Integrated optimization of the command and control systems for computerized machine tools

Integrated optimization was performed on a biaxial contouring system to minimize the tracking time subject to electrical and contour error constraints for elliptical, airfoil, and corner trajectories. The controller and the interpolator were designed together to improve the performance of the system.; The main idea presented in this thesis is the integrated design of the sub-systems of the CNC biaxial contouring system, namely the controller and the interpolator. The controller is designed based on the command signal generated by the interpolator. By taking into account the form of the command signal, the performance of the controller can be improved over the conventional controllers. The controller parameters and the rate (i.e. feedrate) at which the command signal is fed into the system are determined via optimization. We were able to use the solid modelling data directly for control purpose by converting the data into time signals.; In solving the minimum tracking time problems, a method using numerical (composite) optimization was employed to determine the feedrate profile along with the weighting matrices of the discrete linear quadratic regulator (DLQR) controller.; An iterative decomposition procedure was used to solve the minimum tracking time problem when numerical sensitivity became troublesome. The problem is divided into two subproblems, each with its own objective function. One is characterized as the feedrate optimization phase, and the other is characterized as the controller tuning phase. These two subproblems are solved repeatedly and alternately until no further improvements can be made.; Using either the composite or decomposition optimization procedure, it was possible to minimize the tracking time for the contouring system subject to both electrical and contour error constraints. For an elliptical trajectory, the tracking time was found to be about 25% less than the tracking time resulting from an optimal constant feedrate profile.