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Discrete-event-dynamic pump control

Sebastian Roll & Heinz A Preisig

Dept of Chemical EngineeringNTNU, Trondheim

Norway

January 27, 2012

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Contents

Project

DEDS Basics

Hybrid - automaton

Properties

Distillation pump control

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Pump project: Process

condensor

ethanol

waterboiler

dis

till

atio

n

purified

stream splitter

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Pump project: Process

ethanol

water

condensor

boiler

dis

till

atio

n

sensor tube

pump

purified

valve

b probe access

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Retrofit distillation

I Move condenser down and to the side

I Pump reflux back up to header

I Meter flux

I Provide sample point

. . . . . .

Retrofit distillation

I Move condenser down and to the side

I Pump reflux back up to header

I Meter flux

I Provide sample point

. . . . . .

Retrofit distillation

I Move condenser down and to the side

I Pump reflux back up to header

I Meter flux

I Provide sample point

. . . . . .

Retrofit distillation

I Move condenser down and to the side

I Pump reflux back up to header

I Meter flux

I Provide sample point

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Pump : peristaltic

I Volume transporter

I Calibrate →meter

I Kind control →accuracy

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Pump : peristaltic

I Volume transporter

I Calibrate →meter

I Kind control →accuracy

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Pump : peristaltic

I Volume transporter

I Calibrate →meter

I Kind control →accuracy

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Flow measurement: discretely observed volume

I Most instrumentation →expensive

I Discrete volume measure →cheap

I Provides average measure between two eventsI Event period not fixedI →PROCESS IS CLOCKI →depends on process dynamicsI →acceleration as uncertainty

. . . . . .

Flow measurement: discretely observed volume

I Most instrumentation →expensive

I Discrete volume measure →cheap

I Provides average measure between two eventsI Event period not fixedI →PROCESS IS CLOCKI →depends on process dynamicsI →acceleration as uncertainty

. . . . . .

Flow measurement: discretely observed volume

I Most instrumentation →expensive

I Discrete volume measure →cheapI Provides average measure between two events

I Event period not fixedI →PROCESS IS CLOCKI →depends on process dynamicsI →acceleration as uncertainty

. . . . . .

Flow measurement: discretely observed volume

I Most instrumentation →expensive

I Discrete volume measure →cheapI Provides average measure between two eventsI Event period not fixed

I →PROCESS IS CLOCKI →depends on process dynamicsI →acceleration as uncertainty

. . . . . .

Flow measurement: discretely observed volume

I Most instrumentation →expensive

I Discrete volume measure →cheapI Provides average measure between two eventsI Event period not fixedI →PROCESS IS CLOCK

I →depends on process dynamicsI →acceleration as uncertainty

. . . . . .

Flow measurement: discretely observed volume

I Most instrumentation →expensive

I Discrete volume measure →cheapI Provides average measure between two eventsI Event period not fixedI →PROCESS IS CLOCKI →depends on process dynamics

I →acceleration as uncertainty

. . . . . .

Flow measurement: discretely observed volume

I Most instrumentation →expensive

I Discrete volume measure →cheapI Provides average measure between two eventsI Event period not fixedI →PROCESS IS CLOCKI →depends on process dynamicsI →acceleration as uncertainty

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Pump project: Level glass

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Hybrid plant

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

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Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control input

I supervisory controlI trajectory reconstructionI stability

I persistent fault

I fault detectionI fault isolationI fault counteraction supervisory controlI hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control input

I supervisory controlI trajectory reconstructionI stability

I persistent fault

I fault detectionI fault isolationI fault counteraction supervisory controlI hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control inputI supervisory control

I trajectory reconstructionI stability

I persistent fault

I fault detectionI fault isolationI fault counteraction supervisory controlI hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control inputI supervisory controlI trajectory reconstruction

I stability

I persistent fault

I fault detectionI fault isolationI fault counteraction supervisory controlI hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control inputI supervisory controlI trajectory reconstructionI stability

I persistent fault

I fault detectionI fault isolationI fault counteraction supervisory controlI hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control inputI supervisory controlI trajectory reconstructionI stability

I persistent fault

I fault detectionI fault isolationI fault counteraction supervisory controlI hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control inputI supervisory controlI trajectory reconstructionI stability

I persistent faultI fault detection

I fault isolationI fault counteraction supervisory controlI hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control inputI supervisory controlI trajectory reconstructionI stability

I persistent faultI fault detectionI fault isolation

I fault counteraction supervisory controlI hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control inputI supervisory controlI trajectory reconstructionI stability

I persistent faultI fault detectionI fault isolationI fault counteraction supervisory control

I hazop analysis

. . . . . .

Project classes

plant quantizero-hold

discrete-event plant

u(k) u(t) x(t) x(k)

discrete-event input

continuous input signalcontinuous state

discrete-event state

u(k)

I control inputI supervisory controlI trajectory reconstructionI stability

I persistent faultI fault detectionI fault isolationI fault counteraction supervisory controlI hazop analysis

. . . . . .

Discretising the state space 1

1. define state discretisation: vector of lists

2. yields discrete state space : a set of hypercubes

xa

xb

xc

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Discretising the state space 1

1. define state discretisation: vector of lists

2. yields discrete state space : a set of hypercubes

xa

xb

xc

. . . . . .

Discretising the state space 1

1. define state discretisation: vector of lists

2. yields discrete state space : a set of hypercubes

xa

xb

xc

. . . . . .

Discretising the state space 1

1. define state discretisation: vector of lists

2. yields discrete state space : a set of hypercubes

xa

xb

xc

. . . . . .

Event

.Event definition..

......

An event is defined as the crossing of a boundary surface of adiscrete state hypercube. The boundary itself is dynamicallyallocated, that the boundary point itself belongs to the statefrom which one enters the boundary. In case the trajectoryfollows the boundary for a piece of the way, it is the exit pointthat determines the state transition.

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Discretising the state space 2

xa

xb

xc

xc = 0

0 = fc(xa, xb, xc)

a stencil

direction of gradient in xc

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Model system

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The trajectories

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The discrete state space

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The zero surfaces - here lines

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The directions of change

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The direction fields

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The directions

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Automaton table/graph

I adjacency matrix or

I state transition matrix

I output matrix

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Automaton table/graph

change in x1 change in x2state -1 1 -1 11,1 1,21,2 2,2 1,31,3 2,32,1 1,1 2,22,2 1,2 3,2 2,1 2,32,3 3,3 2,23,1 2,13,2 2,2 3,13,3 3,2

next state

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Stability ???

I circle

I converging

I diverging

I Liapunov function in continuous domain: ellipse

I Discrete: if having made a circle inside a boxsystem stays in the box.

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Does it work for more complex systems ?

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Applications

I Fault detection / isolation with K W Lim, NUS(Singapore)

I Supervisory control with Lunze TUHH (Hamburg) nowBochum: application Bosch carburettor control

I Student experiment (coffee machine ETH, washingmachine UNSW, saft machine (TUE, NTNU))

I Pump control (NTNU)

. . . . . .

Applications

I Fault detection / isolation with K W Lim, NUS(Singapore)

I Supervisory control with Lunze TUHH (Hamburg) nowBochum: application Bosch carburettor control

I Student experiment (coffee machine ETH, washingmachine UNSW, saft machine (TUE, NTNU))

I Pump control (NTNU)

. . . . . .

Applications

I Fault detection / isolation with K W Lim, NUS(Singapore)

I Supervisory control with Lunze TUHH (Hamburg) nowBochum: application Bosch carburettor control

I Student experiment (coffee machine ETH, washingmachine UNSW, saft machine (TUE, NTNU))

I Pump control (NTNU)

. . . . . .

Applications

I Fault detection / isolation with K W Lim, NUS(Singapore)

I Supervisory control with Lunze TUHH (Hamburg) nowBochum: application Bosch carburettor control

I Student experiment (coffee machine ETH, washingmachine UNSW, saft machine (TUE, NTNU))

I Pump control (NTNU)

. . . . . .

Pump project: Process

ethanol

water

condensor

boiler

dis

till

atio

n

sensor tube

pump

purified

valve

b probe access

. . . . . .

Pump project: Flow control state diagram

5

4

3

2

1

6

0

5

4

3

2

1

max, alarm

frac of eq up

frac of eq up

set (1+frac) eq

set (1+frac) eqmin, alarm

frac of eq down

frac of eq down

set eqset eq

set eqset eq

frac of eq down

frac of eq down

frac of eq up

frac of eq up

start

level events time events

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I First level event: do nothing

I All level events after first:

Vk := Vposition

tk := tevent

I all level events after second:

∆tk := tk − tk−1

∆V :=Vk − Vk−1

∆tk

Vc := Vp +∆V

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Pump project: Calibration supervisory control state

diagram

fill

callibrate

end

start

set min speed

set overfill timer

start pump

close feed valve

overfill timer

take time, volume, speed

level 6,5,4,3,2,1

level 0

compute flow rates

increment speed

level 6

speed > max

open feed valve

open feed valve

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Pump project: Calibration results

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Conclusion DEDS modelling

I analysis is based on system’s vector field

I component-wise analysis

I limits scopeI thus dimensionI local automata

I local refinement is possible

I property: deterministic continuous system →non-deterministic automaton

I property: Liapunov functions can be discretised too

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Conclusion DEDS modelling

I analysis is based on system’s vector field

I component-wise analysis

I limits scopeI thus dimensionI local automata

I local refinement is possible

I property: deterministic continuous system →non-deterministic automaton

I property: Liapunov functions can be discretised too

. . . . . .

Conclusion DEDS modelling

I analysis is based on system’s vector field

I component-wise analysisI limits scope

I thus dimensionI local automata

I local refinement is possible

I property: deterministic continuous system →non-deterministic automaton

I property: Liapunov functions can be discretised too

. . . . . .

Conclusion DEDS modelling

I analysis is based on system’s vector field

I component-wise analysisI limits scopeI thus dimension

I local automata

I local refinement is possible

I property: deterministic continuous system →non-deterministic automaton

I property: Liapunov functions can be discretised too

. . . . . .

Conclusion DEDS modelling

I analysis is based on system’s vector field

I component-wise analysisI limits scopeI thus dimensionI local automata

I local refinement is possible

I property: deterministic continuous system →non-deterministic automaton

I property: Liapunov functions can be discretised too

. . . . . .

Conclusion DEDS modelling

I analysis is based on system’s vector field

I component-wise analysisI limits scopeI thus dimensionI local automata

I local refinement is possible

I property: deterministic continuous system →non-deterministic automaton

I property: Liapunov functions can be discretised too

. . . . . .

Conclusion DEDS modelling

I analysis is based on system’s vector field

I component-wise analysisI limits scopeI thus dimensionI local automata

I local refinement is possible

I property: deterministic continuous system →non-deterministic automaton

I property: Liapunov functions can be discretised too

. . . . . .

Conclusion DEDS modelling

I analysis is based on system’s vector field

I component-wise analysisI limits scopeI thus dimensionI local automata

I local refinement is possible

I property: deterministic continuous system →non-deterministic automaton

I property: Liapunov functions can be discretised too

. . . . . .

Conclusions: pump control

I Works fine

I Cheap

I Adapts to dynamics ←nature of DEDS

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Conclusions: pump control

I Works fine

I Cheap

I Adapts to dynamics ←nature of DEDS

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Conclusions: pump control

I Works fine

I Cheap

I Adapts to dynamics ←nature of DEDS

. . . . . .

Conclusions: issues

I Volume measurement is dead volume

I →periodic emptying

I →reduce volume

I →compromise accuracy vs refreshing hold-up

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Conclusions: issues

I Volume measurement is dead volume

I →periodic emptying

I →reduce volume

I →compromise accuracy vs refreshing hold-up

. . . . . .

Conclusions: issues

I Volume measurement is dead volume

I →periodic emptying

I →reduce volume

I →compromise accuracy vs refreshing hold-up

. . . . . .

Conclusions: issues

I Volume measurement is dead volume

I →periodic emptying

I →reduce volume

I →compromise accuracy vs refreshing hold-up

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End

Questions ?