EEL 4890 Problem 1 (30 pts)
Exam 1 solution
Fall 2007
A continuous integrator with initial condition x(0) 1 is shown below.
x(0) = 1
u (t ) e 2t
x(t )
Fill in the table below where x(tn ) is the exact value of the integrator output at time tn . Choose T 0
Fall2011Quiz1Solution
Name_
a) Theflowoutofatankwithcrosssectionalarea A isgivenby f0 H1/2 ,H 0 where is
aconstantand H H(t ) isthetanklevelattime t. Foratankwith H(0) H0 andnoinflow,
findtheflowout f0 (t ) .Youmayuseanyequationsfromthetextorprojects.
Fro
EEL 4890
Exam 1 solution
Name_
Fall 2011
SHOW ALL WORK!
Problem 1 (50 pts)
An unforced linear first order system is described by
x(0) 1.
dx
x 0. The initial state is
dt
a) Find the state derivative function f (x ,u).(5pts)
f (x ,u)
dx
x
dt
b) The diffe
EEL 4890
Exam 1 solution
Fall 2007
Problem 1 (30 pts)
A continuous integrator with initial condition x(0) 1 is shown below.
x(0) = 1
u (t ) e 2t
x(t )
Fill in the table below where x(tn ) is the exact value of the integrator output at time tn .
Choose T 0
Fall 2011 Quiz 1
Name _
a) The flow out of a tank with crosssectional area A is given by f0 H1/2 , H 0 where is a constant and H H(t ) is the tank level at time t. For a tank with H(0) H0 and no inflow, find the flow out f0 (t ) . You may use any equati
Fall 2011 Quiz 1 Solution
Name _
a) The flow out of a tank with crosssectional area A is given by f0 H1/2 , H 0 where is
a constant and H H(t ) is the tank level at time t. For a tank with H(0) H0 and no inflow, find the flow out f0 (t ) . You may use
EEL 4890 Fall 2011
Exam 1 solution
Name_
SHOW ALL WORK!
Problem 1 (50 pts) An unforced linear first order system is described by
dx x 0. The initial state is dt
x(0) 1.
a) Find the state derivative function f (x ,u). (5 pts)
f (x ,u)
dx x dt
b) The diffe
EEL 4890 Problem 1 (30 pts)
Exam 1 solution
Fall 2007
A continuous integrator with initial condition x(0) 1 is shown below.
x(0) = 1
u (t ) e 2t
x(t )
Fill in the table below where x(tn ) is the exact value of the integrator output at time tn . Choose T 0
EEL 4890 Fall 2004
Exam 1
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Problem 1 (30 pts) A continuous integrator with initial condition is shown below. x(0) = 1
u (t ) = e -2t
x(t )
Fill in the table below. Choose T = 0.05 for each integrator. Round all answers to 4 places afte
EEL 4890 Fall 2002 Problem 1 (25 pts)
Exam 1
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The flow out of the tank shown below is given by F0 = cH 2 . The cross-sectional area of the tank A = 50 ft 2 and the constant c = 2 ft 3 /min per ft1/2 . The initial level in the tank is H
EEL 5890 Fall 2001 Problem 1 (25 pts)
Exam 1
Name_ SS # _
The flow out of the tank shown below is given by F0 = cH 2 . The cross-sectional area of the tank A = 50 ft2 and the constant c = 2 ft3/min per ft1/2. The initial level in the tank is H(0) = 16 ft.
Homework Chapter 2 Solution a) A dH + F0 = F1 , dt dH H + = F1 dt R dH + H = RF1 dt F0 = H R
A
AR b)
= AR,
K =R
F1 = F , t 0 AR dH + H = RF , dt H (0) = 0
H (t ) = KF (1 - e - t / ) = RF (1 - e - t / ), c) t0
A = 20 ft 2 , R = 0.5 ft per ft 3 / min, F =
1.9 a) A dH + F0 = F1 , dt F0 = H 1/2
dH 1 = ( F1 - H 1/2 ) dt A Aproximating the first derivative using the first order difference quotient, H (t + t ) - H (t ) 1 ( F1 - H 1/2 ) t A Replacing H (t ) with H A ( n), short for H A ( nt ) and H (t + t ) with
EEL 4890 Exam 1, Sp17 Name (UPPERCASE):
Instructions: This is a closed-book, closed notes exam. No calculator permitted. Please use a pencil. Do
not remove the formula sheet. No breaks during the exam. Do Problems 1 & 2 and two of the
remaining three prob