Hybrid NMPC for Switching Systems Applied to a Supermarket Refrigeration System*

Refrigeration systems are characterized by switching behavior and discrete control functions as well as fast and slow dynamics, which make their control a challenging task. This paper proposes an efficient hybrid nonlinear model predictive control (HNMPC) scheme, which can be applied to a broad class of switching systems including refrigeration systems. The proposed approach is based on the embedding transformation technique and the sum-up rounding scheme and hence requires no assumptions on the switching sequence. A mixed integer optimal control problem is formulated based on reformulations of the switching dynamics. In order to circumvent the complexity of solving the resulting discontinuous optimization problem, the switching system is embedded into a family of continuous systems. The resulting problem is purely continuous and can be solved using state of the art Nonlinear Programming (NLP) solvers. The solution is either of bang-bang type or a rounding scheme with tight upper bound on the integer approximation is employed to approximate the solution to the closest feasible integer solution. The simulation results show the excellent performance of the proposed scheme in preventing the problem of display valves synchronization and reducing the switching frequency of the compressors to its minimum. In addition, the computational effort is very low compared to other schemes in the literature.