Question

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 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 1. To simplify the equations, we will assume that 8(t) is a small angle and the velocity v is constant and equal to 25 fts. The state variables of the submarine, considering only vertical control, are Xz(t) = 8(t),xz(t) = o(t) and Xz(t) = a(t), where a(t) is the angle of attack 2016 Velocity Center of gravity 8(1) Control surface Fig.1: Submarine depth control Thus the state vector differential equation for this system, when the submarine has an Albacore type hull, is 1 0=1-00 0 01 -0.11 0.12||X2()+ 0.07 -0.3) (x3) u(t) y(t) = [1 O 01x200 [x3(1)] where (t) = 8(t), the deflection of the stern plane.

Answer 1

CODE :

clc close all A [0 1 0;-0.01 -0.11 0.12;0 0.07 -0.3]; B [0;-0.1;0.1]; % required pole locations P = [-2+4i -2-4i -3]; % required gain matrix k acker (A,B,P); Gain_required vpa (k') = verification check the poles Poles_obtained = eig(A-B*k)||

Result :

Command Window New to MATLAB? See resources for Getting Started. Gain_required = -2473.685227272727388481143862009 15404.765909090912828105501830578 15470.66590909091064531821757555 Poles_obtained = -2.0000 + 4.0000i -2.0000 - 4.0000i -3.0000 + 0.0000i fx >> |