This work presents two different smart control algorithms to manage a novel phase change material system integrated into building walls and roofs. This system is able to move a phase change material layer with respect to the insulation layer inside the building component. With this ability, the system can increase solar benefits in winter and take profit from night free cooling in summer. During the heating season, the system places the phase change material facing outdoors during sunny hours to melt it, and it moves the phase change material back facing indoors to provide space heating when desired. In the cooling season, the phase change material is moved to the outer face of insulation at night time to enhance its solidification process, and it is moved back to face indoors during cooling peak hours. An appropriate control system, referring to the schedule of operation and placement of phase change material layer with respect to the insulation (when phase change material is facing outdoors or indoors) is critical to achieve savings and avoid malfunctioning of the system. In this work, we have developed and numerically compared two different control algorithms based on weather forecast data for space heating and cooling applications. Experimentation has been done under four different climate conditions: Athens, Madrid, Strasbourg, and Helsinki. One of the control algorithms, based on local search (Tabu), provided the set of activations of the dynamic system for a 24 hour period. The other algorithm is based on model predictive control with an horizon of 2.5 and 5 hours. Results proved the feasibility of the two smart control methods, as well as their capacity to improve the energy benefits of the dynamic phase change material system in days with suitable weather conditions. Moreover, the two control algorithms successfully avoided activating the system in days with non-appropriate weather conditions.