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University of Portland
School of Engineering
5000 N. Willamette Blvd.
Portland, OR 97203-5798
Phone 503 943 7314
Fax 503 943 7316
Theory of Operations
Project Blue Heron: Educational Ball and
Beam Feedback Control System
Contributors:
Bryan Weber
David Kim
Thomas Neveu
Approvals
Name
Dr. Osterberg
Date
Name
Date
Dr. Ward
Insert checkmark (√) next to name when approved.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: A. NAME
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Revision History
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Rev.
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0.1
01/6/06 .
THEORY OF OPERATIONS
PROJECT BLUEBIRD
UNIVERSITY OF PORTLAND
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Author
B. Weber; D. Kim;
T. Neveu
Reason for Changes
Initial draft
SCHOOL OF ENGINEERING
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Table of Contents
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Summary.......................................................................................................................
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Introduction ..................................................................................................................
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THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Background .................................................................................................................. 4
Architecture .................................................................................................................. 5
Hardware Architecture ............................................................................................................................5
Desired Position POT ......................................................................................................................5
Power Supply ...................................................................................................................................6
Analog Control Circuit ......................................................................................................................6
DC Motor Control .............................................................................................................................6
Base/Stand .......................................................................................................................................6
Ball and Resistive Wire Beam .........................................................................................................6
Design Overview.......................................................................................................... 7
System Block Diagram............................................................................................................................7
Hardware Design ....................................................................................................................................8
Desired Balance Point Input ............................................................................................................8
PID Control Circuit............................................................................................................................8
DC Motor ..........................................................................................................................................9
Plant/Ball and Beam ........................................................................................................................9
Conclusions ...............................................................................................................10
UNIVERSITY OF PORTLAND
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CONTACT: A. NAME
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List of Figures.
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Figure 1. Block Diagram of.Blue Heron Product...........................................................................................5
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Figure 2. Blue Heron system
. block diagram.................................................................................................7
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Figure 3. Feedback diagram with transfer functions. ...................................................................................7
Figure 4. Full feedback system schematic....................................................................................................8
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List of Tables .
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Table 1. Title of table goes.here. ................................................................ Error! Bookmark not defined.
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THEORY OF OPERATIONS
PROJECT BLUEBIRD
UNIVERSITY OF PORTLAND
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CONTACT: A. NAME
THEORY OF OPERATIONS
PROJECT BLUEBIRD
Chapter
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Summary
Project Blue Heron is a feedback control system demonstration intended to be an
educational tool in the classroom for years to come. As a result, the only users of this
system will be professors, students, and members of the university community. The
benefit of completing this project is that the designers will gain further knowledge of
feedback control systems and students will have a real world example to interact with
when they are learning about controls.
Blue Heron is a control system that is commonly known as the “ball and beam.” The ball
and beam system consists of four main elements: a ball, a beam, a motor, and a PID
feedback control system. The ball is placed on the beam and only moves horizontally
across it. The beam is attached to the motor which is able to adjust the angle of the beam
and thus control the position of the ball. The goal of Blue Heron is to balance the ball at a
user defined position on the beam.
A common example of a control system is cruise control on a car. The driver defines a
speed that they want to maintain and based on whether the car is accelerating,
decelerating, or remaining constant, the cruise control adjusts the throttle of the car to
bring it back to its defined speed. The project is similar to this example but instead of a car
we have a ball, and instead of cruising at a constant speed we want to keep the ball at a
constant point. If the ball moves to the left or right the angle of the beam is adjusted to
bring the ball back to its defined point.
This
document
UNIVERSITY OF PORTLAND
explains
the
theory
of
operations
SCHOOL OF ENGINEERING
for
project
Blue
Heron.
CONTACT: A. NAME
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Introduction
The purpose of this document is to explain the theory of operation of Blue Heron’s Ball
and Beam Feedback Control system. This is done by explaining the architectural design
of the project. This section describes what each piece of the project is and how it relates
to the connected sections. The second half of this document describes in further detail
each individual piece.
The summary and background sections are fundamental descriptions of our project and
would be easy to understand for those without technical understanding. The reader of the
remainder of this document is assumed to have a technical understanding of electronics.
The sections that follow the background include technical descriptions and fundamentals
that can be understood by anyone with a technical background.
An outline for this document:
1. Summary – Describes the project and document in simple, easy-to-understand
terms
2. Introduction – Describes the purpose of this document and outlines the rest of the
document.
3. Background – Describes the techniques used for designing and building this type
of system.
4. Architectural Overview - This describes what each section of the feedback system
is and how it relates to its connecting sections.
a. General Description – Shows a very simplified block diagram to illustrate
how each piece connects.
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b. Hardware Architecture – Describes how the hardware pieces fit together.
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. Overview - Describes in depth each section individually.
Design
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a. Block Diagram – Shows a more detailed design of the feedback system.
b. Hardware Design – Describes the details of each piece of hardware.
6. Conclusion – Recaps the document and states any improvements we would
suggest for future revisions.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: A. NAME
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Background
Project Blue Heron is a feedback control system using analog circuitry.
The
implementation will require the use of Physics, Calculus, Differential Equations, Algebra,
Electronics, and Control System theory. This paper will use mostly basic concepts from
these areas. A few definition will be explained here to help the reader through the
document.
The plant refers to the unstable system the feedback loop is trying to control. For this
project that will be the ball and beam system without anything else connected to it. A
potentiometer is simply a variable resistor, which will output a variable voltage based on
the position of the wiper on the resistor. The PID is the control circuit for the analog
system and will act as a compensator for the feedback loop. These are some common
phrases used in analog control systems. We will be using these techniques with basic
electric circuit design to complete the project.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: A. NAME
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Architecture
Hardware Architecture
Figure 1. Block Diagram of Blue Heron Product.
Figure 1 is a simple block diagram of Blue Heron’s Ball and Beam Feedback Control
System. A desired position is input into the system and compared with the current
position of the ball in the Analog Control Circuit. The circuit then outputs to the motor and
tells it how far and which way to tilt the beam. The ball will roll and the system will
continue to adjust in real time until the ball is balanced at the desired position.
Desired Position POT
The desired position will be determined with a linear potentiometer. A voltage will be read
off the POT, which corresponds to the desired position of the ball.
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CONTACT: A. NAME
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Power Supply
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. will be connected to the system to power the electronics and motor.
A power supply
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Analog Control Circuit
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The analog control circuit will consist of op-amps, resistors, and capacitors. It will compare
the desired position input voltage with the current position input voltage and compensate
the signal to turn the motor in the correct direction to roll the ball closer to the desired
position on the beam. The comparison will be done continuously in real time, adjusting as
needed to stabilize the system and stop the ball in the correct position.
DC Motor Control
The motor control will receive input from the analog control circuit. It will send the signal
through a power driver to increase the current and drive the motor.
Base/Stand
The motor, circuitry, and beam will be mounted to the stand. It will allow the beam to
swing freely and the system will be unstable. With the motor and circuitry attached to it,
the beam will be controlled and the system will become stable.
Ball and Resistive Wire Beam
The beam will act as a linear potentiometer, which will sense the position of the ball. One
side of the beam will be made with an insulating threaded rod wrapped with resistive wire
to generate a large amount of resistance from one end of the beam to the other. The
other beam will be made out of a conductive material. The ball will roll along the two
beams acting as the wiper for the potentiometer.
The voltage will be read off the
conductive beam and input back into the analog control circuit.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: A. NAME
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Design Overview
System Block Diagram
Figure 2. Blue Heron system block diagram.
Figure 2 is a general block diagram of our system. It shows the feedback loop with each
block and where they interface with each other. The current position is subtracted from
the desired position and the result is sent to the PID, or control circuit. The control circuit
will modify the signal to create help the system remain critically damped and stable. The
output from the PID is sent to the DC motor to tilt the beam, and roll the ball to the desired
position. The plant refers to the ball and beam as an open loop, unstable system, which
becomes stable when connected to the rest of the system.
xref
Kp1
+
-
PID
Motor
Plant
K1 K2(11s)
Km
s (1   m s )
Kp
s2
x out
Kp2
Figure 3. Feedback diagram with transfer functions.
Figure 3 is an in depth block diagram of our system. Above each block is its function, while
inside the block there is the transfer function associated with the element.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: A. NAME
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Figure 4. Full feedback system schematic.
Figure 4 shows the entire electrical schematic of the feedback system. Each part of the
system is explained in greater detail below.
Hardware Design
Desired Balance Point Input
The desired balance point will be input into the system with a linear potentiometer. The
POT will either be a 10k or 1k POT. One end will be connected to +5V and the other to
ground. This will create a 5V voltage drop. The wiper will then read off anywhere
between 0 and 5 volts corresponding to the position along the beam where the ball is to be
balanced at.
PID Control Circuit
The control circuit will subtract the current ball position voltage from the desired ball
position voltage with a subtraction circuit using resistors and an op-amp. The values of
the resistors will be determined based off the analysis to find the best step response. The
subtracted values will then go into the lead compensator, which will adjust the zeroes and
poles to achieve the desired system damping.
This will consist of a few op-amp
configurations with resistors and capacitors. The values of these will be determined
UNIVERSITY OF PORTLAND
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through the system analysis, and designed to provide the best step response. We are
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. damped system. RC combinations will be determined to give us this
looking for a critically
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. compensated signal will then feed into a power amplifier motor driver. This
response. The
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will use an op-amp in configuration with two TIP Power Transistors. This will increase the
power of the signal to drive the larger DC motor.
DC Motor
The DC motor will be mounted on the base of the plant. It will receive the boosted signal
from the control circuit and tilt the beam in the correct direction to roll the ball to the desired
position. The motor will be continually corrected in real time by the control circuit to tilt at
the correct angle and the correct direction to level out the beam with the ball in the correct
position.
Plant/Ball and Beam
The plant, or ball and beam, will be made in such a way that it creates a linear
potentiometer. One beam will be made with resistive wire wrapped around an insulated
threaded rod. The resistive beam will be between 500 and 1000 ohms spread over the
length of the 4 foot beam. +5V will be attached to one side with the other attached to
ground. This will create a similar POT to the linear POT used for the desired position.
The other beam will be made out of conductive material and the two beams will be placed
next to each other, but not touching. A metal ball will sit between the two rods and allowed
to roll along them. The ball will act as a swiper for the potentiometer and the voltage will
be read off the conductive beam. This value will go into the PID circuit and compared with
the desired position voltage. If the voltages are equal the beam will stop, and the ball will
be balanced at the desired position.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: A. NAME
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Conclusions
The project will use analog circuitry to control the otherwise unstable ball and beam
system. The position of the ball will be sensed using a linear potentiometer configuration.
The desired position will also use a linear potentiometer. The circuit will compensate for a
critically damped system and control the motor. The motor will tilt the beam until the ball
settles in the desired position along the beam. The entire project is achieved using analog
circuits only, with no digital microcontrollers. The system will become stable.
UNIVERSITY OF PORTLAND
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CONTACT: A. NAME