Bichop R.H. (Ed.) Mechatronic Systems, Sensors, and Actuators: Fundamentals and Modeling

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21-32 Mechatronic Systems, Sensors, and Actuators

storage elements, where the energy is stored in the induced magnetic field. The voltage across an ideal

inductor V

(t) is

(21.15)

where i

(t) is the current going through the inductor and L is the inductance. When the current to the

inductor is suddenly switched off, e.g., by switching off a driving transistor, Equation 21.15 indicates

that there will be a large transient voltage build-up across the inductor. If not properly suppressed this

transient voltage can shorten or even damage the driving transistor. This is sometimes called inductor

kickback.

A simple method of reducing the instantaneous switching voltage surge is to create a loop for the

excess energy to flow. This can be done by placing diodes in parallel with the load, see Figure 21.54.

Figure 21.54 illustrates two methods of using flyback or free-wheeling diodes to suppress switching voltage

surge when driving inductive loads.

Open-Collector Output

For some digital devices, the output stage (pin) is simply the collector of a transistor. This is called an

open-collector output, see Figure 21.55. Since the output of the device is only the collector of a transistor,

it has no output drive capacity. The output value can be measured through a pull-up resistor, see

Figure 21.55. Open-collector output is convenient for driving electromechanical devices if the output

transistor can sink adequate current, see Figure 21.57.

Isolation

Recall that the power amplification/modulation part of an electromechanical actuator contains both low-

and high-energy signals, see Figure 21.2. For safety and reliability reasons, it is desired to prevent transients

or noise spikes in the high power side of the system from the signal processing (low power) side of the

circuit. Mechanical relay is one option. Optoisolators or optocouplers use light to couple the high and low

FIGURE 21.54 Using diodes to reduce swithcing voltage when driving inductive loads.

FIGURE 21.55 Open-collector output.

Loa d

load

Q1 Q2

Load

Open

Collector

Output

Open

Collector

Output

Digital

Device

Pull-up

Resistor

Load

Digital

Device

t() L

-----

t()⋅=

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Actuators 21-33

energy side of the device. Typically, an LED source is combined with either a phototransistor or photo

thyristor, see Figure 21.35. In addition to signal isolation, optoisolators also help to reduce ground loop

issues between the logic and power side of the circuit.

Grounding

It is important to provide common ground among the different devices. For electromechanical actuators,

the high energy side is often switching at high frequency; if the ground point of the high energy side of

the circuit is directly connected to the ground of the low energy side of the circuit, switching noise may

propagate through the ground wire and negatively affect the operation of the low energy side of the

system. It is recommended that separate common grounds are established for the high and low energy

side and the two grounds are then connected at the power supply. In addition, an adequate-sized ground

plane needs to be provided to minimize the possibility of differences among grounding points.

21.2 Electrical Machines

Charles J. Fraser

The utilization of electric motors as the power source in a mechatronic application is substantial. Electric

motors, therefore, often feature as the prime mover in a variety of driven systems. It is usually the

mechanical features of the application that determines the type of electric motor to be employed. The

torque–speed characteristics of the motor and the driven system are therefore very important. It is perhaps

then a paradox that while the torque–speed characteristics of the motor are readily available from the

supplier, the torque–speed characteristics of the driven system are often quite obscure.

21.2.1 DC Motor

All conventional electric motors consist of a stationary element and a rotating element, which are separated

by an air gap. In DC motors, the stationary element consists of salient “poles,” which are constructed of

laminated assemblies with coils wound round them to produce a magnetic field. The function of the

laminations is to reduce the losses incurred by eddy currents. The rotating element is traditionally called

the “armature” and this consists of a series of coils located between slots around the periphery of the

armature. The armature is also fabricated in laminations, which are usually keyed onto a location shaft.

A very simple form of DC motor is illustrated in Figure 21.56.

The single coil is located between the opposite poles of a simple magnet. When the coil is aligned in

the vertical plane, the conventional flow of electrons is from the positive terminal to the negative terminal.

The supply is through the brushes, which make contact with the commutator segments. From Faraday’s

laws of electromagnetic induction, the “left-hand rule,” the upper part of the coil will experience a force

acting from right to left. The lower section will be subject to a force in the opposite direction. Since the

FIGURE 21.56 Single-coil, 2-pole DC motor.

Magnet

+ve

–ve

Brush

Commutator

Coil

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21-34 Mechatronic Systems, Sensors, and Actuators

coil is constrained to rotate, these forces will generate a torque, which will tend to make the coil turn in

the anti-clockwise direction. The function of the commutator is to ensure that the flow of electrons is

always in the correct direction as each side of the coil passes the respective poles of the magnet. The

commutator incorporates brass segments, separated by insulating mica strips. The carbon brushes make

sliding contact with the commutator.

When the coil lies in the horizontal direction, there is maximum magnetic flux linking the coil but a

minimum rate of change of flux linkages. On the other hand, when the coil is in the vertical plane, there

is zero flux linking the coil but the rate of change of flux linkages is a maximum. The resultant change

in torque acting on the coil through one revolution is as shown in Figure 21.57.

If two coils physically displaced by 90° are used in conjunction with two separate magnets, also

displaced by 90°, then the output torque is virtually constant. With the introduction of a second coil,

the commutator needs to have four separate segments. In a typical DC machine there may be as many

as 36 coils, which would require a 72-segment commutator.

The simple DC motor of Figure 21.56 can be improved in perhaps three obvious ways. Firstly, the

number of coils can be increased, the number of turns in each coil can be increased, and finally the

number of magnetic poles can be increased. A typical DC machine would therefore normally incorporate

four poles, wired in such a way that each consecutive pole has the opposite magnetic polarity to each of

its immediate neighboring poles. If the torque generated in the armature coils are to assist one another

then while one side of the coil is passing under a north pole, the other side must be passing under a

south pole. With a two-pole machine the armature coils are wound with one side of the coil diametrically

opposite the other. In a four-pole machine the coils are wound such that one side of the coil is displaced

90° from the other. The size of the machine will generally determine how many coils and the number

of turns on each coil which can be accommodated.

21.2.2 Armature Electromotive Force (emf)

If a conductor cuts a magnetic flux, a voltage of 1 V will be induced in the conductor if the flux is cut

at the rate of 1 Wb/s. Denoting the flux per pole as Φ and the speed (in rev/s), as N, for a single turn

coil and two-pole machine, the emf induced in the coil is given as

(21.15)

For a machine having Z

armature conductors connected in series, i.e., Z

/2 turns, and 2p magnetic

poles, the total induced emf is

(21.16)

FIGURE 21.57 Torque variation through one revolution.

orque

0 180 360

le of rotation [de

rees]

coil

flux per pole

time for half rev

--------------------------------------

1/2N

------------

2NΦ===

2NΦZ

------------------------ 2NΦZ

p==

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Actuators 21-35

The induced emf or back emf will oppose the applied voltage. Since the emf is directly proportional

to the motor speed then on startup, there will be no back emf generated. This will have consequences

on the current, which will be drawn by the coils, and some measures will have to be taken to counteract

this effect. This topic will be considered later.

21.2.3 Armature Torque

The force on a current carrying conductor is given as

(21.17)

where B is the magnetic flux density under a pole, I is the current flowing in the conductor, and L is the

axial length of the conductor.

The torque on one armature conductor is, therefore,

(21.18)

where r is the radius of the armature conductor about the center of rotation, I

is the current flowing in

the armature conductor, L is the axial length of the conductor, and B

is the average flux density under

a pole.

Given that the resultant torque per conductor is

(21.19)

For Z

armature conductors connected in series, the total torque (in Nm) on the armature is given by

(21.20)

21.2.4 Terminal Voltage

Denoting the terminal voltage by V, in normal running conditions we have a balanced electrical system

where:

(21.21)

Since the number of poles and number of armature conductors are fixed, then from Equation 21.16

we have a proportionality relationship between the speed, the induced emf, and the magnetic flux, i.e.,

(21.22)

Using Equation 21.21

(21.23)

Since the value of I

is normally less than about 5% of the terminal voltage then to a reasonable

approximation

(21.24)

FBLI=

TFrB

r==

Φ/(2

rL)/2p[],=

Φ2pLI

---------------------

ΦpI

------------

ΦpI

-----------------

VEI

----

∝

–()

------------------------

∝

----

∝

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21-36 Mechatronic Systems, Sensors, and Actuators

Similarly Equation 21.19 provides a proportionality relationship between the torque, the armature

current, and the magnetic flux, i.e.,

(21.25)

Equation 21.24 shows that the speed of the motor is directly proportional to the applied voltage and

inversely proportional to the magnetic flux. All methods of speed control for DC motors are based on

this proportionality relationship.

Equation 21.25 indicates that the torque of a given DC motor is directly proportional to the product

of the armature current and the flux per pole. It is obvious therefore that speed control methods which

are based on altering the magnetic flux will also have an effect on the output torque.

21.2.5 Methods of Connection

21.2.5.1 The Shunt-Wound Motor

The shunt-wound motor (Figure 21.58) is wired such that the armature and field coils are connected in

parallel with the supply.

Under normal operating conditions, the field current will be constant. As the armature current

increases, the armature reaction effect will weaken the field and the speed will tend to increase. However,

the induced voltage will decrease due to the increasing armature voltage drop and this will tend to decrease

the speed. The two effects are not self cancelling and overall the motor speed will fall slightly as the

armature current increases.

The motor torque increases approximately linearly with the armature current until the armature

reaction starts to weaken the field. These general characteristics are shown in Figure 21.59 where it can

also be seen that no torque is developed until the armature current is large enough to overcome the

constant losses in the machine. Figure 21.60 shows the derived torque-speed characteristic.

Since the torque increases dramatically for a slight decrease in speed, the shunt-wound motor is partic-

ularly suitable for driving equipment like pumps, compressors, and machine tool elements where the

speed must remain “constant” over a wide range of load conditions.

21.2.5.2 The Series-Wound Motor

The series-wound motor is shown in Figure 21.61. As the load current increases, the induced voltage,

will decrease due to the armature and field resistance drops. Because the field winding is connected in series

with the armature, the flux is directly proportional to the armature current. Equation 21.24 therefore

FIGURE 21.58 The shunt-wound motor.

Φ∝

Supply

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Actuators 21-37

suggests that the speed–armature current characteristic will take the form of a hyperbola. Similarly,

Equation 21.25 indicates that the torque–armature current characteristic will be approximately parabolic.

These general characteristics are illustrated in Figure 21.62, along with the derived torque–speed charac-

teristic in Figure 21.63. The general characteristics indicate that if the load falls to a particularly low value

FIGURE 21.59 The shunt-wound motor load characteristics.

FIGURE 21.60 The shunt-wound torque–speed characteristics.

FIGURE 21.61 The series-wound motor.

Applied voltage, V

Speed

Torque

Armature current

Speed

EMF

Torque

Speed

Torque

Supply

E M

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21-38 Mechatronic Systems, Sensors, and Actuators

then the speed may become dangerously high. A series-wound motor should never be used, therefore, in

situations where the load is likely to be suddenly relaxed.

The main advantage of the series-wound motor is that it provides a large torque at low speeds. Series-

wound motors are eminently suitable, therefore, for applications where a large starting torque is required.

This includes, for example, lifts, hoists, cranes, and electric trains.

21.2.5.3 The Compound-Wound Motor

Compound-wound motors are produced by including both series and shunt fields. The resulting char-

acteristics of the compound-wound motor fall somewhere in between those of the series-wound and the

shunt-wound machines.

21.2.6 Starting DC Motors

With the armature stationary, the induced emf is zero. If while at rest, the full voltage is applied across the

armature winding then the current drawn would be massive. A typical 40-kW motor might have an armature

resistance of about 0.06 Ω. If the applied voltage is 240 V, the current drawn is 4000 A. This current would

undoubtedly blow the fuses and thereby cut off the supply to the machine. To limit the starting current a

variable external resistance is connected in series with the armature. On start-up the full resistance is

connected in series. As the machine builds up speed and increases the back emf, the external resistance can

be reduced until at rated speed the series resistance is disconnected. Alternatively, a series resistance can

be momentarily activated in conjunction with the starter switch.

FIGURE 21.62 The series-wound motor load characteristics.

FIGURE 21.63 The series-wound motor torque–speed characteristics.

Applied voltage, V

Torque

Speed

EMF

Torque

Arm

atu

Speed

Torque

eed

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Actuators 21-39

21.2.7 Speed Control of DC Motors

Equation 21.24 shows that the speed of a DC motor is influenced both by the applied voltage and the

magnetic flux. A change in either one of these parameters will therefore effect a change in the motor

speed.

21.2.7.1 Field Regulator

For shunt-wound and compound-wound motors a variable resistor, called a “field regulator,” can be

incorporated in series with the field winding to reduce the flux. For the series-wound motor the variable

resistor is connected in parallel with the field winding and is called a “diverter.” Figures 21.64–21.66 show

the various methods of weakening the field flux for shunt-, compound-, and series-wound motors.

In all of the above methods, the flux can only be reduced and from Equation 21.24 this implies that

the speed can only be increased above the rated speed. The speed may in fact be increased to about three

or four times the rated speed. The increased speed, however, is at the expense of reduced torque since

the torque is directly proportional to the flux which is being reduced.

21.2.7.2 Variable Armature Voltage

Alternatively, the speed can be increased from standstill to rated speed by varying the armature voltage

from zero to rated value. Figure 21.67 illustrates one method of achieving this.

FIGURE 21.64 Speed control by flux reduction: shunt-wound motor.

FIGURE 21.65 Speed control by flux reduction: compound-wound motor.

Supply

E M

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21-40 Mechatronic Systems, Sensors, and Actuators

The potential divider carries the same current as the motor, and this limits this method of speed

control to small machines. Additionally much of the input energy is dissipated in the variable resistance,

which consequently renders the system inefficient.

21.2.7.3 Ward Leonard Drive

In this case the variable DC voltage for the speed controlled motor is obtained from a separate DC

generator, which is in itself driven by an induction motor.

The field coil for the DC generator is supplied from a center-zero potential divider. When the wiper

arm is in the center position, the speed controlled motor is at a standstill. By moving the wiper arm away

from the center position the speed of the motor is increased in either clockwise or anti-clockwise direction.

The Ward Leonard drive is smooth and accurate in either direction and also provides for very responsive

braking. The complexity, however, makes it a very expensive system, and it is only used in high quality

applications.

21.2.7.4 Chopper Control

Figure 21.68 shows a thyristor circuit connected in series with the armature of a DC motor. The thyristor

circuit is triggered such that it operates essentially as a high speed ON/OFF switch. The output waveform

across the armature terminals is depicted in Figure 21.69. The ratio of time on to time off, i.e., the

“mark/space ratio,” can be varied with the result that the average voltage supplied to the armature is

effectively varied between zero and fully on. The frequency of the signal may be up to about 3 kHz and

the timing circuit is quite complex. Speed control of DC motors using thyristors, however, is effective

and relatively inexpensive.

FIGURE 21.66 Speed control by flux reduction: series-wound motor.

FIGURE 21.67 Speed control by varying the armature voltage.

Supply

E M

Supply

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Actuators 21-41

21.2.8 Efficiency of DC Machines

The losses in DC machines can be generally classified as

1. Armature losses:This is the I

R loss in the armature winding, often referred to as the “copper loss.”

2. Iron loss: This loss is attributable to magnetic hysteresis and eddy currents in the armature and

field cores.

3. Commutator losses: This loss is related to the contact resistance between the commutator brushes

and segments. The total commutator loss is due to both mechanical friction and a voltage loss

across the brushes.

4. Excitation loss: In shunt-wound machines, this power loss is due to the product of the shunt

current and the terminal voltage.

5. Bearing friction and windage: Bearing friction is approximately proportional to the speed, but

windage loss varies with the cube of the speed. Both of these losses are fairly minor unless the

machine is fitted with a cooling fan, in which case the windage loss can be quite significant.

Despite the variety and nature of the losses associated with DC machines, they have nonetheless a very

good performance with overall efficiencies, often in excess of 90%.

21.2.9 AC Machines

21.2.9.1 Synchronous Motors

Synchronous motors are so called because they operate at only one speed, i.e., the speed of a rotating

magnetic field. The production of the rotating magnetic field may be actioned using three, 120° displaced,

FIGURE 21.68 Speed control using thyristors.

FIGURE 21.69 Voltage across armature terminals.

Supply

Mark

Space

Average value of V

Time

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