Development of mathematical model for smart intelligent flexible structures using smart intelligent sensor & actuator materials using Timoshenko beam theory & its control using POF

Abstract

In this research paper, the multivariable modelling of intelligent flexible aerospace structures using smart materials with Timoshenko beam theory & state space techniques with multi-sensor data fusion concept & its control using POF strategy is presented in n this research article. Finite Element Method is used in the analysis also. An aerospace aluminum cantilever beam of rectangular cross section with known specifications is considered for the modelling purposes. To start with from the fundamental principles of Timoshenko beam 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. The effect of shear is considered in modelling here, which is neglected in case of Euler – Beam theory, thus giving an accurate beam model. 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 POF controller can be designed and put in loop with the plant, after which the plant vibrations decays to zero in no time. The mathematical model of the POF controller can be used to control the vibrations of the plant using the concept of destructive interference. The work done can also be compared with others to show the authenticity or the profoundness of the methodology that is being developed by us.