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Control systems-I
Introduction
Control systems
• A control system consists of subsystems and
processes (or plants) assembled for the
purpose of obtaining a desired output with desired
performance, given a specified
input.
• Figure 1.1 shows a control system in its simplest
form, where the
input represents a desired output.
Example of an elevator
• When the fourth-floor button is pressed on the first floor, the elevator rises to the
fourth floor with a speed and floor-leveling accuracy designed for passenger
comfort.
•The push of the fourth-floor button is an input that represents our desired
output, shown as a step function in Figure 1.2.
•The performance of the elevator can be seen from the elevator response curve in
the figure.
Measures of performance
• Two major measures of performance are apparent:
(1) the transient response, and
(2) the steady-state error
• In the elevator example, passenger comfort and passenger
patience are dependent upon the transient response.
• If this response is too fast, passenger comfort is sacrificed.
• If too slow, passenger patience is sacrificed.
• The steady-state error is another important performance specification
since passenger safety and convenience would be sacrificed if the
elevator did not properly level.
Advantages of Control Systems
• With control systems we can move large equipment with precision
that would otherwise be impossible.
• We can point huge antennas toward the farthest reaches of the
universe to pick up faint radio signals; controlling these antennas
by hand would be impossible.
• Because of control systems, elevators carry us quickly to our
destination, automatically stopping at the right floor.
• We alone could not provide the power required for the load and
the speed; motors provide the power, and control systems
regulate the position and speed.
Advantages (cont…)
• We build control systems for four primary reasons:
1. Power amplification
2. Remote control
3. Convenience of input form
4. Compensation for disturbances
• For example, a radar antenna, positioned by the low-
power rotation of a knob at the input, requires a large
amount of power for its output rotation. A control
system can produce the needed power amplification,
or power gain
Advantages (cont…)
• Robots designed by control system principles can
compensate for human disabilities.
• Control systems are also useful in remote or
dangerous locations. For example, a remote-controlled
robot arm can be used to pick up material in a radioactive
environment.
• Control systems can also be used to provide convenience by
changing the form of the input. For example, in a
temperature control system, the input is a position on a
thermostat. The output is heat. Thus, a convenient position
input yields a desired thermal output.
Advantages (cont…)
• The system must be able to yield the correct output even
with a disturbance.
• For example, consider an antenna system that points in a
commanded direction. If wind forces the antenna from its
commanded position, or if noise enters internally, the system
must be able to detect the disturbance and correct the
antenna‘s position.
• Obviously, the system's input will not change to make the
correction.
• Consequently, the system itself must measure the amount
that the disturbance has repositioned the antenna and then
return the antenna to the position commanded by the input
System Configurations
• Two major configurations of control systems:
i) open loop systems
and
ii) closed loop systems
Open loop systems
• The toaster in Fig.a can be set for the desired darkness of the
toasted bread.
• The setting of the ‘‘darkness’’ knob, or timer, represents the input
quantity, and the degree of darkness and crispness of the toast
produced is the output quantity.
• If the degree of darkness is not satisfactory, because of the
condition of the bread or some similar reason, this condition can in
no way automatically alter the length of time that heat is applied.
• Since the output quantity has no influence on the input quantity,
there is no feedback in this system.
• The heater portion of the toaster represents the dynamic part of
the overall system, and the timer unit is the reference selector.
Open loop systems
Fig.a Automatic Toaster
Fig.b Electric motor
Open loop systems (cont…)
• The dc shunt motor of Fig.b is another example of an open loop
system.
• For a given value of field current, a required value of voltage is
applied to the armature to produce the desired value of motor
speed.
• In this case the motor is the dynamic part of the system, the
applied armature voltage is the input quantity, and the speed of the
shaft is the output quantity.
• A variation of the speed from the desired value, due to a change of
mechanical load on the shaft, can in no way cause a change in the
value of the applied armature voltage to maintain the desired
speed.
• Therefore, the output quantity has no influence on the input
quantity.
Open loop systems (cont…)
• Systems in which the output quantity has no effect upon the input quantity are
called open-loop control systems.
• The examples just cited (in Figs.a & b) are represented symbolically by a functional
block diagram, as shown in Fig. c.
• In this figure,
(a) the desired darkness of the toast or the desired speed of the motor is the
command input,
(b) the selection of the value of time on the toaster timer or the value of voltage
applied to the motor armature is represented by the reference-selector block, and
(c) the output of this block is identified as the reference input.
The reference input is applied to the dynamic unit that performs the desired
control function, and the output of this block is the desired output
Advantages and disadvantages of open-
loop control systems
Advantages:
1. Simple in construction and easy to maintain
2. Less expensive because of the use of minimum number of control devices
3. The problem of instability does not exist
4. Performs accurately once the calibration of the input is done
5. Open-loop system is convenient when it is very convenient to measure
the output or the measurement is economically not feasible
Disadvantages:
1. Disturbances (internal or external) cause drifts in the desired output
2. Changes in calibration cause errors in the system
3. Re-calibration of the system may be necessary from time to time in order
to maintain the required quality of output.
Closed loop control systems
• A person could be assigned the task of sensing the actual value of
the output and comparing it with the command input.
• If the output does not have the desired value, the person can alter
the reference-selector position to achieve this value.
• Introducing the person provides a means through which the output
is fed back and is compared with the input.
• Any necessary change is then made in order to cause the output to
equal the desired value.
• The feedback action therefore controls the input to the dynamic
unit.
• Systems in which the output has a direct effect upon the input
quantity are called closed loop control systems
Closed loop control systems(cont…)
• To improve the performance of the closed-loop system so that the
output quantity is as close as possible to the desired quantity, the person
can be replaced by a mechanical, electrical, or other form of a
comparison unit.
• The functional block diagram of a single-input, single-output(SISO)
closed-loop control system is illustrated in Fig. d.
• Comparison between the reference input and the feedback signals
results in an actuating signal that is the difference between these two
quantities.
• The actuating signal acts to maintain the output at the desired value.
• This system is called a closed-loop control system.
• The designation closed-loop implies the action resulting from the
comparison between the output and input quantities in order to
maintain the output at the desired value.
• Thus, the output is controlled in order to achieve the desired value.
Fig.d Functional diagram of closed
loop control system
Example of closed-loop control system -A home
heating system
• In a home heating system the desired room temperature (command input) is set
on the thermostat (reference selector).
• A bimetallic coil in the thermostat is affected by both the actual room temperature
(output) and the reference-selector setting.
• If the room temperature is lower than the desired temperature, the coil strip
alters its shape and causes a mercury switch to operate a relay, which turns on the
furnace to produce heat in the room.
• When the room temperature reaches the desired temperature, the shape of the
coil strip is again altered so that the mercury switch opens.
• This deactivates the relay and in turn shuts off the furnace.
• In this example, the bimetallic coil performs the function of a comparator since
the output (room temperature) is fed back directly to the comparator.
• The switch, relay, and furnace are the dynamic elements of this closed-loop
control system
Example of closed-loop control system
–Automatic elevator
• A closed-loop control system of great importance to all
multistory buildings is the automatic elevator.
• A person in the elevator presses the button
corresponding to the desired floor.
• This produces an actuating signal that indicates the
desired floor and turns on the motor that raises or
lowers the elevator.
• As the elevator approaches the desired floor, the
actuating signal decreases in value and, with the
proper switching sequences, the elevator stops at the
desired floor and the actuating signal is reset to zero.
Example of closed-loop control system
–Automatic aircraft landing system
Automatic aircraft landing
system(cont…)
• The system consists of three basic parts:
the aircraft, the radar and the controlling unit.
• The radar unit measures the approximate vertical
and lateral positions of the aircraft, which are
then transmitted to the controlling unit.
• From these measurements, the controlling unit
calculates appropriate commands.
• These commands are then transmitted to the
aircraft autopilots which in turn cause the aircraft
to respond.
Advantages and disadvantages of
closed-loop systems
Advantages:
1.Relatively less accurate and inexpensive components may be used to obtain
an accurate control of a given process
2. The influence of internal and external disturbances on the output can be
made almost ineffective
3. Debilitating effects of plant parameter variations can be effectively
counteracted
4.Transient responses of the system can be improved
5. Steady state error can be reduced
Disadvantages:
1. It requires more number of equipment and components and is thus it is
costlier
2. There is a tendency to overcorrect errors, which may create oscillations
in the system output. This may cause instability of the system
Definitions
(As per the standards of the IEEE)
• System: A combination of components that act together to perform a function not possible
with any of the individual parts. The word system as used herein is interpreted to include
physical, biological, organizational, and other entities, and combinations thereof, which can
be represented through a common mathematical symbolism.
• A system excited by only initial conditions is said to be autonomous and a system having
external input together with or without initial condition is said to be
non autonomous.
• Command input: The motivating input signal to the system, which is independent of the
output of the system and exercises complete control over it (if the system is completely
controllable).
• Reference selector (reference input element): The unit that establishes the value of the
reference input. The reference selector is calibrated in terms of the desired value of the
system output.
• Reference input: The reference signal produced by the reference selector, i.e., the
command expressed in a form directly usable by the system. It is the actual signal input to
the control system.
• Disturbance input: An external disturbance input signal to the system that has an
unwanted effect on the system output.
Definitions (cont...)
• Forward element (system dynamics): The unit that reacts to an actuating signal to produce
a desired output. This unit does the work of controlling the output and thus may be a
power amplifier.
• Output (controlled variable): The quantity that must be maintained at a prescribed value,
i.e., following the command input without responding the disturbance inputs.
• Open-loop control system: A system in which the output has no effect upon the input
signal.
• Feedback element: The unit that provides the means for feeding back the output quantity,
or a function of the output, in order to compare it with the reference input.
• Actuating signal: The signal that is the difference between the reference input and the
feedback signal. It is the input to the control unit that causes the output to have the
desired value.
• Closed-loop control system: A system in which the output has an effect upon the input
quantity in such a manner as to maintain the desired output value.
• Servomechanism (often abbreviated as servo): The term is often used to refer to a
mechanical system in which the steady-state error is zero for a constant input signal.
Sometimes, by generalization, it is used to refer to any feedback control system.
• Regulator : This term is used to refer to systems in which there is a constant steady-state
output for a constant signal. The name is derived from the early speed and voltage
controls, called speed and voltage regulators.
Definitions (cont...)
• Time-invariant control system:
A system is said to be time-invariant if its behaviour or characteristics do not change with
time.
The parameters of the system do not vary with time. The response of a time-invariant
system is independent of the time at which it is applied. It responds identically regardless
of the time of application of the input.
Ex: Elements of an electrical network such as R,L and C.
• Time-variant system:
If the parameters of a control system vary with time, the system is said to be a time-
varying system.
Ex: A space vehicle leaving earth
• Continuous –time and discrete -time control systems:
If all the variables of a control system are continuous functions of time, the system is said
to be continuous –time control system. If one or more system variables of a control system
are known at a certain discrete instants of time, the system is discrete-time system.
Ex: The speed control of a DC motor with tacho-generator feedback is an example of
continuous control system, while a microprocessor or computer based system is an
example of a discrete time system.
Regulator Fan motor
Problem 1.1 Explainbecontrolactionofaceiling-fanregulator anddraw thecoep0n fitbladediagfar0.
A fan regulator is a combination of a
series switch and a speed regulator. For a given
speedsettingonthefanregulator,thefanruns
specific setting on the regulator is the
inputandthevariable voltageapplied
motoristhecontrol signal. Thespeed
reference
to the fan
of the fan
at a specific speed. To obtain a differentspeed,
thesettingontheregulatoristobechanged.This
changes thevoltageapplied tothemotor.The
Voltage
isthecontrolled output.Theoutputspeedisnot
measuredandsothecontrolschemeisopen-loop.
Theblockdiagram isshown inFig.
Actual speed
Reference
input Controller Actuator
Fig. P1.1 Fan regulator
Process
Controlled output
Fan leaves
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CS-1(Ch.1).pdf

  • 2. Control systems • A control system consists of subsystems and processes (or plants) assembled for the purpose of obtaining a desired output with desired performance, given a specified input. • Figure 1.1 shows a control system in its simplest form, where the input represents a desired output.
  • 3. Example of an elevator • When the fourth-floor button is pressed on the first floor, the elevator rises to the fourth floor with a speed and floor-leveling accuracy designed for passenger comfort. •The push of the fourth-floor button is an input that represents our desired output, shown as a step function in Figure 1.2. •The performance of the elevator can be seen from the elevator response curve in the figure.
  • 4. Measures of performance • Two major measures of performance are apparent: (1) the transient response, and (2) the steady-state error • In the elevator example, passenger comfort and passenger patience are dependent upon the transient response. • If this response is too fast, passenger comfort is sacrificed. • If too slow, passenger patience is sacrificed. • The steady-state error is another important performance specification since passenger safety and convenience would be sacrificed if the elevator did not properly level.
  • 5. Advantages of Control Systems • With control systems we can move large equipment with precision that would otherwise be impossible. • We can point huge antennas toward the farthest reaches of the universe to pick up faint radio signals; controlling these antennas by hand would be impossible. • Because of control systems, elevators carry us quickly to our destination, automatically stopping at the right floor. • We alone could not provide the power required for the load and the speed; motors provide the power, and control systems regulate the position and speed.
  • 6. Advantages (cont…) • We build control systems for four primary reasons: 1. Power amplification 2. Remote control 3. Convenience of input form 4. Compensation for disturbances • For example, a radar antenna, positioned by the low- power rotation of a knob at the input, requires a large amount of power for its output rotation. A control system can produce the needed power amplification, or power gain
  • 7. Advantages (cont…) • Robots designed by control system principles can compensate for human disabilities. • Control systems are also useful in remote or dangerous locations. For example, a remote-controlled robot arm can be used to pick up material in a radioactive environment. • Control systems can also be used to provide convenience by changing the form of the input. For example, in a temperature control system, the input is a position on a thermostat. The output is heat. Thus, a convenient position input yields a desired thermal output.
  • 8. Advantages (cont…) • The system must be able to yield the correct output even with a disturbance. • For example, consider an antenna system that points in a commanded direction. If wind forces the antenna from its commanded position, or if noise enters internally, the system must be able to detect the disturbance and correct the antenna‘s position. • Obviously, the system's input will not change to make the correction. • Consequently, the system itself must measure the amount that the disturbance has repositioned the antenna and then return the antenna to the position commanded by the input
  • 9. System Configurations • Two major configurations of control systems: i) open loop systems and ii) closed loop systems
  • 10. Open loop systems • The toaster in Fig.a can be set for the desired darkness of the toasted bread. • The setting of the ‘‘darkness’’ knob, or timer, represents the input quantity, and the degree of darkness and crispness of the toast produced is the output quantity. • If the degree of darkness is not satisfactory, because of the condition of the bread or some similar reason, this condition can in no way automatically alter the length of time that heat is applied. • Since the output quantity has no influence on the input quantity, there is no feedback in this system. • The heater portion of the toaster represents the dynamic part of the overall system, and the timer unit is the reference selector.
  • 11. Open loop systems Fig.a Automatic Toaster Fig.b Electric motor
  • 12. Open loop systems (cont…) • The dc shunt motor of Fig.b is another example of an open loop system. • For a given value of field current, a required value of voltage is applied to the armature to produce the desired value of motor speed. • In this case the motor is the dynamic part of the system, the applied armature voltage is the input quantity, and the speed of the shaft is the output quantity. • A variation of the speed from the desired value, due to a change of mechanical load on the shaft, can in no way cause a change in the value of the applied armature voltage to maintain the desired speed. • Therefore, the output quantity has no influence on the input quantity.
  • 13. Open loop systems (cont…) • Systems in which the output quantity has no effect upon the input quantity are called open-loop control systems. • The examples just cited (in Figs.a & b) are represented symbolically by a functional block diagram, as shown in Fig. c. • In this figure, (a) the desired darkness of the toast or the desired speed of the motor is the command input, (b) the selection of the value of time on the toaster timer or the value of voltage applied to the motor armature is represented by the reference-selector block, and (c) the output of this block is identified as the reference input. The reference input is applied to the dynamic unit that performs the desired control function, and the output of this block is the desired output
  • 14. Advantages and disadvantages of open- loop control systems Advantages: 1. Simple in construction and easy to maintain 2. Less expensive because of the use of minimum number of control devices 3. The problem of instability does not exist 4. Performs accurately once the calibration of the input is done 5. Open-loop system is convenient when it is very convenient to measure the output or the measurement is economically not feasible Disadvantages: 1. Disturbances (internal or external) cause drifts in the desired output 2. Changes in calibration cause errors in the system 3. Re-calibration of the system may be necessary from time to time in order to maintain the required quality of output.
  • 15. Closed loop control systems • A person could be assigned the task of sensing the actual value of the output and comparing it with the command input. • If the output does not have the desired value, the person can alter the reference-selector position to achieve this value. • Introducing the person provides a means through which the output is fed back and is compared with the input. • Any necessary change is then made in order to cause the output to equal the desired value. • The feedback action therefore controls the input to the dynamic unit. • Systems in which the output has a direct effect upon the input quantity are called closed loop control systems
  • 16. Closed loop control systems(cont…) • To improve the performance of the closed-loop system so that the output quantity is as close as possible to the desired quantity, the person can be replaced by a mechanical, electrical, or other form of a comparison unit. • The functional block diagram of a single-input, single-output(SISO) closed-loop control system is illustrated in Fig. d. • Comparison between the reference input and the feedback signals results in an actuating signal that is the difference between these two quantities. • The actuating signal acts to maintain the output at the desired value. • This system is called a closed-loop control system. • The designation closed-loop implies the action resulting from the comparison between the output and input quantities in order to maintain the output at the desired value. • Thus, the output is controlled in order to achieve the desired value.
  • 17. Fig.d Functional diagram of closed loop control system
  • 18. Example of closed-loop control system -A home heating system • In a home heating system the desired room temperature (command input) is set on the thermostat (reference selector). • A bimetallic coil in the thermostat is affected by both the actual room temperature (output) and the reference-selector setting. • If the room temperature is lower than the desired temperature, the coil strip alters its shape and causes a mercury switch to operate a relay, which turns on the furnace to produce heat in the room. • When the room temperature reaches the desired temperature, the shape of the coil strip is again altered so that the mercury switch opens. • This deactivates the relay and in turn shuts off the furnace. • In this example, the bimetallic coil performs the function of a comparator since the output (room temperature) is fed back directly to the comparator. • The switch, relay, and furnace are the dynamic elements of this closed-loop control system
  • 19. Example of closed-loop control system –Automatic elevator • A closed-loop control system of great importance to all multistory buildings is the automatic elevator. • A person in the elevator presses the button corresponding to the desired floor. • This produces an actuating signal that indicates the desired floor and turns on the motor that raises or lowers the elevator. • As the elevator approaches the desired floor, the actuating signal decreases in value and, with the proper switching sequences, the elevator stops at the desired floor and the actuating signal is reset to zero.
  • 20. Example of closed-loop control system –Automatic aircraft landing system
  • 21. Automatic aircraft landing system(cont…) • The system consists of three basic parts: the aircraft, the radar and the controlling unit. • The radar unit measures the approximate vertical and lateral positions of the aircraft, which are then transmitted to the controlling unit. • From these measurements, the controlling unit calculates appropriate commands. • These commands are then transmitted to the aircraft autopilots which in turn cause the aircraft to respond.
  • 22. Advantages and disadvantages of closed-loop systems Advantages: 1.Relatively less accurate and inexpensive components may be used to obtain an accurate control of a given process 2. The influence of internal and external disturbances on the output can be made almost ineffective 3. Debilitating effects of plant parameter variations can be effectively counteracted 4.Transient responses of the system can be improved 5. Steady state error can be reduced Disadvantages: 1. It requires more number of equipment and components and is thus it is costlier 2. There is a tendency to overcorrect errors, which may create oscillations in the system output. This may cause instability of the system
  • 23. Definitions (As per the standards of the IEEE) • System: A combination of components that act together to perform a function not possible with any of the individual parts. The word system as used herein is interpreted to include physical, biological, organizational, and other entities, and combinations thereof, which can be represented through a common mathematical symbolism. • A system excited by only initial conditions is said to be autonomous and a system having external input together with or without initial condition is said to be non autonomous. • Command input: The motivating input signal to the system, which is independent of the output of the system and exercises complete control over it (if the system is completely controllable). • Reference selector (reference input element): The unit that establishes the value of the reference input. The reference selector is calibrated in terms of the desired value of the system output. • Reference input: The reference signal produced by the reference selector, i.e., the command expressed in a form directly usable by the system. It is the actual signal input to the control system. • Disturbance input: An external disturbance input signal to the system that has an unwanted effect on the system output.
  • 24. Definitions (cont...) • Forward element (system dynamics): The unit that reacts to an actuating signal to produce a desired output. This unit does the work of controlling the output and thus may be a power amplifier. • Output (controlled variable): The quantity that must be maintained at a prescribed value, i.e., following the command input without responding the disturbance inputs. • Open-loop control system: A system in which the output has no effect upon the input signal. • Feedback element: The unit that provides the means for feeding back the output quantity, or a function of the output, in order to compare it with the reference input. • Actuating signal: The signal that is the difference between the reference input and the feedback signal. It is the input to the control unit that causes the output to have the desired value. • Closed-loop control system: A system in which the output has an effect upon the input quantity in such a manner as to maintain the desired output value. • Servomechanism (often abbreviated as servo): The term is often used to refer to a mechanical system in which the steady-state error is zero for a constant input signal. Sometimes, by generalization, it is used to refer to any feedback control system. • Regulator : This term is used to refer to systems in which there is a constant steady-state output for a constant signal. The name is derived from the early speed and voltage controls, called speed and voltage regulators.
  • 25. Definitions (cont...) • Time-invariant control system: A system is said to be time-invariant if its behaviour or characteristics do not change with time. The parameters of the system do not vary with time. The response of a time-invariant system is independent of the time at which it is applied. It responds identically regardless of the time of application of the input. Ex: Elements of an electrical network such as R,L and C. • Time-variant system: If the parameters of a control system vary with time, the system is said to be a time- varying system. Ex: A space vehicle leaving earth • Continuous –time and discrete -time control systems: If all the variables of a control system are continuous functions of time, the system is said to be continuous –time control system. If one or more system variables of a control system are known at a certain discrete instants of time, the system is discrete-time system. Ex: The speed control of a DC motor with tacho-generator feedback is an example of continuous control system, while a microprocessor or computer based system is an example of a discrete time system.
  • 26. Regulator Fan motor Problem 1.1 Explainbecontrolactionofaceiling-fanregulator anddraw thecoep0n fitbladediagfar0. A fan regulator is a combination of a series switch and a speed regulator. For a given speedsettingonthefanregulator,thefanruns specific setting on the regulator is the inputandthevariable voltageapplied motoristhecontrol signal. Thespeed reference to the fan of the fan at a specific speed. To obtain a differentspeed, thesettingontheregulatoristobechanged.This changes thevoltageapplied tothemotor.The Voltage isthecontrolled output.Theoutputspeedisnot measuredandsothecontrolschemeisopen-loop. Theblockdiagram isshown inFig. Actual speed Reference input Controller Actuator Fig. P1.1 Fan regulator Process Controlled output Fan leaves