Adaptive fractional-order backstepping sliding mode controller design for an electrostatically actuated size-dependent microplate

Abstract

In this article, adaptive backstepping sliding mode controller and adaptive fractional backstepping sliding mode controller methods are proposed to control an electrostatic microplate with a piezoelectric layer. Based on the modified couple stress theory, a size-dependent mathematical model is proposed, in which the microplate is modeled using the Kirchhoff plate theory. To take into account the geometric nonlinearities, the von Kármán nonlinear strains are considered in the mathematical model. The Hamilton’s principle is used to obtain the nonlinear equation of motion of the system, which is then converted into a nonlinear ordinary differential equation via the Galerkin technique. The validity of the results obtained from the proposed reduced-order model is checked through direct numerical simulation of the partial differential equation using the finite element method. Finally, two Lyapunov-based control approaches that are adaptive backstepping sliding mode and adaptive fractional backstepping sliding mode are applied to the system. In the adaptive fractional backstepping sliding mode controller method, the adaptive control law is used to evaluate the upper bound of uncertainties and random disturbances. The fractional-order form of sliding surface is used to reduce the amount of chattering and also to improve the tracking error. In the results section, first, numerical studies are conducted to study the effect of system parameters, such as material length scale parameter, aspect ratio, fractional order, and robustness of the controller, on the performance of the system. In addition, the performances of the two control methods are compared, and the merits and demerits of each method are discussed.

Robust chaos suppression of uncertain unified chaotic systems based on chattering-free sliding mode control

“…From (3), the augmented state x a ðtÞ includes the matched uncertainty δ 2 ðtÞ, which normally can't be measured. Therefore, when realizing the proposed switching function in (9) and the continuous SMC controllers in (19) and (20), one can use the relation of x a ðtÞ ¼ _ x 2 ðtÞ in ( 8) to obtain x a ðtÞ without using the unmeasurable information of δ 2 ðtÞ:…”

“…Consider the nonlinear unified chaotic system described in (2) with α ¼ 0 which belongs to the original Lorenz system. According to Step1 in Remark 4, we introduce an augmented state as x a ðtÞ ¼ 28x 1 ðtÞ � x 2 ðtÞ � x 1 ðtÞx 3 ðtÞ þ δ 2 ðtÞ þ uðtÞ (25) Therefore, by (11), we have A ¼ The chattering-free SMC uðtÞ is obtained as (19) or (20) with ξ ¼ 2.…”

“…[15][16][17][18] But it can only ensure the sliding motion outside a specified boundary layer, which will affect the control performance. Also, in the recent works, [19][20][21] the adaptive backstepping SMC was proposed to effectively eliminate the chattering and complete the actual engineering system control. However, their methods only developed for matched uncertainties and cannot directly apply to unmatched cases.…”

Fuzzy Fractional-Order PID Control for PMSG Based Wind Energy Conversion System with Sparse Matrix Converter Topology

“…Incorporating FO calculus into control strategies is shown to improve the control system performance and robustness with less control efort [43,44]. FO diferentiator can be represented as a persistent diferential integral operator [45][46][47],…”

Sliding Mode Robust Active Disturbance Rejection Control for Single-Link Flexible Arm with Large Payload Variations

“…One paper [20] proposed an ADRC based on nonlinear sliding mode (SM) controller, which uses SM controller to replace the classical PD feedback controller and achieves better control effect. In [21], a terminal sliding mode control is proposed to obtain a higher convergence rate for SM. Admittedly, the method of using SM as feedback controller can deal with the problem caused by ESO estimation error, but it is still an open problem to suppress the chattering caused by SMC.…”