Nonlinear modeling and tracking control of a single-link micro manipulator using controlled Lagrangian method

Abstract

In this paper a dynamical model and the governing equations of motion of a micro-cantilever beam with rotating joint as an application of under-actuated systems will be developed. The model is based on the geometrically nonlinear equations of motion of the microbeam, employing strain gradient elasticity theory. The Rayleigh–Ritz method is used to discretize partial differential equations to obtain a set of nonlinear ordinary differential equations of motion. Then, a controlled Lagrangian method as a robust procedure for controller design is employed to achieve an acceptable tracking on the hinge’s angle of rotation of a micro-cantilever beam while undesirable vibration of the under-actuated flexible variable is damped. A stability analysis of the closed-loop system is also discussed. The advantages of the controlled Lagrangian method lie in its ability to find the Lyapunov function to prove the stability of the system and its capability of handling under-actuated devices. The performance of the designed control scheme is illustrated through several numerical simulation results and some comparisons are made in various situations.

Nonsingular decoupled terminal sliding-mode control for a class of fourth-order under-actuated nonlinear systems with unknown external disturbance

“…Over the past years, a number of robust and adaptive control techniques have been proposed for uncertain nonlinear systems [1][2][3][4][5][6][7]. Sliding mode control (SMC), due to its robustness against parameter variations and simplicity for handling nonlinear systems with bounded external disturbances, has received much attention [8,9].…”

Vibration control of coupled Duffing oscillators in flexible single-link manipulators

“…In the majority of the existing studies, the structural nonlinearities were ignored for simplicity and the flexible-link manipulators were considered as a linear model with infinite vibrational modes (Chen and Huang, 2017). Recently, the dynamic modeling of several types of flexible-link manipulators was developed from the nonlinear dynamics perspective (Altıner et al, 2019;Cao and Liu, 2020;Chen et al, 2019;Feliu-Talegon and Feliu-Batlle, 2019;Pratiher, 2019, 2020;Meng et al, 2018;Ni et al, 2020;Shafei and Shafei, 2018;Sharifnia, 2020;Tavallaeinejad et al, 2016;Vakil et al, 2012;Wang and Lou, 2019). The nonlinear model can exhibit relatively large-amplitude vibrations and complicated dynamics.…”