Nonlinear control of passive vibratory systems with finite actuation stroke

Abstract

Many vibration response control technologies employ actuators that exhibit finite stroke limits. In this paper, we consider the scenario in which a linear, time-invariant feedback law has been designed to control vibrations in a linear, time-invariant vibratory system, without accounting for the actuation stroke limits. In this scenario, the saturation of the actuator stroke may be viewed as introducing unmodeled dynamics into the closed-loop system response, which can be undesirable for a few reasons. Most importantly, it may destabilize the closed-loop system. Additionally, it introduces impulsive disturbances into the response, and may result in hardware damage. We illustrate a technique whereby the linear feedback law, designed a priori, may be augmented with a nonlinear feedback loop which protects against stroke saturation while simultaneously maintaining closed-loop stability. The nonlinear feedback law is developed around the concept of output-strict passivity, and exploits the known output-strict passivity of the vibratory system. Importantly, the nonlinear feedback law leaves the performance of the linear feedback law unaffected for small-signal responses.