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Chapter 5. Simultaneous Design and Control Optimization of PSA Systems Under Uncertainty the PSA model and controller description, respectively. max obj dP ,dc,v,t∈[0,tf =50cyles] s.t. hd1(xd, xa, dP , v, θm, t)m hc1(xd, xa, dc, v, θm, t)m 99.99 ≤ P urityH2 (θm, tf )m 0 ≤ ISE(θm, tf )m ̇ ̇ m=1 tf = 0 m=1,2...Ns = 0 m=1,2...Ns ≤ 100 m = 1,2...Ns ≤ εc m = 1,2...Ns 0≤Ui (θ,t) viomfm d 0≤Tj (θm,tf)m vio ≤ ε i=1,2 m=1,2...Ns ≤ εd j = 1,2,3,4 m = 1,2...Ns (5.14) ∑ Ns = wθm RecoveryH2 (θm) It should also be noted that ISE is treated as a constraint [90] (instead of being considered as a separate objective function), which makes εc a tuning parameter which can be changed to obtain a stable and fast controller response. Here, the value of εc and εd are fixed at 2 and 10−5, respectively. Furthermore, hd1 represents the PSA design constraints, while hc1 represents the PSA controller constraints. Step 2 In this step, the multi-period dynamic optimization problem formu- lated in the last step is solved [56]. The resulting optimal decision variables and PSA performance indicators are shown in the Table 5.9. The maximum expected closed loop hydrogen recovery in this case comes out to be around 61 % WITH an expected value of ISE at 1.42. Step 3 In this step, the dynamic feasibility test [38] is performed to check whether the optimal design and control system obtained in the last step is feasible for the complete range of uncertain parameter. The dynamic feasibility test problem is formulated, as shown in Eq. 5.15 below. Here, gl are the set of PSA 121PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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