copyright © 2002 douglas j. cooper all rights reserved practical process control using control...

Copyright © 2002Copyright © 2002Douglas J. CooperDouglas J. CooperAll Rights ReservedAll Rights Reserved

Practical Process ControlPractical Process ControlUsing Using Control StationControl Station

Prof. Doug CooperChemical Engineering Dept.

University of Connecticut (Storrs)


1. Fundamental Principles of Process Control1. Fundamental Principles of Process Control

Motivation for Automatic Process Control Safety First:

– people, environment, equipment The Profit Motive:

– meeting final product specs– minimizing waste production – minimizing environmental impact – minimizing energy use– maximizing overall production rate


““Loose” Control Costs MoneyLoose” Control Costs Money

It takes more material to make a product thicker, so greatest profit is to operate as close to the minimum thickness constraint as possible without going under

It takes more processing to remove impurities, so greatest profit is to operate as close to the maximum impurities constraint as you can without going over

3.6

3.8

4.0

4.2

4.4

60 80 100 120 140

Process: Gravity Drained Tank Controller: Manual Mode

Mor

e P

rofit

able

Ope

ratio

n

Time (mins)

30

40

50

60

70

3.4

3.6

3.8

4.0

4.2

80 100 120 140 160


Mor

e P

rofit

able

Ope

ratio

n

Time (mins)

operating constraint

poor control means large variability, sothe process must beoperated in a lessprofitable regionprocess variable


Tight Control = Most Profitable OperationTight Control = Most Profitable Operation

A well controlled process has less variability in the measured process variable, so the process can be operated close to the profitable constraint

3.4

3.6

3.8

4.0

4.2

80 100 120 140 160


Mor

e P

rofit

able

Ope

ratio

n

Time (mins)

30

40

50

60

70

3.4

3.6

3.8

4.0

4.2

80 100 120 140 160

Process: Gravity Drained Tank Controller: Manual ModeM

ore

Pro

fitab

le O

pera

tion

Time (mins)

operating constraint

process variable

tight control permitsoperation near theconstraint, whichmeans more profit


An introductory example


Consider Heating a HouseConsider Heating a House

furnace

heat loss(disturbance)

fuel flow

valve

Temperaturesensor/transmitter

TTset point

Controlsignal

Thermostatcontroller

TC

1. Measurement

2. Computation/Decision

3. Action


Automatic Control isAutomatic Control is Measurement Measurement Computation Computation Action Action

Is house cooler than set point? ( TSetpoint Thouse > 0 )

Action open fuel valve

Error

Is house warmer than set point? ( TSetpoint THouse < 0 )

Action close fuel valve


FFeedbackeedback Control Loop Control Loop BBlocklock DiagramDiagram:: Components Components and Variables for hand Variables for home ome

heating heating

Thermostat Home HeatingProcess

Fuel Valve

TemperatureSensor/Transmitter

Set Point

Heat Loss Disturbance

TSP

dQhouse temperaturemeasurement

signal

Controllererror

Manipulatedfuel flow to

furnace

Housetemperature

Controlleroutputsignal

Tm

T

T

+-

Comparator


Control Objective

Controlled Process Variable

Measured Variable

Set point Error Controller Output

Manipulated Variable

Disturbances

Terminology


General Feedback Control Loop Block General Feedback Control Loop Block DiagramDiagram

Set PointController Process

FinalControlElement

MeasurementSensor/Transmitter

ySP(t)+- y(t)(t) o(t) m(t)

Disturbance

measured variable(feedback signal)

Controllererror

ManipulatedProcessvariable

Controlled Processvariable

Controlleroutput

ym(t)

d(t)

“Actual” controller

Comparator


ExamplesExamples

Measurement Sensors: temperature, pressure, pressure drop, level, flow density, concentration

Final Control Element: solenoid, valve, variable speed pump or compressor, heater or cooler

Automatic Controllers: on/off, PID, cascade, feed forward, model-based Smith predictor, multivariable, sampled data, parameter scheduled adaptive control


3. Graphical Modeling of Dynamic Process Data3. Graphical Modeling of Dynamic Process Data

Process Behavior and Controller Tuning Consider cruise control for a car vs a truck

– how quickly can each accelerate or decelerate – what is the effect of disturbances (wind, hills, etc.)

Controller (gas flow) manipulations required to maintain set point velocity in spite of disturbances (wind, hills) are different for a car and truck because the dynamic behavior of each "process" is different

Dynamic behavior how the measured process variable responds over time to changes in the controller output and disturbance variables


Understanding Dynamic Process BehaviorUnderstanding Dynamic Process Behavior

To learn about the dynamic behavior of a process, analyze measured process variable test data

Process variable test data can be generated by suddenly changing the controller output signal

Be sure to move the controller output far enough and fast enough so that the dynamic behavior of the process is clearly revealed as the process responds

The dynamic behavior of a process is different as operating level changes (nonlinear behavior) so collect process data at normal operating levels (design level of operation)


Modeling Dynamic Process Modeling Dynamic Process BehaviorBehavior

The best way to understand process data is through modeling

Modeling means fitting a first order plus dead time (FOPDT) dynamic process model to the data set:

where:y(t) is the measured process variableu(t) is the controller output signal

The FOPDT model is low order and linear so it can only approximate the behavior of real processes

)()()(

PPP tuKtydt

tdy


FOPDTFOPDT

When a first order plus dead time (FOPDT) model is fit to dynamic process data

The important parameters that result are:The important parameters that result are:– Steady State Process Gain, Steady State Process Gain, KKPP

– Overall Process Time Constant, Overall Process Time Constant, PP

– Apparent Dead Time, Apparent Dead Time, PP

)()()(

PPP tuKtydt

tdy


PID Tuning Guide


The FOPDT Model is All The FOPDT Model is All ImportantImportant

model parameters (KP, P and P) are used in correlations to compute initial controller tuning values

sign of KP indicates the action of the controller

(+KP reverse acting; KP direct acting)

size of P indicates the maximum desirable loop sample time (be sure sample time T 0.1P)

ratio P /P indicates whether MPC (Smith predictor) would show benefit (useful if P P)

model becomes part of the feed forward, Smith predictor, decoupling and other model-based controllers


Step TestStep Test

The controller is set to manual mode Process starts at steady state Controller output signal is stepped to new value Measured process variable allowed to complete response

50

55

60

50

55

60

0 5 10 15 20

Open Loop Step TestProcess: Custom Process Controller: Manual Mode

Pro

cess

Var

iabl

eC

ontro

ller O

utpu

t

Time (mins)

Step Test

50

55

60

50

55

60

0 5 10 15 20


Pro

cess

Var

iabl

eC

ontro

ller O

utpu

t

Time (mins)


Process Gain From Step Test Process Gain From Step Test DataData

KP describes how much the measured process variable, y(t), changes in response to changes in the controller output, u(t)

A step test starts and ends at steady state, so KP can be computed from plot axes

where u(t) and y(t) represent the total change from initial to final steady state

A large process gain means the process will show a big response to each control action

)( Output, Controller in the Change StateSteady

)(Variable, Process Measured in the Change StateSteady

tu

tyKP


KKPP for Gravity Drained Tanks for Gravity Drained Tanks

Steady state process gain has a: size (0.095), sign (+0.095), and units (m/%)

1.8

2.0

2.2

2.4

2.6

2.8

3.0

45

50

55

60

8 9 10 11 12 13 14 15 16 17 18

Gravity Drained Tanks - Open Loop Step TestProcess: Gravity Drained Tank Controller: Manual Mode

Pro

cess

Var

iabl

eC

ontr

olle

r O

utpu

t

Time (mins)

y = (2.88 - 1.93) m

u = (60 - 50) %

%

m095.0

%5060

m 93.188.2

u

yK P


2. Hands-On 2. Hands-On Case StudiesCase Studies

Gravity Drained Tanks

measured process variable level sensor

& controller

disturbancevariable

controller output

manipulated variable

.

.


Non-Interacting Gravity Drained Tanks

TANK 1

I.C.: t=0 h1 = h1s

TANK 2

I.C.: t=0 h2 = h2s

)t(VR

h

dt

dhA 1

1

11

1

1P

2

22

R

h)t(V

R

h

dt

dhA


Overall Time Constant From Step Test DataOverall Time Constant From Step Test Data

Time Constant P describes how fast the measured process variable, y(t), responds to changes in the controller output, u(t)

P is how long it takes for the process variable to reach 63.2% of its total change, starting from when the response first begins

50

55

60

50

55

60

0 5 10 15 20


Pro

cess

Var

iabl

eC

ontro

ller O

utpu

t

Time (mins)

Step Test

50

55

60

50

55

60

0 5 10 15 20


Pro

cess

Var

iabl

eC

ontro

ller O

utpu

t

Time (mins)


PP for Gravity Drained Tanks for Gravity Drained Tanks

1) Locate where the measured process variable first shows a clear initial response to the step change – call this time tYstart

From plot, tYstart = 9.6 min

1.8

2.0

2.2

2.4

2.6

2.8

3.0

45

50

55

60

8 9 10 11 12 13 14 15 16 17 18


Pro

cess

Var

iabl

eC

ontr

olle

r O

utpu

t

Time (mins)

tYstart



2) Locate where the measured process variable reaches y63.2, or

where y(t) reaches 63.2% of its total final change

Label time t63.2 as the point in time where y63.2 occurs

1.8

2.0

2.2

2.4

2.6

2.8

3.0

45

50

55

60

8 9 10 11 12 13 14 15 16 17 18


Pro

cess

Var

iabl

eC

ontr

olle

r O

utpu

t

Time (mins)

tYstart t63.2

y63.2

1.8

2.0

2.2

2.4

2.6

2.8

3.0

45

50

55

60

8 9 10 11 12 13 14 15 16 17 18


Pro

cess

Var

iabl

eC

ontr

olle

r O

utpu

t

Time (mins)

tYstart t63.2

y63.2



y(t) starts at 1.93 m and shows a total change y = 0.95 m

y63.2 = 1.93 m + 0.632(y) = 1.93 m + 0.632(0.95 m) = 2.53 m

y(t) passes through 2.53 m at t63.2 = 11.2 min

1.8

2.0

2.2

2.4

2.6

2.8

3.0

45

50

55

60

8 9 10 11 12 13 14 15 16 17 18


Pro

cess

Var

iabl

eC

ontr

olle

r O

utpu

t

Time (mins)

y = 0.95 m

tYstart t63.2

y63.2 = 2.53 m


PP for Gravity Drained Tanks for Gravity Drained Tanks- The time constant is the time difference between tYstart and t63.2

- Time constant must be positive and have units of time

From the plot: P = t63.2 tYstart = 11.2 min 9.6 min = 1.6 min

1.8

2.0

2.2

2.4

2.6

2.8

3.0

45

50

55

60

8 9 10 11 12 13 14 15 16 17 18


Pro

cess

Var

iabl

eC

ontr

olle

r O

utpu

t

Time (mins)

y = 0.95 m

tYstart t63.2

P = 1.6 minutes

y63.2 = 2.53 m


Apparent Dead Time From Step Test DataApparent Dead Time From Step Test Data

P is the time from when the controller output step is made until when the measured process variable first responds

Apparent dead time, P, is the sum of these effects:

– transportation lag, or the time it takes for material to travel from one point to another

– sample or instrument lag, or the time it takes to collect analyze or process a measured variable sample

– higher order processes naturally appear slow to respond

Notes:– Dead time must be positive and have units of time– Tight control in increasingly difficult as P 0.7P

– For important loops, work to avoid unnecessary dead time



P = tYstart tUstep

= 9.6 min 9.2 min = 0.4 min

1.8

2.0

2.2

2.4

2.6

2.8

3.0

45

50

55

60

8 9 10 11 12 13 14 15 16 17 18


Pro

cess

Var

iabl

eC

ontr

olle

r O

utpu

t

Time (mins)

tYstart

P = 0.4 minutes

tUstep


Workshop 1: Workshop 1: Exploring Dynamics of Gravity Drained TanksExploring Dynamics of Gravity Drained Tanks


Processes Have Time-Varying BehaviorsProcesses Have Time-Varying Behaviors

The predictions of a FOPDT model are constant over time

But real processes change every day because– surfaces foul or corrode – mechanical elements like seals or bearings wear– feedstock quality varies and catalyst activity drifts – environmental conditions like heat and humidity change

So the values of KP, P, P that best describe the dynamic behavior of a process today may not be best tomorrow

As a result, controller performance will degrade with time and periodic retuning may be required


Processes Have Nonlinear BehaviorsProcesses Have Nonlinear Behaviors

The predictions of a FOPDT model are constant as operating level changes The response of a real process varies with operating level

50

60

70

80

50

55

60

65

70

2 4 6 8 10 12 14 16 18 20

Example Nonlinear Behavior Process: Custom Process Controller: Manual Mode

Pro

cess

Var

iabl

eC

ontr

olle

r O

utpu

t

Time (time units)

response shape is different at different operating levels

even though controller output steps are the same

A

B

C


Gravity Drained Tanks is NonlinearGravity Drained Tanks is Nonlinear

A controller should be designed for A controller should be designed for a specific level of operation!a specific level of operation!

1234567

405060708090

0 5 10 15 20 25 30 35 40 45

Nonlinear Behavior of Gravity Drained TanksModel: First Order Plus Dead Time (FOPDT) File Name: TEST.DAT

Gain (K) = 0.075, Time Constant (T1) = 1.15, Dead Time (TD) = 0.53 SSE: 206.0

Mea

sure

d Le

vel (

m)

Con

trolle

r Out

put (

%)

Time

equal u’s

constant parameter FOPDT model

nonlinear processvariable response

copyright © 2002 douglas j. cooper all rights reserved practical process control using control...

Documents

practical process control

action slide

measured process variable

t setpoint t house

control station

tight control

action close fuel valve

profitable constraint