4. Consider the system giveb in the figure below, here tankA is full of water and tankB is empty. The flow directions for pumA and pumpB are given in the figure. PumpA can transfer whole water in tankA in 20 mins while pumpB transfers whole water inside tankB in 100 mins. PumpA and pumpB are activated/deactivated in 10 minutes intervals: (10 minutes on, 10 minutes off, 10 mins. on, 10 mins. off, ..). In this problem, we want to analyze the water levels in tanka and tankB. a. Find the differential equation set describing the system. b. Write the state transition matrix. c. Show the characteristic equation of the system Empty Pump A

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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4. Consider the system giveb in the figure below, here tankA is full of water and tankB is
empty. The flow directions for pumA and pumpB are given in the figure. PumpA can
transfer whole water in tankA in 20 mins while pumpB transfers whole water inside
tankB in 100 mins.
PumpA and pumpB are activated/deactivated in 10 minutes intervals:
(10 minutes on, 10 minutes off, 10 mins. on, 10 mins. off, .).
In this problem, we want to analyze the water levels in tanka and tankB.
a. Find the differential equation set describing the system.
b. Write the state transition matrix.
c. Show the characteristic equation of the system
d. Determine the eigenvalues and eigen vectors
e. What will be the water levels in both tanks after 4 hours?
f. Find the steady state water levels.
Empty
rdung
Pamp
Fall
Transcribed Image Text:4. Consider the system giveb in the figure below, here tankA is full of water and tankB is empty. The flow directions for pumA and pumpB are given in the figure. PumpA can transfer whole water in tankA in 20 mins while pumpB transfers whole water inside tankB in 100 mins. PumpA and pumpB are activated/deactivated in 10 minutes intervals: (10 minutes on, 10 minutes off, 10 mins. on, 10 mins. off, .). In this problem, we want to analyze the water levels in tanka and tankB. a. Find the differential equation set describing the system. b. Write the state transition matrix. c. Show the characteristic equation of the system d. Determine the eigenvalues and eigen vectors e. What will be the water levels in both tanks after 4 hours? f. Find the steady state water levels. Empty rdung Pamp Fall
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