Polynomial spline input design for LPV motion systems

This paper considers the concurrent design of point-to-point trajectories and corresponding feedforward inputs for mechatronic motion systems. This design approach is an extension of a recently developed linear optimization framework for polynomial splines of a chosen degree. This optimization framework minimizes the higher derivatives of the spline, thereby ensuring smoothness of the systems input, and is capable of automatically selecting the optimal number and location of the knots of the polynomial spline inputs. By including a discrete-time linear system model in the optimization framework, the input of the motion system is obtained as a dynamically optimal polynomial spline, taking into account boundary and bound constraints on both system input and output, as well a their derivatives. Numerical results illustrate the potential of the presented design approach for linear parameter varying systems.