Page 225 - Numerical methods for chemical engineering

Problems 211

For various choices of the controller tuning parameters {K C , τ I , τ D }, simulate the closed-
loop response for several perturbations. Start at steady state with u(0) = e(0) = υ in,2 (0) = 0
and immediately change υ in,2 to a constant value chosen at random within 0 ≤ υ in,2 ≤
(0.1)υ in,set . For each response, a measure of how well the controller rejects the disturbance
is
'
t H 2
F(K C ,τ I ,τ D ) = |e(t)| dt (4.257)
0
t H is a horizon time suitably long for the response to be measured; for example, the time
required for the height to approach within 99% of its new steady-state value if we were to
take no control action for υ in,2 = (0.1)υ in,set . Of all the {K C , τ I , τ D } sets that you try, report
the one with the best F(K C , τ I , τ D ), averaged over many disturbances. If at any time during
a simulation, h(t) exceeds 2 or drops below 0, stop and reject the controller design.