A Linear Programming Approach to the Optimal Design of Spline-Based Motion System Inputs

For motion systems such as cam-follower mechanisms and loads driven by servo motors, this paper considers the design of system inputs that are continuous up to their M -th derivative and minimize some design criterion subject to user-defined constraints. This problem is tackled by optimizing a piecewise-linear, continuous parametrization (based on a large number of second-order B-splines) of the M -th derivative of the trajectory, which guarantees the continuity up to derivativeM . As an application, the system input of a linear dynamic system is optimized to reduce the residual vibrations. Both non-robust and robust solutions of the resulting linear optimization problem are presented. For high-speed applications a trade-off in the degree of continuity at the boundaries is shown: for robustness against small plant perturbations this degree needs to be low, while for robustness against unmodeled higher dynamics this degree needs to be large. The numerical optimization results furthermore confirm and outperform earlier results for the considered benchmark.