Single-Link Flexible Manipulator Control Accommodating Passivity Violations: Theory and Experiments

The robust control of a system which is nominally passive, but experiences a passivity violation is considered in this paper. Specifically, we utilize the hybrid passivity and finite gain stability theorem to robustly control a single-link flexible manipulator experiment. This system is nominally passive, but passivity is destroyed by, for example, sensor dynamics. The hybrid theorem is specifically applicable to such a scenario. We review and develop further the hybrid passivity and finite gain stability theorem in a linear time-invariant, single-input-single-output context. Calculation of the various passivity and finite gain parameters that classify a system as hybrid is discussed. In the interest of developing a hybrid controller that is optimal in some sense, we pose a numerical optimization problem which is constrained by the hybrid passivity and finite gain stability theorem. The numerical optimization objective function seeks to have a hybrid controller mimic a nominal controller. Experimental results successfully demonstrate tip-based feedback control of a single-link flexible manipulator.