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For the attitude control satellite system if D(z)=1, K=1, and T=1 s, J=4, and H₂=1, the state space model is given by: x(k + 1) = | -1) - y(k)=[ 1 0 ]x(k) where x₁(k) is angular position and x₂(k) is angular velocity. (a) Show that the closed-loop system is unstable. (b) Using pole-placement design, find the gain matrix K that yields the closed-loop damping ratio <= 0.707 and the time constant T = 4 S. (c) Show that the gain matrix K in part (b) yields the desired closed-loop characteristic equation, ¦ x(4) + 0.1235 (4) [ 11 01

For the attitude control satellite system if D(z)=1, K=1, and T=1 s, J=4, and H₂=1, the state space model is given by: x(k + 1) = | -1) - y(k)=[ 1 0 ]x(k) where x₁(k) is angular position and x₂(k) is angular velocity. (a) Show that the closed-loop system is unstable. (b) Using pole-placement design, find the gain matrix K that yields the closed-loop damping ratio <= 0.707 and the time constant T = 4 S. (c) Show that the gain matrix K in part (b) yields the desired closed-loop characteristic equation, ¦ x(4) + 0.1235 (4) [ 11 01

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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V.2 For the attitude control satellite system if D(z)=1, K=1, and T=1 s, J=4, and H₂ =1, the state space model is given by: x(k+ 1) = - 1 1 |× (4) + 0.125 (4) = 0 y(k)= [ 10 ]x(k) where x₁(k) is angular position and x₂ (k) is angular velocity. (a) Show that the closed-loop system is unstable. (b) Using pole-placement design, find the gain matrix K that yields the closed-loop damping ratio and the time constant T = 4 S. <= 0.707 (c) Show that the gain matrix K in part (b) yields the desired closed-loop characteristic equation, given by zI - A+BK
Transcribed Image Text:V.2 For the attitude control satellite system if D(z)=1, K=1, and T=1 s, J=4, and H₂ =1, the state space model is given by: x(k+ 1) = - 1 1 |× (4) + 0.125 (4) = 0 y(k)= [ 10 ]x(k) where x₁(k) is angular position and x₂ (k) is angular velocity. (a) Show that the closed-loop system is unstable. (b) Using pole-placement design, find the gain matrix K that yields the closed-loop damping ratio and the time constant T = 4 S. <= 0.707 (c) Show that the gain matrix K in part (b) yields the desired closed-loop characteristic equation, given by zI - A+BK
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