and calculate the system matrices for L = 0.5, R1 = 1, R2 = 1and C = 1. %3D %3D From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable. Design a state feedback u(t) = -Kr(t), which will place the closed-loop poles on desired locations: 19 = -1 and 14 = -2.

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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2.
Consider the following electrical system:
R
L
C= Uc
The equations describing the system dynamics are the following:
di(t)
u(t) = Lº
+(R, +R, )i(t)+u̟(t)
dt
c du (t)
= i(t)
dt
Choose as state variables: x, (t) = u.(t) and x, (t) = i(t).
Obtain the following state space model
1
-
C
+ 1 u
R, + R, |X2
L
1
L
y =[1 0]
+ Ou
and calculate the system matrices for L = 0.5, R1 = 1, R2 = 1and C = 1.
From the state space model obtain the transfer function of the system.
By using controllability gramian, check if the system representation R(A,B,C) is
controllable.
Design a state feedback u(t) = -Kx(t), which will place the closed-loop poles on
desired locations: 14 = -1 and 14 = -2.
By using observability matrix, check if the system representation R(A, B,C) is
observable.
Design a reduced-order state observer with desired poles 2d = -2.
Transcribed Image Text:2. Consider the following electrical system: R L C= Uc The equations describing the system dynamics are the following: di(t) u(t) = Lº +(R, +R, )i(t)+u̟(t) dt c du (t) = i(t) dt Choose as state variables: x, (t) = u.(t) and x, (t) = i(t). Obtain the following state space model 1 - C + 1 u R, + R, |X2 L 1 L y =[1 0] + Ou and calculate the system matrices for L = 0.5, R1 = 1, R2 = 1and C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A,B,C) is controllable. Design a state feedback u(t) = -Kx(t), which will place the closed-loop poles on desired locations: 14 = -1 and 14 = -2. By using observability matrix, check if the system representation R(A, B,C) is observable. Design a reduced-order state observer with desired poles 2d = -2.
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