Desensitized minimum power/jerk control profiles for rest-to-rest maneuvers

The focus of this paper is on the development of weighted minimum power/jerk control profiles for the rest-to-rest maneuver of a flexible structure. To account for modeling uncertainties, equations are derived which represent the sensitivity of the system states to model parameters. The original state-space model of the flexible structure is augmented with the sensitivity state equations with the constraint that the sensitivity state variables are forced to zero at the end of the maneuver. This requirement attenuates the residual vibration at the end of the maneuver caused by errors in system parameters. A systematic procedure for the design of the controller is developed by representing the linear-time-invariant system in its Jordan form. This decouples the modes of the system permitting us to address smaller order dynamical systems. The proposed technique is illustrated via a benchmark floating oscillator problem.