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

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[[Category: Frequently Asked Questions]]
 
[[Category: Frequently Asked Questions]]
[[Category: Chapter 8 FAQ]]
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[[Category: Loop Analysis FAQ]]
 
[[Category: Nyquist FAQ]]
 
[[Category: Nyquist FAQ]]

Revision as of 16:21, 17 May 2008

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.