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Chapter 4. Explicit/Multi-Parametric MPC Control of PSA Systems Step 2 For the given values of prediction horizon and control horizon, a con- strained quadratic optimization problem Eq. 4.2 is solved to obtain the future values of the plant input variable. Here, the plant predictive model, as shown in Eq. 4.3, is employed to express the future state predictions in the form of input variables (u), as expressed in Eq. 4.4. D∗(x(t)) = min {12Uc′HUc + x(t)FUc + 12x(t)′Y x(t)} Uc s.t. GU ≤ W + Ex(t) (4.2) Here, Uc is the vector containing the control moves sequence, while H, F, and F are the MPC weight matrices. x(t + ∆t) = Ax(t) + bu(t) y(t) = cx(t) j=0 Note that sometimes, the control horizon for future control move prediction is kept smaller than the prediction horizon, resulting in an optimization formulation of smaller size, where only the control moves till Hu − 1 are determined from the optimization problem, keeping rest of them fixed at the value at Hu − 1. Step 3 From the complete sequence of optimal input trajectory obtained in Step 2, the first control move is applied to the plant while the rest are ignored. The whole procedure is repeated from step 1 as the next measurement from the plant is made available. The above steps indicate that the MPC control law is implicit in nature and 61 x(t+k|t)=A x(t)+ A bu(t+k−1−j) k−1 k∑j (4.3) (4.4)PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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