Table 1 Step response characteristics and worst-case parameter ranges for PI and CMC controllers + linear process
PI controller | |||||
Characteristics | Nominal | Δ=0.2 | Δ=0.5 | Δ=1.0 | Δ=1.2 |
t r (s) | 29 | 44 | 75 | 157 | 173 |
t s (s) | 96 | 113 | 175 | 499 | Unstable |
M OV (%) | 9.14 | 22.83 | 52.25 | 114.17 | Unstable |
e ss (M) | 0.00 | 0.19 | 0.49 | 0.91 | Unstable |
Parameters | Nominal | Δ=0.2 | Δ=0.5 | Δ=1.0 | Δ=1.2 |
γ Sb1 (/s) | 0.400 | 0.431–0.476 | 0.532–0.595 | 0.475–0.791 | 0.584–0.599 |
γ Sb2 (/s) | 0.400 | 0.401–0.471 | 0.400–0.584 | 0.413–0.569 | 0.428–0.875 |
γ Sb3 (/s) | 0.400 | 0.401–0.473 | 0.414–0.593 | 0.466–0.721 | 0.412–0.853 |
K I | 0.045 | 0.048–0.054 | 0.048–0.061 | 0.052–0.086 | 0.058–0.085 |
K P | 1.000 | 1.016–1.165 | 1.130–1.359 | 1.137–1.549 | 1.159–1.367 |
γ K1 (/s) [10 −3] | 0.400 | 0.436–0.477 | 0.424–0.515 | 0.434–0.674 | 0.505–0.795 |
γ K2 (/s) [10 −3] | 0.400 | 0.403–0.466 | 0.401–0.454 | 0.473–0.666 | 0.570–0.683 |
γ Sm1 (/s) | 0.800 | 0.809–0.948 | 0.863–1.099 | 0.827–1.544 | 0.825–1.410 |
γ Sm2 (/s) | 0.800 | 0.835–0.943 | 0.904–1.012 | 0.849–1.205 | 1.152–1.548 |
γ Sm3 (/s) | 0.800 | 0.832–0.958 | 0.823–1.140 | 0.841–1.536 | 0.853–1.279 |
k 1 (/s) | 0.100 | 0.101–0.116 | 0.106–0.142 | 0.111–0.174 | 0.127–0.208 |
k 2 (/s) | 0.100 | 0.101–0.114 | 0.102–0.139 | 0.103–0.199 | 0.123–0.211 |
CMC controller | |||||
Characteristics | Nominal | Δ=0.2 | Δ=0.5 | Δ=1.0 | Δ=1.2 |
t r (s) | 29 | 37 | 65 | 89 | 117 |
t s (s) | 97 | 116 | 155 | 202 | 353 |
M OV (%) | 10.12 | 25.3 | 44.63 | 60.55 | 75.00 |
e ss (M) | 0.00 | 0.18 | 0.46 | 0.92 | 1.12 |
Parameters | Nominal | Δ=0.2 | Δ=0.5 | Δ=1.0 | Δ=1.2 |
γ Sb1 (/s) | 0.400 | 0.403–0.476 | 0.450–0.595 | 0.412–0.781 | 0.626–0.857 |
γ Sb2 (/s) | 0.400 | 0.401–0.477 | 0.406–0.580 | 0.407–0.752 | 0.403–0.745 |
γ Sb3 (/s) | 0.400 | 0.403–0.466 | 0.402–0.594 | 0.577–0.726 | 0.425–0.806 |
k b1 (/M/s) [10 −2] | 0.185 | 0.186–0.221 | 0.202–0.274 | 0.199–0.342 | 0.224–0.365 |
k b2 (/s) | 0.500 | 0.514–0.565 | 0.516–0.683 | 0.621–0.737 | 0.509–0.747 |
k b3 (/M/s) [10 −2] | 0.185 | 0.187–0.213 | 0.187–0.245 | 0.242–0.354 | 0.230–0.318 |
k b4 (/s) | 0.500 | 0.516–0.596 | 0.679–0.723 | 0.553–0.851 | 0.662–1.008 |
k 1 (/s) | 0.100 | 0.100–0.119 | 0.104–0.148 | 0.130–0.199 | 0.101–0.174 |
k 2 (/s) | 0.100 | 0.101–0.114 | 0.105–0.150 | 0.106–0.198 | 0.109–0.209 |