Model-free Adaptive Output Feedback Vibration Suppression in a Cantilever Beam

TL;DR

The paper develops a model-free, output-feedback RCAC framework to suppress vibrations in a lumped-parameter cantilever beam under unknown disturbances. A sampled-data implementation couples RCAC with a lumped-parameter plant, using signal-conditioning filters to accommodate displacement or acceleration sensing, including a pseudo-displacement estimator for acceleration signals. Numerical results show substantial vibration attenuation for all sensing schemes, with displacement feedback generally performing best and the acceleration-based pseudo-displacement approach offering practical advantages when displacement sensing is difficult. The work highlights the method's potential for plug-and-play active vibration control in flexible structures and points to filter optimization and reduced hyperparameter sensitivity as avenues for future improvement.

Abstract

This paper presents a model-free adaptive control approach to suppress vibrations in a cantilevered beam excited by an unknown disturbance. The cantilevered beam under harmonic excitation is modeled using a lumped parameter approach. Based on retrospective cost optimization, a sampled-data adaptive controller is developed to suppress vibrations caused by external disturbances. Both displacement and acceleration measurements are considered for feedback. Since acceleration measurements are more sensitive to spillover, which excites higher frequency modes, a filter is developed to extract key displacement information from the acceleration data and enhance suppression performance. The vibration suppression performance is compared using both displacement and acceleration measurements.

Figures (14)

• Figure 1: Cantilever beam laboratory setup.
• Figure 2: Lumped parameter model of a cantilever beam.
• Figure 3: Sampled-data implementation of adaptive controller for control of the continuous-time system ${\mathcal{M}}.$ For this work, $r \equiv 0$ reflects the desire to minimize the oscillations in the measured signal, ${\mathcal{F}}$ is a filter for signal conditioning, $\sigma$ is the control-magnitude saturation, and ${\mathcal{M}}$ represents the LP model introduced in Section \ref{['sec:LPM']}. The form of filter ${\mathcal{F}}$ depends on whether the available measurement $y$ is a displacement or an acceleration, and more details are given in Subsection \ref{['subsec:filter']}.
• Figure 4: Signal conditioning filter ${\mathcal{F}}$ in which the input $e_k$ is an acceleration measurement and the output $z_k$ is a displacement estimate. $K_{\rm g} > 0$ is the filter gain, and $\nu_{\rm hp} > 0$ determines the high-pass filter cutoff frequency.
• Figure 5: Subsection \ref{['subsec:disp_results']}: Open-loop and closed-loop displacement and acceleration results in the time domain with RCAC using displacement measurements ${\mathcal{C}}_{\rm disp}$ in the case where $i_{\rm u} = 12$ and $f_{\rm dist} = 20$ Hz with $d_{\rm f} = 5$ and $R_u = 1.$