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lecture9 - 9.Poles&Zeros n(s G(s = (s&d(s)are d(s...

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  1 9.  Poles & Zeros Given a Transfer Function                      where n(s) & d(s) are  polynomials in s. Reminder: An example of polynomials in s is: s 3 +4s 2 -s+5 Solving d(s) = 0 for s yields the poles  of the transfer function. Solving n(s) = 0 for s yields the zeros  of the transfer function. Note: These roots are, in general, complex. They can be  plotted on a complex plane. We use x for poles, and o for  zeros. D(s) = 0 is called the Characteristic Equation  of the system. ) s ( d ) s ( n ) s ( G =
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  2 Poles of Transfer Function  Stability The location of the poles tells the stability status of the  system. If all poles are on the left half plane (LHP), then system is  stable. Any poles on the imaginary axis must be single for  stability.
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