Multilayered non‐uniform atomic force microscope piezoelectric microcantilever control and vibration analysis considering different excitation based on the modified couple stress theory

Abstract

Atomic force microscope (AFM) is one of the most powerful tools for surface scanning, force measurement, and nano‐manipulation. To improve its performance, vibration and control of AFM micro‐cantilever (MC) should be studied. Hysteresis, as an undesired phenomenon affecting vibration amplitude and phase, is also another important issue to be examined. In this paper, vibration analysis and control of a ZnO non‐uniform multi‐layered piezoelectric MC has been investigated in non‐contact mode. A modified couple stress theory has been used to obtain the strain energy for modeling the MC. In order to control the amplitude, a sliding mode controller (SMC) has been utilized on AFM, due to its application in uncertain and nonlinear systems. For applying the control signal, two methods of piezo and base actuation are studied. The results are compared with proportional integral derivative (PID) control method and it is demonstrated that SMC method reduces the control input close to the surface and increases the accuracy near the surface. In addition to MC control, hysteresis amplitude and phase differences are investigated by applying the Prandtl–Ishlinskii model. Also, surface topography is studied with hysteresis. The simulations show backward phase difference and an increase in amplitude, accordingly.

Modeling the Piezoelectric Cantilever Resonator with Different Width Layers

“…In the open-loop test, the quality factor of the piezoelectric cantilever resonator is 1411.2, therefore, the static tip displacement is 1.62 nm. Back to the proposed model, let the applied voltage be the drive voltage, that is 0.2 V. Substituting the geometry and material parameters to (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), the static tip displacement is 1.88 nm, which is larger than the measured result. The reason is that there is a feedthrough capacitor in the resonator [32], which will affect the output current.…”

“…The piezoelectric cantilever is one of the most important structures for micro-electro-mechanical system (MEMS) application and it has been used in atomic force microscopes, chemical sensors and biosensors, radio frequency (RF) switches, photon detectors, micromirrors, and energy harvesters [ 1 , 2 , 3 , 4 , 5 , 6 , 7 ]. Tip displacement and resonance frequency are two important characters of the piezoelectric cantilever, especially when setting the height of the cantilever in the RF switch [ 8 ] and tuning the resonance frequency of the energy harvester that matches the ambient vibrating frequency for improving the power efficiency [ 4 ].…”

Fuzzy model-based disturbance rejection control for atomic force microscopy with input constraint

“…In Korayem et al (2021), a lumped-parameters model has been introduced for the AFM system and the problem of control design for the AFM system has been studied based on the proposed model. Since complex nonlinearities of the dynamics of the AFM system have not been taken into consideration in Arjmand et al (2008), Wang et al (2010), Balthazar et al (2014), Keighobadi et al (2019a), Wang et al (2019), Javazm and Pishkenari (2020), Habibnejad Korayem et al (2021), and Korayem et al (2021), they are unable to represent the nanomechanical properties of the samples accurately. In addition, in Arjmand et al (2008), Wang et al (2010, 2019), Keighobadi et al (2019a), Balthazar et al (2014), Javazm and Pishkenari (2020), Habibnejad Korayem et al (2021), and Korayem et al (2021), the dynamical behavior of the AFM system has been approximated with affine models; in other words, the control signal has been assumed as a linear function.…”

“…Since complex nonlinearities of the dynamics of the AFM system have not been taken into consideration in Arjmand et al (2008), Wang et al (2010), Balthazar et al (2014), Keighobadi et al (2019a), Wang et al (2019), Javazm and Pishkenari (2020), Habibnejad Korayem et al (2021), and Korayem et al (2021), they are unable to represent the nanomechanical properties of the samples accurately. In addition, in Arjmand et al (2008), Wang et al (2010, 2019), Keighobadi et al (2019a), Balthazar et al (2014), Javazm and Pishkenari (2020), Habibnejad Korayem et al (2021), and Korayem et al (2021), the dynamical behavior of the AFM system has been approximated with affine models; in other words, the control signal has been assumed as a linear function. On the contrary, the time-delayed feedback control technique has been applied for the stabilization of a distributed-parameters model of the AFM system in dos Santos Rodrigues et al (2014).…”

Study of PID controller gain for active vibration control using FEM based particle swarm optimization in COMSOL multiphysics

“…9 The nonlinearities and mechanical vibration of the micro-cantilever restrict the resolution of these instruments. [10][11][12][13] Zhang et al 10 studied the frequency response of micro-cantilever at different control voltage and feedback gains to cancel the uncertain vibration by developing a dynamic model of a micro-cantilever with piezoelectric actuator. Similarly, Khabaz et al 13 have controlled the vibration of a micro-cantilever using piezoelectric actuator and sensor.…”