Fig 9. Controller performance with first-order autocatalysis in C (Eq 9) and hyperbolic increase of k1.
Phase 1 (not shown): the controller is at steady state at its set-point Aset = 5.0 with constant k1 = 2.0. Phase 1 lasts 1 time unit. Initial concentrations: A0 = 5.0, E0 = 0.9, C0 = 1.0. Phase 2: k1 increases in a hyperbolic fashion (Eq 14), k2 = 1 × 105, k3 = 5 × 105, k4 = 1 × 105, k5 = 10.0, and k6 = 1.0. KM = 1 × 10−6, KI = 0.1, n = 4 (Eq 6). Left panel: k1 and C as a function of time just before k1 reaches the infinity limit; right panel: corresponding A and E concentrations as a function of time.