**1. Introduction**

It is well known that many practical electromechanical devices can be modeled by a coupled equation; they can be understood in the context of simple lumped mechanical masses and electric and magnetic circuits. Electromechanical systems fall into three groups: Conventional electromechanical systems (MACRO), microelectromechanical systems (MEMS), and nanoelectromechanical systems (NEMS) [1].

Many of the "NEMS" device technologies use "MEMS" as a bridge to the nanoworld. "MEMS" will provide a bridge to enable applications of nanotechnology, as illustrated in the cantilever sensor. As an example, the atomic force microscope

(AFM) used in this technique has a tip made of silicon, using a typical MEMS device process, and is of micrometer dimensions. Cantilever sensors recognize resonant frequency shifts with the addition of mass, indicating the presence or absence of specific compounds in the environment tested. First, "MEMS" technology is based on multidisciplinary foundations. Designing a commercially viable microsystem with required dynamic performance requires an in-depth understanding and accurate prediction of its dynamic characteristics. Furthermore, the macro-properties of materials may change as the size of the feature of mechanical elements is reduced, leading to difficulties in modeling their dynamic characteristics [2].

We remark in an AFM that a microscale cantilever with a sharp tip is used to scan the specimen surface, and the vibration of the cantilever is measured to identify the distance between the tip and the specimen surface. The AFM is composed of an elastic cantilever, and the achievable sensitivity and resolution of the AFM are largely dependent on the geometry of the cantilever. Currently, AFM is one of the most effective imaging techniques that is being used at the nanoscale and sub-nanoscale levels. This technique has been applied to multiple problems in the field of natural sciences and can record a range of surface properties of materials in both liquid media and air. Nowadays, AFM includes a wide variety of methods in which the probe interacts with the sample in different ways to characterize various material properties. AFM can characterize a wide array of mechanical properties (e.g., adhesion, stiffness, friction, and dissipation), electrical properties (e.g., capacitance, electrostatic forces, work function, and electrical current), magnetic properties, and optical spectroscopic properties. In addition to imaging, the AFM probe can be used to manipulate, write, or even pull-on substrates in lithography and molecular pull experiments.

A general overview [3] was written concerning nonlinear and chaotic behavior and their controls of an atomic force microscopy (AFM) vibrating problem, which has been dedicated to tapping mode operation, considered the presence of hydrodynamic damping, based on papers of the research group in Brazil. We also discussed an AFM mathematical modeling with phase-locked loops (PLLs), inspired by Ref. [4, 5].

The MEMS-based atomic force microscope (AFM) device consists of a microcantilever beam with a tip that interacts with the surface of a sample. The sample surface topography causes vibrations in the microcantilever beam; the microcantilever reflects a laser beam that is captured by a photodiode. The laser beam deflection is used to generate the topographic images of the sample. The common operation modes of AFMs are noncontact, contact, intermittent, and trolling modes [3, 6, 7] and underserved of others. The atomic force microscope (AFM) was first presented in Ref. [8].

The field of scanning probe microscopy (SPM) began in the early 1980s with the invention of the scanning tunneling microscope (STM) by Gerd Binnig and Heinrich Rohrer, which was awarded the Nobel Prize in Physics in 1986.

Many authors developed theories on this topic. We remarked that mathematical models in (AFM) are used to analyze the behavior of strongly nonlinear dynamics, to determine the presence of irregular displacements that are caused by the interaction forces between the microcantilever tip and the atoms of the sample surface. Another contributing factor to irregular displacement in the microcantilever is the viscoelastic phenomenon. The control design are applied to suppress the irregular (chaotic) displacement of microcantilever the AFM to keep the motion regular (periodic). AFM is an essential technique for the study of surfaces and their interactions with atomic resolution, showing the strong influence of fractional nonlinear dynamics.

#### *MEMS-Based Atomic Force Microscope: Nonlinear Dynamics Analysis and Its Control DOI: http://dx.doi.org/10.5772/intechopen.108880*

It is well known that the nonlinear dynamics of atomic force microscopy (AFM) is an emerging topic of research and is a widely used tool for atomic-level surface analysis. In addition, nanodevices has become an important equipment in the industry for developing nanotechnology, being used to develop substances, compounds, artifacts, and nano chips. In fact, (AFM) is a force sensor. When the surface under investigation attracts or repels the tip, the cantilever bends to or from the surface.

In this unit chapter paper, we will mention an example of a cantilever modeled as being a single spring-mass-damper system, and a nonlinear dynamic model is developed to study the cantilever-sample interaction by using the L. J. potential including the long-range attractive forces and short-range repulsive forces**.** A comprehensive investigation of the nonlinear dynamics and chaos is carried out based on this model, including samples related to damping; it is possible to see that the behavior is not only viscous but viscoelastic and will be discussed, using bifurcation diagrams, phase portraits, Poincare maps, and Lyapunov exponents. An active control strategy has also been proposed by us to be effective in suppressing micro-oscillations, although these methods require significant use of control resources.

Note that active methods also require sensors capable of constantly providing accurate measurements for feedback to the controller. Here, the analysis is performed considering the effects of an optimal active linear control and time-delay control.

Through computer simulations, the efficiency and robustness to parametric errors of each control technique are verified. The results obtained were in complete agreement with earlier theories and experiments. This bending is then measured by position-sensitive photodiodes via the displacement of the laser beam reflected by the back of the cantilever.

In summary, this chapter presents a short review of AFM applications of nonlinear dynamics and control. This is organized as follows. In Section 2, we presented a state of the art to give the position of the problem in the current literature. In Section 3, we exhibit the mathematical model used. In Section 4, we discuss its nonlinear dynamic behavior. In Section 5, we develop a control design to control its chaotic behavior. Finally, we present the concluding remarks and give some acknowledgments. And list the main references used.
