# Difference between revisions of "Why does Z≠0 correspond to instability?"

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* the "loop transfer function" is <math>L(s)=P(s)C(s)</math> | * the "loop transfer function" is <math>L(s)=P(s)C(s)</math> | ||

* the closed loop system is described by <math>\frac{L(s)}{1+L(s)}</math> | * the closed loop system is described by <math>\frac{L(s)}{1+L(s)}</math> | ||

− | * Z=#RHP zeros of <math>1+L(s)</math> | + | * Z = #RHP zeros of <math>1+L(s)</math> |

So we see that if a point is a zero of <math>1+L(s)</math>, then it is a pole of the closed-loop system. Now, if that pole lies in the right half-plane, then the closed-loop system will be unstable. Thus if the function <math>1+L(s)</math> has any RHP zeros, the closed loop system around the loop transfer function is unstable. | So we see that if a point is a zero of <math>1+L(s)</math>, then it is a pole of the closed-loop system. Now, if that pole lies in the right half-plane, then the closed-loop system will be unstable. Thus if the function <math>1+L(s)</math> has any RHP zeros, the closed loop system around the loop transfer function is unstable. | ||

− | [[User:Hines|Hines]] 17:12, 12 November 2007 (PST) | + | [[User:Hines|George Hines]] 17:12, 12 November 2007 (PST) |

[[Category:CDS101/110 | [[Category:CDS101/110 |

## Revision as of 01:12, 13 November 2007

First recall some definitions:

- the "loop transfer function" is
- the closed loop system is described by
- Z = #RHP zeros of

So we see that if a point is a zero of , then it is a pole of the closed-loop system. Now, if that pole lies in the right half-plane, then the closed-loop system will be unstable. Thus if the function has any RHP zeros, the closed loop system around the loop transfer function is unstable.

George Hines 17:12, 12 November 2007 (PST)

[[Category:CDS101/110