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Systematic design of advanced control structures Adriana Reyes-Lúa February 28 th , 2020 Norwegian University of Science and Technology

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Page 1: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

Systematic design of

advanced control structures

Adriana Reyes-Lúa

February 28th, 2020

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Page 2: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Content

• Motivation and scope

• Active constraint switching with advanced control structures (chapter 2)

– Case study: mixing

– Case study: distillation column

– Case study: cooling cycle (chapter 3)

– Case study: cooler (chapter 4)

• MV to MV constraint switching

– Split range control

• Design of standard split range controllers (chapter 5)

• Generalized split range controller (chapter 6)

– Multiple controllers with different setpoints (chapter 7)

• Improved PI control for tank level (chapter 8)

• Conclusions

Page 3: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Motivation and scope

CV: controlled

variable (output, y)• Temperature

• Pressure

• Concentration

MV: manipulated

variable (input, u)• Valve opening

• Compressor rotational

speed

DV: disturbance variable (d)• Ambient temperature

• Raw materials

• Desired production

Page 4: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Motivation and scope

Top-down analysis:S1-S4: Identify steady-state

optimal operation

Bottom-up analysis:S5-S7: Design control

structure

Page 5: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

5

Motivation and scope

Bottom-up analysis:S5: regulatory control layer

S6: supervisory control layer

S7: online optimization layer

Page 6: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

6

Motivation and scope

Bottom-up analysis:S5: regulatory control layer

S6: supervisory control layer

S7: online optimization layer

Keeps operation

in the right

active constraint region

Page 7: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

7

Motivation and scope

Constraint region«region in the disturbance

space defined by which

constraints are active within it»

Disturbance 1

Dis

turb

an

ce

2

Jacobsen and Skogestad (2011) Active constraint regions for optimal operation of chemical processes. Industrial & Engineering Chemistry Research.

S6: supervisory control layer

Page 8: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

8

Motivation and scope

Model predictive control

Advanced control structures

S6: supervisory control layer

Page 9: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

9

Active constraint switching with classical advanced

control structures

Figure taken from www.transmittershop.com/blog/causes-solutions-annoying-noise-control-valves

Page 10: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

10

Active constraint switching with classical advanced

control structures

Figure taken from www.transmittershop.com/blog/causes-solutions-annoying-noise-control-valves

Page 11: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

11

Active constraint switching with classical advanced

control structures

Figure taken from www.transmittershop.com/blog/causes-solutions-annoying-noise-control-valves

Page 12: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

12

Design procedure for active constraint switching with

classical advanced control structures

A1• Define control objectives, CV constraints and MV constraints

A2• Organize constraints in priority list

A3• Identify possible and relevant active constraint switches

A4• Design control structure for optimal operation

A5• Design control structure to handle active constraint switches

Page 13: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

13

Design procedure for active constraint switching

Case study:Mixing of

air and MeOH

Page 14: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

14

Design procedure for active constraint switching

Step A1: Define control objectives, CV constraints and MV constraints

Control objectives:• Keep y1 = xMeOH = 0.10 ideal

• Keep y1 =xMeOH > 0.08

• Control y2 = mtot ideal

2 CVs2 MVs

Page 15: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

15

Design procedure for active constraint switching

Control objectives:• Keep y1 = xMeOH = 0.10

• Keep y1 =xMeOH > 0.08

• Control y2 = mtot

2 CVs2 MVs

u1 is has a maximum value

Step A1: Define control objectives, CV constraints and MV constraints

Page 16: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

16

Design procedure for active constraint switching

Step A2: Organize constraints in priority list

Figure from www.indelac.com/blog/control-valves-vs.-regulators-in-control-applications

Page 17: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

17

Design procedure for active constraint switching

Step A2: Organize constraints in priority list

• Constraint on air flow (u1)

• Constraint on MeOH flow (u2)(P1) Physical MV inequality constraints

• Constraint (max and min) on xMeOH (y1)(P2) Critical CV inequality constraints

• Setpoint on xMeOH (y1)(P3) Less critical CV and MV constraints

• Setpoint on mtot (y2)(P4) Desired throughput

• No unconstrained degrees of freedom(P5) Self-optimizing variables

Page 18: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design procedure for active constraint switching

Step A3: Identify possible and relevant active constraint switches

• Case 1: CV to CV constraint switching

One MV switching between two alternative CVs.

Page 19: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design procedure for active constraint switching

Step A3: Identify possible and relevant active constraint switches

Split range control

Valve position control

Different controllers

with different setpoints

• Case 2: MV to MV constraint switching

More than one MV for one CV.

Page 20: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design procedure for active constraint switching

Step A3: Identify possible and relevant active constraint switches

• Case 3: MV to CV constraint switching

MV controlling a CV that may saturate; no extra MVs

Input saturation pairing rule«an MV that is likely to saturate at

steady-state should be paired with a

CV that can be given up»

Low priority CVHigh priority CV:

always controlled

MV that does not

saturate

Page 21: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

21

Design procedure for active constraint switching

Step A3: Identify possible and relevant active constraint switches

• Case 3: MV to CV constraint switching

MV controlling a CV that may saturate; no extra MVs

Following input

saturation pairing rule

NOT following input

saturation pairing rule

Page 22: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

22

Design procedure for active constraint switching

Step A3: Identify possible and relevant active constraint switches

• At nominal operation point all

constraints are satisfied

• Constraint switch:

• Reach maximum air flow (u1)

• Lose a degree of freedom (case 3)• Must give up controlling the

constraint with the lowest priority

(desired throughput)

Page 23: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design procedure for active constraint switching

Step A4: Design control structure for optimal operation

Case A Case B

NOT following input

saturation pairing rule

Following input

saturation pairing rule

Low

priority

CV

MV likely to saturate

High

priority CV

not always

controlled

MV likely to saturate

Page 24: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design procedure for active constraint switching

Step A4: Design control structure for optimal operation

Case A Case B

NOT following input

saturation pairing rule

Following input

saturation pairing rule

Needs MV to CV

switching

Page 25: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design procedure for active constraint switching

Step A5: Design control structure to handle active constraint switches

Case B-SRC

Split range control+selector

Case B-VPC

Valve position control + selector

Page 26: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design procedure for active constraint switching

Case study: Mixing of air and MeOHMV1 is saturated:

lost degree of freedomHigh priority CV: concentration

Low priority CV (throughput) MV2 is not saturated:

It should be used to control the high priority CV

Page 27: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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MV to MV constraint switching

Split range control Different controllers with

different setpoints

Valve position

control

Page 28: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Classical split range control

Monogram of Instruments and Process Control

prepared at Cornell, NY, in 1945

CV

MV1

MV2

Eckman, D.P. (1945).

Principles of industrial

control, New York.

Page 29: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Classical split range control

v internal signal to split range block limited physical meaning

v* split value

ui controller output physical meaning

αi gain from v to ui slope

Page 30: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Classical split range control

v internal signal to split range block limited physical meaning

v* split value degree of freedom

ui controller output physical meaning

αi gain from v to ui slope

Page 31: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

31

Classical split range control

v internal signal to split range block limited physical meaning

v* split value degree of freedom

ui controller output physical meaning

αi gain from v to ui slope

Page 32: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design of split range control: select slopes

Goal: get desired loop gain |g C|

at crossover frequency

Fast process Slow process

Desired

gain for ui

Common

gain in C

DOFDesired

gain for ui

Common

gain in C

DOF

Page 33: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design of split range control: order of MVs

Define the desired operating point for every MV

Group the MVs according to the effect on the CV

Within each group, define order of use

Page 34: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Design of split range control

u1 = uAC : air conditioning (AC)

u2 = uCW : cooling water (CW)

u3 = uHW : heating water (HW)

u4 = uEH : electrical heating (EH)

Page 35: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Classical split range control: a compromise

1 DOF

2 tuning parameters

Page 36: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized split range controller

Page 37: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized split range controller

«Baton strategy» logic

k is the active input

• Ck computes uk’ (suggested value for uk)

• If ukmin< uk’< uk

max

• Keep uk active and uk uk’

• Keep remaining ui at limiting value

• else

• Set uk= ukmin or uk< uk

max, depending on the reached limit

• New active input selected according to predefined sequence

(j= k-1 or j=k+1)Preliminary step:

• Define order of use of MVs ( j=1,…,N)

• Tune controllers The active input will decide when to switch and

will remain active as long as it is not saturated.

Page 38: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized split range controller

u1 = uAC : air conditioning (AC)

u2 = uCW : cooling water (CW)

u3 = uHW : heating water (HW)

u4 = uEH : electrical heating (EH)

Page 39: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized vs standard split range controller

Page 40: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized split range controller: initialization

How to

start?

This suggested input was

not being applied while

input k was not in use

This accumulated error is

not due to the previous

actions of input kk

Page 41: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized split range controller: initialization

Resetting:Only use error

when I receive

the baton

Initial action proportional to error at tb

k

Page 42: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized split range controller: initialization

Back-calculation:

I was keeping

track of the

applied input

Page 43: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized split range controller: initialization

Resetting:

Back-calculation:

Page 44: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Generalized split range controller vs MPC

Page 45: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints

Does this make sense at any point?

Page 46: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints

Setpoint

deviation

Input

usage

Page 47: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints:

Optimal setpoint deviation

Linear for u and quadratic for Δy Inputs are a linear function of output

Page 48: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints:

Optimal setpoint deviation

Linear for u and quadratic for Δy Inputs are a linear function of output

Cost when using uk as input

Page 49: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints:

Optimal setpoint deviation

Linear for u and quadratic for Δy

Optimal

setpoint deviation

minimizing cost

Inputs are a linear function of output

Cost when using uk as input

Page 50: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints: Case study

QAC : air conditioning

QHW : heating water

QEH : electrical heating

Page 51: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints: Room T

Cost: linear for u and quadratic for Δy

QAC : air conditioning

QHW : heating water

QEH : electrical heating

Inputs (Qi) are a linear function of output (T)

Optimal setpoint deviation minimizing cost

Page 52: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints: Room T

QAC : air conditioning

QHW : heating water

QEH : electrical heating

Optimal setpoint

deviation

minimizing cost

Page 53: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints: Room T

Page 54: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Multiple controllers with different setpoints: Room T

Lower accumulated

cost with minimum

setpoint deviation

Constant setpoint

Page 55: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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Final comments

• Steady-state optimal operation may be easily achieved using PID-based

control structures– Chapters 2,3,4: active constraint switching

– Chapter 7: optimal setpoints

• Useful to systematically define control objectives, feasibility and tools– Priority list of constraints

– Control structures available for each type of switch (CV-CV, MV-MV, MV-CV)

• Possible to improve performance of PID-based advanced control– Chapters 5, 6: design of split range controllers

– Chapter 8: improved level control

Page 56: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

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One final comment

• The “gap” between theory and practice can be in both directions

Åström, K. J., & Kumar, P. R. (2014). Control: A perspective. Automatica, 50(1), 3–43.

Centrifugal governor used in steam

engines in the 1780’s:

Proportionally controls fuel flow to

maintain engine speed.

Theoretical investigation started about

a century later.speed

fuel

Page 57: Systematic design of advanced control structures · 2020-03-05 · Case study: Mixing of air and MeOH. 14 Design procedure for active constraint switching Step A1: Define control

Systematic design of

advanced control structures

Thank you for your attention!

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