Outline Control structure design plantwide control A procedure

Outline • Control structure design (plantwide control) • A procedure for control structure design I Top Down • • Step 1: Degrees of freedom Step 2: Operational objectives (optimal operation) Step 3: What to control ? (self-optimizing control) Step 4: Where set production rate? II Bottom Up • Step 5: Regulatory control: What more to control ? • Step 6: Supervisory control • Step 7: Real-time optimization • Case studies 1

II. Bottom-up • Determine secondary controlled variables and structure (configuration) of control system (pairing) • A good control configuration is insensitive to parameter changes Step 5. REGULATORY CONTROL LAYER 5. 1 Stabilization (including level control) 5. 2 Local disturbance rejection (inner cascades) What more to control? (secondary variables) Step 6. SUPERVISORY CONTROL LAYER Decentralized or multivariable control (MPC)? Pairing? Step 7. OPTIMIZATION LAYER (RTO) 2

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 issues: • What more should we control? (secondary cv’s, y 2, use of extra measurements) • Pairing with manipulated variables (mv’s u 2) y 1 = c y 2 = ? 3

Objectives regulatory control layer 1. 2. 3. 4. 5. 6. 7. 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) 8. Allow for “slow” control in layer above (supervisory control) 9. Make control problem easy as seen from layer above The key decisions here (to be made by the control engineer) are: 1. Which extra secondary (dynamic) variables y 2 should we control? 2. Propose a (simple) control configuration (select input-output pairings) 5

Main objectives control system 1. Implementation of acceptable (near-optimal) operation 2. Stabilization ARE THESE OBJECTIVES CONFLICTING? • Usually NOT – Different time scales • Stabilization fast time scale – Stabilization doesn’t “use up” any degrees of freedom • • 6 Reference value (setpoint) available for layer above But it “uses up” part of the time window (frequency range)

Why simplified configurations? • Fundamental: Save on modelling effort • Other: – – – 7 easy to understand easy to tune and retune insensitive to model uncertainty possible to design for failure tolerance fewer links reduced computation load

Use of (extra) measurements (y 2) as (extra) CVs: Cascade control y 2 s K u 2 G y 1 Primary CV y 2 Secondary CV (control for dynamic reasons) Key decision: Choice of y 2 (controlled variable) Also important (since we almost always use single loops in the regulatory control layer): Choice of u 2 (“pairing”) 8

Degrees of freedom unchanged • No degrees of freedom lost by control of secondary (local) variables as setpoints become y 2 s replace inputs u 2 as new degrees of freedom Cascade control: y 2 s New DOF 9 K u 2 G y 1 y 2 Original DOF

Example: Distillation • Primary controlled variable: y 1 = c = x. D, x. B (compositions top, bottom) • BUT: Delay in measurement of x + unreliable • Regulatory control: For “stabilization” need control of (y 2): – – Liquid level condenser (MD) Unstable (Integrating) + No steady-state effect Liquid level reboiler (MB) Pressure (p) Variations in p disturb other loops Holdup of light component in column (temperature profile) Almost unstable (integrating) Ts 10 T-loop in bottom TC

Cascade control distillation ys With flow loop + T-loop in top y X C Ts T TC Ls L 11 X C FC z

Hierarchical 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: 1. The stability and performance of the lower (faster) layer (involving y 2) is not much influenced by the presence of the upper (slow) layers (involving y 1) Reason: The frequency of the “disturbance” from the upper layer is well inside the bandwidth of the lower layers 2. 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 12

QUIZ: What are the benefits of adding a flow controller (inner cascade)? qs Extra measurement y 2 = q 1. 13 z Counteracts nonlinearity in valve, f(z) • 2. q With fast flow control we can assume q = qs Eliminates effect of disturbances in p 1 and p 2

What are the benefits of adding a flow controller (inner cascade)? qs Extra measurement y’ = q 1. 14 z Counteracts nonlinearity in valve, f(z) • 2. q f(z) 1 v ar With fast flow control we can assume q = qs Eliminates effect of disturbances in p 1 and p 2 (FC reacts faster than outer level loop) e alv e lin 0 0 1 z (valve opening)

Counteracting nonlinearity using cascade control: Process gain variation -> Time constant variation Proof: • Slave controller with u = z (valve position) and y=q (flow) • Nonlinear valve with varying gain k: G = k / (τs+1) • PI-controller with gain Kc and integral time τI= τ. • With slave (flow) controller: Transfer function from ys to y (for master loop): • T = L/(1+L) = 1/(τCL s + 1) – where τCL = τ/(k Kc) • So variation in k translates into variation in τCL • In practise this gives a variation in the effective time delay in the master loop – Low gain k for valve gives large effective time delay (bad) 15

Objectives regulatory control layer 1. 2. 3. 4. 5. 6. 7. 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) 8. Allow for “slow” control in layer above (supervisory control) 9. Make control problem easy as seen from layer above 16 Implications for selection of y 2: 1. Control of y 2 “stabilizes the plant” 2. y 2 is easy to control (favorable dynamics)

1. “Control of y 2 stabilizes the plant” A. “Mathematical stabilization” (e. g. reactor): • Unstable mode is “quickly” detected (state observability) in the measurement (y 2) and is easily affected (state controllability) by the input (u 2). • Tool for selecting input/output: Pole vectors – y 2: Want large element in output pole vector: Instability easily detected relative to noise – u 2: Want large element in input pole vector: Small input usage required for stabilization 17 B. “Practical extended stabilization” (avoid “drift” due to disturbance sensitivity): • Intuitive: y 2 located close to important disturbance • Maximum gain rule: Controllable range for y 2 is large compared to sum of optimal variation and control error • More exact tool: Partial control analysis

Recall maximum gain rule for selecting primary controlled variables c: Controlled variables c for which their controllable range is large compared to their sum of optimal variation and control error Restated for secondary controlled variables y 2: Control variables y 2 for which their controllable range is large compared to their sum of optimal variation and control error controllable range = range y 2 may reach by varying the inputs optimal variation: due to disturbances Want small control error = implementation error n 18 Want large

What should we control (y 2)? Rule: Maximize the scaled gain • • General case: Maximize minimum singular value of scaled G Scalar case: |Gs| = |G| / span • |G|: gain from independent variable (u 2) to candidate controlled variable (y 2) – IMPORTANT: The gain |G| should be evaluated at the (bandwidth) frequency of the layer above in the control hierarchy! • • • span (of y 2) = optimal variation in y 2 + control error for y 2 – – 19 If the layer above is slow: OK with steady-state gain as used for selecting primary controlled variables (y 1=c) BUT: In general, gain can be very different Note optimal variation: This is often the same as the optimal variation used for selecting primary controlled variables (c). Exception: If we at the “fast” regulatory time scale have some yet unused “slower” inputs (u 1) which are constant then we may want find a more suitable optimal variation for the fast time scale.

2. “y 2 is easy to control” (controllability) 1. Statics: Want large gain (from u 2 to y 2) 2. Main rule: y 2 is easy to measure and located close to available manipulated variable u 2 (“pairing”) 3. Dynamics: Want small effective delay (from u 2 to y 2) • “effective delay” includes • • 21 inverse response (RHP-zeros) + high-order lags

Rules for selecting u 2 (to be paired with y 2) 1. Avoid using variable u 2 that may saturate (especially in loops at the bottom of the control hieararchy) • Alternatively: Need to use “input resetting” in higher layer (“midranging”) • Example: Stabilize reactor with bypass flow (e. g. if bypass may saturate, then reset in higher layer using cooling flow) 2. “Pair close”: The controllability, for example in terms a small effective delay from u 2 to y 2, should be good. 22

Cascade control (conventional; with extra measurement) The reference r 2 (= setpoint ys 2) is an output from another controller General case (“parallel cascade”) Special common case (“series cascade”) 23

Series cascade 1. 2. 3. Disturbances arising within the secondary loop (before y 2) are corrected by the secondary controller before they can influence the primary variable y 1 Phase lag existing in the secondary part of the process (G 2) is reduced by the secondary loop. This improves the speed of response of the primary loop. Gain variations in G 2 are overcome within its own loop. Thus, use cascade control (with an extra secondary measurement y 2) when: • The disturbance d 2 is significant and G 1 has an effective delay • The plant G 2 is uncertain (varies) or nonlinear 24 Design / tuning • First design K 2 (“fast loop”) to deal with d 2 • Then design K 1 to deal with d 1

Partial control • Cascade control: y 2 not important in itself, and setpoint (r 2) is available for control of y 1 • Decentralized control (using sequential design): y 2 important in itself 25

Partial control analysis Primary controlled variable y 1 = c (supervisory control layer) Local control of y 2 using u 2 (regulatory control layer) Setpoint y 2 s : new DOF for supervisory control 26 Assumption: Perfect control (K 2 -> 1) in “inner” loop Derivation: Set y 2=y 2 s-n 2 (perfect control), eliminate u 2, and solve for y 1

Partial control: Distillation 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 27

Limitations of partial control? • Cascade control: Closing of secondary loops does not by itself impose new problems – Theorem 10. 2 (SP, 2005). The partially controlled system [P 1 Pr 1] from [u 1 r 2] to y 1 has no new RHP-zeros that are not present in the open-loop system [G 11 G 12] from [u 1 u 2] to y 1 provided • r 2 is available for control of y 1 • K 2 has no RHP-zeros • Decentralized control (sequential design): Can introduce limitations. – Avoid pairing on negative RGA for u 2/y 2 – otherwise Pu likely has a RHPzero 28

Selecting measurements and inputs for stabilization: Pole vectors • Maximum gain rule is good for integrating (drifting) modes • For “fast” unstable modes (e. g. reactor): Pole vectors useful for determining which input (valve) and output (measurement) to use for stabilizing unstable modes • Assumes input usage (avoiding saturation) may be a problem • Compute pole vectors from eigenvectors of A-matrix 29

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Example: Tennessee Eastman challenge problem 32

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”Summary Advanced control” STEP S 6. SUPERVISORY LAYER Objectives of supervisory layer: 1. Switch control structures (CV 1) depending on operating region – Active constraints – self-optimizing variables 2. Perform “advanced” economic/coordination control tasks. – Control primary variables CV 1 at setpoint using as degrees of freedom (MV): • Setpoints to the regulatory layer (CV 2 s) • ”unused” degrees of freedom (valves) – Keep an eye on stabilizing layer • Avoid saturation in stabilizing layer – Feedforward from disturbances • If helpful – Make use of extra inputs – Make use of extra measurements 39 Implementation: • Alternative 1: Advanced control based on ”simple elements” (decentralized control) • Alternative 2: MPC

Summary of some simple elements Feeforward control with Multiple feeds etc. (extensive variables). : Ratio control • Ratio setpoint usually set by feedback in a cascade manner Feedback 1. Use of extra measurements for improved control; : Cascade control – Cascade control is when MV (for master) =setpoint to slave controller – MV 1 = CV 2 s 2. Switch between active constraints: Selectors 3. Make use of extra inputs – Dynamic (improve performance): Input resetting = valve position control = midranging control – Steady state (extend operating range): Split range control 4. Reduce interactions when usingle-loop control: Decouplers (including phsically based) 40

Control configuration elements • Control configuration. The restrictions imposed on the overall controller by decomposing it into a set of local controllers (subcontrollers, units, elements, blocks) with predetermined links and with a possibly predetermined design sequence where subcontrollers are designed locally. Some control configuration elements: • Cascade controllers • Decentralized controllers • Feedforward elements • Decoupling elements • Input resetting/Valve position control/Midranging control • Split-range control • Selectors 41

Most important control structures 1. 2. 3. 42 Feedback control Ratio control (special case of feedforward) Cascade control

Ratio control (most common case of feedforward) General: Use for extensive variables (usually flows) with constant optimal ratio Example: Process with two feeds q 1(d) and q 2 (u), where ratio should be constant. Use multiplication block (x): (q 2/q 1)s (desired flow ratio) q 1 (measured flow disturbance) 43 x q 2 (MV: manipulated variable) “Measure disturbance (d=q 1) and adjust input (u=q 2) such that ratio is at given value (q 2/q 1)s”

Usually: Combine ratio (feedforward) with feedback • Adjust (q 1/q 2)s based on feedback from process, for example, composition controller. • This is a special case of cascade control – Example cake baking: Use recipe (ratio control = feedforward), but adjust ratio if result is not as desired (feedback) – Example evaporator: Fix ratio q. H/q. F (and use feedback from T to fine tune ratio) 44

Example Cascade control • Controller (“master”) gives setpoint to another controller (“slave”) – – • Without cascade: “Master” controller directly adjusts u (input, MV) to control y With cascade: Local “slave” controller uses u to control “extra”/fast measurement (y’). “Master” controller adjusts setpoint y’s. Example: Flow controller on valve (very common!) – – – y = level H in tank (or could be temperature etc. ) u = valve position (z) y’ = flowrate q through valve flow in H Hs LC MV=z MV=qs valve position FC z flow out 45 WITHOUT CASCADE flow out WITH CASCADE q measured flow

What are the benefits of adding a flow controllerq (inner cascade)? s Extra measurement y’ = q 1. 46 z Counteracts nonlinearity in valve, f(z) • 2. q f(z) 1 v ar With fast flow control we can assume q = qs Eliminates effect of disturbances in p 1 and p 2 e alv e lin 0 0 1 z (valve opening)

Example (again): Evaporator with heating From reactor q. F [m 3/s] TF [K] c. F [mol/m 3] evaporation level measurement temperature measurement T ∞ H q [m 3/s] T [K] c [mol/m 3] Heating fluid q. H [m 3/s] TH [K] concentrate NEW Control objective • Keep level H at desired value • Keep composition c (rather than temperature T) at desired value BUT: Composition measurement has large delay + unreliable Suggest control structure based on cascade control 47

Split Range Temperature Control 48

Split Range Temperature Control E 0 49 Note: adjust the location er E 0 to make process gains equal

Use of extra measurements: Cascade control (conventional) The reference r 2 (= setpoint ys 2) is an output from another controller General case (“parallel cascade”) Not always helpful… y 2 must be closely related to y 1 Special common case (“series cascade”) 50

Series cascade 1. 2. 3. Disturbances arising within the secondary loop (before y 2) are corrected by the secondary controller before they can influence the primary variable y 1 Phase lag existing in the secondary part of the process (G 2) is reduced by the secondary loop. This improves the speed of response of the primary loop. Gain variations in G 2 are overcome within its own loop. Thus, use cascade control (with an extra secondary measurement y 2) when: • The disturbance d 2 is significant and G 1 has an effective delay • The plant G 2 is uncertain (varies) or nonlinear 51 Design / tuning (see also in tuning-part): • First design K 2 (“fast loop”) to deal with d 2 • Then design K 1 to deal with d 1 Example: Flow cascade for level control u = z, y 2=F, y 1=M, K 1= LC, K 2= FC

Pressure control distillation • Need to stabilze p using Qc • But want Qc to be max • Use cascade with backoff on Qc ( • Another similar example: reactor temperature control (stabilization) closed to Qmax. 52

Use of extra inputs Two different cases 1. Have extra dynamic inputs (degrees of freedom) Cascade implementation: “Input resetting to ideal resting value” Example: Heat exchanger with extra bypass Also known as: Midranging control, valve position control 2. Need several inputs to cover whole range (because primary input may saturate) (steady-state) Split-range control Example 1: Control of room temperature using AC (summer), heater (winter), fireplace (winter cold) Example 2: Pressure control using purge and inert feed (distillation) 53

Extra inputs, dynamically • Exercise: Explain how “valve position control” fits into this framework. As en example consider a heat exchanger with bypass 54

QUIZ: Heat exchanger with bypass closed q. B Thot • Want tight control of Thot • Primary input: CW • Secondary input: q. B • Proposed control structure? 55

Alternative 1 closed q. B TC Thot Use primary input CW: TOO SLOW 56

Alternative 2 closed q. B Thot TC Use “dynamic” input q. B Advantage: Very fast response (no delay) Problem: q. B is too small to cover whole range + has small steady-state effect 57

Alternative 3: Use both inputs (with input resetting of dynamic input) closed q. B Thot FC q. Bs TC TC: Gives fast control of Thot using the “dynamic” input q. B FC: Resets q. B to its setpoint (IRV) (e. g. 5%) using the “primary” input CW IRV = ideal resting value 58 Also called: “valve position control” (Shinskey) and “midranging control” (Sweden)

Too few inputs • Must decide which output (CV) has the highest priority – Selectors • Implementation: Several controllers have the same MV – Selects max or min MV value – Often used to handle changes in active constraints • Example: one heater for two rooms. Both rooms: T>20 C – Max-selector – One room will be warmer than setpoint. • Example: Petlyuk distillation column – Heat input (V) is used to control three compositions using max-selector – Two will be better than setpoint (“overpurified”) at any given time 59

Divided wall column example 60

Control of primary variables • Purpose: Keep primary controlled outputs c=y 1 at optimal setpoints cs • Degrees of freedom: Setpoints y 2 s in reg. control layer • Main structural issue: Decentralized or multivariable? 61

Decentralized control (single-loop controllers) Use for: Noninteracting process and no change in active constraints + Tuning may be done on-line + No or minimal model requirements + Easy to fix and change - Need to determine pairing - Performance loss compared to multivariable control - Complicated logic required for reconfiguration when active constraints move 62

Multivariable control (with explicit constraint handling = MPC) Use for: Interacting process and changes in active constraints + Easy handling of feedforward control + Easy handling of changing constraints • no need for logic • smooth transition - 63 Requires multivariable dynamic model Tuning may be difficult Less transparent “Everything goes down at the same time”