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SoC Presentation Title 2004
Introduction
! !""#$%&' )*+,-*. /01,"23 4+%.0151 %+# 6"157+
)( sG c )( sG pOutput Input
Controller Plant )()(1
)()(
sG sG
sG sG
Input Output
pc
pc
+=
1. Routh Stability Criterion
2. Root Locus Method
3. Nyquist Stability Criterion
0)()(1 =+ sG sG pc System Stability and Performance
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SoC Presentation Title 2004
Some Reviews
! Polar Plots (also known as Nyquist Plot)
It is the plot of Gain versus Phase Angle , as ! is varied from
zero to innity.
! Nyquist Stability Criterion
It determines the stability of a closed-loop system from its
open-loop frequency response and open-loop poles.
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! Main advantage is that frequency response characteristic of
the system is
depicted in one plot .
Vary ! and see change of Gain and Phase Angle
Usually Negative Angle!
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SoC Presentation Title 2004First Order System
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SoC Presentation Title 2004First Order System
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SoC Presentation Title 2004Second Order System
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Where it begins
8*.%- 8.*,
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Where it ends
8*.%- 8.*,
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Nyquist Stability riterion
Special Case! => Relative Stability
Stable
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9".%:;" /,%$5.5,0
Bode Plot Polar Plot
Note: Only apply for Minimum Phase System(No positive open loop
poles and zeros)! Non-minimum Phase System may have negative phase
margin and gain margin but can still be stable! Always check open
loop poles and zeros before use it!
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SoC Presentation Title 2004Question 1
Rationalizing by multiplying by its conjugate
(Split into Re and Im parts respectively.)
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SoC Presentation Title 2004Question 1
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SoC Presentation Title 2004Question 2
1. Split into Re and Im parts.2. Find Gain and Phase for varying
.
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Nyquist Plot Bode Plot
8*15:;" 8
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SoC Presentation Title 2004Question 3
-1
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-1
Another method: No encirclement of -1 point. N=0
Refer: http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol
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SoC Presentation Title 2004Question 5
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SoC Presentation Title 2004
Li Jiaxin
Email: [email protected]
THANK YOU
