Open and closed loop systems

IC 8451&CONTROL SYSTEMS
Department of Electrical and Electronics Engineering
Approved by AICTE | Affiliated to Anna University | Accredited by NAAC | Accredited NBA | Recognized by UGC under 2(f) and 12(B)
Chennai Main Road, Kumbakonam- 612 501.
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Prepared by
Mrs.K.Kalpana.,M.E.,(Ph.D).,
Department of Electrical and Electronics Engineering
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UNIT I SYSTEMS AND REPRESENTATION 9
Basic elements in control systems: – Open and closed loop systems
– Electrical analogy of mechanical and thermal systems – Transfer function
– AC and DC servomotors – Block diagram reduction techniques – Signal
flow graphs.
UNIT II TIME RESPONSE 9
Time response: – Time domain specifications – Types of test input –
I and II order system response – Error coefficients – Generalized error
series – Steady state error – Root locus construction- Effects of P, PI, PID
modes of feedback control –Time response analysis.
UNIT III FREQUENCY RESPONSE 9
Frequency response: – Bode plot – Polar plot – Determination of
closed loop response from open loop response - Correlation between
frequency domain and time domain specifications
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SYLLABUS

UNIT IV STABILITY AND COMPENSATOR DESIGN 9
Characteristics equation – Routh Hurwitz criterion –
Nyquist stability criterion- Performance criteria – Effect of Lag,
lead and lag-lead compensation on frequency response-
Design of Lag, lead and lag lead compensator using bode
plots.
UNIT V STATE VARIABLE ANALYSIS 9
Concept of state variables – State models for linear and
time invariant Systems – Solution of state and output
equation in controllable canonical form – Concepts of
controllability and observability.
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1. Nagarath, I.J. and Gopal, M., “Control Systems Engineering”, New Age International
Publishers, 2017.
2. Benjamin C. Kuo, “Automatic Control Systems”, Wiley, 2014.
1. Katsuhiko Ogata, “Modern Control Engineering”, Pearson, 2015.
2. Richard C.Dorf and Bishop, R.H., “Modern Control Systems”, Pearson Education,2009.
3. John J.D., Azzo Constantine, H. and Houpis Sttuart, N Sheldon, “Linear ControlSystem
Analysis and Design with MATLAB”, CRC Taylor& Francis Reprint 2009.
4. Rames C.Panda and T. Thyagarajan, “An Introduction to Process Modelling
Identification and Control of Engineers”, Narosa Publishing House, 2017.
5. M.Gopal, “Control System: Principle and design”, McGraw Hill Education, 2012.
6. NPTEL Video Lecture Notes on “Control Engineering “by Prof. S. D. Agashe, IIT
Bombay.
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TEXT BOOKS
REFERENCES

Basic elements in control systems: – Open and closed loop
systems – Electrical analogy of mechanical and thermal
systems– Transfer function – AC and DC servomotors –
Block diagram reduction techniques – Signal flow graphs.
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UNIT I SYSTEMS AND REPRESENTATION
SYLLABUS

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system
• system is a combination of number of
equipments or components connected in a
sequence to perform a specific function.
control system
• In a system, when the output quantity is
controlled by varying the input quantity then
the system is called as a control system.

 OPEN LOOP SYSTEM
Any physical system which does not automatically correct
the variation in its output, is called an open loop system, or
control system in which the output quantity has no effect upon
the input quantity are called open-loop control system. This
means that the output is not fed back to the input for
correction.
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 CLOSED LOOP SYSTEM
Control systems in which the output has an effect upon the
input quantity in order to maintain the desired output value
are called closed loop systems.
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 Practical Examples of Open Loop Control System
 Electric Hand Drier – Hot air (output) comes out as long as you
keep your hand under the machine, irrespective of how much your
hand is dried.
 Automatic Washing Machine – This machine runs according to the
pre-set time irrespective of washing is completed or not.
 Bread Toaster – This machine runs as per adjusted time irrespective
of toasting is completed or not.
 Automatic Tea/Coffee Maker – These machines also function for
pre adjusted time only.
 Timer Based Clothes Drier – This machine dries wet clothes for
pre-adjusted time, it does not matter how much the clothes are dried.
 Light Switch – Lamps glow whenever light switch is on irrespective
of light is required or not.
 Volume on Stereo System – Volume is adjusted manually
irrespective of output volume level.
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 Practical Examples of Closed Loop Control System
 Automatic Electric Iron – Heating elements are controlled by output
temperature of the iron.
 Servo Voltage Stabilizer – Voltage controller operates depending
upon output voltage of the system.
 Water Level Controller – Input water is controlled by water level
of the reservoir.
 Missile Launched and Auto Tracked by Radar – The direction of
missile is controlled by comparing the target and position of the
missile.
 An Air Conditioner – An air conditioner functions depending upon
the temperature of the room.
 Cooling System in Car – It operates depending upon the
temperature which it controls.
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 Advantages of Open Loop Control System
 Simple in construction and design.
 Economical.
 Easy to maintain.
 Generally stable.
 Disadvantages of Open Loop Control System
 They are inaccurate.
 They are unreliable.
 Any change in output cannot be corrected automatically.
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 Advantages of Closed Loop Control System
 Accurate.
 Less affected by noise.
 The sensitivity of system may be made small to make system more stable.
 Disadvantages of Closed Loop Control System
 They are costlier.
 They are complicated to design.
 Required more maintenance.
 Feedback leads to oscillatory response.
 Overall gain is reduced due to presence of feedback.
 Stability is the major problem and more care is needed to design a
stable closed loop system.
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The differences between the open loop and the
closed loop control systems are mentioned in the
following table.
OPEN LOOP CONTROL SYSTEMS CLOSED LOOP CONTROL SYSTEMS
The feedback element is absent. The feedback element is always present.
An error detector is not present. An error detector is always present.
It is stable one. It may become unstable.
Easy to construct. Complicated construction.
It is an economical. It is costly.
Having small bandwidth. Having large bandwidth.
It is inaccurate. It is accurate.
Less maintenance. More maintenance.
It is unreliable. It is reliable.

 EXAMPLES OF CONTROL SYSTEMS
 TEMPERATURE CONTROL SYSTEM
 OPEN LOOP SYSTEM
 The electric furnace shown in figure is an open loop system.
 The output in the system is the desired temperature.
 The temperature of the system is raised by heat generated by the heating element.
 The output temperature depends on the time during which the supply to heater
remains ON.
 The ON and OFF of the supply is governed by the time setting of the relay.
 The temperature is measured by a sensor, which gives an analog voltage
corresponding to the temperature of the furnace.
 The analog signal is converted to digital signal by an Analog to Digital converter
(AD converter).
 The digital signal is given to the digital display device to display the temperature.
 In this system if there is any change in output temperature then the time setting of
the relay is not altered automatically.
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 CLOSED LOOP SYSTEM
 The electric furnace shown in figure is a closed loop system.
 The output of the system is the desired temperature and it depends on the time
during which the supply to heater remains ON.
 The switching ON and OFF of the relay is controlled by a controller which is a
digital system or computer.
 The desired temperature is input to the system through keyboard or as a signal
corresponding to desired temperature via ports.
 The actual temperature is sensed by sensor and converted to digital signal by the
A/D converter.
 The computer reads the actual temperature and compares with desired temperature.
 If it finds any difference then it sends signal to switch ON or OFF the relay through
D/A converter and amplifier.
 Thus the system automatically corrects any changes in output.
 Hence it is a closed loop system.

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 MATHEMATICAL MODELS OF CONTROL SYSTEMS
 A control system is a collection of physical objects (components)
connected together to serve an objective.
 The input output relations of various physical components of a system are
governed by differential equations.
 The mathematical model of a control system constitutes a set of differential
equations.
 The response or output of the system can be studied by solving the
differential equations for various input conditions.
 The mathematical model of a system is linear if it obeys the principle of
superposition and homogeneity.
 This principle implies that if a system model has responses c1(t) and c2 (t)
to any inputs r1 (t) and r2 (t) respectively, then the system response to the
linear combination of these inputs a1r1 (t) + a2 r2 (t) is given by linear
combination of the individual outputs a1 c1(t)+a2 c2(t), where a1 and a2 are
constants.
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 Types of Feedback
There are two types of feedback
 Positive feedback
 Negative feedback
 Positive Feedback
The positive feedback adds the reference input, R(s) and
feedback output C(S).
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For the time being, consider the transfer function of positive
feedback control system is,
Where,
T is the transfer function or overall gain of positive feedback
control system.
G is the open loop gain, which is function of frequency.
H is the gain of feedback path, which is function of frequency.
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 Negative Feedback
Negative feedback reduces the error between the reference input,
R(s) and system output C(S).
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Transfer function of negative feedback control system is,
Where,
T is the transfer function or overall gain of negative feedback
control system.
G is the open loop gain, which is function of frequency.
H is the gain of feedback path, which is function of frequency.
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 Characteristics of negative feedback
 Accuracy in tracking steady state value
 Rejection of disturbance signals
 Low sensitivity to parameter variations
 Reduction in gain
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Open and closed loop systems