ECE 461 - Homework Set #7
Lead, PID, Systems with Delays. Due Monday October 20th
Problem 1-3) The transfer function for controlling the temperature at the tip of a metal bar is
300
Y s1s3s9s20 X
Gain Compensation: K(s) = k
1a) Design a gain comensator wh

Solution to Homework #6 ECE 461
Root Locus - Gain Compensation - Due Monday, October 13
Problem 1-4
50
Gs s1s3s6
1) Sketch the root locus for G(s) including
Real Axis Loci: (-1, -3), (-6, -infinity)
Breakaway Point(s): s = -1.8802
d
s
ds
1s 3s 6 0
jw Cr

Homework #10 ECE 461
Due Monday, November 17th
Let G(s) be sampled at 100ms (T = 0.1):
50
G(s) = (s+1)(s+3)(s+10)
1) A discrete-time model which approximates G(s) is G(z)
0.0273z 2
(z0.9)(z0.74)(z0.37)
1a) Draw the root locus for G(z)
1b) Find k for a

ECE 461 - Homework Set #12
Gain, Lead, Lag Compensatio with Bode Plots. Due Monday, December 1st
1) For the following system:
500
G(s) = (s+1)(s+3)(s+9)
design a compensator, K(s), which results in
No error for a step input,
A 0dB gain frequency of 3 rad

ECE 461 - Homework Set #11
Bode Plots, Nichols Charts, Gain Compensation in the Frequency Domain. Due Monday, November 24th
1) Name That System: Give the transfer function for a system with the following frequency response.
Draw in the straight-line asymp

Solution to Homework #9 ECE 461
Due Monday, November 10th
1) X and Y are related as follows:
0.001z
Y = z 2 1.9z+0.9 X
1a) What is the difference equation that relates X and Y?
Cross multiply
(z 2 1.9z + 0.9)Y = (0.001z)X
Note that zY means "the next valu

Homework #5 ECE 461
Error Constants, Routh Criteria
Error Constants:
1) Determine the system type and the steady-state error for the following systems
G(s)
Type
Kv
Error for a Step
Input
0
10
0
0.0909
0
-10
0
-0.111
1
infinity
10
0
2
100
(s+2)(s+5)
1

Homework #3 ECE 461
Mass Spring Systems, Rotational Systems, Wave Equation, Motor Dynamics. Due Monday, Sept 22
For each problem, let M = 1kg, K = 10 N/m, B = 0.5 Ns/m
1) 3-Mass System
K
K
M1
K
M3
K
F
B
M2
B
B
X2
X1
X3
a) Draw the circuit equivalent
K
K
K

Homework #4 ECE 461
LaGrangian Dynamics
A ball is rolling in a bowl where the height is a funciton of X:
y = cos(x)
.
.
y = sin(x) x
1) Determine the kinetic energy and potential energy of the ball as a funciton of x
PE = mgy = mg cos(x)
.
.
KE = 1 m(x 2

ECE 461 - Homework Set #2
State-Space, Heat Equation, Matlab/SciLab. Due Monday Sept 15th
Problem 1-5)
1) Write N equations to solve for the N unknown voltages
XV
V 2 V
CsV 1 = 100k1 + 200k1
V 1 V
V 3 V
CsV 2 = 200k2 + 300k2
V 2 V
CsV 3 = 300k3
2)