control problems on mechanical systems (1999)

7/29/2019 Control Problems on Mechanical Systems (1999)

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1Control system

EC 2255 CONTROL SYSTEMS 3 0 0 3

AIM

To familiarize the students with concepts related to the operation analysis andstabilization of control systems

OBJECTIVESTo understand the open loop and closed loop (feedback ) systemsTo understand time domain and frequency domain analysis of control systemsrequired for stability analysis.To understand the compensation technique that can be used to stabilize controlsystems1. CONTROL SYSTEM MODELING 9

Basic Elements of Control System Open loop and Closed loop systems - Differentialequation - Transfer function, Modeling of Electric systems, Translational and rotationalmechanical systems - Block diagram reduction Techniques - Signal flow graph2. 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, Analysisusing MATLAB3. FREQUENCY RESPONSE ANALYSIS 9

Frequency Response - Bode Plot, Polar Plot, Nyquist Plot - Frequency Domainspecifications from the plots - Constant M and N Circles - Nichols Chart - Use ofNichols 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 MATLAB5. STATE VARIABLE ANALYSIS & DIGITAL CONTROL SYSTEMS 9

State space representation of Continuous Time systems State equations Transferfunction from State Variable Representation Solutions of the state equations -Concepts of Controllability and Observability State space representation for Discretetime 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 InternationalPublishers, 5th Edition, 2007.2. M.Gopal, Control System Principles and Design, Tata McGraw Hill, 2ndEdition, 2002.REFERENCES:

1. Benjamin.C.Kuo, Automatic control systems, Prentice Hall of India, 7 thEdition,1995.2. M.Gopal, Digital Control and State Variable Methods, 2nd Edition, TMH, 2007.3. Schaums Outline Series,Feedback and Control Systems Tata McGraw-Hill, 2007.4. John J.Dazzo & Constantine H.Houpis, Linear control system analysis anddesign, Tata McGrow-Hill, Inc., 1995.5. Richard C. Dorf & Robert H. Bishop, Modern Control Systems, Addidon

Wesley, 1999.


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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

system.

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.

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


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

system?

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

10. What is block diagram?

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

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.


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15. Define nontouching loop.

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

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

external disturbance are not corrected

automatically

The changes in output due to

external disturbances are corrected

4.They are generally stable Great efforts are needed to design a

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.

PART A

1. What is system and control system?

2. What are the types of control system and explain it?

3. Write the application for open loop and closed loop control system.

4. Distinguish the open loop and closed loop control systems.5. What are the components of control system?

6. Define transfer function.

7. What is differential equation?

8. What are the basic elements used for modeling mechanical

translational system?


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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 modelingmechanical rotational system?

11. Write the torque balance equations for

a. Ideal rotational mass element

b. Ideal rotational Dash-pot

c. Ideal rotational spring

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 masons gain formula.

20. Compare the block diagram representation and

signal flow graph.


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BASIC ELEMENTS OF MECHANICAL SYSTEM

ELEMENT SYMBOL FORCE

Mass(M)

Damper(B)

Spring(K)


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PROBLEMS ON MECHANICAL SYSTEMS

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 newtons law,

(1)

Take laplace transform for (1)


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

mechanical system

Soln:

STEP1: Free hand drawing from Mass (M1)


By newtons law,

(1)


(2)


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By newtons law,

(3)


(4)

SUB/: (4) in (2)


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mechanical system

Soln:


Here applied force =0


By newtons law,

(1)


(2)


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By newtons law,

(3)


(4)

SUB/: (2) in (4)


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mechanical system

Soln:


To find

differential

equation:

By newtons law,

(1)


(2)



By newtons law,


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(3)


(4)

SUB/: (2) in (4)

BASIC ELEMENTS OF ROTATIONAL SYSTEM

ELEMENT SYMBOL FORCE


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Inertia(J)

Damper(B)

Spring(K)

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

rotational system


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Soln:



By newtons law,

(1)


(2)



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(3)


(4)

SUB/: (2) in (4)


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ELECTRICAL ANALAGOUS OF MECHANICAL SYSTEM

Force voltage analogy:

Mechanical system Electrical system

Force ,f(t) Voltage source V

Mass,MInductance L

Damper ,B Resistance, R

Spring ,k Capacitance ,C

Hints

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

ii) if there is Change in displacement put the elements in parallel

Force current analogy:


Force ,f(t) Current source I

Mass,MCapacitance,C


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


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ELECTRICAL ANALAGOUS OF ROTATIONAL SYSTEM

Torque voltage analogy:


Torque Voltage source V

Inertia,JInductance L


Spring ,k Capacitance ,C

Hints

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

ii) if there is Change in displacement put the elements in parallel

Torque current analogy:


Torque Current source I

Inertia,JCapacitance,C


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


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

Solution:

STEP1: Free hand drawing


By newtons law,

Force-Voltage Analogy

Force-Current Analogy



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Soln:



By newtons law,



By newtons law,

Differential Equationare


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I

C1R1

R2

C2R2 L2

L1

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


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Soln:


Here applied force =0


By newtons law,




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By newtons law,




C1

R1

C2

R2

I

L1

L2

R3


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Soln:




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control problems on mechanical systems (1999)

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