Poles and Zeros
“When does a transfer function go to zero or infinity?”
Transfer functions are usually made up of two polynomials, one in the numerator and one in the denominator. When the polynomial in the denominator (known as the pole) goes to zero, the transfer function will become infinitely large, while when the ones in the numerator go to zero, the function becomes a zero (hence the term zero for such functions). If a transfer function has more poles, then it becomes more unstable, while more zeros will make it more stable. Because of this, controls engineers try to maximize the pole-to-zero ratio.