Nonlinear aeroservoelastic control using Euler-Lagrange theory

An Euler-Lagrange (EL) system is a dynamical system governed by the Euler-Lagrange equations. In this paper, we consider asymptotic stabilization of EL systems with arbitrary La grangians arising in aeroelasticity. First, sufficient conditions for local and global asymptotic stability of equilibrium points of EL systems are stated. These conditions are in terms of the Lagrangian and an associated Hamiltonian (storage function). We then give a procedure to design a Lyapunov stable stabilizing controller with its own Lagrangian. This procedure involves shaping the closed loop Lagrangian to satisfy the sufficient conditions for stability. Two examples to illustrate the approach are presented. The first is a simple problem that permits hand calculations; while the second example considers a nonlinear version of the Benchmark Active Control Technology (BACT) wind tunnel model for aeroelasticity.