Design and development of a model free robust controller for active control of dominant flexural modes of vibrations in a smart system

Real physical vibrating smart systems exhibit a lot of nonlinearities in their dynamics. Undesirable vibrations, particularly in the regions of first as well as second resonance, play a very important role in deteriorating the stability of the system as well as its operational efficiency. The work presented in the paper focuses on an analytical technique of mathematical modeling of a vibrating piezoelectric laminate cantilever beam which is considered to be the smart system. The natural frequencies of the vibrating smart system are determined from the ANSYS simulation studies and experimentally, it is found that the vibrations induced voltage is maximum at the first followed by the second natural frequencies. Hence, the smart system is modeled analytically through finite element technique using the Euler-Bernoulli beam theory for the first two flexural modes of vibrations. To account for the possible nonlinearities, a suitable robust controller is designed based on sliding mode technique. Simulation studies on the developed analytical model indicated a high performance of the designed controller in controlling the vibrations at first and second resonance regions. Also, the designed controller was found to be effective in its operations when the excitation varied over a large range covering the first two natural frequencies. In the final stage, the designed robust controller was successfully prototyped on a Field Programmable Gate Array (FPGA) platform using LabVIEW coupled with Compact Reconfigurable Input Output (cRIO-9022) controller configured in its FPGA interface mode and the resulting robust FPGA controller successfully controlled the occurring system vibrations.