Variation of fraction in FOPID controller for vibration control of Euler–Bernoulli beam

摘要

Fractional-order derivatives and integrals have gained serious attention by the researchers in past few decades. It has been observed that fractional calculus is more suitable in modeling real life systems. In this paper, Fractional-Order PID (FOPID) controller is studied to suppress the vibration of cantilever beam modeled by Euler–Bernoulli model. Finite difference method is applied to analyze the behavior of the system at different fractional orders of PID controller, and the governing equations are simulated using MATLAB. The response of the system is evaluated at different fractionalorder control points, under constant PID parameters ( K_p, K_i , and K_d ). Furthermore, the variation of frequency in transient response and 5% settling time is observed. Simulation results reveal that, though system with fractional order controller is more flexible now, the classical model of PID controller can also be properly tuned through PID constants to achieve the resultant response of the system. So, due to more simplified modelling, the classical model has an edge over the fractional order in the vibration control of cantilever beam.