Question

Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1. Fig. 1.1 Satellite tracking control system In this problem we will only consider the control of the angle e (angle of elevation). The dynamic model of the rigid satellite, rotating about an axis perpendicular to the page, can be approximately written as: JÖ = tm - ty - bė where ) is the satellite's moment of inertia, b is the damping coefficient, tm is the applied torque and ty is a disturbance torque due to wind forces. We now define the following parameters: u(t) = "; Wa(t) =; a = 5 1. Show that we can formulate a transfer function on the following form, from the information given above 1 OS) = [u(S) - Wa(s)] 2. While we choose the state variables x; = 0, x2 = 0 and output y = x/, show that we can formulate a state space model as CO=C 368+920+ [] w.com y(0) = [1 0108.2011

Answer 1

Solution:I have done the first question and the second question.

I have uploaded the images of solution in below.

If you will understand the soliusol then please likey solution so that i will be encouraged to golive more efforts to solve more questions.
varte variables. state sea choose e she the 2.x Noce, have we x = 0 x2 = output, y = x = 0 Now, 8. x =0 å = 6 = 22 = x = - x = X2 (1) = X(t) = X2 (2) y = = n =) Y (D = R b ao = ult) – Wa (it) - 0 = ax (t) = uld - Walt) - X2 (t) » X(t) = -2X2(t) - 4 WNCH) + ha le (at) so the state space model coure le, x, Lt) 1 [ ][-]-[:]** • [ 31.6 1= [' :] [ act]