SHAVO control: the combination of the adjusted command shaping and feedback control for vibration suppression

The fast and precise positioning of flexible mechanical structures is often corrupted by the unwanted dynamics in the form of a residual vibration. Therefore, we would like to find an appropriate control strategy that is capable to suppress this effect. The control strategies can be basically divided into two main groups: feedback control and feedforward control. The feedback control with the information from integrated sensors is capable to ensure the stability and robustness, but it may require large actuator effort, and it may be difficult to design satisfactory controllers for rapid movements. The feedforward methods including command/input shaping are based on the model of the system and usually require no additional sensors. They can significantly eliminate residual vibration, but feedforward methods cannot deal with disturbances, and the quality of their performance is strongly determined by the precision of the used model on which they are based. This paper proposes the novel solution to these problems, the so-called SHAVO (SHAper +\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+$$\end{document} serVO control) strategy that combines advantages of both approaches. Compared to other methods combining command shaping and feedback controller, the SHAVO approach differs in two key features. Firstly, it uses a different structure, the model of the system is used not only for shaper synthesis but also for predicting system outputs and states. Secondly, the shaper itself is highly optimized with arbitrary adjustable time length, not an impulse series, not limited by the system’s natural frequency.