Multivariate Statistical Control Thesis

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    MULTIVARIATE STATISTICAL ANDNEURAL CONTROLLER

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    vapor boil-up using PLS based direct synthesis controllers as well as neural controllers. The

    following transfer function equation (4.9) was used to simulate the process when perturbed

    by pseudo random binary signals (1000 samples).

    Inputs:

    # =Reflux flow rate; $ = vapour boil up

    Disturbances:

    # = Feed flow rate; $ = Feed light component mole fraction

    ++

    ++

    ++

    ++

    )175)(1.01(

    )1.01(096.1

    )175)(1.01(

    )1.01(082.1)175)(6.01(

    )6.01(864.0

    )175)(6.01(

    )6.01(878.0

    s s

    s

    s s

    s s s

    s

    s s

    s

    (4.9)

    Both FIR based and ARX based inner models were used to identify the process dynamics in projected

    subspaces. Equations ( 4.10-4.11 ) represent the identified ARX based dynamic models for outputs 1&

    2, respectively. Equations ( 4.12-4.13 ) represent the identified FIR based dynamic models for outputs

    1& 2, respectively.

    # { =".""# # "."" %

    #.' ".'' %(4.10)

    $ { =".#% ".%

    #." ' "."' '(4.11)

    # { ="."# '# "."$%$

    "."#'$ "."#'#(4.12)

    $ { =".' % ".'

    ".$ # ".'(4.13)

    FIR and ARX based inner correlation between the scores T and U were established keeping

    the outer linear structure of the PLS intact. The predicted outputs corresponding to the inputs

    within a PLS framework were obtained by post compensating the scores with matrix.

    The score were generated by post compensating the original I matrix with matrix.

    Figures 4.3 and 4.4 present the comparison of actual plant dynamics involving top product

    composition D X and bottom product composition B X with ARX based PLS predicted

    dynamics.

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    MULTIVARIATE STATISTICAL ANDNEURAL CONTROLLER

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    The desired transfer function for closed loop simulation was selected as second order system.

    The controller were designed as direct synthesis controller in the following way,

    +

    +=

    2)1(

    10

    02)1(

    1

    )(

    s

    s sCLG

    (4.14)

    Where is tuning parameter. Direct Synthesis controller resulted is as follows:

    ))(1)((

    )()(

    sCLG sG

    sCLG sC G =

    (4.15)

    The performances of proposed direct synthesis controllers designed on the basis of equations(4.9-4.13& 4.15 ) and embedded in PLS framework were examined. PLS controller perfectly

    could track the set point (step change in top product composition from 0.99 to 0.996 and step

    change in bottom product composition from 0.01 to 0.005). Figures 4.5 and 4.6 illustrate and

    compare the performance of PLS controllers ( FIR based/ARX based inner dynamic model)

    in servo mode.

    4.3.2 NNPLS Controller

    In the same ( 22 ) distillation process output 1 ( J, input1

    (reflux flow rate) & the output 2 ( J, input 2 (vapour boil-

    up) time series relations were identified using n

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