The satallite system below is controlled using reaction wheels. The torque wheel input for the system is u(s) and the satallite attitude is Ө(s)For a strong communication link Ө needs to be a value where the satallite atenna is pointing at the ground stationThe transfer function for this system will be shown in the picture. Design a feedback control system that sets the closed loop damping ratio at 0.8 and the natural frequency is at 10 rad/sec. This image features a diagram and handwritten notes related to satellite communication and feedback control systems.**Diagram Description:**- A satellite is depicted in orbit around Earth. The satellite is equipped with solar panels and an antenna.- There is a line indicating the satellite's signal path, pointing towards a "ground station" marked on Earth.**Notes:**- "For a strong communication link, θ needs to just be a value where the satellite antenna is pointing at the ground station."- "The transfer function for this system is: \[ \frac{\Theta(s)}{u(s)} = \frac{s + 0.6}{s^2(3s + 1)} \]"- "Design a feedback control system that sets the closed loop damping at 0.8 and the natural frequency at 10 rad/sec." These elements focus on controlling the orientation and communication link of the satellite with a ground station using a transfer function and feedback control system design.

Given: Transfer function: s+0.6s2s+6 To find: Design a feedback control system with ζ=0.8 and ωn=10 rad/secTransfer function of closed loop system: Gs1+GsHs Where, Gs=s+0.6s2s+6, Substituting we get s+0.6s2s+61+s+0.6s2s+6Hs=s+0.6s2s+6+s+0.6Hss+0.6s3+6s2+s+0.6Hs Denominator represents characteristic equation s2+2ζωns+ωn2 Substitute the given values ζ=0.8 and ωn=10 rad/sec s2+16s+100So, the value of H(s) should be such that both these are equal s3+6s2+s+0.6Hs=s2+16s+100Hs=-s3-5s2+15s+1000.6=-1.5s3-7.5s2+22.5s+150 Hence, the feedback system will be

Answered: The satallite system below is…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The satallite system below is controlled using reaction wheels. The torque wheel input for the system is u(s) and the satallite attitude is Ө(s)

For a strong communication link Ө needs to be a value where the satallite atenna is pointing at the ground station

The transfer function for this system will be shown in the picture. Design a feedback control system that sets the closed loop damping ratio at 0.8 and the natural frequency is at 10 rad/sec.

This image features a diagram and handwritten notes related to satellite communication and feedback control systems.

**Diagram Description:**
- A satellite is depicted in orbit around Earth. The satellite is equipped with solar panels and an antenna.
- There is a line indicating the satellite's signal path, pointing towards a "ground station" marked on Earth.

**Notes:**
- "For a strong communication link, θ needs to just be a value where the satellite antenna is pointing at the ground station."
- "The transfer function for this system is:
\[ \frac{\Theta(s)}{u(s)} = \frac{s + 0.6}{s^2(3s + 1)} \]"

- "Design a feedback control system that sets the closed loop damping at 0.8 and the natural frequency at 10 rad/sec."

These elements focus on controlling the orientation and communication link of the satellite with a ground station using a transfer function and feedback control system design.

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