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Chapter 4. Explicit/Multi-Parametric MPC Control of PSA Systems requires repeated online solution of the optimization problem, as the state of the plant evolves in time. A further implication of online optimization is that MPC application to problems with fast dynamics, especially situations where the sam- pling interval duration is comparable to time required to solve the optimization problem, is rather quite limited. 4.1.2 Explicit/Multi-Parametric Model Predictive Con- trol Recent advances made in the field of multi-parametric programming now makes it possible to obtain the governing MPC control law beforehand, or offline. Pis- tikopoulos et al. [119], first demonstrated this by employing multi-parametric techniques to reformulate the original MPC problem into a multi-parametric op- timization problem. In the last decade, there has been tremendous growth in the industrial applications of mp-MPC as outlined in Table 4.1. In contrast to MPC controller, multi-parametric MPC comprises an offline step, where most of computational intensive calculations are performed, making its online implementation much simpler. The functioning of mp-MPC in the form of two main steps, offline and online, is explained here in detail. Offline step The main purpose of this step is to formulate and solve the multi-parametric control optimization problem. In order to achieve this, first the quadratic opti- mization problem in Eq. 4.2 is converted to a multi-parametric quadratic pro- gramming problem by performing the linear transformation shown in Eq. 4.5. zm u+H−1F′xt (4.5) The resulting multi-parametric quadratic optimization formulation is given in 62PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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