Piston extrusion-based 3D bioprinting is a widely used technology in tissue engineering; however, the phenomenon of extrusion hysteresis severely constrained its printing accuracy. This study investigates the hysteresis mechanism using a low-viscosity gelatin hydrogel as a model material and develops effective control strategies through mathematical modeling. Rheological characterization determined the material's gelation point (29.8 ℃)and the optimal printing temperature window. Subsequently, precise syringe temperature control was achieved using a heat transfer model, which exhibited a low prediction error of only 0.0064 ℃. We constructed an extrusion hysteresis model that simultaneously accounts for the elastic deformation of the syringe and the compressibility of the material. A static model derived from mechanical analysis provided a formula for calculating the extrusion hysteresis volume, while a dynamic model revealed that the resulting flow rate follows an exponential decay law. Experimental validation assessed the influences of critical parameters, including piston velocity (0.015-0.03 mm/s), nozzle diameter (0.46-0.75 mm), temperature (30-35 ℃), and various material types. The results demonstrated that the compressible model predictions aligned well with experimental data. However, the finest nozzle (0.46 mm) exhibited larger errors, attributed to rapid heat dissipation and increased susceptibility to premature gelation. Based on the dynamic model, we propose a control strategy employing "premature extrusion stop with adjusted movement speed." Printing experiments confirmed that for low-viscosity hydrogels, this strategy reduced accidental deposition in non-printing areas compared to standard retraction (withdrawal) strategies. This research provides a theoretical for optimizing the accuracy of piston extrusion systems and advances the mitigation of defects caused by extrusion hysteresis in the 3D printing of low-viscosity hydrogels.