SUBJECT
NAME
Control System
ETEL307
th
5 SEMESTER
SUBJECT
NAME
UNIT -1
Introduction to
Control Systems
What is “Control”?
▪
Room temperature control
▪
Car driving
▪
Voice volume control
4
What is System ?
Automatic Control
Applications:
▪ Robotic systems
▪ Aircraft
▪ Missile guidance systems
▪ Industrial processes
▪ Transportations
6
What is “Automatic Control”?
❑
Why do we need automatic control?
▪
Convenient (room temperature, laundry machine)
▪
Dangerous places
▪
Where Impossible for human
7
Manual Liquid-level control system
A manual Control Systems for regulating the level of fluid in a tank by adjusting the output value.
The operator views the level of fluid through a port in the side of the tank.
8
Automatic Liquid-level control system
Manipulated
variable
Desired
Level
Controlled variable
Plant
controller
Pneumatic
Valve
Water Tank
Actual
Level
Reference input
Feedback Signal
Float
Feedback Element
1
Classification of Control Systems
Classification of Control Systems
Control Systems
LTI
t
ar
Automatic
ine
Manual
s(L
em
yst
lS
Man-made
o
ntr
Co
Natural
e
im
Non-linear
linear
linear
m
ste
l sy
Non-linear
Closed-loop
tro
on
tc
an
ari
inv
Open-loop
s)
Time variant
Time invariant
Time variant
Time invariant
Open-loop control systems
Open-loop control systems
• Open-loop control ?
• In the presence of disturbances, an open-loop control system will not perform the desired task.
• Open-loop control can be used, in practice, only if the relationship between the input and output is
known and if there are neither internal nor external disturbances.
10
Open-loop control systems
Disturbance
Plant
input or
reference
input filter
(transducer)
Controller
Control Signal
Actuator
Process
output or
controlled
variable
15
CD player speed control: Open-Loop
20
Open-loop control systems
Advantages:
❑
Simple construction, ease of maintenance, and less expensive.
❑
There is no stability concern.
❑
Convenient when output is hard to measure or measuring the output precisely
is economically not feasible.
17
Open-loop control systems
Disadvantages:
▪ Disturbances and changes in calibration cause errors,and the output may be
different from what is desired.
▪ Recalibration is necessary from time to time.
Open-loop control systems
Applications:
▪ Washing machines
▪ Light switches
▪ Gas ovens
Closed-loop control systems
Closed-loop control systems
• Closed-loop control ?
• In a closed-loop control system the actuating error signal, which is the difference between the
input signal and the feedback signal , is fed to the controller so as to reduce the error and bring
the output of the system to a desired value.
21
Closed-loop (feedback) control
error or
actuating signal
Disturbance
input or
reference input filter
(transducer)
summing junction
or comparator
+
+
Plant
Controller
Control
Signal
Actuator
Process
output or
controlled
variable
_
sensor or
output transducer
sensor noise
14
CD player speed control: Closed-Loop
23
Closed-loop control systems
Advantages:
❑
High accuracy
❑
Not sensitive to disturbance
❑
Controllable transient response
❑
Controllable steady state error
24
Closed-loop control systems
Disadvantages:
▪ More Complex, and More Expensive.
▪ Possibility of instability.
▪ Need for output measurement.
▪ Recalibration is necessary from time to time.
Closed-loop control systems
Applications:
• Refrigerator
• Iron box
Terms used in
Control systems
Definitions
Systems - A system is a combination of components that act together and perform a certain
objective.
Control System – An interconnection of components forming a system configuration that will
provide a desired response.
Input
Output
Process
28
Definitions
Plants – A plant may be a piece of equipment, perhaps just a set of machine parts functioning
together, the purpose of which is to perform a particular operation.
Process – The device, plant, or system under control. The input and output relationship represents
the cause-and-effect relationship of the process.
Input
Process
Output
29
Definitions
Disturbances - A disturbance is a signal that tends to adversely affect the value of the output
of a system. It can be internal or external
Controlled Variable – is the quantity or condition that is measured and controlled.
Manipulated Variable – is the quantity or condition that is varied by the controller so as to
affect the value of the controlled variable.
30
Definitions
Control - means applying the manipulated variable to the system to correct or limit deviation of
the measured value from a desired value.
Feedback Control - In the presence of disturbances, tends to reduce the difference between
the output of a system and some reference input
31
CONTROL SYSTEM DESIGN
32
Control system design process
Control Systems
34
Transfer Function
Signal Flow Graphs
Introduction
• Signal-flow graphs are an alternative to block diagrams.
• Signal flow graphs ?
Introduction
Unlike block diagrams, which consist of blocks, signals, summing junctions, and pickoff
points
signal-flow graph consists only of branches, which represent systems, and nodes, which
represent signals.
Fundamentals of Signal Flow Graphs
• Signal flow graph:
Xi = AijXj
Node: Variable representation
Branch: Every transmission function and unidirectional
Fundamentals of Signal Flow Graphs
• The arrow in the branch denotes the direction of the signal flow.
• The transmission function Aij is represented by a line with an arrow called a Branch.
Signal Flow Graph of Ohm’s Law:
• The Ohm’s law state that E = RI, where
E is a voltage,
I is a current, and
R is a resistance.
• The signal flow graph of the equation is given below;
Construct the signal flow graph using
algebraic equations
Signal Flow Graph Algebra
1. The Addition Rule:
The value of the variable designated by a node is equal to the sum of all signals entering the node.
2. The Transmission Rule:
The value of the variable designed by a node is transmitted on every branch leaving that node.
Example: The signal flow graph of the simultaneous equation
Y = 3X and, Z = -4X,
3. The Multiplication Rule:
A cascaded or series connection of n-1 branches with transmission functions,
can be replace by a single branch with a new transmission function equal to the product of the old ones.
Example:
The signal flow graph of the simultaneous equations
Y = 10X, Z = -20Y
Construct the signal flow graph for the following set of
simultaneous equations
Signal flow graph from the given equations
Four variables (x1,x2,x3,and x4) : four nodes
• Arrange these four nodes from left to right and connect them with the associated branches.
• Another way to arrange this graph is ------------🡪
Terminologies used in signal
flow graphs
Terminologies
• An input node or source contain only the outgoing branches. i.e., X1
• An output node or sink contain only the incoming branches. i.e., X4
Terminologies
• A path is a continuous, unidirectional succession of branches along which no node is passed more than
ones. i.e., X1 to X2 to X3 to X4, X2 to X3 back to X2, X1 to X2 to X4, are paths.
Terminologies
A forward path is a path from the input node to the output node. i.e.,
X1 to X2 to X3 to X4, and X1 to X2 to X4, are forward paths.
Terminologies
• A feedback path or feedback loop is a path which originates and terminates on the same node. i.e.; X2
to X3 and back to X2 is a feedback path.
• A self-loop is a feedback loop consisting of a single branch. i.e.; A33 is a self loop.
Terminologies
• The gain of a branch is the transmission function of that branch when the transmission function is a
multiplicative operator. i.e., A33
• The path gain A21 A32 A43 for the path X1 to X2 to X3 to X4
Terminologies
• The loop gain A32 A23 for the loop : X2 to X3 and back to X2 is
Converting Block Diagram into a
Signal Flow Graph
Block Diagram into a Signal Flow Graph
• Draw the signal nodes for the system.
• Interconnect the signal nodes with system branches.
Block Diagram into a Signal Flow Graph
• The signal nodes for the system are shown in figure (a).
• The interconnection of the nodes with branches that represent the subsystem is
shown in figure (b).
If summing point is placed before take off point in direction of signal flow then both can be
represented by single node
Block Diagram to Signal-Flow Graph
H1
R(s)
E(s)
X1
G1
－
－
－
G2
X2
G3
X3
G4
H2
H3
－H1
R(s)
1
E(s)
G1
X1
G2
－H2
－H3
X2
G3 X3 G4
C(s)
C(s)
Block Diagram to Signal-Flow Graph
• If desired, simplify the signal-flow graph to the one shown in Figure (c) by eliminating signals that have a
single flow in and a single flow out, such as V2(s), V6(s), V7(s), and V8(s).
Convert Parallel System Block Diagram into
Signal Flow Graph
Parallel System Block Diagram into a
Signal Flow Graph
Parallel System Block Diagram into a
Signal Flow Graph
• Draw the signal nodes for the system.
• Interconnect the signal nodes with system branches.
• The signal nodes for the system are shown in figure (c).
• The interconnection of the nodes with branches that represent the subsystem is shown
in figure (d).
Feedback System Block Diagram into a
Signal Flow Graph
Feedback System into a Signal Flow Graph
Feedback System into a Signal Flow Graph
• Draw the signal nodes for the system.
• Interconnect the signal nodes with system branches.
Feedback System into a Signal Flow Graph
• The signal nodes for the system are shown in figure (e).
• The interconnection of the nodes with branches that represent the subsystem is
shown in figure (f).
Calculate the different parameters for given
Signal Flow Graph
Example1: Signal flow graph and identify the following
a) Input node.
b) Output node.
c) Forward paths.
d) Feedback paths.
e) Self loop.
f) Determine the loop gains of the feedback loops.
g) Determine the path gains of the forward paths.
Input and output Nodes
a) Input node
b) Output node
(c) Forward Paths
(d) Feedback Paths or Loops
(d) Feedback Paths or Loops
(d) Feedback Paths or Loops
(d) Feedback Paths or Loops
(e) Self Loop(s)
(f) Loop Gains of the Feedback Loops
(g) Path Gains of the Forward Paths
Block Diagram to Signal-Flow Graph Models
H1
R(s)
E(s)
X1
G1
－
－
－
G2
X2
G3
X3
G4
H2
H3
－H1
R(s)
1
E(s)
G1
X1
G2
－H2
－H3
X2
G3 X3 G4
C(s)
C(s)
Block Diagram to Signal-Flow Graph
－H1
R(s)
1
E(s)
G1
X1
G2
－H2
－H3
X2
G3
G4
X3
1
C(s)
Example2:Signal flow graph and identify the following
a) Determine the path gains of the forward paths.
b) Determine the loop gains of the feedback loops.
c) Non-touching loops gains
Consider the signal flow graph below and identify the following
There are two forward path gains
Consider the signal flow graph below and identify the following
• There are four loops
Consider the signal flow graph below and identify the following
• Nontouching loop gains;
Summary
• There are four loop gains
• Nontouching loop gains;
• There are two forward path gains;
• Non-touching loops;
Block diagram reduction techniques
Block diagram reduction techniques
1. Combining blocks in cascade
X
Y
2. Combining blocks in parallel
X
G1X
G2X
Y=G1G2X
Block diagram reduction techniques
X1
X1
X2
X2
A
Y=G(X1+X2)
B
B
A
Block diagram reduction techniques
4. Moving a summing point ahead of a block
5. Moving a pickoff point behind a block
Block diagram reduction techniques
6. Moving a pickoff point ahead of a block
7. Swap with two neighboring summing points
Block diagram reduction techniques
8. Eliminating a feedback loop
Block Diagram Transformation Theorems
Block Diagram Transformation Theorems
The letter P is used to represent any transfer function, and W, X , Y, Z denote any transformed signals.
Block Diagram Transformation Theorems
Block Diagram Transformation Theorems
Reduction of Complicated Block Diagrams
Block Diagram reduction
Example1: Reduce the Block Diagram to Canonical Form.
Reduce the Block Diagram to Canonical Form.
However in this example step-4 does not apply.
However in this example step-6 does not apply.
Example2: Simplify the Block Diagram.
1
2
3
X
1
3
2
Simplify the Block Diagram.
Mason’s gain Rule
Mason’s Rule
• Use of Mason’s rule ?
• The block diagram reduction technique requires successive application of
fundamental relationships in order to arrive at the system transfer function.
Mason’s Rule:
• The transfer function, C(s)/R(s), of a system represented by a signal-flow
graph is
Where n = number of forward paths.
Pi = the i th forward-path gain
∆i = Determinant of the ith forward path
∆ is called the signal flow graph determinant or
characteristic function.
Since ∆=0 is the system characteristic equation.
Mason’s Rule:
∆ =
1 - ∑ loop gains + ∑ gain products of two non touching loops - ∑ gain products
of three non touching loops + . . .
∆i = value of Δ for the part of the block diagram that does not touch the i-th forward path
(Δi = 1 if there are no non-touching loops to the i-th path.)
Systematic approach
1.
Calculate forward path gain Pi for each forward path i.
2.
Calculate all loop transfer functions
3.
Consider non-touching loops 2 at a time
4.
Consider non-touching loops 3 at a time etc
5.
Calculate Δ from steps 2,3,4 and 5
6.
Calculate Δi as portion of Δ not touching forward path i
Calculate the transfer function using
Mason gain formulae
Apply Mason’s Rule to calculate the transfer function for given Signal Flow Graph
Therefore,
Continued..
There are three feedback loops
Continued..
There are no non-touching loops, therefore
∆ = 1- (sum of all individual loop gains)
Continued..
Eliminate forward path-1
∆1 = 1- (sum of all individual loop gains)+...
∆1 = 1
Eliminate forward path-2
∆2 = 1- (sum of all individual loop gains)+...
∆2 = 1
Continued..
Finally transfer of signal flow graph is
Draw the signal flow graph of the block diagram and
Find the control ratio C/R.
Example1: Draw signal flow graph for the block diagram and find the control ratio C/R.
Continued..
Signal flow graph for above diagram
Continued..
The characteristic function
Since the loop touch the forward path
Continued..
Finally transfer function is
Example2: Determine the control ratio C/R and the canonical block diagram of the feedback
control system.
Continued..
Continued..
Continued..
Exmple3:Find the transfer function C/R for the system in
Where k is constant.
Signal flow graph
Signal flow graph
• The only forward path gain is
• The two feedback loop gains are
Signal flow graph
• There are no non-touching loops, hence
• Both feedback loops touches the forward path, hence
Control ratio T is
Electrical Components:
Servo motor: As the name recommends, a servomotor is a
servomechanism.
•It is a servomechanism that uses position input to control its movement
and last position.
•The data to its control is some signal, either simple or advanced,
speaking to the position directed for the output shaft.
• The Motor is matched with some sort of encoder to give position and
speed input. In the least difficult case, just the position is measured.
•. As the positions approach, the mistake signal lessens to zero and the
Motor stops.
• The exceptionally most straightforward servomotors use position-just
detecting by means of a potentiometer and blast control of their Motor.
•Applications: Robotics, Conveyor belts, solar tracking system, camera
auto focus etc..
Types:
1.AC Servo motor
2.DC Servo motor
Stator of Servomotor
Stepper Motor:
•A stepper motor is an electromechanical device it converts electrical power into
mechanical power.
• Also it is a brushless, synchronous electric motor that can divide a full rotation
into an expansive number of steps.
•The motor’s position can be controlled accurately without any feedback
mechanism, as long as the motor is carefully sized to the application.
•Stepper motors are similar to switched reluctance motors.
•The stepper motor uses the theory of operation for magnets to make the motor
shaft turn a precise distance when a pulse of electricity is provided.
•The stator has eight poles, and the rotor has six poles. The rotor will require 24
pulses of electricity to move the 24 steps to make one complete revolution.
• Another way to say this is that the rotor will move precisely 15° for each pulse of
electricity that the motor receives.
Stepper Motor
Types of Stepper Motor:
•Permanent magnet stepper
•Hybrid synchronous stepper
•Variable reluctance stepper
•Permanent Magnet Stepper Motor: Permanent magnet motors use a permanent magnet
(PM) in the rotor and operate on the attraction or repulsion between the rotor PM and the stator
electromagnets.
•Variable Reluctance Stepper Motor: Variable reluctance (VR) motors have a plain iron rotor
and operate based on the principle that minimum reluctance occurs with minimum gap, hence
the rotor points are attracted toward the stator magnet poles.
•Hybrid Synchronous Stepper Motor: Hybrid stepper motors are named because they use a
combination of permanent magnet (PM) and variable reluctance (VR) techniques to achieve
maximum power in a small package size.
Advantages of Stepper Motor:
•The rotation angle of the motor is proportional to the input pulse.
•The motor has full torque at standstill.
•Precise positioning and repeatability of movement since good stepper motors
have an accuracy of 3 – 5% of a step and this error is non cumulative from
one step to the next.
•Excellent response to starting, stopping and reversing.
•Very reliable since there are no contact brushes in the motor. Therefore the
life of the motor is simply dependant on the life of the bearing.
Applications:
Industrial Machines
Security
Medical
Consumer Electronics
Stepper motor circuit
Operation of Stepper Motor:
•Stepper motors rotate when voltage is applied to their terminals. Stepper motors, on the other hand,
effectively have multiple toothed electromagnets arranged around a central gear-shaped piece of iron. The
electromagnets are energized by an external control circuit, for example a microcontroller.
•To make the motor shaft turn, first one electromagnet is given power, which makes the gear’s teeth
magnetically attracted to the electromagnet’s teeth.
•The point when the gear’s teeth are thus aligned to the first electromagnet, they are slightly offset from the
next electromagnet.
•So when the next electromagnet is turned ON and the first is turned OFF, the gear rotates slightly to align
with the next one and from there the process is repeated.
•Each of those slight rotations is called a step, with an integer number of steps making a full rotation. In that
way, the motor can be turned by a precise.
• Stepper motor doesn’t rotate continuously, they rotate in steps. There are 4 coils with 90 o angle between
each other fixed on the stator.
•The stepper motor connections are determined by the way the coils are interconnected.In stepper motor, the
coils are not connected together.
•The motor has 90o rotation step with the coils being energized in a cyclic order, determining the shaft
rotation direction.
Tachogenerators:
•An electromechanical generator is a device capable of producing electrical
power from mechanical energy, usually the turning of a shaft.
•When not connected to a load resistance, generators will generate voltage
roughly proportional to shaft speed.
• With precise construction and design, generators can be built to produce
very precise voltages for certain ranges of shaft speeds, thus making them
well-suited as measurement devices for shaft speed in mechanical
equipment.
•By measuring the voltage produced by a tachogenerator, you can easily
determine the rotational speed of whatever its mechanically attached to.
•Tachogenerators can be purchased with different “full-scale” (10 volts) speeds for
different applications.
•Tachogenerators can also indicate the direction of rotation by the polarity of the
output voltage.
•When a permanent magnet style DC generator’s rotational direction is reversed,
the polarity of its output voltage will switch.
•In measurement and control systems where the directional indication is needed,
tachogenerators provide an easy way to determine that.
•Tachogenerators are frequently used to measure the speeds of electric motors,
engines, and the equipment they power: conveyor belts, machine tools, mixers,
fans, etc.
•Types:
1.AC tachogenerator
2.DC tachogenerator
Synchros:
The Synchro is a type of transducer which transforms the angular position of the shaft into an electric signal. It
is used as an error detector and as a rotary position sensor. The error occurs in the system because of the
misalignment of the shaft.
Synchros System Types
The synchro system is of two types. They are
1.Control Type Synchro.
2.Torque Transmission Type Synchro.
3.Torque Transmission Type Synchros
This type of synchros has small output torque, and hence they are used for running the very light load like a
pointer. The control type Synchro is used for driving the large loads.
2. Control Type Synchros System
The controls synchros is used for error detection in positional control systems. Their systems consist two
units. They are
• Synchro Transmitter
• Synchro receiver
Synchros Transmitter – Their construction is similar to the three phase alternator. The stator of the
synchros is made of steel for reducing the iron losses. The stator is slotted for housing the three phase
windings. The axis of the stator winding is kept 120º apart from each other.
Magnetic Amplifier:
•Magnetic Amplifier is a amplifying device with high gain which is used to control the output voltage of DC
power supplies. These amplifiers are used instead of electron tube/vacuum tube because the magnetic
amplifiers don’t have any moving parts or any other parts subject to deterioration.
•Basic Magnetic Amplifier Circuit: A magnetic amplifier is a saturable reactor whose output has been rectified
so that a small dc input controls a large dc output. Fig. 2 shows the simplified magnetic amplifier circuit.
Basic Magnetic Amplifier Circuit
The magnetic amplifier has control, bias and load windings which operate in the following manner:
a)The core is driven to saturation by applying pulsating dc through the load windings
b)A bias current is introduced to desaturate the core to an operating point on the knee of the saturation
curve.
c)The control current varies the core saturation about the operating point established by the bias current.
Cascaded Operation of Magnetic Amplifier:
•In dc power supplies, two magnetic amplifiers are used for control. The control winding of the first stage
magnetic amplifier senses changes in power supply output.
•The load winding of this magnetic amplifier is the control winding of the second stage magnetic amplifier.
•The gain of the first magnetic amplifier is therefore multiplied by the gain of the second to produce an
overall gain of 106 .
•The load winding of the second stage magnetic amplifier is the control winding of the power reactors
Applications:
1) Magnetic amplifiers were important as modulation and control amplifiers in the early
development of voice transmission by radio.
2) The ability to control large currents with small control power made magnetic amplifiers
useful for control of lighting circuits, for stage lighting and for advertising signs.
3) Magnetic amplifiers were used extensively as the switching element in early switched-mode
(SMPS) power supplies.
4) Magnetic amplifiers are still used in some arc welders
5) Magnetic amplifiers can be used for measuring high DC-voltages without direct connection
to the high voltage and are therefore still used in the HVDC-technique
6) Magnetic amplifiers were used by locomotives to detect wheel slip
7) Magnetic amplifiers are also still used in instrumentation for measuring current
8) Such instrumentation mag. amps. are commonly found on space craft where a clean
electromagnetic environment is highly desirable.
Servo Amplifiers:
• In servo systems (servomotors), a speed or position of the output device
(motor) is controlled by applying a desired input and a measuring output to the
error detector of the system.
•This error signal generated is not strong enough to provide the actuating signal
required by the final control element.
• So, the servo system requires amplifier called servo amplifier.
•Electronic servo amplifiers may be of ac or dc type.
Feature of servo amplifier:
1)Input Impedance
2)Output Impedance
3)Frequency Response
4)Phase Sensitivity
5)Drift
6)Residual Voltage
7)Noise
Applicatons: in all servo systems