Black-Box versus Grey-Box LPV Identification to Control a Mechanical System

This paper presents a comparison of black-box and grey-box linear parameter varying (LPV) identification techniques to control a mechanical systems. It is illustrated by a practical example that if a physical model of a system is not available or too complicated for controller synthesis, black-box identification techniques may lead to a model and controller which achieves a reasonable performance. As an application, a black-box LPV model of a three-degrees-of-freedom robotic manipulator is identified experimentally from a sufficiently reach input-output data set. After model validation, a polytopic gain-scheduled LPV controller is designed for both models. Another LPV controller is designed based on a grey-box model. To compare the performance of the designed controllers, they are implemented on the manipulator to do a trajectory tracking task. In addition, an inverse dynamics and a PD controller are also implemented for comparison. It is shown that back-box LPV identification can potentially give reasonable performance, but not as high as grey-box modelling.