(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 = Cx Ax+ Bu; where the state vector is x = it VC , 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.

Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
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(a) Using KVL, KCL, the inductor law and Ohm's law, write down a state space model for this circuit
of the form
x Ax+ Bu;
y = Cx
where the state vector is x =
iL
VC
, 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.
(e) Choose a set of parameter values such that the system is not observable and find the corresponding
set of unobservable states.
Transcribed Image Text:(a) Using KVL, KCL, the inductor law and Ohm's law, write down a state space model for this circuit of the form x Ax+ Bu; y = Cx where the state vector is x = iL VC , 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. (e) Choose a set of parameter values such that the system is not observable and find the corresponding set of unobservable states.
+
u
R
iL
L
R₁
R₂
C
vc
ic
-O +
UR2
Figure 2: Electrical Circuit
Transcribed Image Text:+ u R iL L R₁ R₂ C vc ic -O + UR2 Figure 2: Electrical Circuit
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