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Basic Control Engineering
Prof. Wonhee Kim
Ch.2. Modeling in the Frequency Domain
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Laplace Transform Review
- Laplace transform
- Inverse Laplace transform
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Laplace Transform Review
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Laplace Transform Review
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Laplace Transform Review:
- Solution of a Differential Equation
Example 2.3)
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System Modeling in Frequency Domain
r(t)
r(t)
c(t)
c(t)
From input to output: Convolution
0
*t
c g r t g r t d
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System Modeling in Frequency Domain
C s G s R s
r(t) c(t) R(s) C(s)
Laplace
transform
C sG s
R s
Transfer function
0
*t
c g r t g r t d
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System Modeling in Frequency Domain
R(s) C(s)
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System Modeling in Frequency Domain
Example 2.4)
r(t) c(t) R(s) C(s)
Laplace
transform
2
2
1
2
dc tc t r t
dt
sC s C s R s
C sG s
R s s
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System Modeling in Frequency Domain
Example 2.5)
1
2
C sG s
R s s
1
2C s G s R s R s
s
1
R ss
1 1 1/ 2 1/ 2
2 2C s G s R s
s s s s
21 1
2 2
tc t e
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Electrical Network Transfer Functions
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Electrical Network Transfer Functions
Example 2.6)
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Electrical Network Transfer Functions
Example 2.6) For the capacitor:
For the resistor:
For the inductor:
Impedance:
/Ci t Cdv t dt
I s sCV s
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Translational Mechanical System Transfer Functions
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Rotational Mechanical System Transfer Functions
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Translational Mechanical System Transfer Functions
Example 2.16)
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Nonlinearities
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Nonlinearities - Linearization
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Nonlinearities - Linearization
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Nonlinearities - Linearization