For reference-tracking motion control, preview-based linear quadratic (LQ) design methods provide an effective means to balance tracking performance with available actuation capacity. This paper considers a control structure for which the optimal feedforward controller is independent of the feedback controller. In this way, explicit implementation formulas for feedforward controllers are derived that can be applied to a range of rigid-body motion systems. Key aspects of the optimal LQ solutions are identified, particularly how the choice of design weightings affect steady-state error for polynomial tracking. A redesign procedure for finite preview-time is proposed that preserves exact polynomial tracking properties and control bandwidth of the optimal solutions. Comparative experimental results are presented for a motor-driven linear motion stage.
Cole, M. O. T., & Wongratanaphisan, T. (2014). Optimal LQ feedforward tracking with preview: Practical design for rigid body motion control. Control Engineering Practice, 26(1), 41-50. https://doi.org/10.1016/j.conengprac.2013.12.007