Dynamically Compensated and Robust Motion System Inputs Based on Splines: A Linear Programming Approach

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 system input. Furthermore, the design criterion and constraints are chosen such that the resulting optimization problem is a linear program. As an application, the system input of a linear dynamic system is optimized to reduce the residual vibration in a robust manner. The obtained numerical results improve those of an earlier benchmark, based on Bernstein-Bezier harmonics. Furthermore, they suggest that the proposed linear programming approach behaves in practice as an algorithm that is capable of automatically selecting the optimal number and location of the knots of a polynomial spline of order M + 2.