NETE Q-Adaptive Control of the nonlinear dynamics of the cantilever-sample system of an Atomic Force Microscope
Keywords:
Adaptice Control, Q-Control, Lyapunov stability, Nonlinear System, Atomic Force Microscope (AFM)Abstract
The article presents the control of the nonlinear
dynamics of the cantilever-sample system of an atomic force
microscope (AFM) by the combination of Q-control and model
reference adaptive control, when the AFM operates in contact
mode. In this mode the AFM is always in contact with the sample,
being able to measure the topographic characteristics for
different materials and structures at a nanometric scale. For this
task, the AFM uses a cantilever with a micro tip at one end that
explores the surface of the sample during scanning. During this
process, the closed loop feedback control keeps the acting force on
the cantilever beam constant, where the error between the
reference and the output of the plant is equivalent to the
topography of the sample. We know that the nonlinear dynamics
of the cantilever beam system is complex, due to the different
types of nonlinear forces that act. In the contact mode the
interaction force is described by the modified Hertz model when
the cantilever-sample distance is less than 0.2 nm. Here we use an
approximate model of the interaction force to reduce the
complexity of the model, which depends on the Q factor. The
proposed method combine the adaptive control with the control
Q, where the control Q allows to reduce the force of beam
interaction cantilever-sample, reducing the probability of damage
in the sample and in the micro tip due to permanent contact. The
Q control is incorporated to the proposed method through the
design of the reference model and also a design formula for the
effective Q factor is obtained. As a result we have that the
proposed control method is stable, showing good performance for
different surfaces and reference inputs. The stability of the
system is proved by the second Lyapunov method. To show the
effectiveness of the proposed method a variety of simulations are
presented. The proposed method is totally general and can be
applied to any nonlinear complex system.
