Outline Skogestad procedure for control structure design I Top Down Step S1: Define operational objective (cost) and constraints Step S2: Identify degrees of freedom and optimize operation for disturbances Step S3: Implementation of optimal operation What to control ? (primary CV’s) Control Active constraints + self-optimizing variables Step S4: Where set the production rate? (Inventory control) II Bottom Up Step S5: Regulatory control: What more to control (secondary CV’s) ? Step S6: Supervisory control Step S7: Real-time optimization

Step S4. Where set production rate? Very important decision that determines the structure of the rest of the inventory control system! May also have important economic implications Link between Top-down (economics) and Bottom-up (stabilization) parts Inventory control is the most important part of stabilizing control “Throughput manipulator” (TPM) = MV for controlling throughput (production rate, network flow) Where set the production rate = Where locate the TPM? Traditionally: At the feed For maximum production (with small backoff): At the bottleneck

TPM (Throughput manipulator) Definition 1. TPM = MV used to control throughput (CV) = “MV used to set production rate” Definition 2 (Aske and Skogestad, 2009). A TPM is a degree of freedom that affects the network flow and which is not directly or indirectly determined by the control of the individual units, including their inventory control. The TPM is the “gas pedal” of the process Value of TPM: Usually set by the operator (manual control) Operators are skeptical of giving up this MV to the control system (e.g. MPC) The TPM is usually a flow (or closely related to a flow), e.g. main feedrate, but not always. It can be a setpoint to another control loop Example: Reactor temperature can be a TPM, because it changes the reactor conversion, Example: Pressure of gas product can be a TPM, because it changes the gas product flowrate Usually, only one TPM for a plant, but there can be more if there are parallel units or splits into alternative processing routes multiple feeds that do not need to be set in a fixed ratio If we consider only part of the plant then the TPM may be outside our control. throughput is then a disturbance

TPM and link to inventory control Liquid inventory: Level control (LC) Sometimes pressure control (PC) Gas inventory: Pressure control (PC) Component inventory: Composition control (CC, XC, AC)

Production rate set at inlet : Inventory control in direction of flow* TPM * Required to get “local-consistent” inventory control

Production rate set at outlet: Inventory control opposite flow* TPM * Required to get “local-consistent” inventory control

Production rate set inside process* TPM * Required to get “local-consistent” inventory control

General: “Need radiating inventory control around TPM” (Georgakis)

Consistency of inventory control Consistency (required property): An inventory control system is said to be consistent if the steady-state mass balances (total, components and phases) are satisfied for any part of the process, including the individual units and the overall plant. Local*-consistency (desired property): A consistent inventory control system is said to be local-consistent if for any part/unit the local inventory control loops by themselves are sufficient to achieve steady-state mass balance consistency for that unit (without relying on other loops being closed). * Previously called self-consistency 9

QUIZ 1 CONSISTENT?

Local-consistency rule Rule 1. Local-consistency requires that 1. The total inventory (mass) of any part of the process must be locally regulated by its in- or outflows, which implies that at least one flow in or out of any part of the process must depend on the inventory inside that part of the process. 2. For systems with several components, the inventory of each component of any part of the process must be locally regulated by its in- or outflows or by chemical reaction. 3. For systems with several phases, the inventory of each phase of any part of the process must be locally regulated by its in- or outflows or by phase transition. Proof: Mass balances Note: Without the word “local” one gets the more general consistency rule

QUIZ 1 CONSISTENT?

Dynamic simulation case (d)

Local concistency requirement -> “Radiation rule “(Georgakis)

Flow split: May give extra DOF TPM Extra DOF (FC) No extra DOF

Consistent? Local-consistent? QUIZ 2 Note: Local-consistent is more strict as it implies consistent

Closed system: Must leave one inventory uncontrolled QUIZ 3 Closed system: Must leave one inventory uncontrolled

OK? (Where is production set? QUIZ 4 OK? (Where is production set? TPM1 TPM2 NO. Two TPMs (consider overall liquid balance). Solution: Interchange LC and FC on last tank

Example 1: Alternative TPM locations Compressor could be replaced by valve if p1>pG

Alt.1 Alt.2 Alt.3 Alt.4 NOT CONSISTENT

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

Alt.1 Alt.2 Alt.3 Alt.4

Where should we place TPM? TPM = MV used to control throughput Traditionally: TPM = Main feed valve (or pump/compressor) Gives inventory control “in direction of flow” Consider moving TPM if: There is an important CV that could otherwise not be well controlled Dynamic reasons Special case: Max. production important: Locate TPM at process bottleneck* ! TPM can then be used to achieve tight bottleneck control (= achieve max. production) Economics: Max. production is very favorable in “sellers marked” If placing it at the feed may yield infeasible operation (“overfeeding”) If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM inside recycle loop BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck) Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)** *Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control **Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally) saturate with CV that may be given up”

QUIZ. Distillation. OK? LV-configuration TPM

DB-configuration OK??? TPM

TPM

Additional problems See “Kida slides” Exercise 4

Example * ** * Keep p ¸ pmin ** Keep valve fully open

Often optimal: Locate TPM at bottleneck! "A bottleneck is a unit where we reach a constraints which makes further increase in throughput infeasible" If feed is cheap and available: Located TPM at bottleneck (dynamic reasons) If the flow for some time is not at its maximum through the bottleneck, then this loss can never be recovered.

Single-loop alternatives for bottleneck control Want max flow here Traditional: Manual control of feed rate TPM Alt.1. Feedrate controls bottleneck flow (“long loop”…): FC Fmax TPM Alt. 2: Feedrate controls lost task (another “long loop”…): Fmax TPM Alt. 3: Reconfigure all upstream inventory loops: Fmax TPM

Possible improvements Alt. 1D: Feedrate controls bottleneck flow + “feedforward”: FC Fmax TPM Alt. 2D: Feedrate controls lost task + “feedforward”: Fmax TPM Alt. 4: MPC

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

Bottleneck: max. vapor rate in column Example Reactor-recycle process with max. feedrate Alt.1: 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 Example Reactor-recycle process with max. feedrate: Alt. 2 Better economically: Move TPM to bottleneck (MAX). Feedrate used for lost task (xb) Bottleneck: max. vapor rate in column MAX 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. 3: Even better economically: Move TPM to bottleneck (MAX). Reconfigure upstream loops Example MAX LC TPM OK, but reconfiguration undesirable…

Reactor-recycle process: Alt.3: Move TPM + reconfigure (permanently!) Example Reactor-recycle process: Alt.3: Move TPM + reconfigure (permanently!) LC CC TPM F0s For cases with given feedrate: Get “long loop” but no associated loss

Bottleneck: max. vapor rate in column Example Reactor-recycle process with max. feedrate Alt.1D: Alt. 1 “Long loop” + “feedforward” Bottleneck: max. vapor rate in column TPM F/F0 Vs FC “Feedforward”: Send feed change to ALL flows upstream bottleneck Less back-off in V because F closer to V

Example Reactor-recycle process with max. feedrate Alt.2D: Alt. 2 “Long loop” + “feedforward” F/F0 MAX TPM “Feedforward”: Send flow change to ALL flows upstream bottleneck Less back-off in xB because F closer to xB

Alt.4: Multivariable control (MPC) Example 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: E.M.B. Aske, S. Strand and S. Skogestad, ``Coordinator MPC for maximizing plant throughput'', Computers and Chemical Engineering, 32, 195-204 (2008).

May move TPM to inside recycle loop to avoid snowballing Example: Eastman esterification process Alcohol recycle Reach max mass transfer rate: R increases sharply (“snowballing”) Ester product Alcohol + water + extractive agent (e)

First improvement: Located closer to bottleneck

Final improvement: Located “at” bottleneck + TPM is inside “snowballing” loop

Where should we place TPM? TPM = MV used to control throughput Traditionally: TPM = Main feed valve (or pump/compressor) Operators like it. Gives inventory control “in direction of flow” Consider moving TPM if: There is an important CV that could otherwise not be well controlled Dynamic reasons Special case: Max. production important: Locate TPM at process bottleneck* ! Because max. production is very favorable in “sellers marked” TPM can then be used to achieve tight bottleneck control (= achieve max. flow) If placing it at the feed may yield infeasible operation (“overfeeding”) If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM inside recycle loop BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck) Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)** *Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control **Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally) saturate with CV that may be given up”

Conclusion TPM (production rate manipulator) Think carefully about where to place it! Difficult to undo later

Location flow sensor (before or after valve or pump): Does not matter from consistency point of view Locate to get best flow measurement Before pump: Beware of cavitation After pump: Beware of noise Etc. Location of pressure sensor (before or after valve, pump or compressor): Important from consistency point of view

Moving TPM A purely top-down approach: Start by controlling all active constaints at max. throughput (may give moving TPM) Economic Plantwide Control Over a Wide Throughput Range: A Systematic Design Procedure Rahul Jagtap, Nitin Kaistha*and Sigurd Skogestad   Step 0: Obtain active constraint regions for the wide throughput range Step 1: Pair loops for tight control of economic CVs at maximum throughput Most important point economically Most active constraints Step 2: Design the inventory (regulatory) control system Step 3: Design loops for ‘taking up’ additional economic CV control at lower throughputs along with appropriate throughput manipulation strategy Warning: May get complicated, but good economically because of tight control of active constraints

TPM for < max throughput Figure 5. Plantwide control structure for maximum throughput operation of recycle process (Case Study I) A + B  C B + C  D Stripper Column A, B Recycle B A C D FC PC LC TC X RC CCD CCB V1MAX V2MAX 0.98% 0.02% LVLRxrMAX TPM for < max throughput 165 °C xBRxr Opt HS3 TRxrOpt HS2 LS1 SP1 SP3 LC2 SP2 SP1 > SP2 > SP3 LC1 LC3 LS2 TRxrMAX