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

Abstract

Accurate representation of the atomic force microscopy (AFM) system is not only necessary to achieve control objectives, but it is also beneficial for detecting the nanomechanical properties of the samples. To this end, this paper addresses the issue of controller design for the AFM system based on an accurate nonaffine nonlinear distributed-parameters model in which flexibility and distributed mass effects of the microcantilever beam are considered properly. First, a T-S fuzzy model is derived for this dynamical model of the AFM system in order to simplify the procedure of controller design. Then, a fuzzy model-based controller is designed to suppress the chaos and attenuate the disturbance in the AFM system through the linear matrix inequality (LMI) formulation. Moreover, by considering some criteria for disturbance rejection and transient performance, and some constraints on control input and states, new stabilization conditions are proposed based on a fuzzy Lyapunov function. Finally, simulation results are represented to demonstrate the effectiveness of the proposed method.

Robust fuzzy model predictive control for nonlinear discrete‐time systems

“…To stabilize system (5), the non-PDC controller is considered as (7). 25 Non-PDC controller is utilized to design a fuzzy controller. The approach involves designing a state feedback controller for each local linear model.…”

“…To stabilize system (), the non‐PDC controller is considered as () 25 . Non‐PDC controller is utilized to design a fuzzy controller.…”

“…In most of the proposed FMPC for T‐S fuzzy systems, the Parallel Distributed Compensation (PDC) technique has been employed. However, non‐parallel distributed compensation (non‐PDC) technique can provide better performance compared to PDC 25 . Although non‐PDC approach has been considered in 16,23 so as to provide FMPC for T‐S fuzzy systems, disturbance, and system uncertainties have not been noted in References 16 and 23, respectively.…”

Stabilization of nonlinear fractional order faulty systems with time-varying delay

“…On the other hand, dealing with nonlinear systems is a significant challenge in control engineering (Naderi Akhormeh et al, 2019). The Takagi–Sugeno (T-S) fuzzy model approach is a strong tool for representing nonlinear systems accurately (Mahmoudabadi et al, 2022a, 2022b). T-S fuzzy approach was firstly introduced by Takagi and Sugeno in 1985 (Takagi and Sugeno, 1985), and then has been extended to fractional order systems by Zheng et al (2010).…”

Robust tracking control for nonlinear fractional order delayed systems: Modified repetitive control approach

“…Takagi and Sugeno have proposed an effective modeling approach, namely, the Takagi-Sugeno (T-S) fuzzy model, to deal with these difficulties [10,11]. This rule-based modeling approach has been employed in numerous research papers [12][13][14][15][16].…”