Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams

This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations motion for are derived using Hamilton’s principle non-local strain gradient theory. Galerkin method is then applied to transform resulting dimensionless equation into a nonlinear ordinary equation. A novel fault-tolerant terminal sliding mode technique proposed address uncertainties inherent in micro/nano-systems potential faults failures actuators. controller includes finite time estimator, stability which convergence error dynamics established Lyapunov theorem. significance this study lies its application field micro/nano-mechanics, where precise small-scale systems crucial development advanced technologies such as nano-robotics micro-electromechanical (MEMS). addresses these systems, making it valuable choice practical applications. simulation results presented demonstrate effectiveness scheme high accuracy estimation algorithm.