Design of linear & nonlinear observers for a turning process with implicit State-Dependent Delay

Abstract

Analysis and design of present machining methods used in mechanical engineering are based on Taylor series approximations and linearizations which cause erroneous and anomalous results. High precision machining cannot tolerate such errors. We consider and analyze an exact mathematical model of the turning process without performing any kind of linearization of the model. We give a strategic design of an estimator for the position of a machining tool based on first principles. The system's dynamics are characterized by a nonlinear State-Dependent Delay Differential Equation (SD-DDE). This delay is extremely convoluted with the state by an implicit relation. The central tenet is to use inversion of the delay model and to extract the state vector given the delay. We use our recently developed observation technique referred to as Delay Injection. Both linear asymptotic and nonlinear observers with different architectures are designed for the state estimation of a machine tool based on state-dependent delay measurement. Simulation results are depicted at the end which portray the effectiveness, validity and usefulness of the proposed observer schemes.