Natural storage function for passivity-based trajectory control of hydraulic actuators

A passivity framework for hydraulic actuators is developed by considering the compressibility energy function for a fluid with a pressure-dependent bulk modulus. It is shown that the typical actuator's mechanical and pressure dynamics model can be obtained from the Euler-Lagrange equations for this energy function and that the actuator is passive with respect to a hydraulic supply rate which contains, in addition to the flow work (PQ), the compressibility energy also, which has often been ignored. A storage function for the pressure error is then proposed and the pressure error dynamics are shown to be a passive two-port subsystem. Trajectory tracking control laws are then derived using the storage function. A case study is presented to compare the new passivity-based approach and the traditional backstepping approach using a quadratic pressure error term. In this example, the proposed approach has one fewer parameter to tune, is less sensitive to velocity measurement error, and requires lower feedback gains than the traditional approach.