# Impulse-Based Hybrid Motion Control

## TL;DR

This paper extends impulse-based hybrid control to general systems, providing stability conditions under damping uncertainties and demonstrating effectiveness through numerical examples with various damping scenarios.

## Contribution

It introduces a generalized hybrid motion control framework using impulsive actions triggered at state zero crossings, with stability analysis under uncertain damping.

## Key findings

- Stable convergence to zero achieved under damping uncertainties.
- Control method effective for systems with Coulomb friction.
- Numerical examples demonstrate robustness and transient behavior.

## Abstract

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.