Underwater Robots - Gianluca Antonelli.pdf

3.9 Numerical Comparison Among the Reduced Controllers 75
However, to better illustrate this different behavior, asecond simulation
study was developed in which the vehicle is commanded to c hange the sole
roll angle according to the time law inFigure 3.16 while keeping constant the
vehicle position and the other vehicle angles atzero; for the sake ofclarity,
it is assumed that no ocean current isacting on the vehicle. The behavior
of the reduced version of control law E is compared to that of the reduced
version of the control law A in terms of the measured roll angles (Figure 3.17,
left column). Remarkably, inthe simple condition considered, the restoring
moment to be compensated for is mainly acting around the x b axis. In the
simulation, it is possible to compute the restoring moment around this axis
and compare it with the adaptive compensation of the control law E and the
integral compensation plus the model-basedcompensation of thecontroller A
respectively; those plots are reported in the rightcolumn of Figure 3.17. It can
be observed that during the phase in which the roll angle changes from +10 ◦
to − 10 ◦ the compensation built by the control law A has alag with respect
to the acting restoring moment; this is due to the integral charge/discharge
time required tobuild atime-varying compensation term. The control law E ,
instead, performs proper compensation of the restoring moment since it accounts
for the vehicle orientation in the adaptation mechanism.
desired orientation [deg]
20
10
0
−10
roll
−20
0 50 100 150
time [s]
Fig. 3.16. Comparison of the control law A and the control law E in the second
case study: Time history of the desired orientation