دانلود رایگان مقاله کنترل بهینه یک آزمایشگاه ستون تقطیر باینری از طریق منطقه صریح MPC

Abstract

This paper shows how to construct and implement explicit MPC feedback laws for systems with a large number of states. Specifically, the construction of critical regions of the explicit MPC solution is replaced by a two-step procedure. First, all optimal active sets are enumerated off-line and corresponding KKT matrices are pre-factored. Then, in the on-line step, the optimal control inputs are identified by checking primal and dual feasibility conditions using the pre-factored data. The feasibility and performance of the proposed approach are experimentally demonstrated on the control of the laboratory binary distillation column, described by a dynamical model with 10 state variables. We show that the control algorithm requires only modest computational resources on-line. A comparison of the memory and computational demands of the proposed method with the on-line solution of the corresponding quadratic program via the state-of-the-art solver as well as the approximated solution via the first-order method is made.

6. Conclusions

In this paper, we have shown how to control a distillation column using an MPC algorithm. To allow for a fast and simple implementationofthe control strategy, wehaveusedthe regionless explicit approach. Specifically,the feedback law was pre-computed off-line. To avoid the curse of dimensionality typical for the storage requirements of explicit MPC strategies, we have used the direct enumeration of all optimal combinations of active constraints. Moreover, the complexity of the analytical feedback law was kept low by only considering a partial pre-factorization of the KKT system for dual variables. Then the optimal control actions can be obtained by a sequential search procedure, which only needs to check primal and dual feasibility via a series of matrix multiplications and additions. Therefore the whole implementation is division free, fast, and simple to implement. The main advantage of the regionless approach over regionbased approaches is twofold. First,the construction ofthe analytical form of the MPC feedback law does not directly depend on the dimensionality of the parametric space. Therefore such solutions can be obtained even for systems with a high number of system’s states. Secondly, as documented in Section 5.1, the regionless solution requires a significantly smaller memory footprint compared to its region-based alternative. Specifically, the required memory storage is decreased by two orders of magnitude. The computational complexity of the proposed approach was compared with the standard and approximated on-line solutions of the corresponding QP via the state of the art optimization solvers. The results showed that regionless explicit approach can indeed provide significant computational improvements, outperforming the standard on-line QP solution roughly by the factor of 19, with no additional cost to be paid in the sub-optimality of the computed solution. By means of an experiment we have demonstrated that the proposed MPC controller achieves a suitable control performance. The influence of the model-plant mismatch was mitigated by using the disturbance modeling approach.