In this paper, a sliding mode backstepping controller for a pinned-pinned Euler-Bernoulli beam is briefly reviewed and its efficacy in the presence of unknown bounded harmonic disturbances at arbitrary frequencies is analyzed. A brief discussion of the open-loop unstable response to harmonic excitations at resonant frequencies is provided. Motivated by this, particular attention is given to excitations at the natural frequencies of the system. It is shown that in the face of such resonant disturbances, the sliding mode backstepping controller is able to eliminate the vibrations in the beam system where backstepping control alone cannot. Indeed it is shown that if the disturbances are not accounted for, the closed loop system exhibits large (relative to the initial conditions) steady state harmonic vibrations. When the unknown resonant harmonic disturbances are accounted for via the sliding mode backstepping technique, the steady state position is constant and does not exhibit any vibrations, and furthermore it reaches this steady state exponentially at an arbitrarily selected rate.
- Dynamic Systems and Control Division
Robust Boundary Control for an Euler Bernoulli Beam Subject to Unknown Harmonic Disturbances With a Focus on Resonance
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Karagiannis, D, & Radisavljevic-Gajic, V. "Robust Boundary Control for an Euler Bernoulli Beam Subject to Unknown Harmonic Disturbances With a Focus on Resonance." Proceedings of the ASME 2017 Dynamic Systems and Control Conference. Volume 3: Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems; Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems. Tysons, Virginia, USA. October 11–13, 2017. V003T32A009. ASME. https://doi.org/10.1115/DSCC2017-5264
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