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This paper investigates joint trajectory and active beamforming design for unmanned aerial vehicle (UAV)-enabled ultra-reliable low-latency communication (URLLC) systems under finite blocklength (FBL) transmission. Unlike conventional Shannon-capacity formulations, the FBL regime introduces a signal-to-interference-plus-noise ratio (SINR)-dependent dispersion penalty that increases the sensitivity of reliability to mobility-induced channel variations. To address this challenge, we develop a propulsion-aware model predictive control (MPC) framework that performs receding-horizon joint trajectory and multi-user beamforming optimization while enforcing FBL-based rate constraints.