Chapter 2 Emprical Model.pdf

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    Chapter 2 Identification

    (Empirical Modeling)

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    Process Control Prof. Cai Wenjian 2

    Lecture 3

    1. Fundamentals of Empirical Modeling2. Identification from Step Response

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    Process Control Prof. Cai Wenjian 3

    What is Process Modeling?

    Constructing process model from experimentally obtained

    input/output data, with no recourse to physical nature andproperties of system.

    What are three problems in control engineering?

    Given input and model find

    output?

    Given output and model

    find input?

    Given input and output find

    model?

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    Purpose of Modeling

    Improve Process Understanding: Simulation on dynamic and steady-state

    process behavior before plant is constructed, model based simulation caninvestigate process transient without disturb process.

    Train plant operating personnel: Interfacing a process simulator with

    standard process control equipment to create a realistic training environment,

    train plant operators to run complex units and deal with emergency situations

    Develop control strategy for new processes: Process dynamic model

    allows alternative control strategies to be evaluated. For model-based

    control strategies, process model is part of the control law.

    Optimize process operating conditions: Use steady-state model torecalculate optimum operating conditions to maximize profit or minimize

    cost. Use steady-state process model and economic information to

    determine most profitable operating conditions.

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    Models Classification

    Empir ical model:obtained by fitting experimentaldata.

    Hybrid model:combination of the two; values

    of some parameters in a theoretical model arecalculated from experimental data.

    Theoretical model:developed using the

    principles of chemistry, physics, and biology.

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    Procedure of Empirical Modeling

    Empirical modeling (identification) consists of followingsteps:

    1. Problem Definition Step 1. Problem Definition

    2. Model Formulation Step 2. Model Formulation

    3. Input function selection Step 3. Input function Selection

    4. Parameter Estimation Step 4. Parameter Estimation

    5. Model Validation Step 5. Model Validation

    Flow Chart of Process Identification

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    Step 1. Problem Definition

    Different interpretation, resulting different models

    same aspect but various angles, vary degree of complexity.

    how simple or complex, will model have to be?

    model only useful with tool available for solution

    which aspects of process most relevant and be contained in model?

    Impossible to represent all aspect of the physical process,

    capture those aspects that most relevant to problem at hand.

    what do we intend to use the model for?

    Some modeling solved analytically, others by numericalmethods

    how can we test the adequacy of model?

    how much time do we have for the modeling exercise?

    Procedure of Empirical Modeling

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    Step 2. Model Formulation

    In empirical modeling, we analysis of input/output data to detect

    model form capable of explaining the observed behavior

    ( )1

    Ls

    p

    Kg s e

    Ts

    2( )

    ( 1)

    Ls

    p

    Kg s e

    Ts

    Four parameter model

    1 2

    ( )( 1)( 1)

    Ls

    p

    Keg s

    s s

    2

    sL

    p

    eg s

    as bs c

    Five parameter model Procedure of Empirical Modeling

    1 2

    ( 1)( )

    ( 1)( 1)

    Ls

    p

    K s eg s

    s s

    2

    ( 1) sL

    p

    s eg s

    as bs c

    Three parameter model

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    Step 3. Input function Selection

    Process information of output data dependent on input function.

    Input should provide output rich in useful information and easily extracted.

    Typical input functions used in process identification are:

    Sine waves

    Impulse#Pulse (rectangular or arbitrary)#

    White noise

    Pseudo random binary sequences

    Step#

    Relay#

    Procedure of Empirical Modeling

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    Step 4. Parameter Estimation

    After candidate model selected, estimate unknownparameters.

    Fitting experimental data to a predetermined model

    form by finding the parameter values which provide

    the best fit.

    Estimating unknown parameters carried in time

    domain or in the frequency domain.Procedure of Empirical Modeling

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    Step 5. Model Validation

    -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2-1

    -0.8

    -0.6

    -0.4

    -0.2

    0

    0.2

    0.4

    Final step involves checking how the empirical model fits data it supposed to

    represent. Comparing model predictions with additional process data, and

    evaluating the fit.

    Time domain, response to certain signal

    Frequency domain, Nyquist Plot. Procedure of Empirical Modeling

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    Flow Chart of Process Identification

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    Basic Requirement of Step Response

    Obtain process model from a transient response experiment.

    inject step input at the process

    measure response

    Requirement:

    stable process

    Amplitude of step input must be determined before test

    sufficiently large so response is easily visible above noise level

    as small as possiblenot to disturb the process more than necessary

    keep the dynamics linear.

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    Graphic Method( )

    1p

    Kg s

    s

    /( ) (1 )ty t y e

    AyK steady-state gain

    Time Constant

    Deepest Slop

    /( )

    ( )max

    tydy t edt

    ydy t

    dt

    tan to (0) y

    y t

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    Graphic Method

    Ls

    p e

    Ts

    KsG

    1

    )(

    when times greater than the time delay

    )1()( /)( Lt

    eyty

    A

    yK

    steady-state gain

    Time Constant

    Time Delay L:

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    Two Points Method( )

    1

    Ls

    p

    Kg s e

    Ts

    )1()( TLt

    eKAty

    y()% 28.4 39.3 55 59.3 63.2 77.7 86.5

    time(t) T/3+L T/2+L 0.8T+L 0.9T+L T+L 1.5T+L 2T+L

    t1 and t2, the time when response

    with value 28.4% and 63.2%

    )(5.1 12 ttT

    )3(5.0 21 ttL

    Process model and step response

    t1= T/3+L t2=T+L

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    Lecture 4

    Identification from Step Response (2)

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    Log Method ( )1

    Ls

    p

    Kg s e

    Ts

    when times greater than the time delay

    )1()( /)( Lteyty

    yy AK K A

    /)( Ltkey

    yy

    ln y y L t

    y

    steady-state gain

    Time Constant and Time Delay L:

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    Log Method

    Plot against t: a straight line with

    slope of

    intercept y-axis atL / .

    meet the t-axis at the point t=L.

    1/ ln

    y y L t

    y

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    Process Control Prof. Cai Wenjian 21

    Area Method

    0 0 0

    ( )/

    0

    [ ( ) ( )] ( ) [ ( ) ( )]

    [1 (1 )]

    L

    Lar

    Lt L T

    L

    y y t dt y dt y y t dtAT

    K K K

    Kdt K e dtT L

    K

    Average residence time Taris computed form the area ofA0

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    Area Method

    1

    0

    /

    01 ]1[)(

    KTedteKdttyAT

    TtTar

    0 01 1( )

    arT

    ar

    e y t dt AeA eAT L T T

    K K K K

    Measure and compute areaA1

    under step response up to time Tar

    Than TandL can be estimated as

    arT T L

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    Numerical Integration

    Integral of a continuous time signal over 0, ft approximate

    00

    0