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Transcript of Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato...
![Page 1: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/1.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Created atUniversidad de Guanajuato & École Polytechnique de
Montréal
Module 15: Process Control and Module 15: Process Control and Process IntegrationProcess Integration – Tier I – Tier I
Program for North American Mobility in Higher Education (NAMP)
Introducing Process Integration for Environmental Control in
Engineering Curricula (PIECE)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
![Page 3: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/3.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
This module is divided in three essential complements, it will demonstrate the relationship between the use of PI tools to design a process and the control strategies.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Tier one:
•Basic Concepts About Process Control
Tier Two:
•Use of PI tools and especially dynamic simulation to address control strategies
Tier Three:
•Analysis of a real process.
Structure
![Page 5: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/5.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Index:
Tier one:
•Comparison between Steady State and Dynamic State.
•Important Definitions about dynamic state.
• Dynamic Models.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Index:
Tier two:
• Relationship between Process Design and Process Control
• Dynamic Effect on recycle Structures
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Tier 1
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Objective:
Understand the difference between steady state and dynamic state.
Understand basic concepts about control process.
Understand the advantages of Dynamic Simulation.
Tier 1
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Steady State Initial conditions = Final conditions
Process
T2T1
Flow 1 Flow 2
Process
T2T1
Flow 1 Flow 2
INPUT
OUTPUT
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Tier 1 Module 15 PIECE
Process Control and Process Integration
When a system is at steady state, there is no change in the process, input and output remains constant in the time.
Process INPUT OUTPUT
TIMEConstant Constant
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Dynamic State:
Initial conditions Final conditions
In steady state every variable in the process remain constant while dynamic state one or some variables could change thereby affecting the process
KEY PHRASE
CHANGE WITH TIME
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Tier 1 Module 15 PIECE
Process Control and Process Integration
And now……
What does control mean?
Why is it necessary?
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Before the next part it is necessary to understand the next concepts:
Manipulated Variable
A variable that can be changed to maintain constant the controlled variable.
Controlled Variable
A variable which is desirable to control.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
How ??
Changing flows of hot and cold
water.
An adequate temperature of water
is desirable
Next there is a typical example of control, everyone has needed to control the temperature when you wish to take a shower…………
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Let’s identify new concepts about control….
Process
Final Control Element
Sensor
Disturbance
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Temperature
Flows of cold and hot water
Controlled Variable
Variables which help to control
temperature
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Tier 1 Module 15 PIECE
Process Control and Process Integration
It is possible to observe some elements:
It is a feedback control loop.
Cause Effect
Sensor
InputOutput
Disturbances
Final Control Element
Process
Desired Temperature
Controller
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Tier 1 Module 15 PIECE
Process Control and Process Integration
TemperatureEither flow of cold or flow of hot water
Input OutputSingle Single
But if…
In addition if it is used
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Temperature and
Total flow
Flow of cold and
flow of hot water
Input OutputMultiple Multiple
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Tier 1 Module 15 PIECE
Process Control and Process Integration
To Control
To take necessary actions to maintain a system in desired conditions.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Why is important to control processes ?
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Raw Materials
High Quality Manufactured Products
What would happen if there was lower quality raw materials , what should be considered ?
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Raw materials quality and availability
Services quality and availability
Product Quality and throughput
Plant equipment availability
Environmental conditions
Process materials behavior
Plant equipment malfunction
Control system malfunction
Link to other plants
Drifting and decaying factors
Some aspects that should be considered:
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Tier 1 Module 15 PIECE
Process Control and Process Integration
How is a Control System designed?
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Information from existing
plants
Physical and chemical principles
Management Objectives
Process Control theory
Vendor Hardware selection
Experience with existing
plants
Formulate Control
Objectives
Computer Simulation
Computer Simulation
Develop process model
Devise Control Strategy
Select Control
Hardware
Install control system
Adjust controller settings
Final Control system
Steps to design a Control System
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Control System
Safety
Equipment
Protection
Smooth
Operation
Environmental Protection
Profit
Product Quality
Monitoring and
diagnosis
Objectives of a control process system
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Safety
Safety of people in the plant and in the surrounding community is of paramount importance. Working at an industrial plant should involve less risk than any other activity in persons life.
Environmental Protection
Federal, state or local laws regulations require that the effluents of a plant satisfy certain specifications.
Equipment protection
Operating conditions must be maintained within bounds to prevent damage to expensive equipment
Smooth Operation
It is desirable because it results in attenuated disturbances to all the integrated units.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Product Quality
Process Control contributes maintaining the operation required for excellent product quality set by the purchasers.
Optimization
It is concerned with operating the process so that the operation results in producing the highest rate of profit.
Monitoring and Diagnosis
Both the controlled and manipulated variables must be monitored in order to evaluate the performance of a control system.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
When a process control is implemented, the variability of the key parameters is reduced.
Control System
Less Output Variation
Higher Quality
xA
Time
0.97
0.99
0.98
Without control
With control
Time
xA
0.975
0.985
0.98
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Tier 1 Module 15 PIECE
Process Control and Process Integration
A mathematical model is a representation of a process, using mathematical relationships, an equation or a set of equations. These equations are obtained from basic conservation balances as material, energy and momentum.
MATHEMATICAL MODELS
Process Mathematical Model
Constitutive Relationships
Basic Balance
Equations
Are the models necessary?
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Tier 1 Module 15 PIECE
Process Control and Process Integration
When should the reaction be stopped to have a maximum B concentration?
CBA
What would happen if inlet flow stop, how fast will the tank be empty?
Flow
Liquid Level
Models allow to analyze behavior system when any change is made. It is a safe, fast and easy way.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Lumped Parameters
Dependent variables are not function of spatial location
Uses macroscopic balances
Ordinary Differential equations
Distributed parameters
Dependent variables are function of spatial location
Uses microscopic balances
Partial differential equations
Classification of Fundamental Models
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Dynamic state vs. Steady-State.
Steady State
Dynamic State
Model
Basic Equations
No Accumulation
Term
Accumulation Term
Algebraic
Equations
Differential
Equations
![Page 34: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/34.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Mass in Mass consumed
Mass produced
Mass out= - + -
Steady State Conservation Law
Rate of change
Rate of mass in
Rate of mass consumed
Rate of mass
produced
Rate of mass out= - + -
Dynamic State Conservation Law
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Tier 1 Module 15 PIECE
Process Control and Process Integration
The dynamic model gives a relation for determining the output variable as function of time for arbitrary variations in the input.
dt
dAccumulation Term
Variation with time !!
T
L
CA
(Energy)
(Inventory)
(Species)
![Page 36: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/36.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Dynamic models of chemical processes invariably consist of one or more partial or ordinary differential equations. To solve them it is possible to use the Laplace transform. It means that transient responses of the dependent variables can be found.
Differential equations
ModelSolution
LaplaceInverse Laplace
Time Domain
Laplace DomainBUT Just for linear
equations !!
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Linearization
Very often, it is possible to find non-linear models, and linearized methods provide useful result for many process. The application is justified by the small region of a process when under control.
When a system is under control, it is located in a small
region.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
),( yxfdt
dy
)()(),( ssss yyy
fxx
x
fyxf
dt
dy
The linear approximation about (xs,ys) can be obtained by applying a Taylor series expansion to this function truncating the second order and higher order terms.
For this non linear function
ss xxyyt 0
These terms are known because they are evaluated at xs and ys
![Page 39: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/39.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Transfer Functions
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Having the model, now it desirable to make the model as GENERAL as possible in order to analyze the dynamic behavior of different processes.
Subtracting the steady state equation and defining deviation variables.
Changes in variable from initial values or conditions.
Changes in variable from initial values or conditions.
How?
)0( )( )('
)0( )( )('
ututu
ytyty
Deviation variables
Initial conditions
New conditions
![Page 41: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/41.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Model
Deviation variables
Laplace Transform
Transfer Function
G (s)
)()()( sXsGsY
G(s)Y (s)X (s)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
....
.....
)(
)(11
11
nnnn
mm
mm
sasa
sbsb
sX
sY
Input
OutputDynamic relation Input-Output
(Laplace Domain))(
)(
)(sG
sX
sY
mn
Physical Realizability Condition
Transfer function is the Laplace Transform of the output variable Y(s) divided by the Laplace Transform of the input variable X(s) with all the initial conditions equal to zero.
Transfer function is the Laplace Transform of the output variable Y(s) divided by the Laplace Transform of the input variable X(s) with all the initial conditions equal to zero.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Steps to obtain a transfer function
Model
Linear
Non Linear
Linearization
Transfer Function
Laplace
Transfor
m
Deviation variables
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Gain represents the difference between two steady state of the system.
12
12
uu
yyK
Time constant is indicative of the speed of response of the process. It has time units
Large Value
Small Value
Slow process response
Fast process response
u
yK
![Page 45: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/45.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
uKY
u
Steady-State
Transfer function of different systems.
1)(
s
KsG
)()()(
tKutydt
tdyDifferential
Equation
Transfer Function
63%
![Page 46: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/46.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
uKY
u
Steady-State
Testing another transfer function
Time
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Tier 1 Module 15 PIECE
Process Control and Process Integration
)()()(
2)(
2
22 tuKty
dt
tdy
dt
tydp
12)(
22
ss
KsG
Degree of oscillation in a process response after a perturbation.
Differential Equation
Transfer Function
1
10
1 Overdamped
Underdamped
Critically Damped
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Tier 1 Module 15 PIECE
Process Control and Process Integration
110
1
Every process can be characterized in term for its values of time constant and gain.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Key characteristics of an underdamped second order response.
a) Rise Time (trise)
Time required to first cross the new steady state value and is given by
b) Percentage overshoot
1
priset
2
1 1tan
21
exp100
(B/D*100)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
e) Response time
Time required for the response to remain within a ± 5% band, based upon the steady state change in y.
c) Decay Ratio (C/B)
d) Period of oscillation (T )
21
2exp
21
2
pT
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Period of oscillation
D
B
t rise
C
Time
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Time Delay
Change
Impulse
Response
)()( tXtX inout
)()( sXesX ins
out
θ
Time
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Tier 1 Module 15 PIECE
Process Control and Process Integration
And what is stability……?
How is it possible to know if a system is stable?
It is necessary to analyze the poles in the general form of a transfer function
When is a system stable?
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Tier 1 Module 15 PIECE
Process Control and Process Integration
General Form
)(
)()(
sP
sQsG
Numerator Polynomial in s of order m
Denominator polynomial of s of order n
)()()()()( sQsXsFsYsP
Poles are the roots of P(s), it means the values that render P(s) zero.
Poles of transfer function
![Page 55: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/55.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
a) Assume that P(s) can be factorized into a series of real poles Pi
)).....()((
)()(
21 npspspsa
sQsG
Inverse Laplace transform
tpn
tp npt eCeCeCCty ...)( 21 20
Re
Im
xxp>0
p=0
p<0
Time
It grows
to infinity.
![Page 56: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/56.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
b) Assume that one of the factors o P(s) is )( 22 ps
)(
)()(
22 ps
sQsG
The roots are ipsips y
Inverse transform Laplace ptp
Csin Sinusoidal behavior
with amplitude of c/p
Re
Im
x
x
Time
![Page 57: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/57.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
c) Assume that one of the factors of P(s) is (s2+as+b)
)(
)()(
2 bass
sQsG
Inverse transform Laplace)( 2 bass
C
Factoring
2
42
4 22 baas
baas
C
• If a2- 4b>0 apply a)
• If a2- 4b=0 Critically damped behavior.
• If a2- 4b<0 apply the next result:
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Tier 1 Module 15 PIECE
Process Control and Process Integration
P<0
P>0
Time
baiw 42
22iwa
siwa
s
C
Inverse transform Laplace wtCe pt sin
It grows
periodically. Re
●
●●
●
Im
![Page 59: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/59.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
For complex conjugated poles, the larger the magnitude of the imaginary component (further the pole is from x axis ) the more oscillatory the response.
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Process Control and Process Integration
Re
Im
Unstable
Region
Plane Imaginary - Real
If there are positive real roots, even if it is a complex number, it will be unstable
Negative real roots is stable
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Process Control and Process Integration
A system is stable when bounded input changes result in bounded output, otherwise it is unstable.
Stability
The poles of a transfer function indicate very specifically the type of dynamic behavior that the transfer
functions represent for a wide variety of inputs .
A variable is bounded when it does not increase in magnitude to infinity as time
increases.
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Block Diagrams.D
isturb
an
ce
Individual elements Physical Model
Sensor
Process
Final Control Element
Representation
This is the block diagram for the system
Every element has a transfer
function !!
Gv GSGP
GD
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Block Diagram Algebra
It provides the method for combining individual transfer functions into an overall transfer function behavior.
)()()( sXsGsY
G1(s)Y (s)X (s)
Cause Effect
Gn(s)G3(s)G2(s)G1(s)X0 X0 X2 X3 Xn
)()()(
)()()()(
01
211
sXsGsG
XsGsGXsGsX
nn
nnnnnn
n
ii
n sGsX
sX
10
)()(
)(
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Tier 1 Module 15 PIECE
Process Control and Process Integration
G2(s)
G1(s)
22113 )()()( XsGXsGsX
G2(s)
G1(s)X0
0201
213
)()(
)()()(
XsGXsG
sXsXsX
)()()(
)(21
0
3 sGsGsX
sX
G2(s)
G1(s)X0
+X2
X3
2201
301
113
)()(
)()(
)()()(
XsGXsG
sXXsG
sGsXsX
Parallel Structures Recycling Structures
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Process Control and Process Integration
Feedback Control
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Process Control and Process Integration
Open Loop.
G (s)
u (s) Y (s)
Stimulus Response
G (s)
u (s) Y (s)
Stimulus Response
Closed Loop.Control action
depends the output
Action
Comparison open-loop and closed-loop
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Feedback makes use of a output of a system to influence an input to the same system
Negative
Positive
Action tends to reduce the error from desired
Action tends to increase the error from desired
Sensor
Input Output
Disturbances
Final Control Element Process
Desired Temperature
Controller
![Page 68: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/68.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
a) Maintain safe operation.
b) Maintain quality product.
Objectives of a feedback control
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Structure
Measurement Element
Error Detection Element
Control Element
Measurement
Comparison and Calculation
Correction
Basic Elements Basic Actions
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Process Control and Process Integration
Input Output
Gv Gp
Gs
GcE(s) U(s)C(s)
Gd
Ysp(s) Y(s)
D(s)
Measurement
Comparison
CorrectionYsp(s) ≠ Y(s)
+-
ProcessFinal element
Controller
Disturbances
Sensor
Desired Output
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Performance Measurement Element (Sensor)
Span
Zero
Accuracy
Repeatability
Process measurement dynamics
Calibration
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Process Control and Process Integration
Closed Loop Transfer Function
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Process
Defining
)()()()()( sGdsDsGpsUsY
GpU(s)
Gd
D(s)
Y(s)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Actuator
Controller
)()()( sCsGvsU
GvU(s)C(s)
)()()( sEsGcsC
GcE(s) C(s)
![Page 75: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/75.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
Sensor
Error
)()( sYsYspsE
E(s)Ysp(s)
Ys(s)
)()()( sYsGsYs
GsYs(s) Y(s)
![Page 76: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/76.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
1
)()(
scvp
spvcpd
GGGG
YGGGsDGsY
Closed Loop Transfer Function
Characteristic Equation01 GpGaGcGs
1
)(
scvp
vcp
sp GGGG
GGG
Y
sY
0)( sDd
Servo Control
![Page 77: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/77.jpg)
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Process Control and Process Integration
1
)(
scvp
d
sp GGGG
G
Y
sY
0)( sYsp
Analyzing the roots of the characteristic equation is possible to know the dynamic behavior, therefore, to know if the system is stable or unstable.
Regulatory control
![Page 78: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/78.jpg)
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Process Control and Process Integration
PID Controller Tuning
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Process Control and Process Integration
In a real process what is desired is to maintain the controlled variables in a given value despite the presence of disturbances. The control system does this task.
The controller does this task
Set Point
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Process Control and Process Integration
dt
teddtteteKcCtc D
t
I
)( )(
1)()(
0
0
)()( tyyte ssp
Standard form for the PID (Proportional-Integral-Derivative)
algorithm
I
D
Kc
Tuning parameters of controller
![Page 81: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/81.jpg)
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Tier 1 Module 15 PIECE
Process Control and Process Integration
a) Proportional
)()( teKCtC co cKsG )(
Control action is proportional to error.
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Process Control and Process Integration
a) Proportional action does not change the order of the process.
b) Closed Loop time constant is smaller then the open loop time constant. Proportional action makes faster the response of the process.
c) There is an offset. (The manipulated variable will change until the error is constant)
Characteristics of Proportional Action.
![Page 83: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/83.jpg)
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Process Control and Process Integration
b) Integral
)()( teK
CtC co
s
KsG
I
c
)(
Integral
Control action is proportional to the integral of the error.
It allows to reduce the error to zero
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Process Control and Process Integration
Characteristics of Integral Action.
a) All steady state corrections for disturbances or set point changes must come from integral actions.
b) There is no offset at steady state. (The manipulated variable will change until error equal to zero)
c) Integral action increase the order of the process dynamics by 1.
d) Increasing the amount of integral action ( decreasing ) results in a faster responding feedback process, but increases the degree of oscillatory behavior.
I
![Page 85: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/85.jpg)
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Process Control and Process Integration
c) Derivative
dt
tdyKCtC s
Dco
)()( s)( DcKsG
Derivative
Control action that is proportional to the derivative of rate of change or error
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Process Control and Process Integration
Characteristics of Derivative Action.
a) It does not change the order of the process
b) It does not eliminate offset
c) Derivative action tends to reduce the oscillatory nature of feedback, however it amplifies process noise.
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Process Control and Process Integration
Comparison between P, PI and PID action
PID
P
PI Offset
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Process Control and Process Integration
Tuning Criteria
a) Eliminate deviations from set point.
b) Good set point tracking should be minimized.
c) Excessive variations of the manipulated variable should be avoided
d) The controlled process should remain stable for major disturbances upsets.
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Process Control and Process Integration
PID
controller
Kc
I
D
Performance
Reliability
Deviations from set point
Controller’s ability to remain in service while handling major
disturbances
Tuning consists to find the best parameters for the controller to achieve the control objective.
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Process Control and Process Integration
dttYstYsp )()(
dttYstYsp2
)()(
dttYstYspt )()(
dttYstYspt2
)()(
Performance Assessment
IAE (Integral Absolute Error)
ITAE (Integral Time Absolute Error)
ISE (Integral Square Error)
ITSE (Integral Time Square Error)
![Page 91: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/91.jpg)
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Process Control and Process Integration
ISE and ITSE penalize larger deviations more severely than IAE and ITAE
dttYstYsp )()( dttYstYsp2
)()(
dttYstYspt )()( dttYstYspt2
)()(
ITAE and ITSE penalize deviations at long time more severely than IAE and ISE
![Page 92: Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.](https://reader037.fdocuments.in/reader037/viewer/2022110320/56649c9d5503460f9495d094/html5/thumbnails/92.jpg)
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Process Control and Process Integration
Classical Tuning Methods
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Process Control and Process Integration
Cohen and Coon
It assumes that a FOPDT model of the process is available.
FOPDT (First Order plus Delay Time)
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Process Control and Process Integration
Ziegler-Nichols Tuning
The ultimate parameters are obtained by operating a P only controller under sustained oscillations and then measuring the period of the oscillations and noting the gain of the P only controller.
P PI PID
Kc 0.5Kcu 0.45Kcu 0.6 Kcu
I - Pu /1.2 Pu /2
D - - Pu /8
cu wP
2
Ku PuUltimate Gain Ultimate Period
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Process Control and Process Integration
This method is based upon prescribing a desired form for the system’s response and then finding a controller strategy and parameters to give that response.
Direct Method Synthesis
This block diagram
Input Output
Gv GpGcYsp(s) Y(s)
pvc
pvc
sp GGG
GGG
Y
Y
1
has the next closed loop equation for changes in set point:
-+
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spvp
spc
YY
GG
YY
G
1
If the system’s response for the relation Y/Ysp, is specified. Then the controller that will give this closed loop response characteristic is that which satisfies the following equation:
This is called Synthesis Equation
Thus, the required controller can be designed if we have a model of the process, it may have a PID form.
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11
1
11
sGG
sG
cvp
cc
sc
GG
1
~1
1
1
sY
Y
csp
If the desired response form
is
Then
The process model is required
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If the process model is a first order process
1
1~
sG
p
The controller strategy is:
ss
KG
c
c
pc
1
1
1
sKG
pcpc
11
1
c
p
KpKc
pI
This is simply a PI controller with settings
Depending the process model, is possible to have a PID controller.
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• Achieves zero steady state offset for all step-like input.
• Uses only one measurement
• Algorithm and tunes rules available
ADVANTAGES FEEDBACK
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• Process output must be upset before feedback action begin
• Feedback control performance can be poor for some combinations of disturbance frequencies and feedback dynamics
• Poor feedback can cause instability, PID does not provide the best possible control for all process.
DISADVANTAGES
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MIMO SYSTEMS
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There are many industrial systems which have multiple inputs and multiples outputs …..
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Distillation Columns
Steam and reflux affect both top and bottom product compositions
Gas-liquid separator
Gas and liquid product flows affect both tank level and pressure.
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Multi-input Multi-output (MIMO) processes
Several CV’s and several MV’s
The numbers of CV’s and MV’s are not necessary same.
One MV affects all or some of CV’s. ( Process interaction )
Which MV will control which CV? ( Pairing )
One control loop affects the other control loops (Control loop interaction)
Decentralized control: Multiple SISO controllers are applied.
Centralized control: All MV’s will be manipulated to all or some CV’s.
Characteristics
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Single-input single-output (SISO) processes
One CV and one MV: No need of pairing
In contrast
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In a general form
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Affects
U(s) Y(s)
SISO
One Output
One Input
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A multivariable process is said to have interaction when process input (manipulated) variables affect more than one process output (controlled) variable.
Affects
U1(s)
U2(s)
Y1(s)
MIMO
Two* OutputsOne Input
Y2(s)
It means that there is interaction !!
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Controllability
Resiliency
Measures the degree to which a processing system can meet its design despite external disturbances and uncertainties in its design parameters.
The ease with a continuous plant can be held at a specific steady state.
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Controllability is defined for a selected set of manipulated and controlled variables, and a system may be controlled for one selection and uncontrolled for another selection.
In order to control the process is necessary to know the interaction among the variables and how the variables will be pairing.
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• RGA (Relative Gain Array) (Bristol, 1966)
• Niderlinski Index
• Condition Number
Commonly used controllability measures
Resiliency measures
• Relative Disturbance Gain
• Disturbance Cost (Lewin, 1996)
• Disturbance Condition Number (Skogestad & Morari, 1987)
)()()( susPsy
)()()()()( sdsPsusPsy d
Model of the process necessary
Model of the process and disturbances necessary
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G11
G21
G12
G22
+
+Controller
K11 + Δyi
Effect
Interaction
Closed Loop
CL
OL
K
K
11
1111
Gain Open Loop
Gain Closed Loop
11 : measure of the interaction using u1
to control y1
Steady state
u1(s)
u2(s) y2(s)
y1(s)u1 – y1
K11OL
Open Loop
K11CL=
Relative Array Gain
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CL
OL
j
i
j
i
ij
u
y
u
y
2221
1211
0
10 ij
1
0
ji uy
ji uy
ji uy
ji uy
1 ji uy Pair
Do not pair
Avoid
Do not pair
Avoid
Recommendation to pairing
With the other loops open
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n
iiiiG
GNI
0
0det
NI<0Sufficient condition for instability if independently tuned controllers with integral action are used.
NI>0 Necessary condition for stability of the closed loop system in the case of independent controller tuning.
Niderlinski Index
Tool for input-output pairing multi-loop SISO controllers with integral action.
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Singular Value Decomposition
Any matrix can be decomposed as:
TVUK
U is matrix of output singular vectors
(output directions)
V is matrix of input singular vectors
(input directions)
Output and input signals are vectors
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Matrix V
First Column
Last Column
Represents the input direction with the largest amplification.
Represents the input direction with the smallest amplification.
Matrix U
First Column
Last Column
Output direction where inputs are more effective
Output direction where inputs are least effective
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The maximum singular value represents the largest gain for any input direction, while the minimum singular value represents the smallest gain for any input direction.
Σ is a diagonal matrix containing the singular values of G
min
max
000
0.00
00.0
000
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Condition Number
smallest
estlk arg
MatrixGain of Valueingular SnmK
K
K
......
.......
......11
Gain Matrix
k
It is an indicator or directionality of the process gain. CN is obtained by calculating the ratio of the maximum singular value to the minimum singular value of the gain matrix.
If CN is large (CN >10), K is ill-conditioned.
If CN is one, K is perfectly conditioned.
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)(arg Kestl
)(Ksmallestu1
u2
The graphical representation of the condition number is showed next:
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Dynamic Simulations
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Simulation is the imitation of the operation of a real - world process or system over time.
Simulation is used to describe and analyze the behavior of a system, ask "what if" questions about the real system, and aid in the design of real systems.
In order to do a simulation is necessary to have a model of the process, and sometimes to develop the model to simulate is costly and time consuming and therefore is a hard task to carry out.
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Simulation What if …..
However to develop the model is essential part of the simulation.
Dynamic simulation predicts how process variables change with time when moving from one steady-state to another or during a transient upset.
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Process Control and Process Integration
Process Design Analysis
Off line systems
On line systems
Quasi on line systems
Education, Training/Control System
Development
Advancement of plant operations /Optimization
Optimization of plant operations
Application Areas of Dynamic Simulation
The results obtained from the dynamic simulator in the online system are feed back to the actual plant in real-time.
The results obtained from the dynamic simulator are applied to simulated plants
Results obtained from the dynamic simulator in the system are not immediately applied to actual plant operations.
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Process Design
The dynamic response of the process without corrective action by a person or control system is important in the analysis of many process design. Proper use contributes to designing processes that are easily maintained near the desired operating conditions.
In addition a simulation can help to ensure that all of the equipment for a new plant is consistently sized
Contributions of Dynamic Simulation
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What if analysis
Evaluate changes to the process equipment, feed materials and operating conditions faster and lower costs trough modelling than through experimentation.
Evaluate the response of the system when changes in operating conditions and equipment are made
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A control strategy study can be as simple as determining the optimal tuning constants for a controller or as complicated as designing an advanced control strategy for the entire plant.
In general to determining the effectiveness of a process control and develop a control strategy.
Process control design
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Determinate how disturbances propagate trough the system.
Investigate the relative sensitivity of process variables to process upsets.
Investigate process and control loops interactions.
Determine the effect of equipment sizing or arrangements changes on disturbances rejections and overall operability.
Determine the effects of ambient conditions on the process.
Process Control Development Strategy
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Compare the dynamic performance of alternatives control strategies.
Perform control-loop tuning.
Investigate star-up, shut-down, low, mid, max throughput operations.
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Training
The operators need training in how to control the process. Training courses teach how to use the Control System to control "a" plant, and simulation can be used to train operators on how to operate "their" plant during a startup or emergency.
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What if… changes to the process equipment, feed materials and operating conditions ??
Real Plant
Simulation
Two options Faster
Dynamic simulation technology plays a very important role in achieving safer and optimal plant operations.
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Glossary
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Control System
A control system is a system of integrated elements whose function is to maintain a variable process at a desirable value or within a range of desired value.
Input
Control system input is the stimulus applied to a control system from an external source to produce a specified response from the control system.
Output
Control system output is the response to the input applied.
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Open-Loop system
An open-loop control system is a control system in which the control action is independent of the output.
Open Closed-Loop
A closed-loop control system is one in which control action is dependent on the output
Time Delay
It represents the time to have a response of the system.
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Offset
Error between the new set point and the new steady state controlled variable value.
Ultimate period
Period of oscillation of the system at the margin of stability
Ultimate Gain
Controller gain that brings the system to the margin of stability at the critical frequency
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Spam
Is the difference between the largest measurement value made by the sensor/transmitter and de lowest value
Zero
Is the lowest reading available from the sensor/ transmitter.
Accuracy
Is the difference between the value of the measured variable indicate by the sensor and its true value.
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Process measurement dynamic
It indicates how quickly the sensor responds to changes in the value of the measured variable.
Calibration
Involves the adjustment between the sensor output and the predicted measurement
Repeatability
Is related to the difference between the sensor readings while the process conditions remains constant
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Noise
Is the variation in a measurement of a process variable which does not reflect real changes in the process variables. It is caused by electrical interference, mechanical vibrations or fluctuations within the process.
Set Point
It is the desirable value of the controllable variable
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QUIZ
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1.- A dynamic model is :
a) A mathematical representation of a real process. which describes approximately its behavior respect to time.
b) A mathematical representation of a real process which describes its behavior without consider the variation on time.
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2.- A dynamic state differs from steady state:
b) Accumulation term is included in variation equations
a) Accumulation term is not included in variation equations to built a model.
c) There is no difference between them
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3.- To control process is important because:
b) To decrease the variability of key variables of the process without forget the objectives of the control system.
a) To transform raw materials in manufactured products.
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4.- A characteristic of feedback :
b) It uses an output to influence the input to the system.
c) It is just a process control concept
a) It uses an input to influence the output to the system.
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Now you know different basics concepts about process control