Download Theory of Operations - University of Portland

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: BRYAN WEBER
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Revision History
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Rev.
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0.9
01/6/08 .
THEORY OF OPERATIONS
PROJECT BLUEBIRD
1.0
01/9/08
UNIVERSITY OF PORTLAND
REV. 1.0
PAGE II
Author
B. Weber; D. Kim;
T. Neveu
B. Weber; D. Kim;
T. Neveu
Reason for Changes
Initial draft
Grammatical and Functional
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER
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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
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER
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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
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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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 feedback control theory.
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
operation
SCHOOL OF ENGINEERING
for
project
Blue
Heron.
CONTACT: BRYAN WEBER
THEORY OF OPERATIONS
PROJECT BLUEBIRD
Chapter
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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 section describes each piece of the project
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 - Describes each section of the feedback system and how
it relates to its connecting sections.
a. General Description – Shows a very simplified block diagram to illustrate
how each piece connects.
b. Hardware Architecture – Describes how the hardware pieces fit together.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER
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Design Overview - Describes in depth each section individually.
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. Block Diagram – Shows a more detailed design of the feedback system.
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THEORY OF OPERATIONS
PROJECT BLUEBIRD
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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: BRYAN WEBER
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Background
Project Blue Heron is an analog feedback control system. The implementation requires
the use of Physics, Calculus, Differential Equations, Algebra, Electronics, and Control
System theory. A few definitions will be explained to help the reader.
The plant refers to the unstable open loop system the feedback loop is trying to control.
For this project the plant is 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 analog control circuit and will act
as a compensator for the feedback loop.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER
THEORY OF OPERATIONS
PROJECT BLUEBIRD
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Architecture
Hardware Architecture
Beam Movement
Steel Ball
DC Motor
Ball
ion
Posit
or
Se n s
(Line
T)
a r PO
DC Motor Control
Desired Position
POT
Analog Control
Circuit
Power Supply
Base/Stand
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.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER
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Power Supply
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. (+15V, -15V, +5V) will be connected to the system to power the
A power supply
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electronics and motor.
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THEORY OF OPERATIONS
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Analog Control Circuit
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 amplifier 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 insulated 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: BRYAN WEBER
THEORY OF OPERATIONS
PROJECT BLUEBIRD
Chapter
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Design Overview
System Block Diagram
Desired
Position
PID
DC
Motor
(Control
Circuit)
+
-
Ball Position
on Beam
Plant
Figure 2. Blue Heron system block diagram.
Figure 2 is a general block diagram of our system. It shows the feedback loop along with
each block. 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 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 closed loop feedback system.
PID
xref
Kp1
K1  K2s(11s)
+
-
Motor
Plant
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 is the corresponding transfer function associated with the element.
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER
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 subtracted
values will then go into the lead compensator.
This will consist of a few op-amp
configurations with resistors and capacitors. The values of these will be determined
through the system analysis, and designed to provide the best step response. We are
UNIVERSITY OF PORTLAND
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER
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looking for a critically damped system. RC combinations will be determined to give us this
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. compensated signal will then feed into a power amplifier motor driver. This
response. The
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. in configuration with two TIP Power Transistors. This will increase the
will use an op-amp
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THEORY OF OPERATIONS
PROJECT BLUEBIRD
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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 signal from the
control circuit and tilt the beam in the correct direction to roll the ball to the desired position.
The circuit will continuously correct the motor’s angle to roll the ball to the desired 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 3 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 beams and
allowed to roll along them. The ball will act as a wiper 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: BRYAN WEBER
THEORY OF OPERATIONS
PROJECT BLUEBIRD
Chapter
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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
SCHOOL OF ENGINEERING
CONTACT: BRYAN WEBER