Optimal Design of Spline-Based Feedforward for Trajectory Tracking

This paper presents a new feedforward design method for linear time invariant systems. The feedforward design is formulated as a linear program that optimizes a polynomial spline of order M + 2, which is continuous up to the M-th derivative. The desired tracking accuracy is specified in advance and is traded off with the smoothness of the feedforward signal. Avoidance of actuator saturation is handled through imposing input constraints. Simulation results are presented to validate the developed feedforward design method. The considered test case is a flexible one-link robot, which is a nonminimum phase system. The obtained numerical results improve those of an earlier benchmark method, the extended bandwidth zero phase tracking control method. Furthermore, the results show that in practice, the proposed linear programming framework behaves as an algorithm that is capable of automatically selecting the number and location of the knots of a polynomial spline of order M + 2.