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Chapter 5. Simultaneous Design and Control Optimization of PSA Systems Under Uncertainty if violation = true then ∂vio v = violation2 ∂t else ∂viov =0 ∂t end if From a real-time control perspective, it is important to constrain both high and low values of adsorption time (Eq. 5.10) to achieve a safe and economical operation. Very low values of feed step duration translate to shorter PSA cy- cles performing loading and unloading of the adsorbent with the impurities at a quicker rate, while significantly enhancing its degradation in the form of wear and tear [154]. Furthermore, this also demands a faster ON and OFF operation of the switch valves, reducing their lifetime, which is directly related to number of switches per unit time. On other hand, long feed steps can oversaturate the bed since the adsorbent has only a limited capacity for the impurities. In addition to this, large changes in the adsorption time (∆tfeed) should also be constrained to avoid oversaturation (∆th) or avoid sudden surge of inflow (∆tl) [73]. It is important to note that in general practice, the controller constraints mentioned in Eq. 5.10 can be treated as constraints in the original NLP problem itself. In this work, the explicit nature of the PI control law is exploited, and an IF-ELSE logic is built to incorporate these equations along with the general PDAE model of PSA. This approach, enhances the convergence rates of the dynamic optimization problem without compromising its rigor. 118PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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