Longitudinal Submarine Dynamics Velocity The dynamics of a controlled submarine are significantly different from those of an aircraft or surface ship, primarily due to buoyancy of the craft. Consider a submarine with angle of attack a(t) and pitch 0(t), that is controlled by deflecting the stern plane through u(t) = 8(t), as described by the equations of motion Center of gravity Coptrol surface JÖ(t) à(t) + 3a(t) -€1 : 0(t) – 0(t) + a(t) – 6(t) €2 · Ö(t) + 8(t) (1) where J is the moment of inertia, and €1, €2 are positive constants. Note: This 8(t) is a variable, NOT the unit impulse.

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Subject: Control System

Longitudinal Submarine Dynamics
Velocity
The dynamics of a controlled submarine are significantly
different from those of an aircraft or surface ship, primarily
due to buoyancy of the craft. Consider a submarine with
angle of attack a(t) and pitch 0(t), that is controlled by
deflecting the stern plane through u(t) = 8(t), as described
by the equations of motion
Center of
gravity
Coptrol
surface
JÖ(t)
à(t) + 3a(t)
-€1 : 0(t) – 0(t) + a(t) – 6(t)
€2 · Ö(t) + 8(t)
(1)
where J is the moment of inertia, and €1, €2 are positive constants. Note: This 8(t) is a variable,
NOT the unit impulse.
Transcribed Image Text:Longitudinal Submarine Dynamics Velocity The dynamics of a controlled submarine are significantly different from those of an aircraft or surface ship, primarily due to buoyancy of the craft. Consider a submarine with angle of attack a(t) and pitch 0(t), that is controlled by deflecting the stern plane through u(t) = 8(t), as described by the equations of motion Center of gravity Coptrol surface JÖ(t) à(t) + 3a(t) -€1 : 0(t) – 0(t) + a(t) – 6(t) €2 · Ö(t) + 8(t) (1) where J is the moment of inertia, and €1, €2 are positive constants. Note: This 8(t) is a variable, NOT the unit impulse.
1.
Which one of the following correctly describes the system in state-space form,
0(t)
with state vector x(t) =
input u(t) = 6(t), and output y(t) = 0(t)?
a(t)
0 1
0 1/J €1/J
0 0], D = 0.
(a) A =
B =
€2
-3
1.
1.
(b) А —
1/J
-1/J
,C = [ 1 0 0], D = 0.
B =
-3
€2
(c) A
-1/J 1/J -€2/J
, C = [ €2_ 0 0], D = 0.
B =
-3
€1
1
(d) A =
-€1/J -1/J 1/J
0 0], D= 0.
B=
€2
-3
Transcribed Image Text:1. Which one of the following correctly describes the system in state-space form, 0(t) with state vector x(t) = input u(t) = 6(t), and output y(t) = 0(t)? a(t) 0 1 0 1/J €1/J 0 0], D = 0. (a) A = B = €2 -3 1. 1. (b) А — 1/J -1/J ,C = [ 1 0 0], D = 0. B = -3 €2 (c) A -1/J 1/J -€2/J , C = [ €2_ 0 0], D = 0. B = -3 €1 1 (d) A = -€1/J -1/J 1/J 0 0], D= 0. B= €2 -3
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