Electric vertical-take-off-and-landing multirotor aircraft has been emerging as a revolutionary transportation mode for both manned and unmanned applications, but this technology is limited by flight time and range restrictions. In this work, an energy-efficient model-based trajectory planning and feedback control framework is developed to improve the energy performance of a multirotor unmanned aerial vehicle. Target vehicle trajectories are planned by solving a formulated energy consumption optimization problem based on a system-level model, which accommodates the integrated dynamics of key vehicle subsystems. In order to implement the generated target trajectories, the framework also includes a PID feedback control architecture for real-time trajectory following. The framework is first verified under simulation, and shows an average reduction of 10.7% in energy consumption over a range of typical hover-to-hover operations, compared to the commonly used baseline flight control architecture. Through model-based analysis, key relationships that contribute to the improvements are identified and analyzed. These results demonstrate the importance of considering and coordinating all relevant system dynamics for efficient and holistic trajectory planning and control, which is absent in existing literature. The framework also demonstrates similar performance improvement under experimental validation, with an average energy reduction of 10.2% over the baseline controller despite the presence of significant real-world disturbances including wind effect.