Step Response

In general can have poles of its own and thus the system response to will reflect the poles of both the transfer function, , and the LT of the forcing term .

  • The effects of the transfer function are present for any input so it is particularly important to understand the effects of the poles (and zeros) of .

  • We will mostly look at the cases where the input is a unit impulse, , or a unit step, . Recall from A3 Q3 that for a second order DE these terms allow us to effectively set the initial condition at 0+ of for the system.

  • The response to the unit impulse is

  • The response to the unit step impulse is

  • The step response is the integral of the impulse response

In the “real world” it is often easier to physically generate a unit step function than a unity impulse so point 2 above gives us a nice way to compute transfer functions.