Rice membrane-covered cultivation offers notable agronomic advantages, including effective weed suppression and improved moisture retention. However, current mechanized approaches remain constrained by high labor requirements, low operational efficiency, and the inherent fragility of biodegradable membranes. To address these limitations, this study integrates a high-speed synchronous membrane-covering device, governed by a PSO-Fuzzy PID control algorithm, into a conventional rice transplanter. This integration enables precise coordination between membrane-laying and transplanting operations. The mechanical properties of the membranes were analyzed, and a tension evaluation model was developed considering structural parameters and roll diameter variation. Experimental tests on three biodegradable membranes revealed an average thickness of 0.012 mm, a longitudinal tensile force of 0.57 N, and a tensile strength of 2.85 N/mm. The PSO algorithm was employed to optimize fuzzy PID parameters (K = 5.3095, K_p = 10.6981, K_i = 0.0100, K_d = 8.2892), achieving adaptive synchronization between membrane output speed and transplanter travel speed. Simulation results demonstrated that the PSO-Fuzzy PID reduced rise time by 53.13%, stabilization time by 90.58%, and overshoot by 3.3% compared with the conventional PID. In addition, a dedicated test bench for the membrane-covering device was designed and fabricated. Orthogonal experiments determined the optimal parameters for the speed-measurement system: a membrane pressure of 5.000 N, a roller width of 28.506 mm, and a placement angle of 0.690°. Under these conditions, the minimum membrane-stretching tension was 0.55 N, and the rotational speed error was 0.359%. Field tests indicated a synchronization error below 1.00%, a membrane-width variation rate below 1.50%, and strong anti-interference capability. The proposed device provides an effective solution for intelligent and fully mechanized rice transplanting.