Does cancelling poles/zeros make any difference at all?

Tim Chung, 25 Nov 02

For example, let's say we have a transfer function of the form:

          a s^2 + b s 
H(s) = ------------------
       c s^2 + d s^2 + e s

As you can see, you could factor out an "s" in both the numerator and the denominator, and effectively "cancel" them to yield a reduced-order system.

Generally speaking, when designing controllers, we want to avoid cancellation of poles and zeros in the right-half-plane, when forming the loop-gain transfer function, P(jw)C(jw.

Even though a pole/zero at "s" is not in the RHP, it'd be good to get in the habit of avoiding cancelling these pole/zero pairs. The reason why pole/zero cancellation is taboo is because, in practice, the exact poles and/or zeros will not be known precisely, and trying to cancel them out will usually yield catastrophic (i.e. undesirable) results.