Multivariable modelling of intelligent flexible mechanical structures using smart materials with FEM, Euler-Bernoulli beam theory, state space & multi-sensor data fusion techniques

Abstract

In this research paper, the multivariable modelling of intelligent flexible mechanical structures using smart materials with Euler-Bernoulli beam theory & state space techniques is being presented with multi-sensor data fusion concept. To start with from the fundamental principles of E-B theory, a Lagrange equation of motion is obtained both for the regular beam element as well as for the PZT & PVDF sensor actuator pair. Following which, a dynamic equation of motion of the smart intelligent structure developed using the smart materials consisting of PZT& PVDF is obtained. Smart materials have got some special properties that react to the changes in their environmental conditions. This means that some of their special properties can be changed by using an external condition, such as temperature, light, pressure, electricity, voltage, pH, or chemical compounds, which could be considered as the special characteristics and this change is reversible, which can be repeated many times. The dynamic equation is transformed into a state space model with 2 inputs and 2 outputs using the concepts of state space theory in the advanced control engineering. The model is developed considering the first 2 modes of vibration, which are the most dominant modes in the vibration theory. The developed state space model is used for active vibration control. An external force of 1 N is applied at the end of the smart flexible multivariable multimodel cantilever beam after which the beam is subjected to vibrations. A Periodic Output Feedback controller can be designed and put in loop with the plant, after which the plant vibrations decays to zero in no time. The work done can also compared with others to show the authenticity or the profoundness of the methodology that is being developed by us.