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Chapter 5. Simultaneous Design and Control Optimization of PSA Systems Under Uncertainty inequality constraints. If ψ is negative, then the design is feasible for the operating range of uncertain parameter. If it is positive, then the design is infeasible and the critical scenario obtained from the complete solution of Eq. 5.15 is augmented with the list of critical scenarios described in Step 1, and the whole procedure is repeated till feasibility is achieved. [] ψ= max gl(θ∗)= max gl(θ,tf) (5.15) l=1,..N cr θ∈[68%,73%],t∈[0,tf =50cycles] It is important to note that formulation in Eq. 5.15 assumes that there are no time variant decision variables in the optimization problem. The value of ψ (Eq. 5.15), for the current design and control configuration comes out to be -7.5 × 10−5, with the purity lower bound as the limiting constraint. Since this is a negative value, the optimal PSA design obtained here is feasible and the algorithm terminates. 5.4 Computational Results and Discussions For the PSA system shown in Figure 5.1, the resulting design and control config- uration obtained by the employment of the methodology mentioned in previous section is shown in Table 5.9, while the corresponding computational statistics are outlined in Table 5.10. Note that for the two-bed PSA system under con- sideration, the total CPU time to solve the full optimization problem is around 9.2 hours. Table 5.9 also depicts the optimal values of key degrees of freedom related to process design, operation and controller design of the PSA system. In particular, the following remarks can be made: 1. The duration of feed step is the largest as compared to other two steps. For the 2-bed, 6-step PSA cycle under consideration, where feed is provided 124PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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