57348017 problems on mechanical systems
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EC 2255 CONTROL SYSTEMS 3 0 0 3AIMTo familiarize the students with concepts related to the operation analysis andstabilization of control systemsOBJECTIVES
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
systems1. CONTROL SYSTEM MODELING 9Basic Elements of Control System !pen loop and Closed loop systems " #ifferentialequation " Transfer function$ %odelin& of Electric systems$ Translational and rotationalmechanical systems " Block dia&ram reduction Techniques " Si&nal flow &raph2. TIME RESPONSE ANALYSIS 9Time response analysis " 'irst !rder Systems " mpulse and Step esponse analysis of second order systems " Steady state errors *$ * $ *# and * # Compensation$ +nalysisusin& %+T,+B3. FREQUENCY RESPONSE ANALYSIS 9'requency esponse " Bode *lot$ *olar *lot$ -yquist *lot " 'requency #omainspecifications from the plots " Constant % and - Circles " -ichol s Chart " /se of -ichol s Chart in Control System +nalysis. Series$ *arallel$ series"parallel Compensators" ,ead$ ,a&$ and ,ead ,a& Compensators$ +nalysis usin& %+T,+B.4. STABILITY ANALYSIS 9Stability$ outh"0urwitz Criterion$ oot ,ocus Technique$ Construction of oot ,ocus$Stability$ #ominant *oles$ +pplication of oot ,ocus #ia&ram " -yquist Stability Criterion" elati1e Stability$ +nalysis usin& %+T,+B5. STATE VARIABLE ANALYSIS & DIGITAL CONTROL SYSTEMS 9
State space representation of Continuous Time systems State equations Transfer function from State 2ariable epresentation Solutions of the state equations "Concepts of Controllability and !bser1ability State space representation for #iscretetime systems. Sampled #ata control systems Samplin& Theorem Sample 3 0old !pen loop 3 Closed loop sampled data systems.TOTAL 45 PERIODSTE!TBOO"4. 5.-a&rath and %.6opal$7 Control System En&ineerin&7$ -ew +&e nternational*ublishers$ 8 th Edition$ 9::;.9. %.6opal$ uo$
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$oment of inertia (!dashpot or damper & and
spring %
$. %ame two types of electrical analo"o s for mechanical system.
The two types of analogies for the mechanical system are"orce voltage and force current analogy
1&. What is block dia"ram?
A bloc 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 bloc diagram arew bloc ! branch point and
summing point.
11. What is the basis for framin" the r les of block dia"ram red ction
techni' e?
The rules for bloc diagram reduction technique are framed such that any
modification made on the diagram does not alter the input output relation.
12. What is a si"nal flow "raph?
A signal flow graph is a diagram that represents a set of simultaneous
algebraic equations .&y ta ing ).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 so rce?
+ource is the input node in the signal fow graph and it has only outgoing
branches. +in is a output node in the signal flow graph and it has only
incoming branches.
15. Define nonto chin" loop.
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The loops are said to be non touching if they do not have common nodes.
16. Distin" ish between open loop and closed loop system
(pen loop )losed loop
1.Innaccurate Accurate
2.+imple and economical Comple- and costlier
'.The changes in output due to
e-ternal disturbance are not correctedautomatically
The changes in output due to
e-ternal disturbances are corrected
,.They are generally stable reat efforts are needed to design a
stable system
1!. Why is ne"ati*e feedback in*ariably preferred in closed loop system?
The negative feedbac results in better stability in steady state and rejects
any disturbance signals.
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+,- / ,
1. 0hat is system and control system2. 0hat are the types of control system and e-plain it'. 0rite the application for open loop and closed loop control system.,. istinguish the open loop and closed loop control systems./. 0hat are the components of control system3. efine transfer function.4. 0hat is differential equation5. 0hat are the basic elements used for modeling mechanical
translational system6. 0rite the force balance equation for
a. Ideal mass elementb. Ideal ash*potc. Ideal spring
17. 0hat are the basic elements used for modelingmechanical rotational system
11. 0rite the torque balance equations fora. Ideal rotational mass elementb. Ideal rotational ash*potc. Ideal rotational spring
12. 0hat are all the two types of electrical analogous ofmechanical system
1'. 0hat is &loc diagram1,. 0hat are all the components of &loc diagram1/. 0hat is a signal flow graph13. 0hat is transmittance14. efine non*touching loops.15. 0rite the properties of signal flow graph.
16. 0rite the mason8s gain formula.27. Compare the bloc diagram representation andsignal flow graph.
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0, ) % ( )7,% ), 8
ELEMENT SYMBOL FORCE
Mass(M)
Damper(B)
Spring(K)
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9:;&)
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2.0rite the differential equation and find out the transfer function for givenmechanical system
+oln@
+T
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+T
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'.0rite the differential equation and find out the transfer function for givenmechanical system
+oln@
+T
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+T
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,.0rite the differential equation and find out the transfer function for givenmechanical system
+oln@
+T
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'B
Ta e laplace transform for 'B
,B
+ &D@ 2B in ,B
0, ) % ( -( , (%, 8
ELEMENT SYMBOL FORCE
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Inertia(J)
Damper(B)
Spring(K)
1B0rite the differential equation and find out the transfer function for givenrotational system
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+oln@
+T
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:3;
Ta e laplace transform for 'B
:4;
+ &D@ 2B in ,B
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+oln@
+T
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orce> olta"e ,nalo"y
orce>) rrent ,nalo"y
I
C1)4
R2
C2R2 ,9
L1
'.0rite the differential equation and raw force*current and force*voltage analogy
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&y newton8s law!
Differential ' ation are
orce> olta"e ,nalo"y
orce>) rrent ,nalo"y
C1R1
C2
R2
I,4
,9
R3
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,. 0rite the differential equation and raw force*current and force*voltage analogy
+oln@
+T
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+T
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orce>) rrent ,nalo"y
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