The automatic control device is a critical component of absorption refrigeration systems. Its functional enhancement can reduce operating costs, improve energy efficiency, and ensure long-term stable unit operation. Given that absorption refrigeration systems operate under various dynamic conditions, the rational design of control strategies is particularly important. This study analyzes the influence of changes in the cooling water and heat source water flow rates on the outlet temperature of chilled water in the unit based on the open-loop response characteristics of absorption refrigeration systems. It proposes a dual-loop energy-saving control strategy for single-effect hot water lithium bromide absorption refrigeration systems based on the setpoint comprehensive optimization algorithm. Considering the multiple variables, strong coupling, large inertia, long time delay, and nonlinear characteristics of absorption refrigeration systems, as well as the difficulties in modeling these systems, this study applies a model-free adaptive control algorithm to the system’s control. It derives both SISO and MIMO model-free control algorithms with time-delay components. Through simulations comparing MFAC, improved MFAC, and traditional PID control, the dual-loop energy-saving control strategy is demonstrated to effectively reduce system heat consumption by approximately 20%, decrease power consumption by about 10%, and enhance the system’s SCOP by approximately 19.3%.