This paper introduces an approach to manage energy demand within a cluster of air conditioning units utilizing a centralized control system. The air conditioning units work in a thermostatic-based on-off strategy for regulating individual air conditioners. The energy supply for these units combines grid power with renewable energy generated by wind turbines. Achieving an optimal balance between renewable and grid power is facilitated by a fuzzy logic controller, which considers user comfort and energy costs. Additionally, an adaptive nonlinear control system is designed to synchronize air conditioner on-off cycles with the recommendations of the fuzzy logic controller. The proposed control method and system model are implemented in MATLAB, with comprehensive testing conducted across diverse scenarios. Simulation results demonstrate the system's adaptability to varying pricing schemes, showcasing its responsiveness to price signals. This work contributes to advancing energy-efficient air conditioning solutions with broader applications in smart grids and sustainable energy management.