Distillation Column Controllability Analysis through Heat Pump Integration

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From the aforesaid variables, the system approximated linearity and process gain matrices in each case are shown in Table 3. When temperatures were used as manipulated variables instead of heat variables, temperatures were already controlled by pre-existing control loops and then either used to control manually or sent as a set-points for automatic control, which changed the system from what it used to be when provisions were only made for control by heat inputs. Hence, it can be observed in Table 3 that the corresponding open-loop gains of two systems differed even when analyzing loops those other inputs variables.
The definition and ideal values of indices explained in Table 1. It can be seen in Table 4 that controllability indices
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Several pairing possibilities were unfavorable since the corresponding CN, MCN and RGAno were extremely large. So, these pairings which are highlighted in Table 5 were fully neglected in next steps.

For D-VRHP:
As seen in Table 5, 'QG4' and 'TG4' had the best values of MRI, CN, MCN and RGAno; it is therefore perfect to control outputs by them. 'QG2', 'QG6', 'TG2', 'TG5' and 'TG6' had also more acceptable indices than others. According to the results of Table 4, diagonal RGA element of 'TG6' was close to zero, which indicated that interaction between the loops was large; then, performance of the decentralized controller might be poor. Hence, 'TG6' was neglected. However, RGAno of 'TG3' was acceptable; but, MRI was less than others and nearly low.

For D-BFHP:
Since 'QG1' had the best MRI, CN and MCN and an acceptable RGAno, it seems to have the better performance than other pairings. The largest MRI value shows the more controllable the process, so 'QG1' could be selected as the best group of manipulated-controlled variables to have a controllable process.
When temperature was used instead of heat as input to control outputs, 'TG1' (shown in Table 5) had the largest MRI and the lowest CN and best MCN; but, according to Table 4, RGA was extremely low and close to zero. So, 'TG7' was chosen as the best pairing due to high MRI and low CN, MCN and RGAno. Hence, it was said in Table 1 that 'the differences in MRI values of each pairings should be

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