*3.5. Experiment 2. PI Control VT.2–WCr, VT.3–PT.1*

Figure 8 shows the results of Experiment 2. Here, the recommended pairings from the RGA analysis were used, and the results show that PT.1 is controlled much better than in Experiment 1. The variations in WC*r* are less frequent, but this is caused by the slow controller operating VT.2. As can be seen in Figure 8e, from *t* ∼ 500 s to *t* ∼ 700 s, the VT.2 valve opens very slowly. This causes the extraction rate to increase slowly (it increased much faster in Experiment 1) towards the point where a drop in WC*<sup>r</sup>* happens. This occurs at *t* ∼ 700 s, causing the valve to close again. Since the variations in WC*<sup>r</sup>* happen less frequently, the effect on PT.1 from VT.2 opening and closing is also less than in Experiment 1, which may explain why PT.1 is better controlled in Experiment 2. It should be noted, however, that VT.3 is much faster than VT.2, hence the controller could possibly be able to counteract the influence of VT.2 even if the oscillations had been more frequent. The differential pressure dPT.2 oscillates here as well (Figure 8d), due to the lack of control and the dP is quite high, indicating a large amount of oil in the incline. Numerical values for the performance can be found in Table 8.

**Figure 8.** Experiment 2. PI controllers on VT.2 and VT.3, with the pairing recommended by the RGA analysis.

The initial transient is quite oscillatory. This is caused by the large initial error in the PT.1 and the fact that no reference filter is used. After PT.1 stabilizes, so does WC*r*. During the steps in inlet conditions, both controllers are able to keep the controlled variable close to the setpoint. The variations in PT.1 are smaller than in Experiment 1.

#### *3.6. Experiment 3. PI Control VT.2–PT.1, VT.3–dPT.1*

In this experiment, WC*<sup>r</sup>* is not used in the controller. Instead, the dP is controlled to a fixed setpoint. Figure 9 shows the results. Here, we see that the behaviour of the WC*<sup>r</sup>* and the ER is not as in Experiments 1 and 2. Since the dP is controlled, a buffer volume is established in the incline. This buffer volume functions as a filter for the disturbances occurring at the inlet. The WC*<sup>r</sup>* has very few drops below 99% in this experiment (Figure 9b). Numerical values for the performance can be found in Table 8.

The effects of measurement noise in the dP transducer are clearly seen in Figure 9d.

**Figure 9.** Experiment 3. PI controllers on VT.2 and VT.3 with VT.2 controlling PT.1 and VT.3 controlling dPT.2.

### *3.7. Experiment 4. PI Control VT.2–dPT.2, VT.3–PT.1*

This experiment uses the control configuration recommended by the RGA analysis. The results of the experiment are shown in Figure 10. The results are quite similar to those found in Experiment 3, but the oscillations in PT.1 during the disturbances are smaller. It is also clear that VT.2 is changing

significantly more than VT.3 in Experiment 3. The variations and initial overshoot in dPT.2 are larger in this experiment, but this is caused by VT.2 being much slower than VT.3. The behaviour of the WC*<sup>r</sup>* and the ER is quite similar to Experiment 3, but the undershoot at *t* ∼ 950 s is smaller in this experiment. Numerical values for the performance can be found in Table 8.

**Figure 10.** Experiment 4. PI controllers on VT.2 and VT.3 with VT.2 controlling dPT.2 and VT.3 controlling PT.1, as recommended by the RGA analysis.
