Passivity Based Nonlinear Control of Hydraulic Actuators Based on an Euler-Lagrange Formulation

A passivity framework for hydraulic actuators is developed by consideration of the compressibility energy function for a fluid with a pressure dependent bulk modulus. The typical actuator’s mechanical and pressure dynamic model is shown to be the Euler-Lagrange equations for this energy function. A passivity property for the actuator is exhibited in which the hydraulic supply rate contains the compressibility energy, instead of just being P · Q. A storage function for the pressure error is then proposed based on the physical compressibility energy and the pressure error dynamics is shown to be a passive two-port subsystem. Control laws are derived using the storage function. A case study is presented to compare the new passivity based approach and the traditional backstepping approach for a trajectory tracking application. In this example, the proposed approach is less sensitive to velocity measurement error and requires lower feedback gains than the traditional approach.