Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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![u
where the state vector is x =
R
I
L
R₁
iL
VC
R₂
ic
Figure 2: Electrical Circuit
(a) Using KVL, KCL, the inductor law and Ohm's law, write down a state space model for this circuit
of the form
x =
Y =
VC
VR2
]
u is the applied voltage and y = VR₂.
(b) Determine the values of the parameters R, R₁, R2, L, C such that the system is controllable.
(c) Determine the values of the parameters R, R₁, R2, L, C such that the system is observable.
(d) Choose a set of parameter values such that the system is not controllable and find the corresponding
set of controllable states.
Ax + Bu;
Cx
(e) Choose a set of parameter values such that the system is not observable and find the corresponding
set of unobservable states.](https://content.bartleby.com/qna-images/question/cd5e0332-0650-432d-b006-8bd12fae84dd/29ec1582-293d-4d6c-8747-165a800e5ac0/955twy_processed.png)
Transcribed Image Text:u
where the state vector is x =
R
I
L
R₁
iL
VC
R₂
ic
Figure 2: Electrical Circuit
(a) Using KVL, KCL, the inductor law and Ohm's law, write down a state space model for this circuit
of the form
x =
Y =
VC
VR2
]
u is the applied voltage and y = VR₂.
(b) Determine the values of the parameters R, R₁, R2, L, C such that the system is controllable.
(c) Determine the values of the parameters R, R₁, R2, L, C such that the system is observable.
(d) Choose a set of parameter values such that the system is not controllable and find the corresponding
set of controllable states.
Ax + Bu;
Cx
(e) Choose a set of parameter values such that the system is not observable and find the corresponding
set of unobservable states.
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