Difference between revisions of "FAQ: What happens when the Nyquist plot goes exactly through -1?"

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''Posted by [[User:Murray|Murray]] 20:07, 12 November 2005 (PST)''<br />
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''Posted by Tim Chung, 11 November 2002''<br />
 
If the Nyquist plot passes through the critical point, s=-1+0j, then this means that the closed-loop poles, i.e. the zeros of the closed-loop characteristic equation, lie on the jw-axis. Hence, the system cannot be asymptotically stable.  Whether it is stable or unstable depends on the multiplicity of the poles at the origin.
 
If the Nyquist plot passes through the critical point, s=-1+0j, then this means that the closed-loop poles, i.e. the zeros of the closed-loop characteristic equation, lie on the jw-axis. Hence, the system cannot be asymptotically stable.  Whether it is stable or unstable depends on the multiplicity of the poles at the origin.
  
 
From a practical point-of-view, purely imaginary poles in the closed-loop system (as described above) are not usually desirable, in that this means the system will have oscillatory behavior. Thus, a well-designed closed-loop system should avoid such poles.
 
From a practical point-of-view, purely imaginary poles in the closed-loop system (as described above) are not usually desirable, in that this means the system will have oscillatory behavior. Thus, a well-designed closed-loop system should avoid such poles.
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[[Category: Frequently Asked Questions]]
 
[[Category: Frequently Asked Questions]]
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[[Category: Chapter 8 FAQ]]
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[[Category: Nyquest FAQ]]

Revision as of 04:08, 13 November 2005

Posted by Tim Chung, 11 November 2002
If the Nyquist plot passes through the critical point, s=-1+0j, then this means that the closed-loop poles, i.e. the zeros of the closed-loop characteristic equation, lie on the jw-axis. Hence, the system cannot be asymptotically stable. Whether it is stable or unstable depends on the multiplicity of the poles at the origin.

From a practical point-of-view, purely imaginary poles in the closed-loop system (as described above) are not usually desirable, in that this means the system will have oscillatory behavior. Thus, a well-designed closed-loop system should avoid such poles.