Active Vibration Damping by Parametric Control

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Shahidi, R.
Shayman, M.
In recent years, smart composites have been introduced in the market that open up new possibilities for controlling or sensing flexible structures. Internal properties of these composite materials which are either embedded into the structure or bonded to the surface of the structure can be manipulated, through application of magnetic field (in magneto-strictive material), voltage (in piezoelectric material), or heat (in Shape Memory Alloys).<P>This dissertation is primarily concerned with those composites with variable stiffness or modulus of elasticity. The objective is to control the stiffness of the structure to achieve stability. A lumped parameter model of a non-shearable and inextensible beam is derived as an approximation to the continuum model with attached composites. Due to the ability to manipulate the modulus of elasticity of the composite, the spring constants of the finite dimensional model of the beam are identified as the control variables. We design nonlinear feedback control laws to damp vibrations in the resultant simple Hamiltonian control system while satisfying the input constraints. Then, the analysis is specialized to a class of bilinear system which is the state linearized version of the original system. Optimality of the proposed controller is studied and under special conditions a discontinuous control law is proposed which achieves a faster dissipation of the energy than the continuous one for some simulated cases.<P>