Part 3: Regulatory («stabilizing») control Wed AM Part 3: Regulatory («stabilizing») control Inventory (level) control structure Location of throughput manipulator Consistency and radiating rule 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  

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) 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 Reactor temperature can be a TPM, because it changes the reactor conversion, Pressure of gas product can be a TPM, because it changes the gas product flowrate Fuel cell: Load (current I) is usually the TPM 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. 10

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?

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

Flow split: May give extra DOF TPM Split: Extra DOF (FC) Flash: 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: Separator control Alternative TPM locations Compressor could be replaced by valve if p1>pG

Alt.1 Alt.2 Alt.4 Alt.3 Similar to original but NOT CONSISTENT (PC not direction of flow)

Example: Solid oxide fuel cell xH2?? xCH4,s CC PC CH4 CH4 + H2O = CO + 3H2 CO + H2O = CO2 + H2 2H2 + O2- → 2H2O + 2e- H2O (in ratio with CH4 feed to reduce C and CO formation) Solid oxide electrolyte O2- e- TPM = current I [A] = disturbance O2 + 4e- → 2O2- Air (excess O2) PC TC Ts = 1070 K (active constraint)

LOCATION OF SENSORS 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 noisy measurement Location of pressure sensor (before or after valve, pump or compressor): Important from consistency point of view

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

DB-configuration: Level control NOT consistent by itself, but can still work* if we add one (or preferably two) composition/temperature loops cc TPM cc *But DB-configuration is not recommended!

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

QUIZ

LOCATION OF SENSORS 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

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

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 Follows Luyben’s law 1 to avoid snowballing(modified): “Avoid having all streams in a recycle system on inventory control”

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”

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

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

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) (self-optimizing control) Step S4: Where set the production rate? (Inventory control) II Bottom Up Step S5: Regulatory control: What more to control (secondary CV’s) ? Distillation example Step S6: Supervisory control Step S7: Real-time optimization

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  

Regulatory layer II. Bottom-up Determine secondary controlled variables (CV2) and structure (configuration) of control system (pairing, CV2-MV2) A good control configuration is insensitive to parameter changes

Step 5. Regulatory control layer Regulatory layer Step 5. Regulatory control layer Purpose: “Stabilize” the plant using a simple control configuration (usually: local SISO PID controllers + simple cascades) Enable manual operation (by operators) Main structural decisions: What more should we control? (secondary cv’s, CV2, use of extra measurements) Pairing with manipulated variables (mv’s u2) CV1 CV2 = ?

Objectives regulatory control layer Regulatory layer Objectives regulatory control layer Allow for manual operation Simple decentralized (local) PID controllers that can be tuned on-line Take care of “fast” control Track setpoint changes from the layer above Local disturbance rejection Stabilization (mathematical sense) Avoid “drift” (due to disturbances) so system stays in “linear region” “stabilization” (practical sense) Allow for “slow” control in layer above (supervisory control) Make control problem easy as seen from layer above Use “easy” and “robust” measurements (pressure, temperature) Simple structure Contribute to overall economic objective (“indirect” control) Should not need to be changed during operation

Regulatory layer Stabilizing control: Use inputs MV2=u2 to control “drifting” variables CV2 Primary CV CV1 CV2s K u2 G CV2 Secondary CV (control for dynamic reasons) Key decision: Choice of CV2 (controlled variable) Also important: Choice of MV2=u2 (“pairing”) Process control: Typical «drifting» variables (CV2) are Liquid inventories (level) Vapor inventories (pressure) Some temperatures (reactor, distillation column profile)

Degrees of freedom unchanged Regulatory layer Degrees of freedom unchanged No degrees of freedom lost as setpoints y2s replace inputs u2 as new degrees of freedom for control of y1 Cascade control: G K CV2s u2 CV2 CV1 Original DOF New DOF

Example: Exothermic reactor (unstable) Regulatory layer Example: Exothermic reactor (unstable) Active constraints (economics): Product composition c + level (max) u = cooling flow (q) CV1 = composition (c) CV2 = temperature (T) feed CC CV1=c CV1s Ls=max TC CV2=T CV2s LC product u cooling

Optimizer (RTO) PROCESS H2 H y ny d Stabilized process u1 u2 CV1s Supervisory controller (MPC) Regulatory controller (PID) H2 H y1=CV1 CV2s y ny d Stabilized process CV1s y2=CV2 Physical inputs (valves) Optimally constant valves Always active constraints u1 u2 Degrees of freedom for optimization (usually steady-state DOFs), MVopt = CV1s Degrees of freedom for supervisory control, MV1=CV2s + unused valves Physical degrees of freedom for stabilizing control, MV2 = valves (dynamic process inputs)

Details Step 5 (Structure regulatory control layer) Regulatory layer (a) What to control (CV2)? Control CV2 that “stabilizes the plant” (stops drifting) Select CV2 which is easy to control (favorable dynamics) In addition, active constraints (CV1) that require tight control (small backoff) may be assigned to the regulatory layer.* *Comment: usually not necessary with tight control of unconstrained CVs because optimum is usually relatively flat

“Control CV2s that stabilizes the plant (stops drifting)” A. “Mathematical stabilization” (e.g. reactor): Unstable mode is “quickly” detected (state observability) in the measurement (y2) and is easily affected (state controllability) by the input (u2). Tool for selecting input/output: Pole vectors y2: Want large element in output pole vector: Instability easily detected relative to noise u2: Want large element in input pole vector: Small input usage required for stabilization B. “Practical extended stabilization” (avoid “drift” due to disturbance sensitivity): Intuitive: y2 located close to important disturbance Maximum gain rule: Controllable range for y2 is large compared to sum of optimal variation and measurement+control error More exact tool: Partial control analysis

Regulatory layer “Control CV2 that stabilizes the plant (stops drifting)” In practice, control: Levels (inventory liquid) Pressures (inventory gas/vapor) (note: some pressures may be left floating) Inventories of components that may accumulate/deplete inside plant E.g., amine/water depletes in recycle loop in CO2 capture plant E.g., butanol accumulates in methanol-water distillation column E.g., inert N2 accumulates in ammonia reactor recycle Reactor temperature Distillation column profile (one temperature inside column) Stripper/absorber profile does not generally need to be stabilized

Identify MVs (u2) to control CV2, taking into account: Details Step 5b…. Regulatory layer (b) Identify pairings = Identify MVs (u2) to control CV2, taking into account: Want “local consistency” for the inventory control Implies radiating inventory control around given flow Avoid selecting as MVs in the regulatory layer, variables that may optimally saturate at steady-state (active constraint on some region), because this would require either reassigning the regulatory loop (complication penalty), or requiring back-off for the MV variable (economic penalty) Want tight control of important active constraints (to avoid back-off) General rule: ”pair close” (see next slide)

Step 5b…. Main rule: “Pair close” Regulatory layer Step 5b…. Main rule: “Pair close” The response (from input to output) should be fast, large and in one direction. Avoid dead time and inverse responses!

Regulatory layer Sigurd’s pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up” Main reason: Minimizes need for reassigning loops Important: Always feasible (and optimal) to give up a CV when optimal MV saturation occurs. Proof (DOF analysis): When one MV disappears (saturates), then we have one less optimal CV. Failing to follow this rule: Need some “fix” when MV saturates to remain optimal, like reconfiguration (logic) backoff (loss of optimality) BUT: Rule may be in conflict with other criteria Dynamics (“pair close” rule) Interactions (“avoid negative steady-state RGA” rule) If conflict: Use reconfiguration (logic) or go for multivariable constraint control (MPC which may provide “built-in” logic) LV TC T s . loop TC TS (a) Normal: Control T using V (b) If V may saturate: Use L

Regulatory layer Why simplified configurations? Why control layers? Why not one “big” multivariable controller? Fundamental: Save on modelling effort Other: easy to understand easy to tune and retune insensitive to model uncertainty possible to design for failure tolerance fewer links reduced computation load

Hierarchical/cascade control: Time scale separation With a “reasonable” time scale separation between the layers (typically by a factor 5 or more in terms of closed-loop response time) we have the following advantages: The stability and performance of the lower (faster) layer (involving y2) is not much influenced by the presence of the upper (slow) layers (involving y1) Reason: The frequency of the “disturbance” from the upper layer is well inside the bandwidth of the lower layers With the lower (faster) layer in place, the stability and performance of the upper (slower) layers do not depend much on the specific controller settings used in the lower layers Reason: The lower layers only effect frequencies outside the bandwidth of the upper layers

Cascade control distillation ys y Ts T Ls L z With flow loop + T-loop in top y XC Ts T TC Ls L FC z XC

QUIZ: What are the benefits of adding a flow controller (inner cascade)? qs Extra measurement y2 = q q z Counteracts nonlinearity in valve, f(z) With fast flow control we can assume q = qs Eliminates effect of disturbances in p1 and p2

Summary: Sigurd’s plantwide control rules Rules for CV-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 (is 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 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) A special case is a closed system 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

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  

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/

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