The Optimal Machine Tool Control Problem

The optimal machine tool control problem is formulated for a computer-aided manufacturing facility where the costs of transmitting part program information to a continuous path numerical control machine tool should be minimized. The problem is formulated as an optimal sampled-data tracking problem with a performance index that measures both part quality (the tracking error in following a desired cutter path and the surface finish quality) and the costs for computing, storing, and transmitting the programmed control for a particular machining operation on a machine tool. The optimal sampled-data control is assumed to be a polynomial function of time over any sampling interval where the parameters of this polynomial for each sampling interval, the length of each sampling interval, and the number of sampling intervals are control variables. This optimal machine tool control problem is solved for the special case where the form of the polynomial approximation is specified and is a fixed function of the desired cutter path at the sampling times. A computation algorithm is developed and used to compute this optimal control approximation. The results for this example are used to illustrate the performance characteristics of such an optimal control approximation.