Optimal control analysis and Practical NMPC applied to refrigeration systems

TL;DR

This work addresses optimal energy efficiency for a canonical mechanical compression refrigeration cycle under a known cooling demand. It develops a reduced-order moving-boundary model focused on condenser dynamics and couples it with a nonlinear static global optimizer that maximizes COP while meeting the demand, revealing that the optimal cycle is defined by three variables $h_{e,out}$, $h_{c,out}$, and $\dot{m}$ with two inputs $N$ and $A_v$. The study uncovers controllability limitations: the condenser is underactuated with a two-input, three-state structure, so the true optimum cannot be reached from arbitrary initial conditions. To cope with this, it compares Practical Non-linear MPC with a feedback-plus-feedforward strategy, finding that PNMPC achieves faster transient convergence and COPs closer to the optimum, though neither approach attains the global solution due to fundamental underactuation; future work will explore recursive feasibility, stability, robustness, and suboptimal multi-objective control balancing steady-state and transient performance.

Abstract

This work is focused on optimal control of mechanical compression refrigeration systems. A reduced-order state-space model based on the moving boundary approach is proposed for the canonical cycle, which eases the controller design. The optimal cycle (that satisfying the cooling demand while maximizing efficiency) is defined by three variables, but only two inputs are available, therefore the controllability of the proposed model is studied. It is shown through optimization simulations how optimal cycles for a range of the cooling demand turn out not to be achieved by keeping the degree of superheating to a minimum. The Practical NMPC and a well-known feedback-plus-feedforward strategy from the literature are compared in simulation, both showing trouble in reaching the optimal cycle, which agrees with the controllability study.

Figures (13)

• Figure 1: Mechanical compression system
• Figure 2: Classical optimization and control structure
• Figure 3: Open-loop simulation results when simple input profiles are applied to both the original SMB model and the reduced-order one
• Figure 4: Pressure-specific enthalpy chart of a canonical mechanical compression cycle
• Figure 5: Integration of the static model of all cycle components into the optimization procedure

Theorems & Definitions (1)

• Remark