Robust Control Approach by QFT for AFM Nanocantilever Having Dynamic Uncertainties and External Disturbances

Robust Control Approach by QFT for AFM Nanocantilever Having Dynamic Uncertainties and External Disturbances

In this study a robust control technique for a nanocantilever of Atomic Force Microscope (AFM) containing parametric uncertainty and external disturbances have been investigated by Quantitative Feedback Theory (QFT). The nonlinear partial differential equation of governing relations of motion and corresponding boundary conditions have been derived using Hamilton principle, Euler-Bernoulli beam and Eringen’s nonlocal elasticity theories. The nonlinear behavior of the AFM is due to the nonlinear nature of the AFM tip–sample interaction caused by the Van der Waals attraction/repulsion force that modeled by two linear and nonlinear springs. In continuous, the Galerkin procedure is utilized to gain the governing nonlinear ordinary differential equation (NL-ODE). Afterward, the resulting NL-ODE is properly solved by means of Horowitz technique. Subsequently the transfer function of system is determined with parametric uncertainty. Therefore, based on the QFT method, a controller (compensator) and a prefilter have been designed and loop shaped for an uncertain plant with external disturbances. The results illustrate by applying this robust control procedure are accomplished performance specifications in the presence plant changes and external disturbances, robust tracking of inputs, minimum bandwidth (preventing noise amplification).