Optimal Control Approach for Turning Process Planning Optimization

This paper considers the optimal process planning of turning operations where the machining time is minimized subject to a variety of equipment and process constraints. A new approach is proposed, in which virtual dynamics are incorporated, the process planning problem is formulated as a time-optimal dynamic system control problem, and optimal control tools are applied. The independent variable is changed from time to the instantaneous machined length to convert the time-optimal control problem to a finite-horizon control problem. Process and equipment constraints are incorporated using penalty terms in the cost function based on an approximation of the constrained variables. A recently developed method, called the Finite-horizon State Dependent Riccati Equation (Finite-SDRE), is used to solve the problem for the single tool turning process. Then, the developed method is extended and applied to parallel turning operations. Simulation studies are conducted to analyze the performance of the method for single-tool and parallel-tool turning operations, and the proposed method is shown to be very effective for solving such process planning problems.