Motion Control of Nonlinear Actuators using Second Degree Approximations

Many actuators are inherently nonlinear. Usually a first degree approximation, i.e. a linear model, is used, which is valid only in a limited operating region. If higher performance requirements have to be satisfied, this region may prove too small to provide efficient and precise movement. The system designer can improve the overall performance either by widening the linear region through constructive measures, like overdimensioning, or by using nonlinear controls. The latter choice is able to enhance performance and efficiency, but most approaches are very plant-specific or require quite strong conditions on the plant. This paper discusses a general approach based on the use of exact feedback linearization of approximate models derived as second order Taylor expansion of the plant. Using the model of a hydraulic plant, it is shown that a control designed using the complete second order approximation yields a much better energy exploitation.