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CONCERNS IN CONTROL SYSTEM
DESIGN
!! Transient Response
"! Speed of the Response
"! Overshoot Level
!! Stability
!! Steady-State Response
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WE NOW ADDRESS STABILITY
•! The output is
For a system to be stable:
ZIR shouldn!t grow
ZSR shouldn!t grow
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STABILITY
Based on ZIR (Initial conditions should not produce
a growing response)
#! Only left hand plane poles: System is stable
#!Some right hand plane poles: System is unstable
#! Left hand plane poles and imaginary axis poles
(with multiplicity 1): System is marginally stable
#! Some imaginary axis poles with multiplicity
greater than 1: System is unstable
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STABILITY (Based on ZSR)
BIBO Stability
All Bounded (magnitude) Inputs should have
Bounded Outputs.
#! Only left hand plane poles: System is Stable
#! Otherwise: System is Unstable
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Given the Transfer Function
Figure out whether it is a stable
system or not?
Equivalent question= where are the
poles located?
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ROUTH TABLE
•! We use Routh table to determine whether
there exists any unstable poles?
•! So what is a Routh table?
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Suppose we are interested in the roots of the
polynomial
a4s4+a3s3+a2s2+a1s1+a0
Initial layout for
Routh table
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Completed
Routh table
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Routh Hurwitz Method.htm
Slide 4
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EXAMPLE
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Special Case 1: Routh Table Containing
a zero in the first column
T(s)=10/(s5+2s4+3s3+6s2+5s+3)
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Special Case 2: Routh Table Containing all
zeros in a row
Example: T(s)=10/(s5+7s4+6s3+42s2+8s+56)
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Root positions
to generate
even
polynomials:
A , B, C,
or any
combination
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Example: T(s)=20/(s8+s7+12s6+22s5+39s4+59s3+48s2+38s+20)
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Stability Design Via Routh-Hurwitz
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Routh table for antenna control
case study .
Conclusion: 0<K<2623
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