Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 2f = -1 and 2f = -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 24 = -2.
Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 2f = -1 and 2f = -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 24 = -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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Please do only the last sybgroup question - Design reduced-order state observer - the other questions were answered.
Transcribed Image Text:Consider the following electrical system:
R L
C= uc
u
R
The equations describing the system dynamics are the following:
u(1) = 1 di(e)
dt
2+(R, + R, i() + u,(1)
cdu, 0 - i(1)
Choose as state variables: x,(1) = u,(1) and x,(t) = i(t).
Obtain the following state space model
R, +R,
+ Ou
and calculate the system matrices for L = 0.5, R, = 1, R2 = land 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(1), 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 24 = -2.
2.
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