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

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− | ''Posted by | + | ''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]] | ||

+ | [[Category: Chapter 8 FAQ]] | ||

+ | [[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.