Consider a process model,
G=\frac{2e^{-0.633s}}{(s+1)(0.2s+1)(0.04s+1)(0.008s+1)}
and compare four PID controllers that are designed using an FOPTD model:
(a) IMC settings (Table 12.1) with \tau_{c} =\theta= 0.73
(b) AMIGO settings (Table 12.6)
Table 12.6:
|
Model: G(s)=\frac{Ke^{-\theta s}}{\tau s+1} |
Model: G(s)=\frac{Ke^{-\theta s}}{s} |
|
K_{c}=\frac{1}{K}(0.2+0.45\frac{\tau }{\theta } ) |
K_{c}=\frac{0.45}{K} |
|
\tau_{I}=\frac{0.4\theta+0.8\tau}{\theta+0.1\tau} \theta |
\tau_{I}=8\theta |
|
\tau_{D}=\frac{0.5\theta\tau}{0.3\theta+\tau} |
\tau_{D}=0.5\theta |
(c) Z-N settings (Table 12.7)
Table 12.7:
|
Controller |
K_{c} |
\tau_{I} |
\tau_{D} |
|
P |
0.5K_{cu} |
— |
— |
|
PI |
0.45K_{cu} |
P_{u}/1.2 |
— |
|
PID |
0.6K_{cu} |
P_{u}/2 |
P_{u}/8 |
(d) SIMC settings with \tau_{c} = 0.37 (Equation
\tau_{I}=\min \left\{\tau,4(\tau_{c}+\theta)\right\} )
Evaluate these controllers for a unit step change in set point (at t = 0) and a disturbance of magnitude 0.5 at t = 10. Assume that G_{d} = G.
