MODEL BASED CONTROL OF MACHINING PROCESSES: EXPLORATION OF BAYESIAN STATISTICAL METHODS FOR IDENTIFICATION AND CONTROL

Machining process modeling & simulation as well as in-process monitoring and control have been identified as key technological factors to power efficient manufacturing facilities of tomorrow. The effective utilization of process models and in-process control are aimed towards improving profitability of the manufacturing process. To that end, the objective of this research work is to improve machining performance by implementing in-process control using model based control strategies, while considering stochastic models of machining process. Towards satisfying that objective, three research questions are asked. 1) What are metrics of measuring machining performance and which machining process models are important to consider according to these metrics? 2) How does uncertainty in machining process affect the validity and accuracy of these models and how models can be altered to account for these uncertainties? 3) What is the appropriate control strategy to be implemented to use machining models with uncertainty to improve machining performance? Machining performance is derived from its relation to profitability. Single operation level and part machining level profitability relates to peak machining forces, dimensional accuracy and tool life. A holistic system perspective of machining process modeling is presented through which identification of machining performance metric becomes efficient. Since machining models are the relationships between machining performance metrics and the machining inputs and have dependence on the machining application chosen, an application dependence metric map is created. This answers the questions of \u27What to control and what models to pick?\u27 Uncertainty in machining process stems from variability from process and part inputs and complex mechanics of metal cutting process. Thus the uncertainty can be classified as parametric uncertainty (variation in parameter values of model) and systematic uncertainties (simplified description of actual cutting phenomenon). In this work, Bayesian statistical methods are deployed for parameter and state estimation for static and dynamic machining process models. Bayesian methods use probabilistic descriptions of models and leverage the prior knowledge of machining process. This way they combine the best of analytical (first principle based) and numerical (data generated) techniques. Current work explores the Bayesian inference techniques for linear, nonlinear and dynamic models for parameter and state estimation. Computational Bayesian inference is implemented by various methods (Gaussian Approximation, Laplace Approximation, variational approach, Monte Carlo methods, Grid based methods etc). In this work a novel Grid based Markov Chain Monte Carlo (MCMC) method has been proposed. This method alleviates the shortcomings of parent methods (Grid based estimation and MCMC method), and exhibits faster convergence to true parameter values. The proposed method is validated using both synthetic and experimental data. Bayesian Model selection methodology is discussed in short with synthetic and experimental data validation. Machining force is a key performance parameter that relates to the tool wear, energy consumption and machining process stability. Active control of machining force has been explored by various strategies deploying model-free or model based control. The machining force system has time-varying input perturbation, which causes loss of control performance or even instability. This work proposes a novel feed-forward model driven adaptive control architecture using Bayesian methods for parameter adaptation. The machining force control is deployed on CNC lathe for experimental implementation. Using the prior knowledge of the machining process model, the force setpoint is converted in a feed-rate setpoint. The feed-rate is the control input that governs the machining force system. The feed-rate is controlled using feed-rate override knob on CNC machine. The machining force is measured using strain gage instrumented cutting tool. The Bayesian statistical methods developed are used in real-time to update the parameter estimates, converging to true parameter values, thereby satisfying the control objective. It is important to note that this control architecture was found insensitive to sudden changes in cutting load because of its feed forward nature. Also, the control needs to be tuned only for the feed-rate override control system, there is no separate controller required for machining force. As an extension of the single part/operation control framework, a multi-stage manufacturing process application is considered along with a demonstrative case that highlights the usefulness of identifying the process parameters. A multi-stage machining problem for the bar turning is considered, where bar is partially hardened. In case of no active control, the machining forces rise in the hardened part of the bar. When adaptive control architecture is used (as described earlier), the parameters are identified as well as machining force is kept constant by adjusting the feed-rate. The parameters identified can then be supplied to subsequent machine performing next machining operation. The parameters identified can also serve as product quality indicators. This sets the foundation of multiple machine-multiple process manufacturing control using models, which then can further be analyzed for profitability of the manufacturing process and the enterprise