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Integration of Feedback Control with Feedforward Control for Trajectory Tracking Improvements for Very Fast Microscale Systems

Abstract— This article presents three control schemes: (i) feedback control method using LQR approach, (ii) inversionbased feedforward control method, and (iii) integration of the feedback control method with the feedforward control method, which is a control system that combines a feedback control method with a feedforward approach. Each control scheme is implemented to track two types of desired trajectories: triangle wave trajectory and sawtooth wave trajectory of the same frequency of 200 Hz and the same amplitude of 5 µm. The tracking is challenging in that the system is very fast, and the motion takes microscale amplitudes. The performance of tracking for each control method is evaluated by the quantifying tracking errors. The main contributions of this article are to show that: (i) the feedback control method cannot track the desired trajectories properly, and tracking errors are perhaps not acceptable in some applications, (ii) the feedforward method can substantially improve the performance of tracking as it is compared to that of the feedback approach, and (iii) integration of the feedback control scheme with the feedforward control scheme can further enhance the tracking of the trajectories and can achieve the best performance of tracking. The integration of the feedback control method with the feedforward control method can be effectively used in case good tracking is needed. Keywords— feedback control method, feedforward control method, LQR, reduced order inverse scheme, trajectory tracking, very fast microscale systems