Consider the satellite control system of Problem 5.3-14 and Fig. P5.3-14. Let D(z) = 1 , T = 1 s, K = 2 , J = 0.1 , and H

k = 0.02 .

(a) Using the closed-loop transfer function, derive a discrete state model for the system.

(b) Derive a discrete state model for the plant from the plant transfer function. Then derive a state model for the closed-loop system by adding the feedback path and system input to a flow graph of the plant.

(c) Calculate the system transfer function from the state model found in part (b), to verify the state

model.

(d) Verify the results in part (c) using MATLAB.

Problem 5.3-14

Consider the satellite control system of Fig. P5.3-14. The unit of the attitude angle w(t) is degrees, and the range is 0 to 360º. The sensor gain is H_k = 0.05.

(a) Suppose that the input ranges for available A/Ds are 0 to 10 V, 0 to 20 V, 0 to 30 V, ±10 V, ±20 V, and ±30 V. Which range should be chosen? Why?

(b) The input signal r(t) is a voltage. Find the required value of r(t) to command the satellite attitude angle
w(t) to be 80º.

(c) Repeat parts (a) and (b) if the range of w(t) is ±180°.

(d) Let Gp(s) = 1>(Js²), the satellite transfer function. Find the system transfer function as a function of the transfer functions D(z), K, and so on.

(e) Evaluate the system transfer function for D(z) = 1, T = 0.5 s, K = 4, and J = 0.2.

Transcribed Image Text:

R(s) m A/D Digital Controller D(z) DIA Sensor Hk M(s) Amplifier and thrusters K (s) Torque Satellite 1 B (s) 0(t)