means manipulating an
in such a way that it meets the requirements of
the next stage for further proce
ssing. For example, the output of an electronic
, which is probably in
the millivolts range is probably too low for an
(ADC) to process directly. In this case the signal
conditioning is the
necessary to bring the voltage level up to that required by the ADC.
applications, it is common to have a sensing stage (which consists of a
sensor), a signal
conditioning stage (where usually amplification of the signal is done) and a processing stage (normally carried out by an
ADC and a micro
amps) are commonly employed to carry out the amplification of
the signal in the signal conditioning stage.
More generally, signal conditioning can include amplification,
, converting, and any other processes required to
make sensor output suitable for conversion to digital format. It is primarily utilized for
, in which sensor
signals must be normalized and filtered to levels suitable for analog
digital conversion so they can be read by
Types of devices that use signal conditioning include signal filters,
current loop converters
Signal inputs accepted by signal conditioners include
. Sensor inputs can be
or bridge, and LVDT
or RVDT. Specialized inputs include encoder
, counter or
, timer or clock, relay or switch, and other
specialized inputs. Outputs for signal conditioning equipment can be voltage, current, frequency, timer or counter,
resistance or potentiometer, and other specialized outputs.
Control systems play a critical role in
that focuses on mathematical
of a diverse nature,
analyzing their dynamic behavior,
to create a controller that will cause the systems to behave in
a desired manner.
Modern control engineering is closely related to
cal and computer engineering
, as electronic circuits can often be
easily described using control theory techniques. At many universities, control engineering courses are primarily taught
electrical and computer engineering
faculty members. Previous to modern electronics, process control devices were
devised by mechanical engineers using mechanical feedback along with pneumatic and hy
draulic control devices, some
of which are still in use today.
The field of control within
is often known as
. It deals primarily with the control of
variables in a chemical process in a plant. It is taught as part of the undergraduate curriculum of any chemical
engineering program, and employs many o
f the same principles in control engineering.
Other engineering disciplines also overlap with control engineering, as it can be applied to any system for which a
suitable model can be derived.
Control engineering has diversified applications that include s
cience, finance management, and even human behaviour.
Students of control engineering may start with a linear control system course which requires elementary mathematics
and Laplace transforms (called classical control theory). In linear control, the stude
nt does frequency and time domain
analysis. Digital control and non
linear control courses require
and algebra respectively, and could be
said to complete a basic c
ontrol education. From here onwards there are several sub branches.
Control engineering is the enginee
that focuses on the
of a diverse range of
) and the design of
that will cause these systems to behave in the desired manner.
Although such controllers need not be electrical many are and hence control eng
ineering is often viewed as a subfield of
electrical engineering. However, the falling price of microprocessors is making the actual implementation of a control
system essentially trivial
. As a result, focus is shifting back to the mechanical engineering discipline, as
intimate knowledge of the physical system being controlled is often desired.
digital signal processors
can all be used to implement
engineering has a wide range of applications from the flight and propulsion systems of
present in many modern
Control engineers often utilize
. For example, in an
is continuously monitored and fed back to the system which adjusts the
accordingly. Where there is regular feedback,
can be used to determine how the system responds to such
feedback. In practicall
y all such systems
is important and
can help ensure stability is achiev
Although feedback is an important aspect of control engineering, control engineers may also work on the control of
systems without feedback. This is known as
. A classic example of
open loop control
that runs through
determined cycle without the use of
whereby some proportion of the output sign
al of a system is passed (fed back) to the
is often used to control the dynamic behavior of the
. Examples of fe
edback can be found in most
, such as
was applied by
Harold Stephen Black
to electrical amplifiers in 1927, but he could not get his idea
patented until 1937.
, a Mexican researcher and physician, co
authored a seminal 1943 paper
Behavior, Purpose and Teleology
that, according to
author of the paper), set the basis for
the new science of
. Rosenblueth proposed
that behavior controlled by negative feedback, whether in animal,
human or machine, was a determinative, directive principle in nature and human creations.
. This kind of
feedback is studied in
, feedback is a process of sharing observations, concerns and suggestions between persons or divisions
of the organization with an intention of improving both personal and organ
izational performance. Negative and positive
feedback have different meanings in this usage, where they imply criticism and praise, respectively.
Feedback is both a mechanism, process and signal that is looped back to control a
within itself. This loop is
called the feedback loop. A
usually has input and output to the system; when th
e output of the system is
fed back into the system as part of its input, it is called the "feedback."
Feedback and regulation are self related. The negative feedback helps to maintain stability in a system in spite of
external changes. It is related to
. Positive feedback amplifies possibilities of divergences (evolution, change
of goals); it is the condition to change, evolution, growth; it gives the system the ability to
access new points of
For example, in an organism, most positive feedback provide for fast autoexcitation of elements of endocrine and
nervous systems (in particular, in
stress responses conditions) and play a key role in regulation of morphogenesis,
growth, and development of organs, all processes which are in essence a rapid escape from the initial state.
Homeostasis is especially visible in the
when considered at organism level.
Types of feedback
Types of feedback are:
: which tends to reduce output (but in amplifiers, stabilizes and linearizes operation),
: which tends to increase output, or
feedback: which can either increase or decrease output.
Systems which include feedback are prone to
, which is
of output resulting from improperly tuned
inputs of first positive then negative feedback. Audio feedback typifies this form of oscillation.
ack is present in many natural and human systems. Feedback is usually bipolar
that is, positive and
in natural environments, which, in their diversity, furnish synergic and antagonistic responses to the output of
In control theory
back is extensively used in
, using a variety of methods including
state space (controls)
and so forth.
The most common general
ng a control
loop feedback mechanism is a
(PID) controller. Each term of the PID controller copes with time. The proportional term handles the
state of the system, the integral term handles its past, and the derivative or slope term tries to predict and handle the
In electronic engineering
The processing and control of feedback is engineered into many
and may also be
If the signal is inverted on its way round the control loop, the system is said to have
; otherwise, the
feedback is said to be
. Negative feedback is often deliberately introduced to increase the
of a system. This scheme can fail if the input changes faster than the system can respond to it. When this happens, the
lag in arrival of the feedback signal results in positive feedback, causing the output to
feedback is usually an u
nwanted consequence of system behaviour.
for assessing the
stability of feedback systems. An easier assessment, but
less general, is based upon gain margin and phase margin using
). Design to
insure stability often involves
, one method of compensation being
In ancient times, the
was used to regulate the flow of water in Greek and Roman
; similar float
valves are used to regulate fuel in a
and also used to regulate tank water level in the
as enhanced in 1745 by blacksmith Edmund Lee who added a fantail to keep the face of the windmill
pointing into the
. In 1787
regulated the speed of rotation of a windmill by using a centrifugal
pendulum to adjust the distance between the bedstone and the runner stone (i.e. to adjust the load).
The use of the
in 1788 to regulate the speed of his
was one factor
leading to the
. Steam engines also use float valves and pressure release valves as mechanical
of Watt's governor was done by
was one of the largest steamships of its time and employed a steam powered rudder with feedback
mechanism designed in 1866 by J.McFarla
ne Gray. Joseph Farcot coined the word
in 1873 to describe steam
powered steering systems. Hydraulic servos were later used to position guns.
Elmer Ambrose Sperry
designed the first
in 1912. Nicolas Minorsky published a theoretical analysis of automatic ship
steering in 1922 and described the
Internal combustion engi
nes of the late 20th century employed mechanical feedback mechanisms such as vacuum
) but mechanical feedback was replaced by electronic
engine management systems
small, robust and powerful single
Feedback Loop Control System
There are four elements in any feedback loop control system.
of the position to be controlled
that specifies the value the controlled variable should have
that compares the a
ctual sensed position, or feedback signal, with the
desired position or reference signal. The output of the comparator is usually called an
error signal, whose polarity determines which way a correction needs to be made.
which is activat
ed by the error signal and results in a correction of
the position. This is often called an actuator.
In our levitator, the sensor is the optical device that measures the position (or lack) of the suspended object. The
reference input is establish by anot
her optical device to measure the ambient light. The comparator is an electrical
device that subtracts and amplifies the two inputs. The control mechanism is the electromagnetic lifting coil.
Since the four elements just mentioned are all essential to clo
sed loop systems, it follows that any scheme to
control something that lacks one or more of these items is
a feedback control system. Thus, it is easy to
examine many legislative programs and obvious why so many of them fail. It also follows, from look
ing at things in a
general way, that nothing can be controlled by feedback unless it can be measured.
Benefits of Feedback
The desired position of the suspended object is the only intentional input to the system. But several other factors
such as weight an
d gravity, power supplies, and air currents can affect the position. Such inputs, being unwanted,
are often called
. Since they are subject to nonlinear effects and unknown change with time, they are
responsible for the impossibility of merely
balancing the coil strength with the weight of the object. The main reason
for feedback control is to measure and compensate for the effect of disturbances.
In other types of systems, feedback allows the apparent response speed of a component such as a mot
or can be
increased by overdriving it when rapid response is needed. Still another reason to use feedback is to provide a stiff
output, which means an output that is not susceptible to being changed by disturbances. And in other instances, it
to have the output exactly proportional to the input, but the amplifiers and other components may not be
perfectly linear. The use of feedback can greatly reduce nonlinearities in all other system components except the
sensor used to provide the feedback s
ignal. Finally, when systems are being mass
produced with inexpensive
components that may have a considerable variation in values, feedback can greatly reduce the effect of differences
between one unit and another.
Problems of Feedback
If all these benefit
s sound almost too good to be true, it is time for a reality check. Actually, they are true enough,
but there is always the Dark side of the Force. There are two main costs:
There is an increase in system complexity, which may increase component count.
etimes this may be offset by the possibility of using cheaper components.
Feedback introduces a stability problem, and this is much more serious. This problem is
sufficiently troublesome that 90% of the pages on books about feedback are devoted to
we mean a tendency to overcontrol, or overshoot, when the input or a disturbance is felt.
Alternatively, when looking at the frequency response, the gain may rise near the upper end of the passband, which
is usually undesireable. In an e
xtreme case the gain can become high enough to cause oscillation, that is, a
sustained cyclic response without any input. This effect generally renders the system useless or even destructive.
Causes of Instability
The stability problem is inevitable. It re
sults from the fact that the feedback, which is connected so as to be negative
at low frequencies, usually becomes positive at high frequencies. Good stability is usually possible provided the
loop gain is low enough.
The main reason the feedback ultimatel
y becomes positive as the frequency increases is that both the control
system and the load it is driving contain components that can store energy.
electrical energy storage elements, and
and raising an object
energy storage elements.
Since the drive to physical devices is not infinite, the response
must dwindle toward zero as the frequency approaches infinity,
with an associated phase shift approaching 90
. Several phase
an add up so that the total around the loop equals 360
, which is positive feedback. Only 180
shift from the energy storage elements is needed to cause positive feedback, since the connection at the
comparator introduces 180
to make the fee
dback negative at low frequencies.
Historically, the stability problem was first clearly recognized when centrifugal fly
ball governors were applied to
early steam engines shortly after their invention around the middle of the eight
eenth century. It was approximately
another century before the first mathematical analysis of this problem was carried out by the eminent scientist
James Clerk Maxwell. (He is far more widely known for his electromagnetic theory of light, which became know
It was not until well into the twentieth century that Nyquist, Bode, and many others laid the foundations of modern
This diagram shows the basic model for any feedback control system. It shows
the four elements in an abstract
Signal flow is clockwise around the loop. Arrows indicating direction are shown, although they are usually used only
at the summing junction, or comparator, which is the circle with the X in it. The inputs (two in t
his case but there can
be any number) have
signs to indicate whether each input is added or subtracted. With two inputs and the
polarities shown, the summing junction is simply subtracting one signal from the other, in effect performing the
on that is one of the functions needed for every feedback loop.
The input is labeled
eference which, in this design, is the ambient light measured by a photodetector in units
of volts. The output is
ontrolled variable, which is the position m
easured in millimeters from the center
position of the photodetector. The output of the summing junction is
rror signal. Photodetector
position into voltage, and the letter B also represents the sensitivity of the detector in units of vol
represents all the stages that process the error signal and drive the lifting coil.
From the equations in the diagram above, we eliminate E, since it is an internal parameter. Solving for the overall
gain of the system, we get:
The second form, with 1/B factored out, looks a bit more complicat
ed but is actually more convenient for most
purposes, since C/R will be almost exactly 1/B for all useful feedback loops. The reason is that AB will usually be
much greater than one, making the other factor in the second form almost unity.
, is called the
closed loop gain
since it is the gain from input to output with the loop closed and
operating. It is the only gain of any final interest. This gain represents how much the input (reference) signal is
amplified at the output.
The real loop gain is the product of all the gains around the loop,
, and is referred to as the
open loop gain
. This gain could be measured (theoretically!) by opening the loop anywhere,
inserting a small test signal, measuring the signal that appears on
the other end of the break, and
calculating the ratio.
Despite the simplicity of this equation, it completely describes the behavior of all feedback loop control systems in
the world. The
A and B are arbitrary. These two blocks represen
t all the signal processing in the
forward and reverse directions, and may be fantastically complicated. They may (and usually do!) have frequency
dependent elements and even nonlinear parts. This equation covers them all. The designer's big challenge is t
characterize their particular circuit design into these two transfer functions.
The characteristics of loop components can be described either by mathematical expressions, called
, or by graphs. Transfer function is a
fancy name for gain.
In the simplest situation the gain of a network or component is just a number that the input is multiplied by to give
the output. For example, a two
resistor voltage divider network. Since a voltage divider attentuates a signal, inst
of amplifying it, the gain is less than unity, which means that if it is given in decibels, it is negative. This transfer
function is V
If several components are connected in series, the individual gains are multiplied together
to give the overall gain.
For example, if two such resistor networks are cascaded together, with buffering to prevent loading effects, the
overall gain (attentuation) would be the product of the individual network gains.
For a voltage divider, multiplying
the input by the gain will give the output, regardless of the nature of the input.
Whether the input is a dc value, sine wave, square wave, or a transient, the output is always the same fraction of
the input at every instant. The reason for this simplicit
y in the case of a voltage divider is that no energy can be
stored, so there is no time dependency between the input and output.
When energy storage elements are present, the output at any instant depends on the current value of the input, and
also to some
degree on previous values. Further, the way previous values affect the output depends on the
waveform of the input. For example, the position of the object being lifted depends on its position an instant earlier,
along with its previous speed and forces o
f gravity versus the lifting coil.
A graphical approach is usually the easiest way to analyze and design feedback loops. So we will review how to
represent the transfer function graphically. There are several ways to do so, but the method suggest
ed by H. W.
Bode in the 1930s is particularly useful.
Bode's method consists of plotting two curves, the
log of gain
, and phase, as functions of the
log of frequency
Usually the gain in decibels, abbreviated dB, and the phase are plotted linearly along t
he y axis on graph paper that
has several cycles of a log scale on the x axis. Each cycle represents a factor of ten in frequency. This special
paper is known as semilog graph paper, and it or a computer program with log
log graphing are essential for
ng Bode plots.
Definition of Decibel
The decibel is a logarithmic measure of a voltage ratio, or gain. It is defined as
Or by the equivalent exponential for
The calculation can be done mentally with the aid of a small table of values. Memorization is practical because
reciprocal values of gain convert to th
e same value of decibel, except for sign.
Because of the properties of logarithms, when networks are cascaded so their gains
multiply, the overall gain in
decibels is obtained by adding the decibels of the networks.
Therefore, three cascaded networks with gains of 2, 2, and 10 would have a total gain of 2
example, and the gains in decibels would combine as 6
32dB. The same idea makes it easy to convert to
and from decibels by breaking down a total into its components.
Another example going the other way is 34 dB, which is 14
dB, so the gain is 5
Phase Lag Network
Whew. Having c
overed all this background, we are ready to make a Bode plot. Let's start with a "phase lag
network" as shown in this schematic, also known as a low
The sole parameter characterizing this network is its time constant
, and we will arbitraril
y take this to be 1 ms for
this exercise. The break frequency is thenf
At low frequencies the gain is flat and unity, or 0 dB. At h
igh frequencies the gain rolls off inversely with frequency,
decreasing by a factor of 2 (or 6 dB) for every frequency doubling. This is an increase of one octave wherever it
Alternatively, the roll
off rate can be expressed as 20 dB per decade (a
factor of 10 in frequency), which results in a
straight line on semilog graph paper with a slope of
6 dB per/octave. It intersects the low
frequency curve at the
The straight line segments show an asymptotic representation of the lag char
acteristic, which is not quite exact
near the break frequency. There the gain is actually 1/SQRT(2) = 0.707, or
3 dB. Calculating more points enables
us to draw the curve as accurately as desired, but the single 3 dB down point and the two asymptotes suff
ice to get
the picture. Even that extra graphing is seldom done, however, since the process entails extra effort. The
asymptotic form is generally more useful, since it shows the break frequency explicitly.
Although the x axis is a log frequency scale, the
values of frequency are indicated directly for convenience. So, as
far as the numbers are concerned, it is a frequency scale, but the markings are not spaced uniformly.
Looking at the phase plot, we see it is 0 degrees well below cutoff,
90 degrees well
45 degrees at the
break frequency. We see the transition is more gradual than that of the gain plot. A good approximation to the curve
is a straight
line asymptote: 0 degrees at one
tenth of the break frequency and
90 degrees at ten times the
On a Bode plot the line will be exact at the break frequency, showing a phase of
For this lag network and for many others that constitute a subset known as
minimum phase networks
phase characteristic contains no information
in addition to that carried by the gain plot. Therefore, the phase curve
is often not plotted at all.