For the FOPTD model,
G=\frac{e^{-s}}{s+1}
compare four PI controllers:
(a) IMC settings (Table 12.1) with \tau_{c} = 1
(b) AMIGO settings (Table 12.5)
Table 12.5:
|
Model: G(s)=\frac{Ke^{-\theta s}}{\tau s+1} |
Model: G(s)=\frac{Ke^{-\theta s}}{s} |
|
K_{c}=\frac{0.15}{K}+(0.35-\frac{\theta \tau }{(\theta +\tau )^{2}} )\frac{\tau }{K\theta } |
K_{c}=\frac{0.35 }{K\theta } |
|
\tau_{I}=0.35\theta +\frac{13\theta \tau^{2}}{\tau^{2}+12\theta \tau +7\theta ^{2}} |
\tau_{I}= 13.4\theta |
(c) ITAE settings for disturbances (Table 12.4)
(d) 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 |
Evaluate these controllers for unit step changes in set point (at t = 0) and a step disturbance of magnitude 1 at t = 20. Assume that G_{d} = G.
