Modal-Based Nonlinear Model Predictive Control for 3-D Very Flexible Structures

In this article a novel nonlinear model predictive control (NMPC) scheme is derived, which tailored to the underlying structure of intrinsic description geometrically exact beams (in velocities and strains are primary variables). This an important class partial differential equation (PDE) models whose behavior fundamental performance flexible structural systems (e.g., wind turbines, high-altitude long-endurance aircraft). Furthermore, contains much-studied Euler–Bernoulli Timoshenko beam models, but has significant additional complexity (to capture 3-D effects arbitrarily large displacements) requires explicit computation rotations in PDE dynamics account for orientation-dependent forces. A challenge presented by formulation that uncontrollable modes necessarily appear any finite dimensional approximation dynamics. We show, however, NMPC can be constructed error introduced explicitly controlled. It demonstrated asymptotic made insignificant (from practical perspective) using our excellent obtained even when applied highly resolved numerical simulation PDEs. also present generalization Kelvin–Voigt damping beams. Finally, special emphasis placed on constructing framework suitable real-time control, where particular PDEs exploited obtain both efficient finite-dimensional schemes.