Download The Balls-in-Tubes Experiment - OSU ECE

The Balls-in-Tubes Experiment
Alvaro E. Gil, Nicanor Quijano, and Kevin M. Passino
Dept. Electrical and Computer Engineering
The Ohio State University
2015 Neil Avenue, Columbus, OH 43210
April 5, 2004
Abstract
This document provides a general guide for students who want to implement real-time control
strategies for the balls-in-tubes experiment. This inexpensive experiment is designed to be
a testbed for the implementation and evaluation of distributed dynamic resource allocation
strategies. In this document, we describe the apparatus, its main components, the challenges
that we need to face, and we show how to interface dSPACE with the experiment.
Contents
1 Introduction
2
2 dSPACE: Hardware and Software
2
3 Experimental Apparatus
3.1 Height Sensors . . . .
3.2 Actuators . . . . . . .
3.3 Electrical Connections
3.4 Power Supply . . . . .
3.5 Simulink Blocks . . . .
3.5.1 Height Sensors
3.5.2 Actuators . . .
3.5.3 Controllers . .
and
. . .
. . .
. . .
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Challenges
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1
Introduction
The ubiquitous presence of networked computing is significantly impacting the field of control
systems. There are already many “distributed control systems” (DCS) in industry and significant
current research on networked multi-agent systems. These networked control systems are typically
decentralized, large-scale, may be hierarchical, and are often quite complicated from a dynamical
systems perspective. They typically have a blend of significant nonlinearities, nondeterministic
behavior, random delays, constrained information flow (e.g., only via the topology defined by
the communication network), high-dimensionality, etc. Since their main purpose is control of
a dynamical system they contain many (if not all) of the challenges typically found in control
systems (e.g., disturbance rejection, tracking, robustness), and additional challenges due to the
presence of a computer network that synergistically interacts with the dynamical system. They
represent a significant departure from typical, say classical DC motor control or inverted pendulum
control problems, and demand many of the same tools/skills and more such as expertise in software
engineering, object-oriented programming, or real-time operating systems. Moreover, they demand
that more attention be given to a number of other nontraditional control objectives, including
dynamic resource allocation, scheduling of tasks, and control over large networks, than in the past.
The balls-in-tubes experiment was designed to provide a testbed for distributed networked
feedback control systems. Compared to past experiments, it provides interesting challenges to
perform dynamic resource allocation.
2
dSPACE: Hardware and Software
We use dSPACE hardware and software for the balls-in-tubes experiment experiment described in
this document. The dSPACE software is based on Matlab/Simulink. To develop the block diagrams
in Simulink for the balls-in-tubes experiment we use several processes. First, we will acquire the
data, and store this information in some global variables that will be used in the next process.
Second, we develop several subsystems (i.e., the name used in Simulink to designate each of the
elements that a complex block diagram has to make everything more compact and easy to read)
that will be in charge of making decisions concerning the control, or other tasks such as to update
variables to be used in the last process. Third, we will update the digital/analog outputs.
In the combined dSPACE-Matlab package we have Simulink and the graphical user interface
(GUI) that is provided in dSPACE. In Simulink we develop the controller and all the necessary
functions to run the experiment. Once we have the code, that they call the “model,” we compile
it and following some steps that are transparent to the user, we obtain a file that will run the
code in real time, and provide the ability to set up a user interface. This GUI in dSPACE can be
viewed as a diagnostic tool, since we can change some variables, and we can see in real time some
of the variables defined by the user in the model. The students can find a tutorial introduction to
dSPACE at http://www.ece.osu.edu/˜passino/dSPACEtutorial.doc.pdf.
3
Experimental Apparatus and Challenges
This experiment was designed to be an inexpensive testbed for dynamic resource allocation strategies. Below, we describe the elements of the experiment, its challenges, and we show how to
interface both the sensors and actuators to the dSPACE card. Figure 1 shows the balls-in-tubes
experiment. There are four tubes, each of which holds a ball inside, a fan at the bottom to lift
the ball, and a sensor at the top to sense the ball’s height. For each tube there is a box that the
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fan pressurizes. You can think of this box as a stiff balloon that is “blown up” by the fan, but
which has an outlet hole used to blow air into the tube. The tubes are connected at the fan inlets
via an input manifold which has an inlet at the bottom as indicated. Also, there is an output
manifold at the top of the tubes with an outlet as shown. The presence of the manifolds is a key
part of the experiment. These manifolds force the sharing of air at the input, or constrain its flow
at the output, so that there is significant coupling between the four tubes. Characteristics of the
coupling can be adjusted by, for instance, making both the inlet and outlet have different opening
sizes or by placing solid objects in the manifold to obstruct airflow to some fans. For a range of
inlet sizes, if one fan succeeds at lifting the ball to near the top, it can only do this at the expense
of other balls dropping. This feature leads to the need for “resource allocation” where here the
resource is the air that elevates the balls. Flow characteristics in the manifolds are very complicated
due to, for instance, air turbulence in the manifolds and pressurized box. Finally, note that the
experiment was designed to be easily extended to more tubes, different arrangement patterns, and
to have different manifolds and hence interaction effects. There are a number of control objectives
465 mm
Close-up view
of output manifold
Output
manifold
outlet
1710 mm
Ball 1
Tube 1
Ultrasonic
sensor 3
DC fan 4
Input
manifold
Close-up view
inlet
of input manifold
470 mm
Pressurized
box 1
Figure 1: Balls-in-tubes experiment (tubes 1-4, numbered left to right).
and challenges that can be studied for this experiment, beyond the obvious isolated balancing of a
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single ball in a tube:
1. Balancing the balls inside the tubes, trying to allocate air pressure to keep all the balls at
fixed positions or alternatively, a uniform height but maximally elevated.
2. Balancing and reallocation dynamics in the presence of disturbances such as changes in manifold inlet sizes or flow obstructions in a manifold. Also, effects of using decentralized and
networked decision making in the presence of an imperfect communication network could be
studied.
The actuators that we selected are DC fans commonly found inside computers. In total, there
is one digital input (DI) and one digital output (DO) for each sensor, and one digital output for
each fan for a total of 12 digital input-output lines that we connect to a DS1104 dSPACE card.
3.1
Height Sensors
To sense the ball height for each tube we use a Devantech SRF04 ultrasonic sensor shown in
Figure 2(a). Figure 2(b) depicts the sensor connections. Table 1 shows the specifications of the
Devantech SRF04 sensor (http://www.robot-electronics.co.uk/htm/srf04tech.htm). The raw data
obtained from the sensor is very noisy. For example, the spikes that we get from it correspond to
errors greater than 10 centimeters. We developed a filter to smooth the sensor output. For our
sampling rate Ts = 100µ sec., after filtering we achieved a resolution of ± 1 centimeter. The
a. Devantech SRF04
Ultrasonic sensor
b. Sensor connections
Figure 2: Ultrasonic sensor used in the balls-in-tubes experiment.
ultrasonic sensor timing diagram is shown in Figure 3. There are two digital signals (one DI and
one DO) needed to obtain raw data from this sensor, which is the travel time of the ultrasound
wave between the sensor and the ball. The DO is connected to the trigger input to start the ball
height measurement. After the application of a signal to the trigger input, the sensor will send out
an 8 cycle sonic burst at 40kHz and set its echo line high. It then waits for an echo, and when it
detects it, the echo line is reset. The pulse width of the echo line is therefore proportional to the
ball height and it is connected to a dSPACE DI.
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Table 1: Specifications of the ultrasonic sensor.
Voltage (DC)
Current
Frequency
Maximum Range
Minimum Range
Weight
Size
5v
30mA Typ. 50mA Max
40KHz
3m
3 cm
0.4 oz.
1.75” w x 0.625” h x 0.5” d
Figure 3: Timing diagram of the ultrasonic sensor.
3.2
Actuators
The actuators that we selected are Dynatron DF1209BB DC fans (Figure 4) commonly found inside
computers and their specifications are shown in Table 2. We use a pulse width modulation (PWM)
signal as an input to the fan. The sampling period is 100 µsec. the period for the PWM is 0.01
sec., and the duty cycle is varied in order to command the ball inside the tube either to reach a
desired height or to raise as much as possible during a certain time interval. One limitation present
in the actuators is that they possess an internal temperature sensor that changes the revolutions
per minute (rpm) of the fan when the ambient temperature changes; this fact makes the rpm of
the fan temperature-dependent. For single runs of the experiment this is not a problem since the
room temperature is relatively constant in such a short time interval. Another more significant
problem is that the fans are of relatively low bandwidth.
Table 2: Specifications of the Dynatron DF1209BB DC fan.
Voltage (DC)
Range Voltage (DC)
Max Current
Operating Temperature
Weight
Size
12v
10.2-13.8v
300mA
-10C to + 65C
80 gm
92mm w x 92mm h x 25.4mm d
5
Figure 4: Fan used in the balls-in-tubes experiment.
3.3
Electrical Connections
Here we show all the electrical connections in this experiment. Figure 5 shows a side view of the
apparatus where you can see all the terminal blocks. There are two terminal blocks (i.e., TOP-1
and TOP-2) on the output manifold, three terminal blocks (i.e., BOT-1, BOT-2, and BOT-3) on
the input manifold, and one terminal block on the pressurized block. Figures 6, 7, and 8 show
detailed information on all the connections found in the output manifold, pressurized block, and
the input manifold respectively. The nomenclature used in this case lists first where the connection
comes/goes from/to, and second also lists the terminal block in parenthesis (if applicable) associated
with this connection.
3.4
Power Supply
Two power supplies are used in the balls-in-tubes experiment. A 15 DC volt power supply is used
to power all the fans. This power supply was designed by undergraduates in an EE 682P design
project. You must use one 15 DC voltage source for powering just one fan; otherwise, an overload
could occur causing a malfunctioning in the fans. The other one is a 5 DC voltage power supply
Tektronix CPS250, which powers all the ultrasonic sensors.
3.5
Simulink Blocks
Here we explain the Simulink blocks that the students need to interface to the height sensors and
the actuators. Next, we describe these key blocks in more detail.
3.5.1
Height Sensors
The height of the ball inside the tube is determined by means of the Simulink blocks shown in
Figure 9. Notice that the logic implemented here corresponds to the specifications of the timing
diagram depicted in Figure 3. The block “Pulse Generator” sends out a signal with amplitude
1, frequency 0.05 s, and duty cycle 0.02 to the trigger input of the sensor. All these values were
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TOP-1
TOP-2
Multipair cable
Tube # 1
MID
BOT-3
BOT-2
BOT-1
Figure 5: Side view of the terminal blocks in the balls-in-tubes experiment.
determined from the timing diagram of the ultrasonic sensor. The block “EchoLine” is the digital
input used for the echo line of the ultrasonic sensor. The travel time of the sound wave is the
difference between the negative edges of the trigger input signal and the echo line of the ultrasonic
sensor. We then use this travel time divided by two and the sound velocity (i.e., 331.1 m
s ) to obtain
the height of the ball. The block “Discard Values” avoids having negative values at the variable
“Travel time of sound wave” at every time.
We have to cope with three limitations presented by this sensor: changes of the sound velocity
with respect to the ambient temperature, the sensor noise, and the resolution of the sensor. If the
temperature in the laboratory changes, then the absolute value of the ultrasonic sensor changes
also, which makes the height measurement temperature-dependent. The raw data obtained from
the sensor is very noisy so we have to filter these data in order to reject undesirable values. We
consider that a signal is “noisy” here when the difference between two consecutive ultrasonic sensor
readings is greater than 10 centimeters. Hence we have two variables: the actual measurement
that could be corrupted, and the filtered measurement. If the measurement does not have noise,
we update the second variable (i.e., we assign the same value that the actual measurement has),
otherwise we will not, and the value will be the same as the previous iteration. The resolution of
the sensor depends on the sampling time used in the experiment. In this particular case, we chose
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S1: Sensor 1
S2: Sensor 2
S3: Sensor 3
S4: Sensor 4
TOP-1
From
Echo
S2
From
Trigger
S2
From
Gnd
S2
From
+5V
S2
From
Echo
S1
From
Trigger
S1
From
Gnd
S1
From
+5V
S1
1
3
5
7
9
11
13
15
17
19
21
23
2
4
6
8
10
12
14
16
18
20
22
24
To
To
To
To
To
To
To
To
Pin 47 Pin 45 Pin 43 Pin 41 Pin 39 Pin 37 Pin 35 Pin 33
(BOT-1) (BOT-1) (BOT-1)(BOT-1) (BOT-1) (BOT-1) (BOT-1) (BOT-1)
From
+5V
S3
From
Gnd
S3
25
27
29
26
28
30
From
+5V
S4
From
Gnd
S4
From
Trigger
S4
From
Echo
S4
31
33
35
37
39
32
34
36
38
40
From From
Trigger Echo
S3
S3
TOP-2
To
To
To
To
To
To
To
To
Pin 24 Pin 22 Pin 20 Pin 18 Pin 55 Pin 53 Pin 51 Pin 49
(BOT-2) (BOT-2) (BOT-2) (BOT-2) (BOT-1) (BOT-1) (BOT-1) (BOT-1)
Figure 6: Electrical connections at the terminal blocks in the output manifold.
MID
To Pin 26 (BOT-2)
To Pin 28 (BOT-2)
To Pin 30 (BOT-2)
To Pin 32 (BOT-2)
Ground
1
2
3
4
5
6
7
9
INA
INB
INC
IND
INE
INF
ING
OUTA
OUTB
OUTC
OUTD
OUTE
OUTF
OUTG
16
15
14
13
12
11
10
From Pin 10 (BOT-3)
From Pin 12 (BOT-3)
From Pin 14 (BOT-3)
From Pin 16 (BOT-3)
COM
DS2003
Figure 7: Electrical connections at the terminal block in the pressurized box.
a sampling time Ts = 100µsec. and achieved a resolution of the sensor equal to ±1 centimeter.
3.5.2
Actuators
The actuators are used to supply the air needed to lift the ball inside the tube. The amount of air
supplied for lifting a ball is proportional to the voltage applied to the fan, which is proportional
to the duty cycle of the PWM signal. Figure 10 shows the blocks necessary to generate a PWM
signal. What you need to do here is to assign a value between 0 and 1 (representing from 0 to 100
% duty cycle) to the memory block “A1” depending on the voltage that you want to apply to a fan.
This duty cycle value will depend on the controller design that you will use for the ball-in-tubes
experiment.
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BOT-3
BOT-2
From Power
IO 5
Supply
P1B 44
+15 Vdc
dSPACE
From Power
IO 11
Supply
P1B 43
+15 Vdc
dSPACE
From Power
Ground
Supply
and
+15 Vdc
P1B 1 dSPACE
From Power
Supply
+5 Vdc
+15 Vdc
From
Pin 24
(TOP-1)
From
Pin 22
(TOP-1)
33
34
35
36
From
Pin 20
(TOP-1)
37
38
IO 5
P1A 44
dSPACE
24
From
Pin 26
(TOP-2)
From
Pin 18
(TOP-1)
39
40
IO 11
P1A 43
dSPACE
25
26
42
28
From
Pin 16
(TOP-1)
From
Pin 14
(TOP-1)
41
27
From
Pin 1
(MID)
From
Pin 2
(MID)
43
44
30
From
Pin 3
(MID)
From
Pin 12
(TOP-1)
45
46
32
From
Pin 5
(MID)
From
Pin 10
(TOP-1)
From
Pin 40
(TOP-2)
From
Pin 38
(TOP-2)
From
Pin 36
(TOP-2)
From
Pin 34
(TOP-2)
47
48
49
50
51
52
53
54
55
56
1
2
3
4
To
Red wire
(FAN-3)
5
6
To
Red wire
(FAN-4)
7
8
To
Black wire
(FAN-4)
To
Black wire
(FAN-3)
9
10
From
Pin 16
(MID)
11
12
From
Pin 15
(MID)
IO 19
P1B 9
dSPACE
IO 13
P1B 10
dSPACE
29
31
To
Black wire
(FAN-2)
To
Black wire
(FAN-1)
13
14
From
Pin 14
(MID)
IO 7
P1B 11
dSPACE
15
16
From
Pin 12
(MID)
IO 1
P1B 12
dSPACE
BOT-1
From
Pin 32
(TOP-2)
From
Pin 30
(TOP-2)
From
Pin 28
(TOP-2)
To
Red wire
(FAN-1)
To
Red wire
(FAN-2)
17
18
19
20
21
22
23
+5 Vdc
Ground
+5 Vdc
Ground
IO 0
P1A 12
dSPACE
IO 7
P1A 11
dSPACE
IO 13
P1A 10
dSPACE
IO 19
P1A 9
dSPACE
Power Supply (Ground)
and P1A 1
dSPACE
Power
Supply (+5 Vdc)
Figure 8: Electrical connections at the terminal blocks in the input manifold.
(boolean)
Pulse
Generator
TriggerInput
DS1104BIT_OUT_C4
Data Type
Conversion
In1
Clock
Out1
In1
Out1
Discard Values
Negative Edge
of TriggerInput
Travel time
of sound
wave
EchoLine
Ball height
165
DS1104BIT_IN_C10
Conversion Factor
In1
medida1
Data Store
Write1
Out1
Negative Edge
of EchoLine
Figure 9: Simulink blocks used to determine the ball height.
3.5.3
Controllers
Two control strategies will be discussed here to give you an idea of how controllers operate for
this plant. First, a conventional controller can be designed to float the ball inside each tube at a
desired height. For this case, you need to define for each tube a variable in Simulink for the desired
height, take the difference between the desired height and the actual one, and this value will be the
input to the designed controller. Other additional inputs can be considered depending on whether
you want to design a proportional-integral or proportional-integral-derivative controller. Second,
you can try to balance the balls around a certain common height. In this case, the peak-to-peak
oscillations of each ball height are allowed to be relatively large, but we want the time averages of
9
<
A1
Duty Cycle
Product2
1/100
Period
1
u
Frequency
1
0
floor
Product1
prevent missing an
entire pulse period
0
(boolean)
PWM
Fan1
1
Out1
Product
Figure 10: Simulink blocks used to generate a PWM signal.
the heights of each of the four balls to be the same. This goal can be achieved by allowing only
one fan enough percentage of PWM duty cycle to raise its ball at a time; hence we think of this as
juggling the balls. Such juggling is a type of allocation of the air resource from the common input
manifold to each ball. The allocation strategy must be designed to persistently seek to minimize
the differences between the average ball heights in spite of air turbulence, inter-tube coupling via
the manifolds, fan bandwidth constraints, and significant sensor noise. The dynamics of allocation
rely critically on feedback information on ball heights, and the distributed decision-making that
implements the allocation strategy.
For the details of the design and operation of two resource allocation strategies for this experiment see [1].
References
[1] N. Quijano, A. E. Gil, and K. M. Passino, “Experiments for decentralized and networked
dynamic resource allocation, scheduling, and control,” Submitted to IEEE Control Systems
Magazine, 2003.
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