BE 402
Homework #9
100 points
Due Tuesday
04/09/2013
Please include any code you used to arrive at your solution; figures are unnecessary.
Problem 1
A simplified block diagram of a human pupil servomechanism is shown in the figure below. Use
MATLABs rlocu
Boston University
Department of Biomedical Engineering
ENG BE 402
Control Systems in Biomedical Engineering
Spring 2013
Professor Jim Collins
Oce: ERB 307
Tele. 30390
email: jcollins@bu.edu
Oce hours: Th 122 pm
Content: Mathematical analysis of dynamic
BE 402
Homework #11
Due Thursday
05/02/2013
100 points
Problem 1
For the system shown below:
R(s)
+

K
s +1
C(s)
1
( s + 2) 2
a. Find the value of K that will result in a gain margin of 5 dB
b. For K = 4, find the gain margin of the system.
(10 points)
(
BE 402
Homework #10
100 points
Due Thursday
04/25/2013
Problem 1
You are modeling a metabolic process with a percent overshoot of 6.1%. You added the
proportional differential (PD) compensator GC(s) to decrease the settling time of the system by a
factor
BE 402
Homework #8
Due Tuesday
April 2, 2013
100 points
Problem 1
1
s + 2 s + 4 s 3 + 8s 2 + s + 2
using a Routh table and an auxiliary polynomial. Solve for all system poles.
(20 points)
Determine the stability of the system with transfer function T ( s
BE 402
Homework #7
100 points
Due Tuesday
03/26/2013
Problem 1
Given the following transfer functions, determine if the system is stable, unstable, or marginally
stable by evaluating the quadratic approach or through factoring. Plot the poles and zeros in
BE 402
Homework #6
Due Tuesday
03/19/2013
100 points
Problem 1
(20 points)
For the following unitygain feedback system:
R(s)
+
G(s)
C(s)

1
A
and G ( s ) = 2
, find values of A, a, and b that will give a Type 1 system
2
s
s + as + b
with a steadystate
BE 402
Homework #5
100 points
Problem 1
Reduce the following block diagram and present the simplified equivalent
C (s)
transfer function GEQ ( s ) =
. Show all steps.
R( s)
Problem 2
Reduce the following block diagram and present the simplified equivalent
BE 402
Homework #4
100 points
Due Tuesday
02/19/2013
Problem 1
a) Find the transfer function G(s) =
I L (s)
.
Vin (s)
b) Find the circuits natural frequency n and damping ratio in terms of
R, L, and C.
(4 points)
(6 points)
c) Given R = 3 and assuming zer
BE 402
Homework #3
Due Tuesday
02/12/2013
100 points
Problem 1
(20 points)
H ( s)
2s 5s 3s 1
s 7 s 3 s 2 2s 9
3
2
4
Represent the transfer function H(s) in statespace using phase variables. Assume all initial
conditions to be zero, and provide the repre
BE 402
Homework #2
100 points
Problem 1
Due Tuesday
5 Feb. 2013
(10 points)
Solve this system of equations using the Inverse Matrix Method:
2 x + 5 y ! 9 z = !14
5 x ! y + 3 z = !12
! x + 2 y + 6 z = 11
Problem 2
(20 points)
Derive the statespace represe
BE 402
Homework #1
Due Tuesday
29 Jan 2013
100 points
Problem 1
Given Y(s), use the Inverse Laplace Transform to find y(t).
3s + 7
.
( s 2s 3)
s + 12
b. Y ( s ) = 2
.
s ( s + 3)
a. Y ( s ) =
(10 points)
2
(10 points)
Problem 2
Solve the following ODEs usi