Day: August 10, 2017 # Transfer functions

Transfer functions

08/10/17

“What causes controls systems to change input to output?”
All controls systems have an input (usually some sinusoidal wave) and an output (the wave modified either through addition, multiplication, differentiation, or integration). However, what exactly causes this mathematical change? Well, the key behind this is something known as the transfer function. The transfer function H(s) is defined as the ratio of the output function Y(s) over the input function X(s) (H(s) = Y(s)/X(s)). If we rearrange this formula, then we can see that the input function multiplied by the transfer function is equal to the output function (H(s)*X(s) = Y(s)). # Poles and Zeros

Poles and Zeros

08/10/17

“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.