(a) Using KVL, KCL, the inductor law and Ohm's law, write down a state space model for this circuit of the form i = Y = where the state vector is x = Ax + Bu; Cx iL [ [the] VC (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. u is the applied voltage and y= VR₂.
(a) Using KVL, KCL, the inductor law and Ohm's law, write down a state space model for this circuit of the form i = Y = where the state vector is x = Ax + Bu; Cx iL [ [the] VC (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. u is the applied voltage and y= VR₂.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd5e0332-0650-432d-b006-8bd12fae84dd%2F29ec1582-293d-4d6c-8747-165a800e5ac0%2F955twy_processed.png&w=3840&q=75)
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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