Pathologies affecting the respiratory system can lead to a debilitating decrease in quality of life and can be fatal. To test medical devices and implants for the human respiratory system, a simulation system that can reproduce multiple respiratory features is necessary. Currently available respiratory simulators only focus on reproducing flow rate profiles of breathing while coughing simulators focus on aerosol analysis. In this paper we propose a novel, bioinspired robotic simulator that can physically replicate both breathing and coughing flow rate characteristics of healthy adults. We conducted a study on 31 healthy adult participants to gather the flow rate measurement of normal breathing, deep breathing, breathing while running and coughing. Coughing flow rate profiles vary considerably between participants, making an accurate simulation of coughs a challenge. To enable cough flow rate simulation, a new methodology based on the identification of four cough phases, Attack, Decay, Sustain and Release (ADSR) and their parametrization was devised. This methodology leads to the unprecedented ability to reproduce diverse and complex coughing flow rate profiles. Our simulator is able to reproduce respiratory flows with a root mean square error (RMSE) of 1.8 L/min between normal participant breathing and its simulation, 5% of the maximum flow rate simulated for that participant (pMFR), an RMSE of 10.08 L/min for deep breathing, 18% of the pMFR and an RMSE of 13.29 L/min for exertion breathing, 17% of pMFR. For the simulation of an average cough we recorded an RMSE of 51.43 L/min, 13% of the pMFR and for a low flow rate cough an RMSE of 12.38 L/min, 9.5% of the pMFR. The presented simulator matches the fundamentals of human breathing and coughing, advancing the current capability of respiratory system simulators.