Given a spacecraft attitude control system shown in Fig. 2: R(s) ● Control Law ● K(s) ● Actuator 2 s+10 Figure 2 (a) Show that a proportional control cannot stabilize the closed-loop system (b) Given the following requirements: Peak time tp ≤, seconds Settling time at 2% error t ≤4, seconds Natural frequency , <2, radians/second • Damping ratio > 0.4 20 0.08s +1 Sensor Spacecraft 1 10,² Y(s) (1) Design a PD control law K(s) of the form K(s+1) such that the closed-loop step response satisfies the above requirements (show the possible locations of the closed-loop poles on the complex plane; use Matlab to plot the system root locus and choose the smallest value of Kc that satisfies the given response requirements) (2) Compute the steady-state error to a unit step input (3) Compute the steady-state error to a unit ramp input

Given a spacecraft attitude control system shown in Fig. 2: R(s) ● Control Law ● K(s) ● Actuator 2 s+10 Figure 2 (a) Show that a proportional control cannot stabilize the closed-loop system (b) Given the following requirements: Peak time tp ≤, seconds Settling time at 2% error t ≤4, seconds Natural frequency , <2, radians/second • Damping ratio > 0.4 20 0.08s +1 Sensor Spacecraft 1 10,² Y(s) (1) Design a PD control law K(s) of the form K(s+1) such that the closed-loop step response satisfies the above requirements (show the possible locations of the closed-loop poles on the complex plane; use Matlab to plot the system root locus and choose the smallest value of Kc that satisfies the given response requirements) (2) Compute the steady-state error to a unit step input (3) Compute the steady-state error to a unit ramp input

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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Question

Given a spacecraft attitude control system shown in Fig. 2:
R(s) +
●
Control Law
●
K(s)
●
Actuator
2
S+10
Figure 2
(a) Show that a proportional control cannot stabilize the closed-loop system
(b) Given the following requirements:
Peak time Sπ, seconds
tp
Settling time at 2% error t ≤4, seconds
Natural frequency , <2, radians/second
n
• Damping ratio >0.4
20
0.08s +1
Sensor
Spacecraft
1
10.5.2
(2) Compute the steady-state error to a unit step input
(3) Compute the steady-state error to a unit ramp input
Y(s)
(1) Design a PD control law K(s) of the form K(s+1) such that the closed-loop step
response satisfies the above requirements (show the possible locations of the
closed-loop poles on the complex plane; use Matlab to plot the system root locus
and choose the smallest value of Kc that satisfies the given response requirements)

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