Robust Control for an Underwater Vehicle Body Motion

A0172 Jean-Pierre Folcher Laboratoire d' Infomatique, Signaux et Systemes de Sophia Antipolis (I3S)

Classical design methods for underwater vehicle body motion (see [2]),

consider linear identified models. These methods cannot predict the

real systems behavior and they ensure only localrobustness. Recent

results in feedback synthesis theory has bred methodologies with a

garanteed (global) robustness and performance for a given mathematical

model of a physical system. For these guarantees to also hold on the

actual system, a robust control design methodology is needed, that

takes the discrepancies between the physical and mathematical model

into account.

Global robustness imply that performance properties should be ensured

for a system family. Numerous theory ( H optimisation, quadratic

stability, Linear Matrix Inequalities optimisation) consider and solve

robust problems for the synthesis of feedback controllers. The

control problem is expressed in terms of an optimisation problem over

a family of systems. H optimisation which is related to the 2 L

induced norm has specific properties and permits the use of the small

gain theorem. Numerous resulting properties will be highlighted in

this paper and will be used to build a robust framework to solve a

synthesis problem.

In the sequel of this paper, this design methodology is applied to the

control of an underwater vehicle body motion. The global dynamic

model of the body motion is given by the Euler-Lagrange equations

which relate body-referenced linear and angular velocities to the

propeller efforts. A vehicle equipped with only one vertical and two

horizontal thrusters is considered. The propellers are driven by a

speed closed loop controller. The number of degree of freedom is

smaller than the number of actuators. A common pragmatic approach

(see, e.g., [2]) consists in dividing the control problem in three

decoupled control problems of longitudinal speed motion, of diving

motion and of steering motion.

To obtain a model suitable for control design, a simplified model for

each motion is considered (Some linear and angular body-referenced

velocities are zero). The motion is described by a first order non

linear model for an acceleration input. The effort delivered by the

vertical thrusters depends quadratically on the rotation speed of the

DC motor (see [1]). The use of the small gain theorem permits to

ensure stability and performances of the closed loop system for a

family of systems (including the non linearities). Major advantages

of the proposed synthesis methodology are to take into account

directly the non linearities and to allow the designer to ensure a

trade off between the performances and the robustness. This synthesis

method is applied to an underwater vehicle the Remotely Operated

Vehicle (ROV) Phantom 500, 1 see Fig. 1. Numerical experiments and

experiments performed with the real plateform at sea will demonstrate

the effectiveness of the proposed synthesis approach which is able to

maintain performance under a wide set of operational regimes.

1 Phantom is an underwater robot produced by Deep Ocean Engineering,

Palo Alto, USA.