The graph below shows the response of a system where the input is a step function. The equation shows the transfer function multiplied by the input step function - recall that ℒ μ(t) = 1/s. The poles (x) and zeros (o) of the transfer function are plotted on the complex plane. In addition the system is multiplied by an adjustable gain (in green).
Use the controls to change the order of the numerator (number of zeros) and denominator (number of poles). Drag the poles and zeros on the complex plane to change their location. As you change the transfer function the gain is automatically adjusted so the steady-state response to the step input is 1. After changing the transfer function you can readjust the gain.