Example stabilizing control Distillation 5 dynamic DOFs L

Example “stabilizing” control: Distillation 5 dynamic DOFs (L, V, D, B, VT) Overall objective: Control compositions (x. D and x. B) “Obvious” stabilizing loops: 1. Condenser level (M 1) 2. Reboiler level (M 2) 3. Pressure 1 E. A. Wolff and S. Skogestad, ``Temperature cascade control of distillation columns'', Ind. Eng. Chem. Res. , 35, 475 -484, 1996.

LV-configuration used for levels (most common) “LV-configuration”: L and V remain as degrees of freedom after level loops are closed Other possibilities: DB, L/D V/B, etc…. 2

BUT: To avoid strong sensitivity to disturbances: Temperature profile must also be “stabilized” Ttop Temperature 3

Data “column A” • • • Binary ideal mixture with relative volatility 1. 5 Equimolar feed (z. F=0. 5) Both products 99% purity (x. D, x. B) 41 stages, feed at stage 20 Liquid lag: 1. 5 min (from top to bottom) • Level control: Tight • Temperature control: Kc=1. 84 (1 min closed-loop time constant) – Assume top product (x. D) most important → Close loop at top (L) • Composition control (supervisory layer): Decentralized PID – Measurement delay for composition: 6 min 4

Temperature control: Which stage x? 5

Singular value rule: Tray 34 is most sensitive 6

Temperature control: Ts is DOF for layer above 7

Partial control Supervisory control: u 1 = V Primary controlled variables y 1 = c = (x. D x. B)T Regulatory control: Control of y 2=T using u 2 = L (original DOF) Setpoint y 2 s = Ts : new DOF for supervisory control 8

Disturbance sensitivity with partial control (Pd 1) 9

10

RGA with temperature loop closed 11

Disturbance sensitivity with decentralized control: CLDG 12

Closed-loop response with decentralized PIDcomposition control Interactions much smaller with “stabilizing” temperature loop closed … and also disturbance sensitivity is expected smaller 13

Integral action in temperature loop has little effect 14

May get improvement with L/D V/B configuration for level loops 15 Simulations are with decentralized PID-control in supervisory layer Difference smaller if we use multivariable control (MPC)

No need to close two inner temperature loops 16

Conclusion: Stabilizing control distillation • • Control problem as seen from layer above becomes much simpler if we control a sensitive temperature inside the column (y 2 = T) Stabilizing control distillation 1. 2. 3. 4. • Condenser level Reboiler level Pressure (sometimes left “floating” for optimality) Column temperature Most common pairing: – “LV”-configuration for levels – Cooling for pressure – V for T-control (alternatively if top composition most important: L for Tcontrol) 17

Conclusion stabilizing control: Remaining supervisory control problem Ls Ts 18 TC + may adjust setpoints for p, M 1 and M 2 (MPC)