A Very Strictly Passive Gain-Scheduled Controller: Theory and Experiments

This paper considers gain-scheduled control within a passive systems framework. Inspired by the passivity theorem and linear parameter varying systems theory, a very strictly passive gain-scheduled controller is introduced. The proposed gain-scheduled controller is used in tandem with an actuator saturation prevention technique. The actuator saturation prevention technique does not violate the passive properties of the controller, can account for feedforward control, and can have variable saturation limits. Scheduling signals are bounded and square integrable on finite time intervals. They have no restrictions on their derivatives, can be nonlinear, and can be functions of system states, exogenous signals, or time. The controller is applied to a trajectory tracking problem of a two-link flexible manipulator's heavy payload. The proposed controller is compared to two other gain-scheduling paradigms through experimentation. The theoretical and experimental results of this paper show that the proposed control architecture with a fixed number of integrating states is able to have improved stability properties over a traditional linear parameter varying controller without compromising performance. In addition, the proposed controller is able to asymptotically track a trajectory while avoiding actuator saturation.