1. CONTROL SYSTEMS unit1

2. Introduction
System – An interconnection of elements and devices for a desired purpose.
Control System – An interconnection of components forming a system configuration that will provide a desired response.
Process – The device, plant, or system under control. The input and output relationship represents the cause-and-effect relationship of the process.
Plant
Input
Output
Block diagram of control system

3. Basic Types of Control SystemsPP
Controller
Plant
Open-Loop Control Systems
Any physical system which does not automatically correct the variation in its output.(no feed back)
Input
Output
Closed-Loop Control Systems
The system in which the output has an effect upon the input quantity
It utilizes feedback to compare the actual output to the desired output response.

4. Advantages & Dis advantages of open loop control Systems
Simple in construction and design.
Economical.
Easy to maintain.
Generally stable.
Convenient to use as output is difficult to measure.
Disadvantages
They are inaccurate.
They are unreliable.
Any change in output cannot be corrected automatically.

5. Advantages & Dis advantages of Closed loop control Systems
Closed loop control systems are more accurate even in the presence of non-linearity.
Highly accurate as any error arising is corrected due to presence of feedback signal.
Bandwidth range is large.
Facilitates automation.
The sensitivity of system may be made small to make system more stable.
This system is less affected by noise.
Disadvantages
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.

6. Differences b/w Open loop & Closed loop
No.
OPEN LOOP CONTROL SYSTEM
CLOSED LOOP CONTROL SYSTEM 1
The feedback element is absent.
The feedback element is always present. 2
An error detector is not present.
An error detector is always present. 3
It is stable one.
It may become unstable. 4
Easy to construct.
Complicated construction. 5
It is an economical.
It is costly. 6
Having small bandwidth.
Having large bandwidth. 7
It is inaccurate.
It is accurate. 8
Less maintenance.
More maintenance. 9
It is unreliable.
It is reliable. 10
Examples: Hand drier, tea maker
Examples: Servo voltage stabilizer, perspiration

7. 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.

8. 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 & 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.

9. Classification of control systems
Natural Control Systems
Manmade Control Systems
Combinational Control Systems
Time variant & Invariant
Linear & Nonlinear
Continuous & Discrete time
Deterministic & stochastic
Lumped & Distributed
SISO & MIMO
Open loop & Closed loop

10. Feed-Back & its characteristics
Feedback is a property of the system by which it permits the output to be compared with the reference input to generate the error signal based on which the appropriate controlling action can be decided.
Characteristics
Reduced steady state error
Reduced sensitivity to parameters variation ( Enhance robustness)
Improved rejection of disturbances
Improve dynamic performance or adjust the transient response

11. Sensitivity of system to parameter variations
System are time-varying in its nature because of inevitable uncertainties such as changing environment , aging , and other factors that affect a control process.
All these uncertainties in open-loop system will result in inaccurate output or low performance. However, a closed-loop system can overcome this disadvantage.

12. Effect of parameter variations
If process is change as
Open-loop system
Closed-loop system

13. Contd…
In the limit, for small incremental changes, last formula is

14. Sensitivity comparison
Open-loop system
Closed-loop system

15. Sensitivity to parameters
If system TF is
System sensitivity to is

16. Disturbance in a feedback control system
Disturbance signal is an unwanted extraneous input signal that affects the system’s output signal, such as noise for amplifier, wind gusts for radar antennas, etc.
Feedback control can completely or partially eliminate the effect of disturbance signal.

17. Steady-state error
Steady-state error is the error after the transient response has decayed, leaving only the continuous response.
Feedback can reduce the steady-state error of control system

18. Only for unit feedback H(s)=1,We have E a (s)= E (s)
How to define the error
From input point:
From output point:
E a (s)=R(s)-H(s)Y(s)
E (s)=R(s)-Y(s)
Only for unit feedback H(s)=1,We have
E a (s)= E (s)

19. Comparison of error
Open-loop system
Closed-loop system

20. Contd… Open-loop system under unit step input
Closed-loop system under unit step input

21. Mathematical Modelling Of Control Systems

22. Differential Equations & Transfer Function
The mathematical modelling of a control system constitutes a set of differential equations
The input output relations of various physical components of a system are governed by differential equations.
The mathematical model of a system is linear if it obeys the principle of superposition & homogeneity.
T.F is defined as the ratio of Laplace transform of output to the Laplace transform of input with zero initial conditions.

23. Mechanical Systems

24. Basic Types of Mechanical Systems
Translational
Linear Motion
Rotational
Rotational Motion

25. Basic Elements of Translational Mechanical Systems
Translational Spring i)
Translational Mass
ii) MM M
Translational Damper
iii)

26. Translational Spring
A translational spring is a mechanical element that can be deformed by an external force such that the deformation is directly proportional to the force applied to it.
Translational Spring i)
Resistor
Circuit Symbols
Translational Spring

27. Translational Spring If F is the applied force
Then is the deformation if
Or is the deformation.
The equation of motion is given as
Where is stiffness of spring expressed in N/m

28. Translational Mass Translational Mass is an inertia element.
A mechanical system without mass does not exist.
If a force F is applied to a mass and it is displaced to x meters then the relation b/w force and displacements is given by Newton’s law. M

29. Translational Dashpot
When the viscosity or drag is not negligible in a system, we often model them with the damping force.
All the materials exhibit the property of damping to some extent.
If damping in the system is not enough then extra elements (e.g. Dashpot) are added to increase damping.
Translational Dashpot

30. Common Uses of Dashpots
Door Stoppers
Vehicle Suspension
Bridge Suspension
Flyover Suspension

31. Guidelines to determine the T.F
Identify the nodes in the system
Draw the Free body diagrams
Write the torque balancing equations using Newton’s second law
Write the differential equations
Apply Laplace transform with zero initial conditions
Rearrange D.E to obtain T.F

32. Example-1 M Consider the following system
Free Body Diagram of Mass Element M

33. Example-2
Find the transfer function of the mechanical translational system given in Figure-1.
Free Body Diagram M
Figure-1

34. Example-3
Find the transfer function X2(s)/F(s) of the following system.
Free Body Diagram M2 M1

35. Mechanical Rotational Systems

36. Basic Elements of Rotational Mechanical Systems
Rotational Spring

37. Basic Elements of Rotational Mechanical Systems
Rotational Dashpot

38. Basic Elements of Rotational Mechanical Systems
Moment of Inertia

39. Guidelines to determine the T.F
Identify the nodes in the system
Draw the Free body diagrams
Write the torque balancing equations using Newton’s second law
Write the differential equations
Apply Laplace transform with zero initial conditions
Rearrange D.E to obtain T.F

40. Practice-1

41. Practice-2

42. Practice-3 ↑ J1 J2

43. Practice - 4 ↑ J1 J2