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Controller with temperature measured after holding tubes

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Figure 7-13 : Disturbance rejection criteria, for the third and first DSI unit controller

configurations.

Cascade controller

We will now consider the third controller configuration in Figure 7-8. This is a cascade controller, which measures the tube surface temperature before the holding tubes and the milk temperature after the holding tubes. The tube surface temperature response has an additional first order dynamic, which we have modelled with a 2 second time constant. The resulting transfer functions are similar to those shown in Figure 7-9. We can now determine the closed loop transfer functions by choosing controller parameters for the cascade controller. Using the

Parameters r = 20s and _I

K

_c =

�

₆ for the inner controller and T _I =1 50s and

Kc

=

�

for the outer 60

controller we can produce the disturbance rejection criteria and this is shown in Figure 7-1 3 . Also shown i s the criteria for the first controller configuration i n Figure 7-8. Clearly the cascade controller provides significantly better disturbance rejection.

Evaporator Controllability Studies

Finally we are interested in the controller input saturation for the DSI unit temperature control loop. The criteria for this was discussed earlier (i.e.,

IG(j.@) I

�

IG

d

(j.@ � - 1 V @ )

and we can see

from Figure 7-9 and Figure

7- 10

that it is satisfied. We can also determine the manipulations required for a unit disturbance and the resulting magnitude plots are shown in Figure 7- 14. The magnitude is smaller than one across the entire frequency range, so there are no saturation problems.

Temperature measured after DSI unit Temperature measured after holding lubes

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_ .. .. ... .. .. .. .. .. .. .. .. .. , , , , ,

Figure 7-1 4 : Closed loop manipulations required for a unit disturbance. 7.4.4) MVR section control

Here we are interested in the control of the

MVR

evaporator section evaporation temperature

( Tel ) and the product dry matter ( W p5

)

. In the previous section we showed that decentralised controllers could be used if the process cross-over frequencies were above

0.01

rad/s. Furthermore, the results of the static

RGA

analysis shows that the correct control loop pairings are Tel

/ M

c and W pS

/ N

camp . Figure 7-1 5 shows the

MVR

evaporator section, with the temperature and product dry matter control loops.

MVR

section temperature

The MVR evaporator temperature can be controlled using a cascade controller connected with

the preheat plate heat exchanger. Earlier we calculated the

RGA

by considering the heat

exchanger condensate flow

(Mc)

as the manipulated variable. However, the cascade controller in

Figure 7- 1 5 provides better disturbance rejection for the plate heat exchanger outlet temperature. The set-point for the outlet temperature controller

(Tmcsp)

is then the manipulated variable for the

MVR

evaporator temperature control loop. In Chapter 4 we developed the linear state space representation for the

MVR

evaporator section. This includes the transfer function between the preheat condenser inlet temperature

(Tmcsp)

and the evaporator temperature

(r.J

The resulting

Bode plot for this transfer function is shown in Figure 7-1 6. It should be remembered that this transfer function neglects the preheat plate heat exchanger dynamics. These have been neglected because of the disturbance rejection capabilities of the plate heat exchanger temperature control loop. MVR FAN

:

e-.---J

1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ ._. - . . . _ . . _ . _ . . . _ • . . _ . _ • • ' · ' . - . 0 - _ . _

.

...

.

... ... ...

.

... ... ... ....•.•.. ... _ . . . ...

.

...

Figure 7-1 5 : The MVR evaporator section density (DC) and temperature (TC) control

loops.

There are not many direct disturbances to the

MVR

evaporator section. In fact, the control loops for the preheat plate heat exchanger and DSI unit temperature would suggest that there are no disturbances. Strictly the feed temperature disturbances are removed by the heat exchanger outlet temperature control loop. In addition the potential steam pressure disturbances are removed by the DSI unit temperature control loop. However, there are many indirect disturbances which cause changes in the DSI preheat section flash vessel temperatures. For example the presence of air in the flash vessels was shown in Chapter 6 to cause changes in their temperature. As a result,

the preheat section flash vessel temperatures can be a significant disturbance to the

MVR

Evaporator Controllability Studies

We now consider the

MVR

evaporator section in isolation from the DSI preheat section. In Chapter 4 the linear dynamic model was developed by combining the DSI preheat section with the

MVR

evaporator section. However, for the consideration of the

MVR

evaporator section temperature control, we consider the

MVR

evaporator section in isolation. This is done to simplify the analysis and to make the flash vessel temperatures a disturbance to the evaporator. The transfer functions shown in Figure

7-1 6

are for the

MVR

evaporator section and do not include the feedback through the DSI preheat section.

The phase cross-over frequency of the

T.l(S)

transfer function is determined from Figure

7-1 6

as

Tmcsp(s)

0.3 rad/s. Figure

7-1 6

also shows the Bode plot for the

T.l(S)

transfer function, from which we

Tph2(s)

can determine a gain cross-over frequency of 0.0 1 rad/s. This is a very low frequency and more importantly it is considerably lower than the process transfer function phase cross-over frequency. As a result, we do not expect there to be any disturbance rejection problems with this control loop. We can confirm this by calculating the closed loop transfer function. Choosing the

controller parameters Ti = 1 00 s and Kc = 5 , we can determine the disturbance rejection criteria

and this is plotted in Figure

7- 18.

Clearly the gain is low across the frequency range and this

reflects the good disturbance rejection characteristics of the control loop.

�

0 _ _ _ _ _ _ _ _ _ _ _ _ _ _

6, -20

Figure 7-16 : Bode plots for the MVR evaporator temperature transfer functions.

The potential problem of controller input saturation can be investigated using the criteria of Section 7.2 (i.e.,

IGCi·w) I

2:

IGd (j.w� - 1

at frequencies where

IGd Ci.w� >I ).

Figure

7-16

shows

that the process transfer function gain is larger than the disturbance gain at frequencies below 0.25 rad/s. This is consistent with the criteria and therefore we do not expect any controller saturation problems. We can confirm this result by determining the closed loop manipulations

required for a unit disturbance, which are shown in Figure 7-1 9. Clearly the manipulations are small and so no serious saturation problems will occur.

MVR

product dry matter

F or the product dry matter control loop, the disturbance is the feed dry matter

(wjc2)

and the

manipulated variable is the MVR compressor speed

(Ncomp).

In Chapter 4 we developed the state space representation of the MVR evaporator. Using the linear dynamic model we can determine the Bode plots between the

MVR compressor speed (Nco",p)'

the feed dry matter

(wfc2)

and the

product dry matter

( wps).

The model combines the DSI preheat section with the

MVR

evaporator section, but the feedback through the plate heat exchanger is neglected. It should also be

remembered that the model considers the entire

MVR

evaporator as a single pass, whereas it actually contains five passes. Later we show that this assumption causes some differences in the process dynamic response. However, the basic conclusion of the controllability analysis is the same when the five passes are modelled as a single pass.

Figure 7-17 : Bode plots for the

MVR

evaporator product dry matter transfer functions. The Bode plots for the process and disturbance transfer functions (i.e.,

wps(s)

and

wps(s)

are

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