Hi,

The main mathematical tool engineers use in control is Laplace transforms which enable one to take an ordinary differential
equation(s) and express it in the form of a transfer function.

For example, given

x_dot_dot + 3 x_dot + 2x = u

we can create the transfer function

x/u = 1/((s+1)(s + 2)) = h(s)

The poles are -1 and -2, and there are no zeros.

Now, if I where to construct a Bode or Nyquist plot I would set s = jw and evaluate the magnitude and phase of h(s = jw). My question is, why can we do this? Where does this idea of setting s=jw come from? Shouldn't we be setting s = sigma + jw because s is a complex variable with a real and imaginary part?

If anyone has a decent explanation I would appreciate. Or even better, if someone has a few links I could look at that would be good too.

JRF

The main mathematical tool engineers use in control is Laplace transforms which enable one to take an ordinary differential

For example, given

x_dot_dot + 3 x_dot + 2x = u

we can create the transfer function

x/u = 1/((s+1)(s + 2)) = h(s)

The poles are -1 and -2, and there are no zeros.

Now, if I where to construct a Bode or Nyquist plot I would set s = jw and evaluate the magnitude and phase of h(s = jw). My question is, why can we do this? Where does this idea of setting s=jw come from? Shouldn't we be setting s = sigma + jw because s is a complex variable with a real and imaginary part?

If anyone has a decent explanation I would appreciate. Or even better, if someone has a few links I could look at that would be good too.

JRF