Design

Conceptual Design

Because the cooling of the first compartment depends on both the flashing of part of the compartment‟s content and return of colder slurry, it is important to note that the mass control of the flash tank is an important part of the temperature control of the first compartment. Defining the control of the temperature of compartment 1 and the mass of the flash tank as two separate loops that need to be tuned separately is therefore not ideal. At Lonmin, tuning is done separately, while the flow rate of the flash recycle stream (m₉) is limited to 95% of the returning flow (m₇). While this ensures that the net rate into the first compartment is positive, the temperature control of this compartment is limited by limiting its MV.

A better approach would be to design a controller that can react rapidly to changes in flow rate of flash recycle stream (m9), while also ensuring that the flash tank does not overflow or run dry due to

changes in the other flow rates. Incorporating these two aspects into one PI controller is done by establishing feed-forward feedback control on the flow controller.

Before formally designing a feed-forward controller, it is important to ensure that this control form is indeed desired and, if so, that it is possible to implement it. According to Marlin (2000) feed-forward control is desired when feedback control does not provide satisfactory control performance, and if a measured feed-forward variable is available. As mentioned, the first criterion as satisfied, due to the limitation placed on the cooling of compartment when using only feedback control. The second criterion is met by the fact that the flash recycle flow rate can serve as feed-forward variable.

Marlin (2000) further recommends three criteria that have to be satisfied by the chosen feed-forward variable in order for feed-forward control to be possible. The first of these is that the feed-forward variable has to indicate the occurrence of an important disturbance. Since the flash recycle stream typically makes up the bulk of the stream entering the flash tank, changes in this flow rate will be an important disturbance to the level control system. The second criterion notes that there must not be causal relationship between the MV (of the level controller, in this case) and the feed-forward variable. A change in the flash tank‟s effluent stream (m7) does not change the flow rate of the flash

recycle stream under open-loop conditions, and hence the second criterion is met. Lastly, the disturbance dynamics should not be significantly faster than the dynamics between the CV and the MV when the feed-forward control is added to the feedback control. Note that the CV is the tank level, while the MV and the feed-forward variables are entering (m9) and exit (m7) streams,

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balance for the flash tank needs to be examined. The unsteady state mass balance of 400-TK-20 is as follows:

[44]

Here, m9 represents the flash recycle stream (measured disturbance), while m7 refers to the exit stream.

The other variables follow the same numbering system as is used in Figure 23. It can be seen that a change in m9 would result in similar dynamic response in the mass of the tank‟s contents, as a change

in the effluent flow would have, albeit opposite in sign. With this, the final criterion of Marlin (2000) is met – affirming the flash recycle stream as a suitable feed-forward variable, in an application suitable to receive feed-forward control.

The design of a feed-forward controller starts with defining the feed-forward transfer function (in the Laplace domain), as the following equation shows (Marlin, 2000):

( )

( ) ( )

[45]

Here, Gd is the disturbance transfer function, while Gp’ is the product of the transfer functions of the

valve and the process. Below is a diagram illustrating the control structure in question:

Figure 24: Block diagram of a feedback control system with feed-forward control (Redrawn from Marlin, 2000)

Note that in this case Dm represents the flash recycle stream, while CV represents the level or mass of

148 ( ) ( ) ( ) ( )( ) ( ) [46]

Here, X(25) is the mass of 400-TK-20 and m_9 is the flash recycle flow rate. Similarly, the process transfer function is defined as follows:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [47]

It is important to note that, while the flow rate of stream 7 (the flow rate from the flash tank) is controlled by a cascade controller on the plant, the inner loop of this cascade controller is assumed to be very fast and in automatic mode during this derivation.

With these terms defined, the transfer functions thereof need to be defined, in order to determine the feed-forward transfer function. This is done by reviewing the differential equation wherein the tank mass is calculated:

[48]

In the Laplace domain, this translates into the following equations:

( ) ( ) ( ) ( ) ( ) ( ) [49] ( ) ( ) ( ) [50] Similarly, ( ) ( ) ( ) [51]

These two equations make sense, since a tank serves as an integrator in a process, and it has been stated that the flash recycle stream and effluent stream have the same type of effect on the tank mass, albeit opposite in its signal. The feed-forward controller transfer function can now be calculated by equation 45, giving the following result:

( )

( )

( )

[52]

The fact that this transfer function is unity means that the measured mass flow rate of the flash recycle stream is to be added to the output of the feedback controller. This means that the initial MV output of the mass controller of 400-TK-20 is the difference between the initialisation terms of m7

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This ensures that there will always be a positive ratio between m7 and m9, that the temperature control

of the first compartment will work quickly and efficiently and that the mass controller will work as designed. It should be noted that the feedback controller should not be a tight mass controller and should rather be tuned loosely, since only the flash recycle stream variations will be quickly rejected. If it is found that large deviations in the flash recycle stream lead to undesired deviations in m₇, a signal sampler (in the form of a zero-order hold) can be added in the place of a feed-forward transfer function, to ensure lower frequency changes.

Below a block diagram of the controller is given:

Figure 25: Block diagram of the feed-forward and feedback temperature controller.

Note that valve dynamics are replaced by a linear correlation and are therefore not included in the diagram.

Tuning

Marlin (2000) notes that the best practice for tuning a feed-forward-feedback controller is to tune each controller separately. Having already designed the feed-forward control component, the feedback controller has to be tuned. Since this is entails inventory control, the same tuning method is used as with the mass controllers in the base case model. Instead of using the coefficients of variance of data values to determine the maximum variation in the tank mass and flow rate of stream 7, for tuning, the tank is tuned for averaging mass control. According to Marlin (2000) a maximum change of 40% in both directions is noted to given averaging behaviour. The maximum change in flow rate of stream 7 is maintained at the base case value. The difference between the initial flow rates of streams 7 and 9 is used as mean flow rate. The resulting tuning parameters are a Kc value of -0.1755 and 1/TI

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The plots used for the fine-tuning of the feedback component of the mass controller and the temperature controller in compartment are shown in Appendix F3. Note that no adaption of the tuning parameters was found to be necessary.