Affiliations: Applied Mechanics Research Laboratory, Tunisia
Polytechnic School, La Marsa, Tunisia | Department of Engineering Sciences and Mechanics,
Virginia Tech, Blacksburg, VA, USA
Abstract: We propose a two-step strategy for the design of passive controllers
for the simultaneous confinement and suppression of vibrations (SCSV) in
mechanical structures. Once the sensitive and insensitive elements of these
structures are identified, the first design step synthesizes an active control
law, which is referred to as the reference control law (RCL), for the SCSV. We
show that the problem of SCSV can be formulated as an LQR-optimal control
problem through which the maximum amplitudes, associated with the control input
and the displacements of the sensitive and insensitive parts, can be regulated.
In the second design step, a transformation technique that yields an equivalent
passive controller is used. Such a technique uses the square root of sum of
squares method to approximate an equivalent passive controller while maximizing
the effects of springs and dampers characterizing passive elements that are
added to the original structure. The viability of the proposed control design
is illustrated using a three-DOF mechanical system subject to an excitation. It
is assumed that all of the masses are sensitive to the excitation, and thus the
vibratory energy must be confined in the added passive elements (insensitive
parts). We show that the vibration amplitudes associated with the sensitive
masses are attenuated at fast rate at the expense of slowing down the
convergence of the passive elements to their steady states. It is also
demonstrated that a combination of the RCL and the equivalent passive control
strategy leads to similar structural performance.
Keywords: LQR-optimal control, state and input bounds, active control, passive control, confinement of vibrations
