Impulse-Based Hybrid Motion Control
For control engineers dealing with second-order motion systems with damping uncertainties, this work provides a hybrid control framework with guaranteed stability under bounded uncertainties.
This paper extends impulse-based discrete feedback control to a general hybrid motion control form, deriving stability conditions for convergence to zero equilibrium with only the upper bound of damping uncertainties known. Numerical examples demonstrate effectiveness for underdamped dynamics, time-varying damping, and Coulomb friction.
The impulse-based discrete feedback control has been proposed in previous work for the second-order motion systems with damping uncertainties. The sate-dependent discrete impulse action takes place at zero crossing of one of both states, either relative position or velocity. In this paper, the proposed control method is extended to a general hybrid motion control form. We are using the paradigm of hybrid system modeling while explicitly specifying the state trajectories each time the continuous system state hits the guards that triggers impulsive control actions. The conditions for a stable convergence to zero equilibrium are derived in relation to the control parameters, while requiring only the upper bound of damping uncertainties to be known. Numerical examples are shown for an underdamped closed-loop dynamics with oscillating transients, an upper bounded time-varying positive system damping, and system with an additional Coulomb friction damping.