Two Degree-of-Freedom Robust Digital Controller Design With Bouc-Wen Hysteresis Compensator for Piezoelectric Positioning Stage

The compensation of nonlinear hysteretic behavior is one of the mandatory requirements in order to achieve precise reference tracking performance from a piezoelectric positioning stage. A common practice of employing an inverse hysteresis model as a feed-forward compensator must deal with modeling complexity; consequently, real-time tracking performance suffers due to modeling errors. In this paper, a two degree-of-freedom robust digital feedback controller design scheme in the presence of a simple Bouc-Wen hysteresis feed-forward compensator is proposed to deal with the dual challenge of modeling complexity and modeling errors. The proposed control scheme takes into account the performance and robustness requirements simultaneously. The desired performance and robustness requirements are expressed by means of constraints on the shapes of closed-loop sensitivity functions (CLSFs). Then, pole placement with sensitivity function shaping methodology is adopted so that the CLSFs respect their respective constraints and the desired performance with robustness could be achieved. The presented experimental results verify the effectiveness of the proposed control scheme in achieving the peak-to-peak reference tracking error of 0.36% for the desired displacement of 12 μm with tracking frequency of 10 Hz, whereas the peak-to-peak tracking error of 4.33% is observed with a Bouc-Wen hysteresis feed-forward compensator (without the feedback controller). Overall, 91% improvement is achieved in reducing the reference tracking error with the proposed control scheme.