• Author / Uploaded
• Sheikameer Batcha

Citation preview

EC 2255 CONTROL SYSTEMS 3003 AIM To familiarize the students with concepts related to the operation analysis and stabilization of control systems OBJECTIVES  To understand the open loop and closed loop (feedback ) systems  To understand time domain and frequency domain analysis of control systems required for stability analysis.  To understand the compensation technique that can be used to stabilize control systems 1. CONTROL SYSTEM MODELING 9 Basic Elements of Control System – Open loop and Closed loop systems - Differential equation - Transfer function, Modeling of Electric systems, Translational and rotational mechanical systems - Block diagram reduction Techniques - Signal flow graph 2. TIME RESPONSE ANALYSIS 9 Time response analysis - First Order Systems - Impulse and Step Response analysis of second order systems - Steady state errors – P, PI, PD and PID Compensation, Analysis using MATLAB 3. FREQUENCY RESPONSE ANALYSIS 9 Frequency Response - Bode Plot, Polar Plot, Nyquist Plot - Frequency Domain specifications from the plots - Constant M and N Circles - Nichol’s Chart - Use of Nichol’s Chart in Control System Analysis. Series, Parallel, series-parallel Compensators - Lead, Lag, and Lead Lag Compensators, Analysis using MATLAB. 4. STABILITY ANALYSIS 9 Stability, Routh-Hurwitz Criterion, Root Locus Technique, Construction of Root Locus, Stability, Dominant Poles, Application of Root Locus Diagram - Nyquist Stability Criterion - Relative Stability, Analysis using MATLAB 5. STATE VARIABLE ANALYSIS & DIGITAL CONTROL SYSTEMS 9 State space representation of Continuous Time systems – State equations – Transfer function from State Variable Representation – Solutions of the state equations Concepts of Controllability and Observability – State space representation for Discrete time systems. Sampled Data control systems – Sampling Theorem – Sample & Hold – Open loop & Closed loop sampled data systems. TOTAL : 45 PERIODS TEXTBOOK: 1. J.Nagrath and M.Gopal,” Control System Engineering”, New Age International Publishers, 5th Edition, 2007. 2. M.Gopal, “Control System – Principles and Design”, Tata McGraw Hill, 2nd Edition, 2002. REFERENCES: 1. Benjamin.C.Kuo, “Automatic control systems”, Prentice Hall of India, 7th Edition,1995. 2. M.Gopal, Digital Control and State Variable Methods, 2nd Edition, TMH, 2007. 3. Schaum’s Outline Series,’Feedback and Control Systems’ Tata McGrawHill, 2007. 4. John J.D’azzo & Constantine H.Houpis, ’Linear control system analysis and design’, Tata McGrow-Hill, Inc., 1995. 5. Richard C. Dorf & Robert H. Bishop, “ Modern Control Systems”, Addidon –

Control system modelling

Control system1

Wesley, 1999. 1

Control system2

1. What is control system? A system consists of a number of components connected together to perform a specific function . In a system when the output quantity is controlled by varying the input quantity then the system is called control

2. What are the two major types of control system? the two major types of control system are open loop and closed loop

3. Define open loop control system. The 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 feedback to the input for correction.

4. Define closed loop control system.

Control system modelling

system.

The control system in which the output has an effect upon the input quantity so as to maintain the desired output value are called closed loop control system.

5. What are the components of feedback control system? the components of feedback control system are plant , feedback path elements, error detector and controller.

6. Define transfer function. The T.F of a system is defined as the ratio of the laplace transform of output to laplace transform of input with zero initial conditions.

7. What are the basic elements used for modeling mechanical translational system. Mass M, spring K and dashpot or damper B

8. What are the basic elements used for modeling mechanical rotational system? 2

Control system3

Moment of inertia J,dashpot or damper B and spring K

9. Name two types of electrical analogous for mechanical system. The two types of analogies for the mechanical system are Force voltage and force current analogy

A block diagram of a system is a pictorial representation of the functions performed by each component of the system and shows the flow of signals.The basic elements of block diagram arew block, branch point and summing point.

11. What is the basis for framing the rules of block diagram reduction technique? The rules for block diagram reduction technique are framed such that any

Control system modelling

10. What is block diagram?

modification made on the diagram does not alter the input output relation.

12. What is a signal flow graph? A signal flow graph is a diagram that represents a set of simultaneous algebraic equations .By taking L.T the time domain differential equations governing a control system can be transferred to a set of algebraic equations in s-domain.

13. What is transmittance? The transmittance is the gain acquired by the signal when it travels from one node to another node in signal flow graph.

14. What is sink and source? Source is the input node in the signal fow graph and it has only outgoing branches. Sink is a output node in the signal flow graph and it has only incoming branches.

15. Define nontouching loop.

3

Control system4

16. Distinguish between open loop and closed loop system Open loop

Closed loop

1.Innaccurate

Accurate

2.Simple and economical

Complex and costlier

3.The changes in output due to

The changes in output due to

external disturbance are not corrected automatically

external disturbances are corrected

4.They are generally stable

Great efforts are needed to design a

Control system modelling

The loops are said to be non touching if they do not have common nodes.

stable system

17. Why is negative feedback invariably preferred in closed loop system? The negative feedback results in better stability in steady state and rejects any disturbance signals.

4

Control system5

1. 2. 3. 4. 5. 6. 7. 8.

What is system and control system? What are the types of control system and explain it? Write the application for open loop and closed loop control system. Distinguish the open loop and closed loop control systems. What are the components of control system? Define transfer function. What is differential equation? What are the basic elements used for modeling mechanical translational system? 9. Write the force balance equation for a. Ideal mass element b. Ideal Dash-pot c. Ideal spring 10. What are the basic elements used for modeling mechanical rotational system? 11. Write the torque balance equations for a. Ideal rotational mass element b. Ideal rotational Dash-pot c. Ideal rotational spring

Control system modelling

PART – A

12. What are all the two types of electrical analogous of mechanical system? 13. What is Block diagram? 14. What are all the components of Block diagram? 15. What is a signal flow graph? 16. What is transmittance? 17. Define non-touching loops. 18. Write the properties of signal flow graph. 19. Write the mason’s gain formula. 20. Compare the block diagram representation and signal flow graph.

5

Control system6

BASIC ELEMENTS OF MECHANICAL SYSTEM ELEMENT

SYMBOL

FORCE

Damper(B)

Control system modelling

Mass(M)

Spring(K)

6

Control system7

PROBLEMS ON MECHANICAL SYSTEMS

Control system modelling

1. Write the differential equation and find out the transfer function for given mechanical system

Solution: STEP1: Free hand drawing

To find differential equation: By newton’s law,

(1) Take laplace transform for (1)

7

Control system8

Control system modelling

2.Write the differential equation and find out the transfer function for given mechanical system

Soln: STEP1: Free hand drawing from Mass (M1)

To find differential equation: By newton’s law,

(1) Take laplace transform for (1)

(2)

8

Control system9

STEP2: Free hand drawing from Mass (M2)

By newton’s law,

(3)

Control system modelling

To find differential equation:

Take laplace transform for (3)

(4) SUB/: (4) in (2)

9

Control system10

3.Write the differential equation and find out the transfer function for given mechanical system

Control system modelling

Soln: STEP1: Free hand drawing from Mass (M1)

Here applied force =0 To find differential equation: By newton’s law,

(1) Take laplace transform for (1)

(2)

10

Control system11

To find differential equation: By newton’s law,

(3)

Control system modelling

STEP2: Free hand drawing from Mass (M2)

Take laplace transform for (3)

(4) SUB/: (2) in (4)

11

Control system12

4.Write the differential equation and find out the transfer function for given mechanical system

Soln:

To find differential equation: By newton’s law,

Control system modelling

STEP1: Free hand drawing from Mass (M1)

(1) Take laplace transform for (1)

(2)

STEP2: Free hand drawing from Mass (M2)

To find differential equation: By newton’s law, 12

Control system13

(3)

Control system modelling

Take laplace transform for (3)

(4) SUB/: (2) in (4)

BASIC ELEMENTS OF ROTATIONAL SYSTEM

ELEMENT

SYMBOL

FORCE

13

Control system14

Damper(B)

Control system modelling

Inertia(J)

Spring(K)

1)Write the differential equation and find out the transfer function for given rotational system

14

Control system15

Soln:

Control system modelling

STEP1: Free hand drawing from Mass (M1)

To find differential equation: By newton’s law,

(1) Take laplace transform for (1) (2)

STEP2: Free hand drawing from Mass (M2)

15

Control system16

(3)

(4) SUB/: (2) in (4)

Control system modelling

Take laplace transform for (3)

16

Control system17

ELECTRICAL ANALAGOUS OF MECHANICAL SYSTEM Force voltage analogy: Mechanical system

Electrical system

Force ,f(t)

Voltage source V Inductance L

Damper ,B

Resistance, R

Spring ,k

Capacitance ,C

Hints i) if there is one displacement put the elements in series

Control system modelling

Mass,M

ii) if there is Change in displacement put the elements in parallel Force current analogy: Mechanical system

Electrical system

Force ,f(t)

Current source I

Mass,M

Capacitance,C

Damper ,B

Resistance, R

Spring ,k

Inductance L

Hints i) if there is one displacement put the elements in parallel ii) ii) if there is Change in displacement put the elements in series

17

Control system18

ELECTRICAL ANALAGOUS OF ROTATIONAL SYSTEM Torque voltage analogy: Mechanical system

Electrical system

Torque

Voltage source V Inductance L

Damper ,B

Resistance, R

Spring ,k

Capacitance ,C

Hints i) if there is one displacement put the elements in series

Control system modelling

Inertia,J

ii) if there is Change in displacement put the elements in parallel Torque current analogy: Mechanical system

Electrical system

Torque

Current source I

Inertia,J

Capacitance,C

Damper ,B

Resistance, R

Spring ,k

Inductance L

Hint i) if there is one displacement put the elements in parallel ii) if there is Change in displacement put the elements in series

18

Control system19

1. Write the differential equation and Draw force-current and force-voltage analogy

STEP1: Free hand drawing

To find differential equation: By newton’s law,

Control system modelling

Solution:

Force-Voltage Analogy

Force-Current Analogy

2. Write the differential equation and Draw force-current and force-voltage analogy 19

Control system20

Soln:

To find differential equation:

Control system modelling

STEP1: Free hand drawing from Mass (M1)

By newton’s law,

STEP2: Free hand drawing from Mass (M2)

To find differential equation: By newton’s law,

Differential Equation are

20

Control system21

Control system modelling

Force-Voltage Analogy

Force-Current Analogy

R2 L1 C1 I

R1

C2

R2

L2

3.Write the differential equation and Draw force-current and force-voltage analogy

21

Control system22

Soln:

Here applied force =0 To find differential equation: By newton’s law,

Control system modelling

STEP1: Free hand drawing from Mass (M1)

STEP2: Free hand drawing from Mass (M2)

To find differential equation: 22

Control system23

By newton’s law,

Control system modelling

Differential Equation are

Force-Voltage Analogy

Force-Current Analogy

C2 R2

C1

R1

R3

L2 L1

I

23

Control system24

Control system modelling

4. Write the differential equation and Draw force-current and force-voltage analogy

Soln: STEP1: Free hand drawing from Mass (M1)

STEP2: Free hand drawing from Mass (M2) 24

STEP3: Free hand drawing from Mass (M3)

Control system modelling

Control system25

Differential Equation are

Force-Voltage Analogy

25

Force-Current Analogy

Control system modelling

Control system26

26

Control system modelling

Control system27

27

Control system modelling

Control system28

28

Control system modelling

Control system29

29

Control system modelling

Control system30

30

Control system modelling

Control system31

31

Control system modelling

Control system32

32

Control system modelling

Control system33

33

Control system modelling

Control system34

34

Control system modelling

Control system35

35

Control system modelling

Control system36

36

Control system modelling

Control system37

37

Control system modelling

Control system38

38

Control system modelling

Control system39

39

Control system modelling

Control system40

40

Control system modelling

Control system41

41

Control system modelling

Control system42

42

Control system modelling

Control system43

43

Control system modelling

Control system44

44

Control system modelling

Control system45

45

Control system modelling

Control system46

46

Control system modelling

Control system47

47

Control system modelling

Control system48

48

Control system modelling

Control system49

49

Control system modelling

Control system50

50

Control system modelling

Control system51

51

Control system modelling

Control system52

52