Numerical algorithms for subspace system identification (N4SID) are a powerful tool for generating the state space (SS) representation of any system. The purpose of this work was to use N4SID to generate SS models of the flowrate and pressure generation within an ex vivo vascular perfusion system (EVPS). Accurate SS models were generated and converted to transfer functions (TFs) to be used for proportional integral and derivative (PID) controller design. By prescribing the pressure and flowrate inputs to the pumping components within the EVPS and measuring the resulting pressure and flowrate in the system,_four TFs were estimated;_two for a flowrate controller ( and ) and two for a pressure controller ( and ). In each controller,_one TF represents a roller pump ( and ),_and the other represents a roller pump and piston in series ( and ). Experiments to generate the four TFs were repeated five times from which average TFs were calculated. The average model fits, computed as the percentage of the output variation (to_the_prescribed_inputs) reproduced by the model, were for , for , for , and for . The simulated step, impulse, and frequency responses indicate that the EVPS is a stable system and can respond to signals containing power of up to 70_Hz.