Table 2 Step response characteristics and worst-case parameter ranges for PI and CMC controllers + nonlinear process
PI controller | ||||
Characteristics | Nominal | Δ=0.2 | Δ=0.5 | Δ=1.0 |
t r (s) | 11,139 | 18,959 | 31,673 | Unstable |
t s (s) | 26,304 | 44,138 | 48,482 | Unstable |
M OV (%) | 2.42 | 24.88 | 44.44 | Unstable |
e ss (M) | 0.00 | 0.19 | 0.48 | Unstable |
Parameters | Nominal | Δ=0.2 | Δ=0.5 | Δ=1.0 |
γ Sb1 (/s) [10 −3] | 0.400 | 0.445-0.480 | 0.492-0.596 | 0.472-0.730 |
γ Sb2 (/s) [10 −3] | 0.400 | 0.402-0.475 | 0.400-0.453 | 0.533-0.735 |
γ Sb3 (/s) [10 −3] | 0.400 | 0.427-0.467 | 0.433-0.591 | 0.402-0.473 |
K I [10 −3] | 0.300 | 0.301-0.353 | 0.310-0.420 | 0.486-0.504 |
K P | 0.650 | 0.673-0.771 | 0.790-0.908 | 0.806-1.282 |
γ K1 (/s) [10 −3] | 0.400 | 0.432-0.461 | 0.446-0.573 | 0.498-0.747 |
γ K2 (/s) [10 −3] | 0.400 | 0.401-0.422 | 0.446-0.586 | 0.404-0.740 |
γ Sm1 (/s) [10 −3] | 0.400 | 0.427-0.479 | 0.424-0.587 | 0.641-0.791 |
γ Sm2 (/s) [10 −3] | 0.400 | 0.423-0.462 | 0.469-0.553 | 0.615-0.730 |
γ Sm3 (/s) [10 −3] | 0.400 | 0.409-0.478 | 0.418-0.539 | 0.401-0.431 |
k r1 (/M/s) [10 −4] | 0.500 | 0.509-0.594 | 0.536-0.734 | 0.737-0.945 |
k r2 (/s) | 1.600 | 1.633-1.865 | 1.749-2.232 | 1.860-2.843 |
k r2 (/s) [10 −3] | 0.800 | 0.812-0.904 | 0.819-1.102 | 0.844-0.891 |
CMC controller | ||||
Characteristics | Nominal | Δ=0.2 | Δ=0.5 | Δ=1.0 |
t r (s) | 11,147 | 15,501 | 25,753 | 30,838 |
t s (s) | 28,848 | 28,324 | 42,494 | 49,196 |
M OV (%) | 2.84 | 13.12 | 26.25 | 56.37 |
e ss (M) | 0.00 | 0.19 | 0.46 | 0.98 |
Parameters | Nominal | Δ=0.2 | Δ=0.5 | Δ=1.0 |
γ Sb1 (/s) [10 −3] | 0.400 | 0.426-0.479 | 0.534-0.597 | 0.542-0.798 |
γ Sb2 (/s) [10 −3] | 0.400 | 0.400-0.478 | 0.404-0.511 | 0.403-0.798 |
γ Sb3 (/s) [10 −3] | 0.400 | 0.406-0.457 | 0.425-0.578 | 0.403-0.633 |
k b1 (/M/s) [10 −5] | 0.550 | 0.567-0.644 | 0.577-0.808 | 0.619-1.075 |
k b2 (/s) | 12.50 | 12.64-14.75 | 16.57-17.84 | 16.99-17.95 |
k b3 (/M/s) [10 −4] | 0.180 | 0.182-0.207 | 0.203-0.238 | 0.196-0.274 |
k b4 (/s) | 140.00 | 144.48-163.09 | 165.38-205.25 | 143.15-278.30 |
k r1 (/M/s) [10 −4] | 0.500 | 0.503-0.593 | 0.523-0.712 | 0.538-0.807 |
k r2 (/s) | 1.600 | 1.635-1.893 | 1.839-1.950 | 1.789-2.861 |
k r2 (/s) [10 −3] | 0.800 | 0.803-0.943 | 0.804-1.162 | 0.808-1.525 |