class 3 - modeling of electrical systems
TRANSCRIPT
System Modeling Coursework
P.R. VENKATESWARANFaculty, Instrumentation and Control Engineering,
Manipal Institute of Technology, ManipalKarnataka 576 104 INDIAPh: 0820 2925154, 2925152
Fax: 0820 2571071Email: [email protected], [email protected]
Blog: www.godsfavouritechild.wordpress.comWeb address: http://www.esnips.com/web/SystemModelingClassNotes
Class 3: Mathematical Modeling of Electrical Systems
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 2
WARNING!
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I claim no originality in all these notes. These are the compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation.
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For best results, it is always suggested you read the source material.
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Contents
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Basic elements of an electrical system•
Equations for the basic elements
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Numerical and its solutions•
Summary
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Unsolved Problems•
References
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Basic elements of the electrical system
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The basic components that are used in electrical systems are resistance, inductance and capacitance.
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These systems are analyzed by the application of Kirchhoff’s voltage and current laws.
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Governing equations for the basic elements
R
L
C
V (t) = R i(t)di(t)V (t) = Ldt
1V (t) = (0)C
idt V+∫
In Laplace domain, the equations are
( ) ( )
( ) ( )
( ) ( )
R R
L L
c c
V s I s R
V s LsI s
I s CsV s
=
=
=
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Mathematical functions of electrical quantities
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Problem No.1
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Consider the electrical system with Resistor, Inductor and Capacitor in Series shown in figure. Find the Transfer function of the system
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Solution to Problem No.1
i
0
di(t) 1V (t) =Ri(t) +L ( )dt
1V (t) = ( )
i t dtC
i t dtC
+ ∫
∫i
0
i
0
i
1V (s) =RI(s) +LsI(s) I(s)
1V (s) = ( )
1V (s) = R +Ls I(s)
V (s) 11 1V (s) R +Ls
Cs
I sCs
Cs
Cs Cs
+
⎡ ⎤+⎢ ⎥⎣ ⎦
=⎡ ⎤+⎢ ⎥⎣ ⎦
02
i
V (s) 1V (s) LCs RCs 1
=⎡ ⎤+ +⎣ ⎦
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Problem No.2
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Find the transfer function of the following circuit in Figure.
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Solution to Problem No.2
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Solution to Problem No.2
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Summary
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Always identify the basic elements in the given circuit
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Write equations for the basic elements using governing laws for the circuit
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Relate them in terms of specified input and output•
If necessary, do the computation in laplace
domain
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Review Questions
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Given the electrical network as in figure, solve for the transfer function I2
(s)/V(s) of the system.
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Review Questions
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Find the transfer function G(s) = V0
(s)/Vi
(s) for the networks in figure (a) and (b).
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References
• MIT OCW material: Lecturer: Penmen Gohari
amongst others…
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And, before we break…
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THY will be done
Thanks for listening…