The dynamics of a controlled submarine are significantly different from those of an

Chapter 0, Problem P3.16

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The dynamics of a controlled submarine are significantly different from those of an aircraft, missile, or surface ship. This difference results primarily from the moment in the vertical plane due to the buoyancy effect. Therefore, it is interesting to consider the control R.O+ K2O +Or, "*02 (a) FIGURE P3.10 Two-axis system. (a) Signal-flow graph, (b) Block diagram model. y,(s) 1*- >Uv) (b) 223 of the depth of a submarine. The equations describing the dynamics of a submarine can be obtained by using Newton's laws and the angles defined in Figure P3.16. To simplify the equations, we will assume that 8 is a small angle and the velocity v is constant and equal to 25 ft/s.The state variables of the submarine, considering only vertical control, are X\ = 6, x2 = dOldt, and x$ = a, where a is the angle of attack. Thus the state vector differential equation for this system, when the submarine has an Albacore type hull, is