Consider the linear state-space model of a damped inverted pendulum. 0 1 b ml² 0 +-+₁ ml² a. Design a full-state feedback controller that leads to a critically-damped closed-loop response characterized by a single (repeated) pole p such that p<0 (express the control gains in terms of p and the system parameters). b. Find the threshold of the feedback gains required for stable response. c. From the two controllers: u=-k₁x₁ and u=-k₂x₂ which one can and which one cannot be used to stabilize this system (justify your answer)?
Consider the linear state-space model of a damped inverted pendulum. 0 1 b ml² 0 +-+₁ ml² a. Design a full-state feedback controller that leads to a critically-damped closed-loop response characterized by a single (repeated) pole p such that p<0 (express the control gains in terms of p and the system parameters). b. Find the threshold of the feedback gains required for stable response. c. From the two controllers: u=-k₁x₁ and u=-k₂x₂ which one can and which one cannot be used to stabilize this system (justify your answer)?
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
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Transcribed Image Text:Consider the linear state-space model of a damped inverted pendulum.
0.
1
b.
1 u
ml²
ml²
a. Design a full-state feedback controller that leads to a critically-damped closed-loop response characterized
by a single (repeated) pole p such that p<0 (express the control gains in terms of p and the system
parameters).
b. Find the threshold of the feedback gains required for stable response.
c. From the two controllers: u=-k,x, and u =-k,x, which one can and which one cannot be used to
stabilize this system (justify your answer)?
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