Consider the satellite control system of Fig P7 5 6 This system is described in Problem 1 4 1 For this problem, T 0 1 s, J 0 1, H k 0 02, and D(z) 1 From the z transform table, (a) Write the closed loop system characteristic equation (b) Use the RouthHurwitz criterion to show that the system is uns...

a 1 KGzH 22z10001Kz0001K 0 b c chareq z 00012z ...

Consider the satellite control system of Fig. P7.5-6. This system is described in Problem 1.4-1. For this

Question:

Consider the satellite control system of Fig. P7.5-6. This system is described in Problem 1.4-1. For this problem, T = 0.1 s, J = 0.1, H_k = 0.02, and D(z) = 1. From the z-transform table, z (1-2) (I + 2)50'0 S 01 SL-3-

(a) Write the closed-loop system characteristic equation.
(b) Use the Routh–Hurwitz criterion to show that the system is unstable for all K.
(c) Check the results of part (b) using the Jury test. R(s) + r(t) A/D Digital controller D(z) DIA Sensor Hk M(s) Amplifier and thrusters K T(s) Torque Satellite 1