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

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21-12 Mechatronic Systems, Sensors, and Actuators

The coupling between the electrical and mechanical property of the material can be modeled by the

following sets of linear constitutive equations:

(21.11)

where

E = electric field strength [V/m]

D = charge-density (dielectric) displacement [C/m

]

T = stress [N/m

]

S = strain

s = compliance

= permittivity [F/m]

d, g = piezoelectric coupling coefficients

Design/Selection Considerations

Figure 21.17 shows the common orientation for piezoelectric actuation. With a typical strain of less

than 0.3%, the amount of deflection or deformation is usually the limited factor for piezoelectric

actuators. The most common architectures are the stacked and bending actuation. Piezoelectric actu-

ators are most suited for high bandwidth, large force, and small stroke/deflection applications. They

are widely used in noise and acoustical applications, as well as optical applications, where precision

motion is critical.

Piezoelectric actuators are usually specified in terms of their free deflection and blocked force. Free

deflection (X

) refers to displacement attained at the maximum recommended voltage level when the actuator

is completely free to move and is not asked to exert any force. Blocked force (F

) refers to the force exerted

at the maximum recommended voltage level when the actuator is totally blocked and not allowed to move.

Figure 21.18 shows the static performance curve of a typical piezoelectric actuator (force vs. deflection).

Generally, a piezo actuator must deform a specified amount and exert a specified force, which determines

its operating point on the force vs. deflection line. An actuator is considered optimized for a particular

FIGURE 21.17 Common piezoelectric actuation geometries. (Courtesy of Piezo Systems, Inc.)

Bimorph bending

∆

∆T

out

∆

out

∆

out

2 Layer transverse

Transverse

Stack actuator

Longitudinal

T = nt

–

TdE⋅+⋅=

DdT

E⋅+⋅=

E −gT

()

−1

D⋅+⋅=

TgD⋅+⋅=

⇔

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Actuators 21-13

application if it delivers the required force at one half its free deflection. High operating voltage, hysteresis,

creep, and fatigue are the main mechanical design considerations.

21.1.2.4 Efficiency

Efficiency is one of the major considerations for any energy conversion process. In most cases, the wasted

energy is converted to heat and increases the device temperature. For electromechanical actuators, heat

(temperature) is one of the most prominent performance-limiting factor as well as failure mode. As

device temperature increases, the underlying conversion efficiency will suffer and dump more energy

into heat, which further increases the device temperature. This is often referred to as thermal runaway.

Therefore, it is very important when designing electromechanical actuators to prevent thermal runaway

and guarantee that under normal operating condition the actuator system achieves thermal equilibrium.

The equilibrium temperature should be maintained below the lowest rated temperature of the compo-

nents, such as the electrical insulation for the windings. The temperature rating for electrical insulations

are listed in Table 21.1.

21.1.3 Power Amplification and Modulation—Switching Power Electronics

As described in the previous section and depicted in Figure 21.2, there are two main functions in an

extended definition of an actuator for mechatronics systems. We have introduced a few energy conversion

mechanisms and the associated actuators. In the second part of this chapter, we will focus on the power

amplification and modulation portion of the actuator. This part of the actuator is traditionally called

the power amplifier or the driver for the corresponding actuator. However, as miniaturization and system

integration become more pervasive, power electrics are being embedded into either the controller (infor-

mation processing unit) or the actuator. It is also the portion where intelligence and additional func-

tionality/feature can be incorporated. For electromechanical actuators, the unmodulated energy source

is electricity. The power amplifier acts as a buffer between the low energy part of the system, where

actuation command is given in low energy electrical signals, and the high energy density electrical signal

that will be converted.

Power amplification can roughly be categorized into two methods, linear and switching. The main

advantage of linear power amplification is the “cleanness” of the signal as compared to the switching

amplifiers. The main drawback is in efficiency, where linear amplifiers tend to run hotter than similar

sized switching amplifiers. However, as with any engineering design, this is only a rule-of-thumb; the

designer needs to analyze the application and select or design the appropriate driver.

Switching amplifiers are made of semiconductor components such as diodes and transistors. These

semiconductor devices either function as a switching element that controls the current flow to the energy

conversion element such as a winding coil, or as an amplification element that modulates the amount of

current flowing into the winding coil. Another advantage of using switching type power amplifiers is that,

with switching, the amplifier stage can be directly controlled by a digital signal from an information

processing device (see Figure 21.1) such as a microcontroller or a microprocessor. This eliminates the need

FIGURE 21.18 Static performance curve of a typical

piezoelectric actuator. (Courtesy of Piezo Systems, Inc.)

Direction of

increasing

voltage

Force

max

Deflection

Operating point

optimized produce

maximum work

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21-14 Mechatronic Systems, Sensors, and Actuators

for an ADC, which reduces the cost and size of the required electronics. Pulse-width modulation (PWM)

is one good example using binary signal to control electromechanical actuators. Figure 21.19 shows one

simple example of using a switching device to interface with a PMDC motor. As discussed in the previous

section, torque is generated when current is flowing into the armature winding of a PMDC motor. To

turn the motor on and off, we can connect the motor with a DC power source in series with a switch.

When the switch is closed, current flows through the motor and the motor turns. If the switch is opened,

current stops and the motor will eventually stop. Of course, more sophisticated circuit and switching

design is needed for actual implementation.

Nevertheless, this example illustrates the fundamentals of switching power amplification. In this section,

we will focus on switching amplifiers by introducing the fundamental building blocks.

21.1.3.1 Semiconductors

Semiconductors are typically materials consisting of elements from group IV of the periodic table, e.g.,

silicon (Si), germanium (Ge), and cadmium sulfide. Unlike conductors and insulators, semiconductors’

current-carrying capability is significantly affected by the temperature and the amount of incident photons

and the type and amount of impurities in the material. By introducing carefully controlled group V or

III elements (called dopants) into the semiconductors, we can increase or decrease the number of valence

electrons in the semiconductors, respectively. Depending on the type of the dopants, semiconductors

can be separated into:

•

n-type semiconductors: semiconductors doped with donor elements (e.g., arsenic or phosphor group

V elements ) that result in one additional electron freed (free electron) from the crystal lattice as

a charge carrier that is available for conducting.

•

p-type semiconductors: semiconductors doped with acceptor elements (e.g., boron or gallium group

III elements) that results in a missing electron in the lattice structure, which is called a hole. Holes

can be viewed as positive charge carriers or places that accept free electrons.

As will be discussed shortly, the interaction between the n-type and p-type semiconductors under

different orientation forms the basis for all the semiconductor electronic devices. One of the more

interesting aspects of modern electronics is the variety of features that can be obtained with a simple

switching device that opens or closes a connection in a controlled manner. We will discuss a few electronic

elements that are widely used, mainly as a controlled switching element, in power electronics for con-

structing power amplifiers/drivers for electromechanical actuators.

21.1.3.2 Diodes

A diode is a two-terminal electronic device that is constructed by joining a p-type and an n-type

semiconductor together to form a pn junction. Figure 21.20 shows the schematic symbol of a generic

diode. The terminal associated with the p-type material is called the anode and the terminal associated

with the n-type material is called the cathode. If the anode has higher electrical potential (>0.7 V) than

FIGURE 21.19 DC motor under switching control.

FIGURE 21.20 Diode.

Vcc

Cathode

Anode

−

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Actuators 21-15

the cathode, the diode is said to be forward biased, i.e., V

> 0.7 V. Conversely, if V

< 0.7 V, the diode

is reverse biased.

As shown in Figure 21.21, depending on the applied voltage, a diode can operate in three different

regions:

•

Forward biased region: V

> V

, where V

is called the forward bias voltage and is typically around

0.7 V for silicon and 0.3 V for germanium. The diode acts as a closed switch, and the anode and

cathode become short-circuited with a slight reverse potential (forward voltage drop) that is equal

to V

, see Figure 21.22.

•

Reverse biased region: V

< V

, where V

is the reverse breakdown voltage of the diode. The

diode acts as an opened switch and the circuit is open, see Figure 21.22.

•

Breakdown region: V

< V

. The diode again acts as a closed switch and a large current flows

through the diode. This is called the avalanche effect. If the magnitude of the reverse current i

is larger than the critical reverse bias current, the device will fail.

A diode is analogous to a fluid check valve, which allows fluid (current) to flow in only one direction if

the forward pressure is sufficient to overcome the spring force, see Figure 21.23. Table 21.3 summarizes

properties of some typical diodes.

Maximum allowable current through a diode and the reverse breakdown voltage are the two major

design considerations for diodes. The voltage across a diode times the current it carries is the power

loss across the diode that is completely converted into heat. The temperature of a diode can rise

rapidly due to its small size and mass. For safe operation, the temperature of the diode junction should

not exceed 200°C. To improve heat transfer, diodes are commonly mounted on metallic heat sinks.

Signal diodes are rated between

and 1 W. Power diodes can be rated as high as several hundred

kilowatts.

FIGURE 21.21 Diode characteristics.

FIGURE 21.22 Approximating a diode in a circuit.

Reverse

bias region

Forward bias

region

Reverse

breakdown

region

Open

circut

–

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21-16 Mechatronic Systems, Sensors, and Actuators

For switching applications, the reverse-recovery time is another important design parameter. The

reverse-recovery time imposes an upper bound on the frequency at which the diode can be switched on

and off. Attempts to operate a diode above this frequency will result in a decrease in switching efficiency

and may cause severe overheating.

Diodes are widely used in electronic power circuits. They are most widely used for rectification and peak

detection. Figure 21.24 illustrates some of the common diode applications. If multiple diodes are to be

TABLE 21.3 Typical Diode Properties

Relative Power

Maximum

Average Forward

Current [A]

Voltage Drop at

Maximum Average

Forward Current [V]

Maximum

Peak Forward

Current [A]

Reverse

Breakdown

Voltage [V]

Maximum

Junction

Temperature

[°C]

Low 1 0.8 30 1000 175

Medium 12 0.6 240 1000 200

High 100 0.6 1600 1000 200

Very High 1000 1.1 10,000 2000 200

Source: T. Wildi, Electrial Machines, Drivers and Power Systems, Prentice Hall, 2000.

FIGURE 21.23 Analogy between diodes and check valves.

FIGURE 21.24 Common diode applications.

Peak detector

BA157GP

–1.0

–2.0

–3.0

–4.0

–5.0

–4.0

–3.0

–2.0

–1.0

Bridge rectifier

Half-wave rectifier

load

Time

Volatge

Time(seconds)

OUT

5.0

4.0

3.0

2.0

5.0

3.0

2.0

1.0

4.0

1.0

0.1

0.1 0.2 0.2

0.2

0.3

0.3 0.4

0.4

9258_C021_Sect001.fm Page 16 Wednesday, October 10, 2007 7:09 PM

Actuators 21-17

used, diode array can be used. In general, the term diode array implies four or more diodes in a single

package. The most efficient packaging scheme is typically eight diodes or more in a dual inline package

(DIP). Other packages are the single inline package (SIP), the flat pack, and even a surface mount

diode array. Although multiple diode arrays can incorporate different type diodes, the most popular

arrays incorporate a fast, small signal diode such as the 1N4148, and the core driver arrays, which employ

a fast switching, higher current, 100-mA diode.

Zener Diode

Recall the current–voltage curve of a diode shown in Figure 21.21.

If a diode is reverse biased to the breakdown region, a large

reverse current will flow through the diode. For most diodes, this

voltage is usually larger than 50 V and may exceed kilovolts.

Zener

(

Avalanche

) diodes are a class of diodes that exhibit a steep break-

down curve with a well-defined reverse breakdown voltage

This unique breakdown characteristic makes Zener diodes good

candidates for building

voltage regulators

, since they can maintain a stable source voltage under

variable supply as well as varying load impedance. Figure 21.25 shows the special symbol that represents

a Zener diode.

To use the Zener diode as a voltage regulator, it should be reverse biased with a supply voltage higher

than the rated reverse breakdown voltage V

, see Figure 21.26. For an ideal Zener diode, in Figure 21.26,

> V

, the voltage across the load will equal to V

; hence the load current i

load

and the Zener diode

current can be written as

Zener diodes are often rated by their power dissipation, which is

Therefore, when selecting Zener diode for voltage regulation applications, it is important to ensure that

Zmax

does not exceed the allowable limit. The most common range of the reverse breakdown voltage for

Zener diodes is from 3.3 to 75 V. However, voltages out of this range are available. Some typical power

ratings for Zener diodes are 1/4, 1/2, 1, 5, 10, and 50 W.

21.1.3.3 Thyristors

A thyristor, or a silicon-controlled rectifier (SCR), is a 4-layer semiconductor switch, similar to a diode,

but with an additional terminal to control the instant of conduction. A thyristor has three terminals: an

anode, a cathode, and a gate, see Figure 21.27. One can think of a thyristor as a controllable diode that

the gate terminal provides as a mean of precise control of the instance when the thyristor is to be turned

on, i.e., it is a controlled switch.

FIGURE 21.26 Use Zener diode as simple voltage regulator.

FIGURE 21.25 Zener (avalanche) diode.

−

load

----------

and i

–

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

Zmax

⋅=

Load

---

−

Unregulated

source

Voltage

regulator

−

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21-18 Mechatronic Systems, Sensors, and Actuators

Figure 21.28 shows the current–voltage characteristics of a thyristor. To turn on (short or conduct) a

thyristor, two conditions have to be satisfied:

1. The anode (A) and cathode (K) terminal has to be forward biased, i.e., the anode voltage needs

to be higher than the cathode voltage.

2. A gate current I

has to flow into the gate for a sufficient amount of time, typically, a few

microseconds. The gate current can be generated by a short positive voltage pulse applied across

the gate (G) and cathode (K) terminal. The minimum amount of gate current that is required to

turn on a thyristor is called the latching current.

When the thyristor is turned on, the amount of current flowing through the device I

SCR

is limited by

the rest of the circuit impedance. Once the thyristor is turned on, the gate terminal loses control of the

device, i.e., we cannot use the gate to turn off the device. The thyristor will only turn off if the anode

current I

SCR

goes to zero, after which the gate terminal can assert control to turn on the device again.

Obviously, the thyristor can also be switched on by exceeding the forward breakdown voltage V

However, this is usually considered a design limitation and switching is normally controlled with a gate

voltage. If the gate (G) terminal is shorted with the cathode (K), the thyristor cannot be turned on, even

if V

is forward biased. One can think of the thyristor as a normally opened switch with a detent. Once

the switch is closed, no additional control is needed. Figure 21.29 shows the operation of a thyristor

driving a simple resistive load under a sinusoidal bipolar source voltage V

. In Figure 21.31, the gate

voltage V

will be the command or control input.

When the thyristor is reverse biased, the gate (G) to cathode (K) terminals should not be forward

biased to prevent reverse breakdown of the first pn junction of the thyristor, see Figure 21.27. The reverse

breakdown voltage V

, the latching current, the current and power rating, and the rate of rise of voltage

are the more important design parameters for selecting a thyristor. When the voltage across the thyristor

is suddenly applied or increased rapidly, the thyristor may turn on even if the gate current (voltage) is

FIGURE 21.27 Thyristor and its schematic symbol.

FIGURE 21.28 Thyristor (SCR) characteristics.

Gate (G)

Cathode (K)

SCR

Anode (A)

Forward voltage drop

(conducting)

Reverse breakdown

voltage

Forward breakdown

voltage

1Ð2 [V]

< I

SCR

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Actuators 21-19

zero. A typical rate of voltage change that will induce thyristor turn-on is about 50 V/

s. To prevent

undesired conduction due to a large rate (high frequency) of voltage variation, a snubber circuit, see

Figure 21.30, is often connected in parallel with the thyristor to filter out the high frequency voltage

variations. The snubber circuit is essentially a passive RC low-pass filter. The selection of the snubber

resistance R

and capacitance C

can use the following formula:

(21.12)

where R

and L

are the load inductance and load resistance, respectively. V

Amax

is the maximum anode

voltage and (dV/dt)

max

is the maximum expected rate of raise of voltage across the anode and cathode.

Unlike diodes used in rectifier circuits that can only rectify the input AC voltage to an average DC

voltage, thyristors can be used to build controlled rectifiers that can rectify AC sources and modulate the

average output DC voltage by modulating the firing timing of the gate voltage/current, see Figure 21.31.

FIGURE 21.29 Thyristor driving a resistive load.

FIGURE 21.30 Snubber circuit.

FIGURE 21.31 Controlled (thyristor) and uncontrolled (diode) rectifications.

Load

, L

Snubber

Load

Half-wave rectification using diode

−

Half-wave rectification usin

ristor

Amax

dV/dt()

max

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

and R

----- R

–==

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21-20 Mechatronic Systems, Sensors, and Actuators

Tr i a c

The thyristor can only be turned on in the forward biased direction. A triac is a controlled switch that

is equivalent to a pair of thyristors that are connected in an anti-parallel configuration, see Figure 21.32.

As depicted in Figure 21.32, a triac can be turned on in both the reverse and forward directions.

21.1.3.4 Transistors

A transistor is a semiconductor device that has three or more terminals and can provide power amplifi-

cation and switching. As we have seen in the previous discussions, electronic switching can be accom-

plished through either diodes or thyristors. Diode switching does not provide any control freedom. A

thyristor is a three-terminal device and the third (gate) terminal can be used to control and switching

instant. However, one drawback of thyristor switching is that the switching control is only in one direction,

i.e., the gate terminal can only be used to turn on the device. The thyristor switch can only be turned

off by dropping the anode current to zero.

A transistor is a special semiconductor device that can be used for power amplification by modulating

a relatively large current between or voltage across two terminals using a small control current or voltage,

and switching by effectively opening and closing the connection between two terminals using a controlled

signal on the third terminal.

Transistors form the basis of modern electronics and are the fundamental building blocks for digital

electronics, operational amplifiers, and power electronics. There are three common types of transistors,

bipolar junction transistors (BJTs), metal-oxide field effect transistors (MOSFETs), and insulated gate

bipolar transistors (IGBTs).

Bipolar Junction Transistors (BJTs)

A bipolar junction transistor is a three-layer device that is made of the p-n-p or the n-p-n combinations

of semiconductors, see Figure 21.33. BJTs have three terminals connected to each of the three layers called

FIGURE 21.32 Tr ia c cha r a c terist i c.

FIGURE 21.33 Biploar junction transistors (BJTs).

–

triac

Gate

n-p-n transistor

Collector (C)

Emitter (E)

Base (B)

Collector (C)

Base (B)

p-n-p transistor

Emitter (E)

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Actuators 21-21

collector (C), emitter (E), and base (B). Figure 21.34 shows the operation of an n–p–n type BJT under

a common emitter type connection. BJTs can operate in three regions:

1. Cutoff—When the base-emitter voltage is less than the turn-on voltage V

, the base current i

will

be negligible. The transistor is in the cutoff region and no current will flow through the collector

and emitter terminal, i.e.,

Typically, V

= 0.6 − 0.7 V. In this mode, the transistor from C to E can be viewed as an open

connection. This is analogous to the closed flow control valve.

2. Active Linear—When V

= V

, the transistor is in the active linear region, where

In this mode, the transistor can be viewed as a current-controlled current amplifier, where the

collector current i

is proportional to the base current i

. The proportionality constant (current

amplification factor or current gain)

= 20 ~ 200, is often denoted as h, hf, or h

in the data

sheets. In this mode, the connection between the terminals C and E can be viewed as closed. This

is analogous to a partially opened flow control valve, where the amount of the fluid (current) flow

is proportional to the size of the valve opening (base current magnitude). The power dissipation

across the transistor P

BJT

= i

· V

3. Saturation—When the base current i

is larger than the maximum available collector current i

the transistor is in the saturation region, where

(21.13)

In this mode, the transistor can be viewed as a closed switch between the terminals C and E. The

collector current i

is controlled (determined) by the collector circuit. This is analogous to a

completely opened flow control valve, where the flow is determined by the source and the load.

Note also that when the transistor is in saturation, the collector-emitter voltage drop is maintained

at a small value called the saturation voltage V

SAT

FIGURE 21.34 Characteristics of a common emitter n–p–n BJT.

Active

linear

Saturation

(mA)

Cutoff

Breakdown

–

0≈

0≥

= V

and

⋅=

and V

SAT

0.2 V≈=

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