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[PSUBS-MAILIST] dive plane control scheme
I recently spent a bit of time wondering how the position of the bow
planes and stern planes, on submarines so equipped, are properly
co-ordinated for dynamic manoeuvers. An internet search didn't turn up
much information, so I did the next best thing - I sat down and reasoned
it out. Assuming a vessel is equipped with dive planes that can be
independently controlled, I came up with what I think is a good
automated control scheme, for a sub with a computer of some sort to
manage the automatic control. I post it here for comment or criticism -
not on the practicality of automated dive plane control (expensive for a
psub, I know), but rather on the suitability and robustness of the
algorithm.
-Sean
The following description of hydroplane positioning logic is applicable
to a submarine vessel with control surfaces consisting of independently
operated port side bow plane, starboard side bow plane, port side stern
plane and starboard side stern plane. The vessel is also assumed to
have one or more rudders for steering control, but the rudder position
will always correspond to the commanded rudder position according to the
desired rate of turn, and is therefore not addressed herein.
NOMENCLATURE
alpha
the commanded angle of the bow planes
beta
the commanded angle of the stern planes
gamma
the maximum angle that a control plane can assume before turbulence
occurs (velocity dependent), subject to mechanical limits (in the case
of near-zero velocities)
theta
the current angle of roll of the vessel
theta-c
the commanded angle of roll of the vessel (special purposes -
ordinarily zero)
phi
the current angle of pitch of the vessel
phi-c
the commanded angle of pitch of the vessel
delta
pitch leveling threshold corresponding to the minimum distance from
target depth at which a leveling manoeuvre must be initiated in order to
reach the target depth without overshoot. This value is a function of
both ascent / descent rate and of phi, and shall be determined
experimentally with the vessel in a neutral buoyancy condition. (i.e.
dynamic manoeuvering only)
ANTI-ROLL STABILIZATION
Except where specifically disabled by command, all control planes
act in conjunction to stabilize the vessel dynamically. This behaviour
occurs as follows: each plane will act in opposition to vessel roll,
with a commanded angle proportional to the difference between theta and
theta-c. The zero position (commanded position when theta is equal to
theta-c), will be equal to alpha and beta for the bow and stern planes,
respectively. In this fashion, the dynamic anti-roll stabilization
behaviour superimposes itself on commanded plane positions for vessel
manoeuvres. When the vessel is in the surfaced condition, the maximum
correction will occur when theta equals (or exceeds) the maximum
standard banking angle during normal operation (maximum commandable
angle of roll when submerged). When the vessel is submerged, the
maximum correction will occur when theta equals (or exceeds) the maximum
permissible angle of roll. In either case, at maximum correction, the
control planes will be oriented at an angle of +/- gamma with respect to
the vessel.
HYDROPLANE BEHAVIOUR - SURFACED CONDITION
When the vessel is in the surfaced condition, any commanded roll
angle (theta-c) is disregarded - trim tank and control surface systems
all act to maintain theta equal to zero with respect to gravity. Trim
in pitch (phi-c) may still be commanded, subject to limits determined by
permissible propellor depth and/or available freeboard and hatch coaming
height. Ordinarily, the vessel will operate in the surfaced condition
with a phi-c of zero; however, it may be desireable to command a
different pitch angle under certain circumstances, such as when towing
or being towed, or when facilitating the launch or recovery of personnel
or materials between the sea and the weather deck. Regardless of
commanded pitch angle (phi-c), when the vessel is in the surfaced
condition alpha and beta will correspond to horizontal positions with
respect to gravity.
HYDROPLANE BEHAVIOUR - DIVE MANOEUVER FROM SURFACE
When a dive manoeuvre from surface is initiated, alpha is initially
set hard down at an angle of -gamma, and assumes subsequent values
proportional to the difference between phi and phi-c. The stern plane
angle beta acts similarly in the opposite direction; however, the
initial value of beta can not be set to gamma immediately, since this
would act to raise the propellor depth above the normal surfaced
propellor depth at the beginning of the dive manoeuvre. Accordingly,
the initial value of beta, (the value which controls the magnitude of
the proportional response), is not gamma, but rather a value which
starts at zero (horizontal with respect to gravity) and rapidly
increases to gamma in a manner which keeps the propellor below the
normal surfaced propellor depth.
HYDROPLANE BEHAVIOUR - DIVE MANOEUVER IN MIDWATER
When a dive manoeuver is initiated while submerged, the bow plane
angle alpha is initially set hard down at an angle of -gamma, and
assumes subsequent values proportional to the difference between phi and
phi-c. The stern plane angle beta is initially set hard up at an angle
of gamma, and assumes subsequent values proportional to the difference
between phi and phi-c.
HYDROPLANE BEHAVIOUR - ASCENT MANOEUVER
When an ascent manoeuver is initiated, the bow plane angle alpha is
initially set hard up at an angle of gamma, and assumes subsequent
values proportional to the difference between phi and phi-c. The stern
plane angle beta is initially set hard down at an angle of -gamma, and
assumes subsequent values proportional to the difference between phi and
phi-c.
HYDROPLANE BEHAVIOUR - BANK CONTROL
Commanded roll angles (theta-c) for specific purposes aside, the
vessel will normally operate in an upright condition, with theta-c equal
to zero. Under this condition, at high speeds, a turn will result in a
normal component acceleration which moves the apparent gravity normal
away from perpendicular to the vessel normal. To correct this, a roll
correction will be applied which increases theta-c to bring the apparent
gravity normal back to perpendicular to the vessel, subject to the
limits of +/- gamma angle on the control surfaces, and maintaining theta
within the maximum permissible theta. Thus, in a sustained turn at a
high rate of speed, vessel trim will be as comfortable as possible for
the occupants.
HYDROPLANE BEHAVIOUR - RATE CONTROL
The above description of hydroplane behaviour details how the dive
control surfaces function with respect to the commanded pitch angle,
phi-c. Response time of the control planes must be rapid in order for
the dynamic stabilization system to function effectively; however, rapid
rotation of control surfaces to extreme positions should not be confused
with extreme manoeuvers. Such extreme control surface positions are
generally short lived under the control scheme. Extreme manoeuvers, on
the other hand, are generally associated with a large magnitude rate of
change of phi-c or theta-c.
A comprehensive description of dive control surface behaviour must
also include the behaviour necessary to level off the vessel as it
approaches the target dive depth, to prevent the vessel from
overshooting the desired depth during dynamic manoeuvering. This is
accomplished by varying phi-c as follows: If the difference between the
vessel's current depth and the target depth is greater than delta (a
function of ascent / descent rate), then phi-c is maintained at the
setpoint. If this difference is less than delta, then phi-c is reduced
in a manner proportional to this difference, becoming zero when the
target depth is reached.
HYDROPLANE BEHAVIOUR - MAINTENANCE OF DEPTH
When levelled off at the desired depth setpoint, alpha and beta will
be adjusted by a common angle (i.e. in the same direction) to compensate
for a difference between the current depth and the setpoint depth. The
amount of correction shall be proportional to this depth difference,
subject to the limits of +/- gamma on the dive plane positions. In the
event of a persistent difference (indicating a buoyancy condition other
than neutral), the ballast system should be automatically compensating,
reducing the required dynamic correction to zero.
MANUAL OPERATION
When control of the vessel is not by the autopilot, but rather by
the operator, provided power is available, all functions of the
automatic system described above will continue to operate, with the
exception of rate control. In this case, phi-c will correspond directly
to operator input.
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