The dynamic flexibility index (FI_d) is a popular performance measure of the unsteady chemical processes. In computing this index for an open-loop system, it has always been assumed that the manipulated variables can be adjusted freely to compensate the instantaneous effects of random disturbances. To produce more practical assessments, it is necessary to impose additional constraints on these variables. Thus, the present study is aimed to derive the necessary conditions of the corresponding constrained optimization problem and also to develop the numerical algorithms needed to produce a suitable flexibility metric. Furthermore, since the maximum value of FI_d can be viewed as the upper bound for the closed-loop counterpart, a novel tuning strategy can also be devised to identify the PID controller parameters accordingly.
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