To carry out stable and dissipative contact tasks with an arbitrary environment, it is critical for a pneumatic actuator to be passive with respect to a supply rate consisting of the spool valve position input and the actuation force output. A pseudo-bond graph model with the inner product between spool valve position input and actuation force output as a pseudo-supply rate is developed. Using this pseudo-bond graph model, an open-loop pneumatic actuator controlled by a four-way proportional valve can be proven to not be passive with respect to the pseudo-supply rate. Conversely, it can also be proven to be passive with respect to the pseudo-supply rate under a closed-loop feedback control law. The passivity of the closed-loop pneumatic actuator is verified in impact and force control experiments. The experimental results also validate the pseudo-bond graph model. The pseudo-bond graph model is intended for passivity analysis and controller design for pneumatic actuation applications where contact stability (such as robotic assembly) and/or stable interaction with a passive environment (such as human-robot interaction) is required.

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