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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.

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.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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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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