Find the closed-loop, optimal control law u*(t) in terms of the states x* (t) asu* (t) = −KLQRX*(t) for the systemand the performance indexJ=*₁(t)*₂(t)==x₂(t) + u₁(t),u₂(t),[ [x²{(t) + x²(t) + u²(t) + u²(t)] dt.Sketch the state-space block diagram showing the controller.

Given: Performance index: J=∫0∞x12t+x22t+u12t+u22tdt. System equations: x˙1t=x2t+u1t,x˙2t=u2t.…

Find the closed-loop, optimal control law u*(t) in terms of the states x* (t) as u* (t) = -KLQRX* (t) for the system and the performance index J = *₁(t) i₂(t) = = x₂(t) + u₁(t), u₂(t), √ [x²(t) + x²(t) + u²(t) + u²(t)] dt. Sketch the state-space block diagram showing the controller.

Find the closed-loop, optimal control law u(t) in terms of the states x (t) as u* (t) = -KLQRX* (t) for the system and the performance index J = *₁(t) i₂(t) = = x₂(t) + u₁(t), u₂(t), √ [x²(t) + x²(t) + u²(t) + u²(t)] dt. Sketch the state-space block diagram showing the controller.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

Find the closed-loop, optimal control law u*(t) in terms of the states x* (t) as
u* (t) = −KLQRX*(t) for the system
and the performance index
J
=
*₁(t)
*₂(t)
=
=
x₂(t) + u₁(t),
u₂(t),
[ [x²{(t) + x²(t) + u²(t) + u²(t)] dt.
Sketch the state-space block diagram showing the controller.

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