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UBC Theses and Dissertations

A real time and time optimal trajectory generator for Cartesian machine tools Zarif Mansour, Sepehr


This work focuses on control and trajectory optimization strategies for high speed contouring of machine tools. In the first part, control strategies are studied. Studied strategies are divided into three major categories. Axial error controllers, contour error controllers, and feed forward controllers. The control strategies are benchmarked on a biaxial XY table. The least contouring error was recorded for the control structure consisting of Cartesian Servo Control (CSC) with a Proportional Derivative Integral (PID) regulator + Torque Feed Forward (TFF). As for the trajectory optimization, a new real time algorithm to select time-optimal feedrates has been proposed. The algorithm is independent of the spline representation of the nominal path, and incorporates both velocity and acceleration constraints. The fact that the proposed algorithm is independent from the spline representation (since it simply adjusts sampling times for position increments), makes it more flexible than conventional algorithms in the literature that require particular spline representations of the reference trajectory. Also the proposed algorithm is computationally efficient because: 1) an analytical solution to the optimization is applied at every time step rather than a global numerical optimization procedure, and 2) other analytical solutions in the literature require a forward and a backward pass over the compete trajectory. The new algorithm only backtracks over a short window before decelerations. Finally, this study also introduces two new reference path generation techniques that use part tolerance values to reduce machining time.

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