Control of fluctuations of a tethered unmanned-underwater-vehicle

The analysis of oscillating systems controlled by mechatronic devices, relies classically on differential equations, and the problem is frequently attacked in the frequency domain, for linear systems based on more conventional controls, or in the time space-state formulation to include also nonlinearities. In this paper we are faced with a system that exhibits memory effects. These are borne because of the presence of added mass and damping that are due to the rigid body motion coupling with the surrounding water. Memory effects are also generated by the presence of lifting surfaces (control wings) due to vortex shedding and transport along the wake. The mathematical formulation of the system dynamics, relies in these cases on an integral-differential equation. This paper introduces a novel formulation for the control of the vehicle that can include in the optimal control integral terms besides the more conventional differential ones.