Cooling and refrigeration based on solid sorption is an attractive technology especially when it is powered by solar energy. The development of the Continuously-Operated Solar-driven Adsorption Refrigeration (CO-SAR) system has offered a method to overcome the problem of the intermittent production of cold. In this study, the ability of the CO-SAR system to control the production of cooling effect under different operating schemes is studied. The studied CO-SAR system uses activated carbon and methanol solid sorption pair. The governing mathematical relations are introduced to solve the coupling behavior of heat and mass transfer inside the adsorption reactor and the integrated solar collector. Furthermore, the feasibility of controlled cold production of the CO-SAR system is investigated. Three different cooling strategies of the CO-SAR system operating mode are demonstrated. In the first operating scheme, the refrigerant flow valve is fully opened and the produced cooling effect is self-controlled by the process of refrigerant adsorption. Moreover, a refrigerant fixed mass flow rate is allowed to flow towards the evaporator in the second controlled operating schedule. The third controlled operating strategy of the CO-SAR system demonstrated in this work represents a more practical and realistic working scheme. It is found out that the CO-SAR system is superior to the traditional intermittent solar-operated single-bed adsorption cooling system because it has the potential to be controlled. In other words, the CO-SAR system has the capability of managing the desired output cooling effect, the required cooling starting time, the duration of the cooling effect, as well as the required cooling ending time. The continuity in cold production and the steady temperature of the cold delivered are noteworthy, especially. This potential makes the system, more reliable, more dependable, and better in functionality than the conventional intermittent solar-operated single-bed adsorption cooling system.