Modeling and Model Predictive Control (MPC) of an Underwater Double Inverted Pendulum (UDIP)

Resumo

The Inverted Double Pendulum (IDP) is a classical nonlinear and unstable mechanical system used as
a benchmark model for the application of innumerous control techniques. However, such a model was never treated
in an off-the-self environment, which represents a gap in its applications range since the demand for underwater

robotics is increasing together with the ocean engineering activities. Thus, to fill this gap and build a new bench-
mark model for the control development of underwater robotics, this paper presents the modeling and control of

an Underwater Double Inverted Pendulum (UDIP). The dynamic model is formulated using the formalism of An-
alytical Mechanics and considering the pertinent hydrodynamic and hydrostatic effects. To keep straight with the

control techniques trends, a Model Predictive Control (MPC) is designed for the UDIP. This controller is tested
through numerical simulations in MATLAB/Simulink© environment considering two scenarios: 1) in the absence
of disturbances, and 2) in the presence of a time-varying water current. The obtained results for the disturbances
case reveal an increase in the control effort in comparison with the case without disturbances. In such a way, this
reflect the difficulty associated to the control of underwater robots in unstructured environments.