EE 233 Laboratory Exercise 02

We investigate the open-loop response and closed-loop response
of a system based on a Maglev model.  Determining the
continuous-time response of the system allows us to later
appreciate how discrete-time control performs in
comparison to a continuous-time implementation.

Given the Maglev transfer function

Gs = ku11/(m*s^2 + m*beta*s + k11)

where ku11, m, beta, k11 are constants, or for simplicity,

               56.54          
G(s) =  ------------------------
        0.12 s^2 + 0.6 s + 58.31


1. Determine the step response using the step command.
Comment on the response, i.e., what are the overshoot, settling time,
steady-state output, etc.

2. A PID controller that yields an acceptable closed-loop response is

D(s) = 0.21 + 19.95/s + 0.04s

Determine the continuous-time closed-loop response of the Maglev system.
Assume the desired output is 2.5 (cm).  

 a. Compute the response by first computing the closed-loop TF,
and then using the step command on the closed-loop TF.
Comment on the closed-loop response of the system.

 b. Compute the response by "approximating" the closed-loop operation.
This is done by iterating over the following steps.

  i. Calculate the input to the forward path by subtracting the
the forward path output from the reference input.
  ii. Determine the forward path response to the input calculated in i.
by using lsim command.
  iii. Determine the lsim output at the "end" time of the iteration.
Feed this back to the forward path and repeat from i.

A 10 ms "sampling" time should be enough for this experiment.
Do 100 iterations for a total of 1 second simulation time.

3.  Compare the results from 2a and 2b. What would be a reason
for using the procedure in 2b instead of 2a?