EEE 481
Homework 1
Problem 1.
Suppose that we measure a signal 010V with a 8bit 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/
EEE 481
Lecture 7: Quantization 1
Quantization



Analog to digital conversion performs discretization in time and in statespace.
Discretization in statespace is quantization.
Quantization occurs due the use of finiteword lengths in the
microprocesso
EEE 481
Lecture 8: Vector Spaces & Norms
Vector Spaces

A linear vector space is comprised of a set of elements, called vectors,
defined over a scalar number field , which satisfies the following
conditions for addition and multiplication by scalars
For
EEE 481
Lecture 6: ADC & DAC
DigitaltoAnalog Conversion

A DAC or D/A converts a binary number into an analog voltage.
Output voltage of a D/A is represented as
0 = [1 21 + 2 22 + + 2 ]
Vfs is the full scale voltage, An are the bits from MSB to LSB (A1
Lab Report Template
Md Ashfaque Bin Shafique
2/13/2013
ABSTRACT
Summary of the experiment and results. (<200 words)
1. INTRODUCTION
Brief background, outline of the experiment methods and
purpose.
2. EXPERIMENTAL SETUP
Detailed description. Include any us
EEE 481, Test 1.
Name: _
75, Closedbook, ClosedNotes, 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
Lecture 4: Parallel & Serial I/O
Parallel Communication

Means of conveying data parallelly through a wired connection.
Bytes/words can be sent in one clock cycle.
Requires at least as many wires as the number of bits + control.
Increase in cross
EEE 481
Lecture 9: Quantization 2
Quantization in Filtering & Control


Finite precision introduces errors in the computations as well as in the filter
implementation.
Fixedpoint arithmetic: bounded noise
3 classes of errors:
Type1 errors: Seen in A/D
EEE 481
Lecture 10: Quantization 3
Quantization in Filtering & Control


Due to the sensitivity of roots of polynomials to perturbations, the
quantization of the filter coefficients can result in a different, possibly
unstable filter
Different filter re
EEE 481
Homework 1
Problem 1.
Suppose that we measure a signal 05V with a nbit 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 Test 2
NAME: _
75, Closedbook, ClosedNotes, 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, Test 1.
Name: _SOLUTIONS_
75, Closedbook, ClosedNotes. 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 05V A/D Converter indicate that its
EEE 481
Lecture 11: Quantization HW Example
Quantization HW Example

Consider the system + 1
1
32
=
1
4
+ 1/2( 1), where the
1
.
128
multiplications and the addition are quantized to
Use simulation to
assess the mean, worstcase magnitude and variance
EEE 481
Lecture 1: Introduction
The Big Picture


What is Feedback?
A mechanism to control systems or processes
The purpose of feedback is to reduce effects of uncertainty (modeling
errors, disturbances) and change system dynamics(stability, bandwidth).
EEE 481
Lecture 5: Computer Interface for DAQ &
Control
DAQ & Control

A typical configuration for data acquisition (DAQ) and control of a plant.
Plant
uProcessor
physical
quantities
digital
signal
ADC
Signal
Conditioning
analog (Amplify/Filter)
electric
EEE 481
Homework 1 Solutions
Problem 1.
Suppose that we measure a signal 010V with a 8bit 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 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 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 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 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
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 1.
Name: _
75, Closedbook, ClosedNotes, 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_
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 05V, and transmit the results over the RS232 serial port.
1. What is the m
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