Parameter Identification and Adaptive Control Of Carbon Nanotube Resonators

In this paper, we exploit an adaptive control scheme to adjust highly sensitive oscillations of fluid conveying carbon nanotube (CNT) resonators. Firstly, we focus on the nonlinear vibrations of the fluid conveying CNTs, considering an added mass using nonlocal Euler-Bernoulli beam theory. CNT rests on nonlinear Winkler and Pasternak foundations. We use the Galerkin method to extract the nonlinear ordinary differential equation models of the CNT oscillations. We elicit a linear parametric model for estimating the added mass and other parameters of the system. Numerical simulations delineate that the developed model has sensitivity to added mass at the yoctogram level. It is known that CNT vibrations are very sensitive to small perturbations. Accordingly, a small perturbation results in significantly abrupt changes in the vibrational parameters of the targeted system. For that reason, it is crucial to have a potent apparatus for identifying the system parameters in case of sudden changes in the vibrational parameters. For such parameter identification, a least squares (LS) parameter identification algorithm and an extended Luenberger observer are integrated to a pole placement controller for online estimation of the system parameters as well as vibration control of the objective system. It is well-known that CNTs are potentially ideal atomic force microscopy (AFM) probes, and accordingly, the proposed method is potentially beneficial for identifying highly sensitive motions in AFM. In addition, numerical simulations are presented, showing that the proposed adaptive controller has the potential to be used for vibration control of the CNT resonators even in the case of chaotic motions.