Download - Transient response analysis
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TRANSIENT-RESPONSE ANALYSISFIRST ORDER SYSTEM
SECOND ORDER SYSTEM
TRANSIENT RESPONSE AND STEADY STATE
RESPONSE
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TRANSIENT RESPONSE AND STEADY STATE RESPONSE
Transient Response
Transient Response
Steady-State Response
Steady-State Response
Figure 1 Figure 2
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FIRST ORDER SYSTEM
K 12s+1
R(s) C(s)
Transfer function:
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Plot of Response System
t = (tau)
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EXAMPLE 1K 5
3s+9R(s) C(s)
◦ Plot rensponse system control
◦ Constant time
◦ Steady state error (Ess)
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Answer:
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Error steady state
Output (respon steady state)
Constant time
= constant time
c(t)= input x 63% = 1 x 0.63 = 0.63
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Error steady state is defined by
Ess = Input-Output
Ess = 1- 0.847
= 0.153
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SECOND ORDER SYSTEM
K1
(𝑠+1)(𝑠+2)C(s)R(s)
Transfer function: =
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CHART OF RESPONSE SYSTEM
tr
tp
ts
0.02 or 0.05
Steady state
overshoot
A B C
D
E FG H
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EXAMPLE 2
Plot response control systemPeak time (tp)Maximum overshootSettling time (ts)Steady state error (Ess)
K 9(𝑠+3)(𝑠+5)
C(s)R(s)
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error steady state
Output (respon steady state)
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error steady state
Output (respon steady state)
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QUESTION ???
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CONCLUSIONOn first order system the value of (tau) will decide accelerate of response system from start statecondition until steady state. The fewer the constant time, response will be better.
While on second order system influenced by the value of and . The more the value of , response will be deeper.
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THANK YOU