Abstract
This paper deals with modelling and control of Euler-Bernoulli smart beam interacting with a fluid medium. Several distributed piezo-patches (actuators and/or sensors) are bonded on the surface of the target beam. To model the vibrating beam properly, the effect of the piezo-patches and the hydrodynamic loads should be taken into account carefully. The partial differential equation PDE for the target oscillating beam is derived considering the piezo-actuators as input controls. Fluid forces are decomposed into two components: 1) hydrodynamic forces due to the beam oscillations, and 2) external (disturbance) hydrodynamic loads independent of beam motion. Then the PDE is discretized using the Galerkin approach to obtain standard multi-modal equations. An adaptive approximation control structure is proposed to suppress the beam vibration. The controller consists of a proportional-derivative PD control plus an adaptive approximation compensator AAC with guaranteed stability. A simply supported beam with 2 piezo-patches interacting with fluid is simulated. The disturbance hydrodynamic force that excites the beam vibration is assumed as a harmonic force with 50 Hz frequency and 1 N amplitude. The results prove the efficacy of the proposed control architecture.
Highlights
Modelling, design and motion regulation of fluid-flexible structures witness much attention since they are used in many life applications such as underwater robotic systems, space vehicles or resonant beams for measurement purposes [1,2,3]
In view of the above, this work is concerned with modelling and adaptive approximation control of a linear smart beam model interacting with fluid
The proposed control law consists of three terms: PD term, an adaptive approximation compensator term, and a robust sliding term for compensation of modelling errors if exist
Summary
Design and motion regulation of fluid-flexible structures witness much attention since they are used in many life applications such as underwater robotic systems, space vehicles or resonant beams for measurement purposes [1,2,3]. These structures would be destabilized if undesired disturbance loads are applied. In view of the above, this work is concerned with modelling and adaptive approximation control of a linear smart beam model interacting with fluid.
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