Function approximation technique (FAT)-based nonlinear control strategies for smart thin plates with cubic nonlinearities

The current work introduces three nonlinear control solutions for the regulation of a vibrating plate considering model uncertainty. These are feedback linearization (FBL), virtual velocity error-based (VVEC), and backstepping (BSC). In FBL control, law is designed with linear closed-loop dynamics such that dynamic stability ensured. Whereas, by VVEC (or so-called passivity-based approach in robotics community) limitations overcome. On other side, BSC selects variables stabilized intermediate laws based on Lyapunov theory. Systematic modeling target piezo patches described. effect, influence makes resulted mode shapes structure highly coupled careful design required. Using Galerkin approach, partial differential equation smart transformed into definite ordinary equations; multi-input multi-output established. aforementioned strategies evaluated investigated detail. essence, they powerful tools dealing systems, however, could be considered superior comparison since does not include inertia inverse matrix modal coordinate acceleration make computational problems. As result, simulation experiments were focused strategy, latter was implemented simply supported thin collocated piezo-patches. results show validity proposed architecture.