Practical plantwide process control Part 1 Sigurd Skogestad, NTNU Thailand, April 2014

Part 1 (3h): Plantwide control Introduction to plantwide control (what should we really control?) Part 1.1 Introduction. Objective: Put controllers on flow sheet (make P&ID) Two main objectives for control: Longer-term economics (CV1) and shorter-term stability (CV2) Regulatory (basic) and supervisory (advanced) control layer Part 1.2 Optimal operation (economics) Active constraints Selection of economic controlled variables (CV1). Self-optimizing variables. Part 1.3 -Inventory (level) control structure Location of throughput manipulator Consistency and radiating rule Part 1.4 Structure of regulatory control layer (PID) Selection of controlled variables (CV2) and pairing with manipulated variables (MV2) Main rule: Control drifting variables and "pair close" Summary: Sigurd’s rules for plantwide control  

Course Summary Find active constraints + self-optimizing variables (CV1). (Economic optimal operation) Locate throughput manipulator (TPM) “Gas pedal” Select stabilizing CV2 + tune regulatory loops SIMC PID rules Design supervisory layer (control CV1) Multi-loop (PID) ++ MPC Difficulties: Optimization! May need to guess active constraints (CV1) Handling of moving active constraints Want to avoid reconfiguration of loops

Summary: Sigurd’s plantwide control rules Rules for CV1-selection: 1. Control active constraints Purity constraint on expensive product is always active (overpurification gives loss):   2. Unconstrained degrees of freedom (if any): Control “self-optimizing” variables (c).   The ideal variable is the gradient of J with respect to the inputs (Ju = dJ/du), which always should be zero, independent of disturbances d, but this variable is rarely available Exception (if available!): Parallel systems (stream split, multiple feed streams/manifold) with given throughput (or given total gas flow, etc.) Should have equal marginal costs Jiu = dJi/du, so Ju = J1u - J2u, etc. Heat exchanger splits: equal Jächke temperatures, JT1 = (T1 – Th1)^2/(T1-T0) In practice, one prefers to control single variables, c=Hy (where y are all available measurements and H is a selection matrix), which are easy to measure and control, and which have the following properties: Optimal value for c is almost constant (independent of disturbances): Want small magnitude of dcopt(d)/dd. Variable c is sensitive to changes in input: Want large magnitude of gain=dc/du (this is to reduce effect of measurement error and noise). If the economic loss with single variables is too large, then one may use measurement combinations, c=Hy (where H is a “full” matrix). 3. Unconstrained degrees of freedom: NEVER try to control a variable that reaches max or min at the optimum (in particular, never control J) Surprisingly, this is a very common mistake, even (especially?) with control experts Ruke for TPM location: Locate TPM at the next constraint to become active as throughput is increased (bottleneck) Rules for inventory control: 1. Use Radiation rule (PC, LC, FC ++) 2. Avoid having all flows in a recycle system on inventory control (this is a restatement of Luyben’s rule of “fixing a flow inside a recycle system” to avoid snowballing) Rules for selecting stabilizing CVs (CV2): Control sensitive variablkes Rules for pairing: 1. General: “Pair close” (large gain and small effective time delay) 2. CV1: Sigurd’s pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up” 3. CV2 (stabilizing loop): Avoid MV that may saturate

PLANTWIDE CONTROL CASE STUDIES Distillation: regulatory control Distillation: Economics (CV1) Single column Two columns in series Reactor/separator/recycle problem Economics (CV1) TPM location Max. throughput (Bottleneck)

Case study: Distillation control S. Skogestad, ``The dos and don'ts of distillation columns control'', Chemical Engineering Research and Design (Trans IChemE, Part A), 85 (A1), 13-23 (2007).

Typical “LV”-regulatory control Assume given feed 5 dynamic DOFs (L,V,D,B,VT) Overall objective (CV1): Control compositions (xD and xB) “Obvious” stabilizing loops (CV2): Condenser level (M1) Reboiler level (M2) Pressure (p) + “non-obvious” CV2 4. Column temperature (T)

Issues distillation control TC Ts L V The “configuration” problem (level and pressure control) Which are the two remaining degrees of freedom? e.g. LV-, DV-, DB- and L/D V/B-configurations The temperature control problem Which temperature (if any) should be controlled? Composition control problem Control two, one or no compositions? Always control valuable product at spec

Control “configurations” (pairing u2-y2 for level control) “XY-configuration” X: remaining input in top after controlling top level (MD): X= L (reflux), D, L/D,… Y: remaining input in bottom after controlling MB: Y = V (boilup, energy input), B, V/B, ...

Top of Column “Standard” : LY-configuration (“energy balance”) Configurations Top of Column cooling LC VT LS “Standard” : LY-configuration (“energy balance”) L+D D L Set manually or from upper-layer controller (temperature or composition) Set manually or from upper-layer controller VT LC DS “Reversed”: DY-configuration (“material balance”) D L

Top of Column x Similar in bottom... XV, XB, X V/B Configurations VT D LC D L D Ls Set manually or from upper-layer controller x (L/D)s Similar in bottom... XV, XB, X V/B

How do the configurations differ? Has been a lot of discussion in the literature (Shinskey, Buckley, Skogestad, Luyben, etc.). Probably over-emphasized, but let us look at it Level control by itself (emphasized by Buckley et al., 1985) Interaction of level control with composition control Related to “local consistency” (Do not want inventory control to depend on composition loops being closed) “Self-regulation” in terms of disturbance rejection (emphasized by Skogestad and Morari, 1987) Remaining two-point composition control problem (steady-state RGA - emphasized by Shinskey, 1984)

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

BUT: To avoid strong sensitivity to disturbances: Temperature profile must also be “stabilized” D feedback using e.g. D,L,V or B LIGHT F TC HEAVY B Even with the level and pressure loops closed the column is practically unstable - either close to integrating or even truly unstable ( e.g. with mass reflux: Jacobsen and Skogestad, 1991) To stabilize the column we must use feedback (feedforward will give drift) Simplest: “Profile feedback” using sensitive temperature

Stabilizing the column profile Should close one “fast” loop (usually temperature) in order to “stabilize” the column profile Makes column behave more linearly Strongly reduces disturbance sensitivity Keeps disturbances within column Reduces the need for level control Makes it possible to have good dual composition control P-control usually OK (no integral action) Similar to control of liquid level

Stabilizing the column profile (T) Regulatory layer Stabilizing the column profile (T) LV TC T s . loop TC TS (a) Common: Control T using V (b) If V may saturate: Use L T at which end? Prefer “important” end with tightest purity spec, T at which stage? Choose “sensitive” stage (sensitive to MV change) Pair T with which input (MV)? Generally “pair close” But avoid input that may saturate Dynamics: V has immediate effect, whereas L has delay Prefer “same end” (L for Ttop, V for Tbtm) to reduce interactions Note: may not be possible to satisfy all these rules

Bonus 1 of temp. control: Indirect level control TC Disturbance in V, qF: Detected by TC and counteracted by L -> Smaller changes in D required to keep Md constant!

Bonus 2 of temp. control: Less interactive Setpoint T: New “handle” instead of L Ts TC

Less interactive: RGA with temperature loop closed

Less interactive: Closed-loop response with decentralized PID-composition control Interactions much smaller with “stabilizing” temperature loop closed … and also disturbance sensitivity is expected smaller %

Integral action in inner temperature loop has little effect %

Note: No need to close two inner temperature loops % Would be even better with V/F

Would be even better with V/F: Ts TC F (V/F)s x V

A “winner”: L/F-T-conguration x Ts (L/F)s Only caution: V should not saturate

Temperature control: Which stage? TC

Binary distillation: Steady-state gain G0 = ΔT/ΔL for small change in L BTM TOP

Summary: Which temperature to control? Rule 1. Avoid temperatures close to column ends (especially at end where impurity is small) Rule 2. Control temperature at important end (expensive product) Rule 3. To achieve indirect composition control: Control temperature where the steady-state sensitivity is large (“maximum gain rule”). Rule 4. For dynamic reasons, control temperature where the temperature change is large (avoid “flat” temperature profile). (Binary column: same as Rule 3) Rule 5. Use an input (flow) in the same end as the temperature sensor. Rule 6. Avoid using an input (flow) that may saturate.

Conclusion stabilizing control: Remaining supervisory control problem TC Ts Ls Would be even better with L/F With V for T-control + may adjust setpoints for p, M1 and M2 (MPC)

Summary step 5: Rules for selecting y2 (and u2) Selection of y2 Control of y2 “stabilizes” the plant The (scaled) gain for y2 should be large Measurement of y2 should be simple and reliable For example, temperature or pressure y2 should have good controllability small effective delay favorable dynamics for control y2 should be located “close” to a manipulated input (u2) Selection of u2 (to be paired with y2): Avoid using inputs u2 that may saturate (at steady state) When u2 saturates we loose control of the associated y2. “Pair close”! The effective delay from u2 to y2 should be small

CASE STUDIES

Example (TPM location): Evaporator (with liquid feed, liquid heat medium, vapor product) Present structure has feed pump as TPM: May risk “overfeeding” PROBLEM: Objective: “Keep p=ps (or T=Ts) if possible, but main priority is to evaporate a given feed” CVs in order of priority: CV1 = level, CV2 = throughput, CV3 = p MV1 = feed pump, MV2 = heat fluid valve, MV3= vapor product valve Constraints on MVs (in order of becoming active as throughput is increased): Max heat (MV2), Fully open product valve (MV3), Max pump speed (MV1) Where locate TPM? Pairings?

Note: Fully open gas product valve (MV3) is also the bottleneck Pairing based on Sigurd’s general pairing rule**: CV1=level with MV1 (top-priority CV is paired with MV that is least likely to saturate) CV2=throughput with MV3 (so TPM =gas product valve) CV3=p with MV2 (MV2 may saturate and p may be given up) Note: Fully open gas product valve (MV3) is also the bottleneck Rules agree because bottleneck is last constraints to become active as we increase throughput * General: Do not need a FC on the TPM **Sigurd’s general pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up”

CASE STUDY: Recycle plant (Luyben, Yu, etc.) Part 1 -3 Recycle of unreacted A (+ some B) 5 Feed of A 4 1 2 Assume constant reactor temperature. Given feedrate F0 and column pressure: 3 Dynamic DOFs: Nm = 5 Column levels: N0y = 2 Steady-state DOFs: N0 = 5 - 2 = 3 Product (98.5% B)

Recycle plant: Optimal operation Part 1: Economics (Given feed) Recycle plant: Optimal operation mT 1 remaining unconstrained degree of freedom, CV=?

J=V as a function of reflux L Optimum = Nominal point With fixed active constraints: Mr = 2800 kmol (max), xB= 1.5% A (max)

Control of recycle plant: Conventional structure (“Two-point”: CV=xD) LC TPM LC xD XC XC xB LC Control active constraints (Mr=max and xB=0.015) + xD

Luyben law no. 1 (to avoid snowballing): “Fix a stream in the recycle loop” (CV=F or D)

Luyben rule: CV=D (constant) LC LC XC LC

“Brute force” loss evaluation:Disturbance in F0 Luyben rule: Conventional Loss with nominally optimal setpoints for Mr, xB and c

Loss evaluation: Implementation error Luyben rule: Loss with nominally optimal setpoints for Mr, xB and c

Conclusion: Control of recycle plant Active constraint Mr = Mrmax Self-optimizing L/F constant: Easier than “two-point” control Assumption: Minimize energy (V) Active constraint xB = xBmin

Modified Luyben’s law to avoid snowballing Luyben law no. 1 (“Plantwide process control”, 1998, pp. 57): “A stream somewhere in all recycle loops must be flow controlled” Luyben rule is OK dynamically (short time scale), BUT economically (steady-state): Recycle should increase with throughput Modified Luyben’s law 1 (by Sigurd): “Avoid having all streams in a recycle system on inventory control” Good economic control may then require that the stream which is not on inventory control is chosen as the TPM (throughput manipulator).

Part 2: TPM location Example Reactor-recycle process: Given feedrate (production rate set at inlet) TPM

Part 2: TPM location PC TC D L F0 F V B Note: Temperature and pressure controllers shown; Otherwise as before

Alt.1 Alt.2 Alt.3 Alt.4 More? Alt. 5? Alt.6? Alt. 7? T fixed in reactor Alt.1 Alt.2 Follows Luyben law 1: TPM inside recycle Alt.3 Alt.4 More? Alt. 5? Alt.6? Alt. 7? Not really comparable since T is not fixed Unconventional TPM

What about TPM=D (Luyben rule)? Alt. 5 What about TPM=D (Luyben rule)? Control xB, xD, Md Not so simple with liquid feed….. PC TC TPM LC LC ? XC LC XC

What about TPM=D (Luyben rule)? Alt. 5 What about TPM=D (Luyben rule)? Another alternative: Top level control by boilup Get extra DOF in top OK! PC TC TPM LC LC XC LC XC

NOTE: There are actually two recycles One through the reactor (D or F) One through the column (L) One flow inside both recycle loops: V Alt.6: TPM=V if we want to break both recycle loops! PC TC

TPM = V Alt. 6 PC LC LC L XC F TC TPM XC LC L and F for composition control: OK!

What about keeping V constant? Alt. 7 What about keeping V constant? PC TC LC TPM L LC F0 F V LC XC With feedrate F0 fixed (TPM) L for compostion control in bottom (xB) Top composition floating NO! Never control cost J=V

Bottleneck: max. vapor rate in column   Reactor-recycle process: Want to maximize feedrate: reach bottleneck in column Bottleneck: max. vapor rate in column TPM

Bottleneck: max. vapor rate in column Reactor-recycle process with max. feedrate Alt.A: Feedrate controls bottleneck flow Bottleneck: max. vapor rate in column TPM Vs FC Vmax V Vmax-Vs=Back-off = Loss Get “long loop”: Need back-off in V

Bottleneck: max. vapor rate in column Reactor-recycle process with max. feedrate: Alt. B Move TPM to bottleneck (MAX). Use feedrate for lost task (xB) Bottleneck: max. vapor rate in column MAX TPM =Alt.6 TPM Get “long loop”: May need back-off in xB instead…

Reactor-recycle process with max. feedrate: Alt Reactor-recycle process with max. feedrate: Alt. C: Best economically: Move TPM to bottleneck (MAX) + Reconfigure upstream loops MAX LC TPM OK, but reconfiguration undesirable… =Alt.6 TPM

Reactor-recycle process: Alt.C’: Move TPM + reconfigure (permanently!) LC CC TPM F0s =Alt.6 TPM For cases with given feedrate: Get “long loop” but no associated loss

Alt.4: Multivariable control (MPC) Can reduce loss BUT: Is generally placed on top of the regulatory control system (including level loops), so it still important where the production rate is set! One approach: Put MPC on top that coordinates flows through plant By manipulating feed rate and other ”unused” degrees of freedom (including level setpoints): E.M.B. Aske, S. Strand and S. Skogestad, ``Coordinator MPC for maximizing plant throughput'', Computers and Chemical Engineering, 32, 195-204 (2008).

Comments on case study Operate with L=0 (column is a flash). Not optimal nominally, but good enough? Many papers, a lot of confusion Stupid recommendations of “balanced schemes” with reactor level not at maximum (Luyben , Yu) Gives economic loss Not understood: Distillation column itself is also a recycle Recommended reading: T. Larsson, M.S. Govatsmark, S. Skogestad, and C.C. Yu, ``Control structure selection for reactor, separator and recycle processes'', Ind. Eng. Chem. Res., 42 (6), 1225-1234 (2003).

Plantwide control. Main references The following paper summarizes the procedure: S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, 28 (1-2), 219-234 (2004). There are many approaches to plantwide control as discussed in the following review paper: T. Larsson and S. Skogestad, ``Plantwide control: A review and a new design procedure'' Modeling, Identification and Control, 21, 209-240 (2000). The following paper updates the procedure: S. Skogestad, ``Economic plantwide control’’, Book chapter in V. Kariwala and V.P. Rangaiah (Eds), Plant-Wide Control: Recent Developments and Applications”, Wiley (2012). More information: http://www.nt.ntnu.no/users/skoge/plantwide All papers available at: http://www.nt.ntnu.no/users/skoge/

PC TC