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Problem 6: The inverted pendulum mechanism shown in Fig. 3(a) has been commonly used as a model for designing the attitude control of a space booster on takeoff. You may assume that O is small such that cos0 =1 and sin 0 z 0 , and the link (length L) has negligible mass. 1. Show that the transfer function of the inverted pendulum has the form f(t) mg G(s) = (s) F(s) s-a² A Find a and A in terms of the system parameters (such as L, m etc.). 2. Can the final value theorem be used to find the steady state value of 0? If no, explain why.

Problem 6: The inverted pendulum mechanism shown in Fig. 3(a) has been commonly used as a model for designing the attitude control of a space booster on takeoff. You may assume that O is small such that cos0 =1 and sin 0 z 0 , and the link (length L) has negligible mass. 1. Show that the transfer function of the inverted pendulum has the form f(t) mg G(s) = (s) F(s) s-a² A Find a and A in terms of the system parameters (such as L, m etc.). 2. Can the final value theorem be used to find the steady state value of 0? If no, explain why.

Elements Of Electromagnetics
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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Problem 6: The inverted pendulum mechanism shown in Fig. 3(a) has been commonly used as a model for designing the attitude control of a space booster on takeoff. You may assume that O is small such that cos 0 =1 and sin 0 - 0 , and the link (length L) has negligible mass. 1. Show that the transfer function of the inverted pendulum has the form f(t) mg 0(s) _ _ A F(s) s -a² G(s) =- Find a and A in terms of the system parameters (such as L, m etc.). 2. Can the final value theorem be used to find the steady state value of 0? If no, explain why.
Transcribed Image Text:Problem 6: The inverted pendulum mechanism shown in Fig. 3(a) has been commonly used as a model for designing the attitude control of a space booster on takeoff. You may assume that O is small such that cos 0 =1 and sin 0 - 0 , and the link (length L) has negligible mass. 1. Show that the transfer function of the inverted pendulum has the form f(t) mg 0(s) _ _ A F(s) s -a² G(s) =- Find a and A in terms of the system parameters (such as L, m etc.). 2. Can the final value theorem be used to find the steady state value of 0? If no, explain why.
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