Use of smart intelligent sensor & actuator mechanical materials (PVDF / PZT) in developing MIMO mathematical model of the smart structure and its use to control the active vibrations using discrete sliding mode control theory with output samples

Abstract

A multi-input, multi-output based modelling of intelligent flexible mechanical aluminium structures using smart materials with Euler-Bernoulli beam theory & state space techniques is being presented with multi-sensor data fusion concepts. An aluminium cantilever beam of rectangular cross section with known specifications is considered for the modelling purposes. 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. The dynamic equation is transformed into a state space model with 2 i/o’s using the concepts of state space theory in 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 Discrete Sliding Mode Control (DSMC) based controller on the o/p samples is designed and put in loop with the plant, after which the plant vibrations decays to zero in no time. The mathematical model of the DSMC controller is used to control the vibrations of the plant using the concept of destructive interference. The mathematical model of the DSMC controller can be used to control the vibrations of the plant using the concept of destructive interference.