which the individ-

ual elements (blocks) are represented in terms of their transfer

functions in terms of the Laplace operators.

Here, G

(s), G

(s), H

(s), and H

(s) represent the

transfer functions of the power converter plus the motor, the

controller, the load, the sensor (of speed in this example), and

the ﬁlter following the sensor respectively. The reference input

for speed and the feedback signal are connected to a summing

junction of an operational ampliﬁer through resistors R

and

, respectively.