EE 518
Physiological Control System Analysis Spring 2007/08
IMPORTANT NOTE: PLEASE READ BEFORE STARTING

There are four questions, attempt all.

Read the questions carefully.

Show complete work for full credit.

Include units in your answers.

ORGANIZE YOUR WORK AND WRITE LEGIBLY.
GOOD LUCK
Last
Name:
First
Name:
Student
ID:
Signature:
Q1
Q2
POINTS SCORE
25
25
Q3
Q4
25
25
TOTAL 100
1

EE 518
Physiological Control System Analysis Spring 2007/08
Q1. (25 pts.)
(a) Obtain the transfer function of the system defined by



 x 
1 x x


2
3










1
0
0
1

1
0

1
1
2







 x
1 x
2 x
3







0


0
1



 u y


1 0 0




 x
1 x x
2
3




(b) Obtain the state-space model of the system shown below.
U(s)
1/s
X
2
(s)
10/(s+5)
X
1
(s)
Y(s)
X
3
(s)
1/(s+1)
2

EE 518
Physiological Control System Analysis Spring 2007/08
Q2. (25 pts.)
F i
X i
C m
R m
Derive the equation of operation for changes (x) about the reference position X i
.
F i
is the force required to maintain the mass in equilibrium at the reference position X i
.
Q3. (25 pts. )
The cardiac output curve of a heart that has been transplanted into a patient is given in tabular form as follows:
Right
Atrial
Pressure
(mmHg)
Cardiac output
(Lmin
-1
)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0 0.3 1.0 2.5 4.8 7.0 9.0 10.5 11.0 11.3 11.5 11.6 11.6 11.6
(a)
Deduce the patient’s steady-state right atrial pressure (P ra
) and cardiac output, assuming the transplant operation is successful.
(b) What would be the steady-state values for cardiac output and P ra
if the total circulatory resistance were to be doubled?
(c) To counteract the increased circulatory resistance in (b), suppose a sufficient quantity of blood is transfused into the patient so that mean systemic pressure is raised by 5 mmHg. What would be the new steady-state values for P ra
and cardiac output?
3

EE 518
Physiological Control System Analysis Spring 2007/08
Q4. (25 pts.)
Determine the open-loop and closed loop responses for the system shown below when the input is a unit step.
X
(1-Ts/2)/(1+Ts/2)
Y
4