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

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[[User:Hines|George Hines]] 17:12, 12 November 2007 (PST)
[[User:Hines|George Hines]] 17:12, 12 November 2007 (PST)
[[Category: CDS 101/110 FAQ - Lecture 7-1]]
[[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]]

Latest revision as of 01:12, 13 November 2007

First recall some definitions:

  • the "loop transfer function" is L(s)=P(s)C(s)
  • the closed loop system is described by {\frac  {L(s)}{1+L(s)}}
  • Z = #RHP zeros of 1+L(s)

So we see that if a point is a zero of 1+L(s), 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 1+L(s) has any RHP zeros, the closed loop system around the loop transfer function is unstable.

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