“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)).