Robust stabilization of the internal dynamics of flexible robots without measuring the velocity of the deflection

In the study of control for multilink flexible robots two important issues are often ignored: (1) the velocity of the deflection is not available (i.e. not measurable), thus, any proposed design based on the velocity of the deflection is not directly implementable; and (2) any finite dimensional model is just an approximation of the true system, which is infinite dimensional, therefore, the designed control should be guaranteed to stabilize the original infinite dimensional systems, otherwise, there may be an effect of spillover. As a whole, any realistic design should consider these two issues. In this paper the authors develop a robust compensation strategy to deal with these two factors simultaneously. First, a time-scale separation is applied and the dynamical system is transformed to a singularly perturbed system, whose boundary-layer is a family of unstable infinite dimensional linear systems parameterized by the slow variables. A single finite dimensional robust compensator is designed for this family of systems, and it is proved that this compensator is able to stabilize every system in this family. The slow part of the control is designed according to the reduced-order system, and the fast part is generated via the designed compensator. It is shown that the full dynamical system is uniformly bounded, which implies that the tracking error is uniformly bounded by a small term and the vibration is damped out. Moreover, schemes for computation are presented, and simulations show excellent path tracking and vibration rejection properties. Numerical experiments show that the authors´ approach can deal with much lower stiffness than most existing two-time scale methods