Mapping AUV Depth Control System

The depth control algorithm consists of two Proportional-Integral-Derivative
(PID) loops, one nested within the other.  The inner loop moves the elevator
to achieve a desired vehicle pitch angle.  The elevator angle is computed
from the vehicle pitch angular error and angular rate.  The outer loop computes
a desired vehicle pitch angle based on the error between commanded and
measured depth.  Figure 1 shows this structure.

Figure 1 Caption:  AUV Pitch and Depth Control Algorithm

The depth control performance was improved recently by the addition of a
depth rate term and gain redesign.  The depth rate is easily extracted
from the Kearfott INS/DVL navigation system, and was not previously available
directly.  Also, the pitch integrator has been removed from the depth control
loop. Figure 2 shows the depth control step response of the original system.
Figure 2a shows the same step response after the redesign.

Figure 2  Caption: AUV Depth Step Response with Original Control
Figure 2a Caption: AUV Depth Step Response After Control Redesign

Figure 3 shows a root locus of the original depth control, generated by
varying gain at the elevator command, denoted delta_E in Figure 1.  Figure
4 shows the same locus with the new control gains and rate term.  The complex
zero pair (blue squares) near Z=1 in Figure 3 have moved deeper into the unit
circle in Figure 4, drawing the dominant pole pair with them.  Damping has
increased from zeta = 0.29 to 0.59, and the closed loop bandwidth has
increased by a factor of four.

Figure 3 Caption: Root Locus of the Original Depth Controller
Figure 4 Caption: Root Locus of the New Depth Controller