EEE 481 Test 2
NAME: _
75, Closed-book, Closed-Notes, Calculators and One 8 1/5 x 11 sheet (2pages) of notes and formulae allowed.
1. Design a PID controller to achieve a crossover of 0.1 rad/s,
50deg phase margin, for the plant with transfer function (al
EEE 481
Test 1
NAME _SOLUTIONS_
Open Book, Closed Notes, 30
Problem 1
In a data acquisition application we would like to use the Diamond MM board to sample 16 channels with
range 0-5V, and transmit the results over the RS-232 serial port.
1. What is the m
EEE 481 Test 2
NAME: _
75, Closed-book, Closed-Notes, Calculators and One 8 1/5 x 11 sheet (2pages) of notes and formulae allowed.
1. Design a PID controller to achieve a crossover of 0.1 rad/s,
50deg phase margin, for the plant with transfer function (al
EEE 481
Homework 2 SOLUTIONS
Problem 1.
Compute the z-transforms of the following sequences (here u(.) denotes the unit step)
cfw_2 0.1 ( ),
0.9 ( 1)
( 2), sin ,
6
cfw_( 2) = 2 cfw_( ) =
1
( 1)
For a single-sided transform, (k>=0), sin =
For a double-side
EEE 481
Homework 3
Problem 1.
3 +2
Consider the continuous time system with transfer function () = 2 +5+4.
1. Realize G(s) in state-space and use Forward Euler to compute its discretization, using sampling
time T = 0.1. Find the transfer function of the c
EEE 481
Homework 4
SOLUTIONS
Problem 1.
Consider the following system with transfer function P ( s ) =
1
.
( s + 0.1)( s + 1)
1. Design a PID so that the crossover is at 7rad/s and the phase margin is 50o.
2. Select a method and the sampling frequency and
EEE 481
Homework 1 Solutions
Problem 1.
Suppose that we measure a signal 0-10V with a 8-bit A/D.
1. What is the resolution?
2. What is the maximum error?
3. How many bits are needed to achieve a maximum error less than 2mV?
4. Assuming that the clock used
EEE 481, Test 1.
Name: _
75, Closed-book, Closed-Notes, Calculators and One 8 1/5 x 11 sheet (2pages) of notes and formulae allowed.
Problem 1. Provide brief answers to the following questions:
1. What is the resolution of a 10bit A/D converter?
2. What i
EEE 481, Test 1.
Name: _SOLUTIONS_
75, Closed-book, Closed-Notes. Calculators and One 8 1/5 x 11 sheet (2pages) of notes and formulae allowed.
Problem 1:
Provide brief answers to the following questions:
1. Data from a 0-5V A/D Converter indicate that its
EEE 481 Test 2
NAME: _
75, Closed-book, Closed-Notes, Calculators and One 8 1/5 x 11 sheet (2pages) of notes and formulae allowed.
1. Design a PID controller to achieve a crossover of 2 rad/s, 50deg
phase margin, for the plant with transfer function (also
EEE 481
Homework 1
Problem 1.
Suppose that we measure a signal 0-5V with a n-bit A/D. What should be the value of n so that
1. The maximum error is less than 1mV?
2. The maximum error is less than 1%?
3. Assuming that the clock used in the A/D conversion
EEE 481
HW 3
P.1
The read arm on a computer disk drive has transfer function H ( s ) =
1000
.
s2
1. Design an analog PID controller to achieve a bandwidth of approx. 100Hz with 50deg phase margin.
2. Design a digital PID with a sampling rate 1kHz and simu
EEE 481
Test 2
NAME _SOLUTIONS_
Open Book, Closed Notes, 45
Problem 1
When
, write the closed loop response for the feedback system, sampled at kT. Find the
maximum T for which the system is stable. How is that value related to the Phase Margin of G(s)?
G
EEE 481
Test 2
NAME _SOLUTIONS_
Open Book, Closed Notes, 45
Problem 1
When
, write the closed loop response for the feedback system, sampled at kT. Find the
maximum T for which the system is stable. How is that value related to the Phase Margin of G(s)?
G
EEE 481
Test 1
NAME _SOLUTIONS_
Open Book, Closed Notes, 30
Problem 1
In a data acquisition application we would like to use the Diamond MM board to sample 16 channels with
range 0-5V, and transmit the results over the RS-232 serial port.
1. What is the m
EEE 481, Test 1.
Name: _
75, Closed-book, Closed-Notes, Calculators and One 8 1/5 x 11 sheet (2pages) of notes and formulae allowed.
Problem 1. Provide brief answers to the following questions:
1. What is the resolution of a 10bit A/D converter?
2. What i
EEE 481
HW 3
P.1
The read arm on a computer disk drive has transfer function H ( s ) =
1000
.
s2
1. Design an analog PID controller to achieve a bandwidth of approx. 100Hz with 50deg phase margin.
2. Design a digital PID with a sampling rate 1kHz and simu
EEE 481, Homework 6
SOLUTIONS
Problem 1.
Consider the pendulum model with input the torque applied at the pivot point and output the angle of the
pendulum. (Assume that the pendulum is a rigid rod of length 0.5m, mass 200g evenly distributed, and its
rota
EEE 481, Homework 5, Solutions
Problem 1.
1. Design a PID controller to achieve a bandwidth of 1Hz, 50deg phase margin, and to be
discretized with a sampling frequency of 10Hz for the system with transfer function
0.1 + 1
1 () = 2
+ 4 + 2
1
2. An additiv
EEE 481
Homework 4
SOLUTIONS
Problem 1.
Consider the following system with transfer function P ( s ) =
1
.
( s + 0.1)( s + 1)
1. Design a PID so that the crossover is at 7rad/s and the phase margin is 50o.
2. Select a method and the sampling frequency and
EEE 481
Homework 3
Problem 1.
3 +2
Consider the continuous time system with transfer function () = 2 +5+4.
1. Realize G(s) in state-space and use Forward Euler to compute its discretization, using sampling
time T = 0.1. Find the transfer function of the c
EEE 481
Homework 2 SOLUTIONS
Problem 1.
Compute the z-transforms of the following sequences (here u(.) denotes the unit step)
cfw_2 0.1 ( ),
0.9 ( 1)
( 2), sin ,
6
cfw_( 2) = 2 cfw_( ) =
1
( 1)
For a single-sided transform, (k>=0), sin =
For a double-side
EEE 481
Homework 1 Solutions
Problem 1.
Suppose that we measure a signal 0-10V with a 8-bit A/D.
1. What is the resolution?
2. What is the maximum error?
3. How many bits are needed to achieve a maximum error less than 2mV?
4. Assuming that the clock used
EEE 481, Homework 5, Solutions
Problem 1.
1. Design a PID controller to achieve a bandwidth of 1Hz, 50deg phase margin, and to be
discretized with a sampling frequency of 10Hz for the system with transfer function
0.1 + 1
1 () = 2
+ 4 + 2
1
2. An additiv
EEE 481
Homework 1
Problem 1.
Suppose that we measure a signal 0-10V with a 8-bit A/D.
1. What is the resolution?
2. What is the maximum error?
3. How many bits are needed to achieve a maximum error less than 2mV?
4. Assuming that the clock used in the A/