Model error compensation and robust observer design. II. Bearing temperature and preload estimation

A two-step observer design methodology is developed for a class of nonlinear, uncertain systems which can be separated into a linear, accurately modeled subsystem and a nonlinear uncertain subsystem. This class of systems is reasonably general and quite common in manufacturing systems. The first step is the design of a model error compensator (MEC) to account for the uncertain subsystem. Error dynamics analysis can then be derived based on the compensated model for designing a conventional observer. In this paper, the two-step observer design strategy is applied to construct a monitor for estimating bearing internal temperature and preload of a machine tool spindle. Several observer schemes with or without the MEC are compared to demonstrate the effectiveness of the MEC loop.