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Consider the inverted-pendulum system shown below. Assume that the mass of the inverted pendulum is m and is evenly distributed along the length of the rod. (The center of gravity of the pendulum is located at the center of the rod.) Assuming that is small, derive mathematical models for the system in the forms of differential equations, transfer functions, and state-space equations. y M 0 x'

Consider the inverted-pendulum system shown below. Assume that the mass of the inverted pendulum is m and is evenly distributed along the length of the rod. (The center of gravity of the pendulum is located at the center of the rod.) Assuming that is small, derive mathematical models for the system in the forms of differential equations, transfer functions, and state-space equations. y M 0 x'

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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5. Consider the inverted-pendulum system shown below. Assume that the mass of the inverted pendulum is m and is evenly distributed along the length of the rod. (The center of gravity of the pendulum is located at the center of the rod.) Assuming that is small, derive mathematical models for the system in the forms of differential equations, transfer functions, and state-space equations. y u➡ M y'. 0 G е x' X
Transcribed Image Text:5. Consider the inverted-pendulum system shown below. Assume that the mass of the inverted pendulum is m and is evenly distributed along the length of the rod. (The center of gravity of the pendulum is located at the center of the rod.) Assuming that is small, derive mathematical models for the system in the forms of differential equations, transfer functions, and state-space equations. y u➡ M y'. 0 G е x' X
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