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Chapter 5. Simultaneous Design and Control Optimization of PSA Systems Under Uncertainty that the estimated CSS state is in the vicinity of the actual one. yp0 = yp0 − J−1e (5.3) j+1 j j j A challenging task in the employment of the direct determination approach is the evaluation of the large Jacobian matrix J, for each iteration, which contains the CSS sensitivity information with respect to all PSA system variables. Jj= ∂e (5.4) ∂[yp, d] [yp0j ,dj] Towards this, Ding and LeVan [39] used hybrid Newton-Broyden method to directly update J−1, while employing an iterative secant method to estimate its initial value (for the first iteration). Jiang et al. [68], also used direct deter- mination approach for PSA optimization and incorporated CSS condition as an constraint in the overall optimization formulation, as shown in Eq. 5.5. Conse- quently, the decision variables and the PSA state variables simultaneous converges to their final optimal values and CSS, respectively. max dP ,yp0 s.t. h1(y ̇p,yp,dP,t) g1(y ̇p, yp, yp0, dP , t) eCSS=yp−yp0 LB≤[yp0,dP] φ(yp, yp0, dP ) = 0 ≤0 =0 ≤ 0 (5.5) Furthermore, Ayoub et al. [7] used direct determination approach to perform PSA modelling simulations by posing CSS evaluation as an optimization problem 105PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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