Integrated Process Control Research Proposal.doc

May 23, 2017 | Autor: Venkat Gopal | Categoria: Process Control
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Descrição do Produto

1. INTRODUCTION:

The (feedback) integral regulator algorithm to minimise output standard
deviation in the presence of dead time and (stochastic) disturbance
(modelled by ARIMA (0,1,1)), is derived with the help of Figure 1 shown
below.

Equation (1)

The Block Diagram for the feedback integral regulator shown in Figure 1.


2. Mathematical Notation used in the integral regulator algorithm, and
practical realisation (Figure 2) :

Xt Process Input;

Yt Controlled Output;

xt is the adjustment in the input manipulated variable;

et is the 'one-step' ahead 'forecast error' and of 'integral' over time of
past errors;

d1 and d2 are the parameters that represent the 'inertial' characteristics
of the dynamic process model;


Zt represents the drifting behaviour of the process due to disturbance;

et = Zt + Yt ;

d1 = e-T// t1 and d2 = e-T// t2 are dynamic process parameters. t1 and t2
are the process time constants for the

second-order process model and T is the sampling period.

b is the process dead time (time delay) in integral units of time (seconds,
minutes, hours), b > 0;

Q is the integrated moving average (IMA) parameter that represents noise, 0
< Q < 1.

PG represents the process gain realised by total effect in output caused by
a unit change in the input variable after the completion of the dynamic
response (Baxley [1991]).

It is shown in (Venkatesan [2002a, 2002b]) that for a 'critically damped'
'second-order' dynamic system when conditions for feedback control
stability are satisfied,


w = PG(1-d1 -d2) = 1 and (ii) PG = 1/(1-d1 -d2) = g, the 'steady-state
gain'.

'w' is the magnitude of the process response to a unit step change in the
first period following the dead time, which carries over, into additional
sample periods (Baxley [1991]).



Figure 2 Practical realisation of integral regulator.
3. Description of Quality Regulator Function:

The Process Control and Quality Integral Regulator will use Box and Jenkins
('s) Auto Regressive Integrated Moving Average (ARIMA) (time series) model
for describing the stochastic output when identical, independent and
Normally distributed (0,1) random shocks (white noise) pass through a
second-order filter (process model).

Smith's predictor for dead time compensation and Dahlin's algorithm
principles are also incorporated in the integral regulator algorithm term
and the dead time (time delay) term which has both integral controller and
dead time compensation properties to reduce product variability at the
output.

The integral regulator element in the integral regulator calculates the
input adjustment required to bring the control error standard deviation of
the outgoing product quality control variable as close to the regulator set
point (target). Simulation of the integral regulator algorithm yields
control data about the number of adjustment intervals, (sampling periods),
required to bring the output product quality variable close to the desired
target, (regulator set point). The Digital Control Implementaion of Quality
Regulator is shown in Figure 3.


Controlled process


(Controlled)



Figure 3. Digital Control Implementation of Integral (Quality) Regulator .
The Process Control and Product Quality Integral Regulator helps in
automatic process control of industrial processes such as oil refining,
petrochemical industries, ores dressing etc. by means of input feedback
control adjustments and yields the number of adjustment intervals,
(sampling periods), during which the process has to be adjusted when
inflicted by white noise (disturbances) using the time constants and
inertial (dynamic) properties of the (stable) process through a second
order filter.

It minimizes control error variance of outgoing product quality bringing
the product quality variable close to the Regulator control set point
(target).

The integral quality regulator functions to control product quality through
regulation schemes which use some combinations (not specific) of the IMA
parameter Θ and the process dynamic parameters d1 andd2 and for each set of
combinations of δ1 and δ2, that satisfy feedback control stability
conditions, as it iterates through the values of Θ from 0.05 to 0.95. The
combinations of these parameters are obtained for any large or small value
of Θ. The process computer uses the regulator algorithm and performs the
required computations that are necessary for the calculations.

4. Research Problem:
An example of developing a second order dynamic model for process is shown
below in the process model and Block Diagram that is given by the linear
difference equation

Yt (1- δ1B1 - δ2B2) = (ω0 - ω1B) Bb+1 Xt.
Equation (2)

Step 1:

Box and Jenkins [1970, 1976] described generic dynamic models of the order
(r,s) by
δr(Β)Yt = ωs(B)BbXt
(3), (Table 9.1, page 330, Box and
Jenkins [1970, 1976]),

'b' being the number of whole periods of dead time, where δr(B) and ωs(B)
are polynomials in B and BXt = Xt-1, B bXt = Xt-b; B is the backward shift
operator.



Step 2:

The general form of representation of an ARIMA (p, d, q) time series model,
is

Φp(B) dZt = Θq(B)at ,
(4)

where

Φp(B) = 1- ΦB1 -Φ2B2 - . . . ΦpBp, and Θq(B) = 1- ΘB1 -Θ2B2 - . . . ΘqBq
are polynomials in B of degree p and q respectively and Φp(B) is called the
auto regressive operator and Θq(B) the moving average operator.

Step 3:

Considering practical situations of process control, sometimes it may be
incorrect to assume that all stochastic outputs due to (white noise)
disturbance can be modelled as ARIMA (0, 1, 1) process.

Some process outputs may have the stochastic element in them for certain
parts and may not be stochastic at all for the remaining portions of the
process, as the process operates, there is every likelihood that the drifts
may have disappeared or absorbed in the syste.

Instead of using the ARIMA (0, 1, 1) for all stochastic outputs due to
disturbance 'carte blanche', the general form of ARIMA model in θ, (Box and
Jenkins [1970, 1976]), the moving average parameter and ø, the auto
regressive operator polynomial functions combinations for different values
of p, d and q can be evaluated by proper simulation studies and appropriate
values determined for a particular stochastic output





 
 
Lastly, and most importantly, similar to the equation in polynomials L1(B)
, L2(B), L3(B) and L4(B) developed by Box and Jenkins that will yield and
lead to minimum variance, special purpose equations in polynomials have to
be developed that will fit in with the higher order dynamic models and
ARIMA models developed by steps (i) and (ii) above as shown in Figure 3.

Conclusion:

Combine the general mathematical expressions for the generic process model
given by equation (3) and similar to the stochastic model given by equation
(4) and develop a research that will consider consider all types of
disturbance, cyclic, step or ramp nature and will apply to most of the
commonly occurring industrial processes utilising the modern mathematical
modelling and computing tools and methods available with fast-processing,
high-speed, high-data-capacity computers




-----------------------




Process Computer

Controlled Process


1 Quality Analysis



2 Set points


Measurement Values

Production Data
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