Robust nonlinear control of atomic force microscope via immersion and invariance

Abstract

This paper reports an immersion and invariance (I&I)-based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed-loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov-based analysis of the closed-loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method. KEYWORDSatomic force microscope, chaos, disturbance rejection control, immersion and invariance, output feedback control INTRODUCTIONAtomic force microscopes (AFMs) are useful tools for measuring intermolecular forces in electronics, identification of biological materials, materials science, and semiconductors. The main component of an AFM is a microcantilever with a sharp tip, which is connected to a piezoelectric. A photodiode sensor, which is sensitive to the microcantilever's end position, determines the tip displacement. When the tip approaches the sample substrate, the atomic force interaction changes the dynamics of the AFM tip and, consequently, the whole microscope. The AFMs can operate in different modes including contact, noncontact, and tapping modes. In the contact mode, the tip operates within the range of the repulsive Int J Robust Nonlinear Control. 2019;29:1031-1050.wileyonlinelibrary.com/journal/rnc

Dynamic scaling‐based adaptive control without scaling factor: With application to Euler–Lagrange systems

“…A novel scaling factor ( 19) is proposed, which ensures the properties ( 21) and ( 22) by virtue of the saturation function s(r). Note that the feedback gains (39) have nothing to do with R or r aided by (22), while the feedback gains in conventional dynamic scaling-based I&I adaptive controller have a quadratic growth with respect to scaling factor. In other words, the introduction of scaling factor R and r is just to prove the perturbance term brought by estimation error can be directly cancelled by constant feedback gains, and hence the information about scaling factor is no longer required in the proposed controller implementations, which significantly reduces the complexity of the closed-loop system.…”

“…[15][16][17] Most existing literatures pertaining to I&I philosophy considered the one-dimensional PDE, which can directly solved. [18][19][20][21][22] When the parametric regressor matrix is not integrable, the limitation is bypassed by introducing low-pass filters for the state and regressor matrix, and the typical merits in basic I&I-based control scheme are maintained simultaneously. [23][24][25][26] While an evident shortcoming is that a huge burden of calculation should be undertaken due to the filtering of regressor matrix, especially when applied to a large dimensional system.…”

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

“…In Kuiper and Schitter (2012), a feedback controller design has been proposed for a linear model of the AFM system. Moreover, some controller design techniques have been established for the AFM system based on lumped-parameters models in Arjmand et al (2008), Wang et al (2010), Balthazar et al (2014), Keighobadi et al (2019a), Wang et al (2019) and Javazm and Pishkenari (2020). A nonlinear delayed feedback controller has been applied to control chaos in an AFM system modeled by the lumped-parameters modeling approach in Arjmand et al (2008).…”

“…In Balthazar et al (2014), the problem of motion control for the AFM system has been studied based on this modeling method. In Keighobadi et al (2019a), a robust nonlinear controller has been employed for AFM system applications based on a lumped-parameters model. An adaptive scan for the AFM system has been studied based on this modeling approach in Wang et al (2019).…”

Dynamical Investigation of Cam-Follower Profile Under Space - 100 to + 120°C Temperature Condition

“…Further new immersion and invariance observer for inertial MEMS attitude-heading reference systems, an enhanced fuzzy H∞ estimation algorithm [20,21] and nonlinear disturbance rejection-based controller of a triaxial MEMS vibratory gyroscope [22,23] are presented. The nonlinear control [24][25][26][27][28][29][30], linear and nonlinear observer and filters [31][32][33][34][35][36][37][38][39][40] and predictive techniques [41][42][43] properly explained space mechanism related control systems.…”