Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato...

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)

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.

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

Index:

Tier one:

•Comparison between Steady State and Dynamic State.

•Important Definitions about dynamic state.

• Dynamic Models.

Index:

Tier two:

• Relationship between Process Design and Process Control

• Dynamic Effect on recycle Structures

Tier 1

Objective:

Understand the difference between steady state and dynamic state.

Understand basic concepts about control process.

Understand the advantages of Dynamic Simulation.

Tier 1

Steady State Initial conditions = Final conditions

Process

Flow 1 Flow 2

Process

Flow 1 Flow 2

OUTPUT

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

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

And now……

What does control mean?

Why is it necessary?

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.

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…………

Let’s identify new concepts about control….

Process

Final Control Element

Sensor

Disturbance

Temperature

Flows of cold and hot water

Controlled Variable

Variables which help to control

temperature

It is possible to observe some elements:

It is a feedback control loop.

Cause Effect

Sensor

InputOutput

Disturbances

Process

Desired Temperature

Controller

TemperatureEither flow of cold or flow of hot water

Input OutputSingle Single

But if…

In addition if it is used

Temperature and

Total flow

Flow of cold and

flow of hot water

Input OutputMultiple Multiple

To Control

To take necessary actions to maintain a system in desired conditions.

Why is important to control processes ?

Raw Materials

High Quality Manufactured Products

What would happen if there was lower quality raw materials , what should be considered ?

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:

How is a Control System designed?

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

Develop process model

Devise Control Strategy

Select Control

Hardware

Install control system

Adjust controller settings

Final Control system

Steps to design a Control System

Control System

Safety

Equipment

Protection

Smooth

Operation

Environmental Protection

Profit

Product Quality

Monitoring and

diagnosis

Objectives of a control process system

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.

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.

When a process control is implemented, the variability of the key parameters is reduced.

Control System

Less Output Variation

Higher Quality

Without control

With control

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?

When should the reaction be stopped to have a maximum B concentration?

What would happen if inlet flow stop, how fast will the tank be empty?

Liquid Level

Models allow to analyze behavior system when any change is made. It is a safe, fast and easy way.

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

Dynamic state vs. Steady-State.

Steady State

Dynamic State

Basic Equations

No Accumulation

Accumulation Term

Algebraic

Equations

Differential

Equations

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

The dynamic model gives a relation for determining the output variable as function of time for arbitrary variations in the input.

dAccumulation Term

Variation with time !!

(Energy)

(Inventory)

(Species)

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 !!

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.

),( yxfdt

)()(),( ssss yyy

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

Transfer Functions

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.

)0( )( )('

Deviation variables

Initial conditions

New conditions

Deviation variables

Laplace Transform

Transfer Function

)()()( sXsGsY

G(s)Y (s)X (s)

OutputDynamic relation Input-Output

(Laplace Domain))(

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.

Steps to obtain a transfer function

Linear

Non Linear

Linearization

Transfer Function

Laplace

Transfor

Deviation variables

Gain represents the difference between two steady state of the system.

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

Steady-State

Transfer function of different systems.

)()()(

tKutydt

tdyDifferential

Equation

Transfer Function

Steady-State

Testing another transfer function

)()()(

22 tuKty

Degree of oscillation in a process response after a perturbation.

Differential Equation

Transfer Function

1 Overdamped

Underdamped

Critically Damped

Every process can be characterized in term for its values of time constant and gain.

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

priset

1 1tan

exp100

(B/D*100)

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 )

Period of oscillation

t rise

Time Delay

Change

Impulse

Response

)()( tXtX inout

)()( sXesX ins

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?

General Form

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

a) Assume that P(s) can be factorized into a series of real poles Pi

)).....()((

21 npspspsa

Inverse Laplace transform

tp npt eCeCeCCty ...)( 21 20

It grows

to infinity.

b) Assume that one of the factors o P(s) is )( 22 ps

The roots are ipsips y

Inverse transform Laplace ptp

Csin Sinusoidal behavior

with amplitude of c/p

c) Assume that one of the factors of P(s) is (s2+as+b)

2 bass

Inverse transform Laplace)( 2 bass

Factoring

4 22 baas

• If a2- 4b>0 apply a)

• If a2- 4b=0 Critically damped behavior.

• If a2- 4b<0 apply the next result:

baiw 42

Inverse transform Laplace wtCe pt sin

It grows

periodically. Re

●●

For complex conjugated poles, the larger the magnitude of the imaginary component (further the pole is from x axis ) the more oscillatory the response.

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

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.

Block Diagrams.D

isturb

Individual elements Physical Model

Sensor

Process

Representation

This is the block diagram for the system

Every element has a transfer

function !!

Gv GSGP

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

)()()(

)()()()(

sXsGsG

XsGsGXsGsX

nnnnnn

n sGsX

22113 )()()( XsGXsGsX

G1(s)X0

)()()(

XsGXsG

sXsXsX

)()()(

3 sGsGsX

G1(s)X0

)()()(

XsGXsG

sGsXsX

Parallel Structures Recycling Structures

Feedback Control

Open Loop.

u (s) Y (s)

Stimulus Response

u (s) Y (s)

Stimulus Response

Closed Loop.Control action

depends the output

Action

Comparison open-loop and closed-loop

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

a) Maintain safe operation.

b) Maintain quality product.

Objectives of a feedback control

Structure

Measurement Element

Error Detection Element

Control Element

Measurement

Comparison and Calculation

Correction

Basic Elements Basic Actions

Input Output

GcE(s) U(s)C(s)

Ysp(s) Y(s)

Measurement

Comparison

CorrectionYsp(s) ≠ Y(s)

ProcessFinal element

Controller

Disturbances

Sensor

Desired Output

Performance Measurement Element (Sensor)

Accuracy

Repeatability

Process measurement dynamics

Calibration

Closed Loop Transfer Function

Process

Defining

)()()()()( sGdsDsGpsUsY

GpU(s)

Actuator

Controller

)()()( sCsGvsU

GvU(s)C(s)

)()()( sEsGcsC

GcE(s) C(s)

Sensor

)()( sYsYspsE

E(s)Ysp(s)

)()()( sYsGsYs

GsYs(s) Y(s)

spvcpd

YGGGsDGsY

Closed Loop Transfer Function

Characteristic Equation01 GpGaGcGs

sp GGGG

0)( sDd

Servo Control

sp GGGG

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

PID Controller Tuning

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

teddtteteKcCtc D

)()( tyyte ssp

Standard form for the PID (Proportional-Integral-Derivative)

algorithm

Tuning parameters of controller

a) Proportional

)()( teKCtC co cKsG )(

Control action is proportional to error.

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.

b) Integral

)()( teK

CtC co

Integral

Control action is proportional to the integral of the error.

It allows to reduce the error to zero

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.

c) Derivative

tdyKCtC s

)()( s)( DcKsG

Derivative

Control action that is proportional to the derivative of rate of change or error

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.

Comparison between P, PI and PID action

PI Offset

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.

controller

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.

dttYstYsp )()(

dttYstYsp2

dttYstYspt )()(

dttYstYspt2

Performance Assessment

IAE (Integral Absolute Error)

ITAE (Integral Time Absolute Error)

ISE (Integral Square Error)

ITSE (Integral Time Square Error)

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

Classical Tuning Methods

Cohen and Coon

It assumes that a FOPDT model of the process is available.

FOPDT (First Order plus Delay Time)

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

Ku PuUltimate Gain Ultimate Period

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)

sp GGG

has the next closed loop equation for changes in set point:

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.

If the desired response form

The process model is required

If the process model is a first order process

The controller strategy is:

This is simply a PI controller with settings

Depending the process model, is possible to have a PID controller.

• Achieves zero steady state offset for all step-like input.

• Uses only one measurement

• Algorithm and tunes rules available

ADVANTAGES FEEDBACK

• 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

MIMO SYSTEMS

There are many industrial systems which have multiple inputs and multiples outputs …..

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.

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

Single-input single-output (SISO) processes

One CV and one MV: No need of pairing

In contrast

In a general form

Affects

U(s) Y(s)

One Output

One Input

A multivariable process is said to have interaction when process input (manipulated) variables affect more than one process output (controlled) variable.

Affects

Two* OutputsOne Input

It means that there is interaction !!

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.

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.

• 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

+Controller

K11 + Δyi

Effect

Interaction

Closed Loop

Gain Open Loop

Gain Closed Loop

11 : measure of the interaction using u1

to control y1

Steady state

u2(s) y2(s)

y1(s)u1 – y1

Open Loop

K11CL=

Relative Array Gain

1 ji uy Pair

Do not pair

Recommendation to pairing

With the other loops open

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.

Singular Value Decomposition

Any matrix can be decomposed as:

U is matrix of output singular vectors

(output directions)

V is matrix of input singular vectors

(input directions)

Output and input signals are vectors

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

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

Condition Number

smallest

estlk arg

MatrixGain of Valueingular SnmK

......

.......

......11

Gain Matrix

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.

)(arg Kestl

)(Ksmallestu1

The graphical representation of the condition number is showed next:

Dynamic Simulations

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.

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.

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.

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

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

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

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

Compare the dynamic performance of alternatives control strategies.

Perform control-loop tuning.

Investigate star-up, shut-down, low, mid, max throughput operations.

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.

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.

Glossary

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.

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.

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.

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

Is the difference between the largest measurement value made by the sensor/transmitter and de lowest value

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.

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

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

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.

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

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.

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.

Now you know different basics concepts about process control

Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato...

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