Abstract
This work presents an alternative method to solve the nonlinear program (NLP) for nonlinear model predictive control (NMPC) problems. The NLP is the most computational demanding task in NMPC, which limits the industrial implementation of this control strategy. Therefore, it is important to consider algorithms that can solve the nonlinear program, not only in real time but also guaranteeing feasibility. In this work, the restricted enumeration method is proposed as alternative to solve the NLP for NMPC problems, showing successful results for pH control in a sugar cane process plant. This method enumerates in restricted way a set of final control element possible positions around the current one. Next, it tests all positions in that set to find the best one, taken as the optimization solution.
Highlights
Model predictive control (MPC) is a successful control technique for plants with slow dynamics like chemical and petrochemical processes
The main disadvantage of nonlinear MPC (NMPC) is the complexity related with the resulting nonlinear optimization problem, which is usually nonconvex (Mishra, 2011) and must be solved in real time (Camacho & Bordons, 2007; Chen & Allgöwer, 1998)
Available numerical methods to solve the non-convex optimization problems for NMPC can be classified in three sub-groups: i) Direct enumeration, which is not very efficient at the computation level when the process model is not compact enough, but with models that can be evaluated at a good speed, this technique always produces feasible solutions and quite close to the global optimum; ii) dynamic programming, like iterative dynamic programming (Luus, 1996) and blurred dynamic programming (Alkan, Erkmen, & Erkmen, 1994), but the disadvantage of dynamic programming methods is the high computation costs; and iii) heuristic methods such as genetic algorithms, Bacterial Chemotaxis (BCh) and simulated annealing
Summary
Model predictive control (MPC) is a successful control technique for plants with slow dynamics like chemical and petrochemical processes. Available numerical methods to solve the non-convex optimization problems for NMPC can be classified in three sub-groups: i) Direct enumeration, which is not very efficient at the computation level when the process model is not compact enough, but with models that can be evaluated at a good speed, this technique always produces feasible solutions and quite close to the global optimum; ii) dynamic programming, like iterative dynamic programming (Luus, 1996) and blurred dynamic programming (Alkan, Erkmen, & Erkmen, 1994), but the disadvantage of dynamic programming methods is the high computation costs; and iii) heuristic methods such as genetic algorithms, Bacterial Chemotaxis (BCh) and simulated annealing Those methods provide feasible solutions very close to the global optimum, they consume a lot of computation time (Holland, 1992).
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