Description
MAAE 3500 Feedback Control Systems
Laboratory Assignment 1
Due: Feb 12 at 5:00pm – submit a single pdf to CULearn.
The purpose of this lab assignment is to model and characterize the response
of a system based on a specific dc motor. The overall question is to determine if
the given motor is an appropriate choice for this application. The goal provide a
platform that can be quickly and precisely moved up and down a vertical shaft.
The motor to be used is the Maxon DCX 10 S and the data sheet for this
motor is attached. The reason for the choice of this motor is that the company
has several on hand. They want to know how well it will work. (See Figure 1.)
Rope
Pulley
Motor
G
m1
Figure 1: System configuration
The small platform is constrained to move up and down in a vertical shaft
(like an elevator). From high above the platform a cable hangs down. The task
is to use an electric motor (which is attached to the platform) and, by means
of a transmission (gear reduction, G) and pulley to which the cable is attached,
move the platform up and down. Consider only one-dimensional motion, up and
down the shaft. Assume the bearings are frictionless. The goal is to create a
system that will achieve the highest upward speed possible after 0.5
seconds of acceleration. After 0.5 seconds the speed is to remain constant.
1
Make the following assumptions:
? the total moving mass in the system (including the motor, platform and
gear box) is equal to ten (10) times the mass of the motor. Everything
else is to be considered massless.
? the cable is flexible and can be modelled assuming that under the the
static weight of the system the platform can deflect no more than 0.15
mm.
? the diameter of the pulley is the same as the outer diameter of the motor
(based on physical space).
? the gear reduction is assumed to be massless – you will choose the gear
ratio.
? the rotational inertia of the pulley is assumed to be twice the rotor inertia
of the motor.
The motor can be modelled electrically with the circuit shown in Figure 2.
The motor speed depends is found based on the speed constant (!m = K! em )
and the motor torque depends on the motor current (?m = KT im ). Values
for these are found in the specification sheet – be careful of units. In this lab
assignment use Matlab.
~i
+
Vin
Rm
Lm
+
~?m
!
~m
em
Figure 2: Motor Circuit
2
Questions:
Answer the following questions, include in your submission any relevant plots
and all m-files used.
? Assuming the motor is 100% e?cient, em i = ?m !m . Use this equation
to find a relationship between KT and K! . Check the values given in
the motor specifications (unit conversions will be needed). Do the stated
values agree with the theory? Comment.
? Choose a gear ratio and justify your choice. It may be based on power,
or speed or torque or some other criteria. You will complete the analysis
for this value – you are not expected to refine this choice even if this first
value is not optimal.
? Create a block diagram for the system. The input will be voltage and
the output will be the height of the platform (x). Clearly indicate the
variables and the transfer functions. Find all parameter values.
? Based on this model find a transfer function relating the input voltage to
the vertical (upward) speed of the platform.
? Find the poles and zeros of this transfer function. What can you conclude
from these about the expected performance of the system?
? Simulate the step response of the system. Do not exceed the nominal
voltage. Comment. Can this design meet the performance requirement.
Perform any other simulations (there may be none) you think are relevant
to the task.
? What would you do at t = 0.5 seconds to change to a constant speed
operation?
? How would all of this change if the platform was dropping?
? Based on the results, comment on your choice of gear ratio.
? Is this motor appropriate for this task? Comment on what might make a
di?erent choice better. Do not iterate the design.
3
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DETAILS
CONFIGURABLE
OK
RECOMMENDED
DCX 10 S ?10 mm, Precious Metal Brushes CLL, ball bearings
PRICE SCALES
Quantity Price per unit
Prices excluding VAT and shipping
costs
1-4
?94.27*
5-19
?82.36*
20-49
?70.09*
from 50
On request
*Configurable products must be configured before ordering.
Prices may vary.
Start combination
Configure
Specifications
Specifications
TECHNICAL ILLUSTRATIONS
Dimension drawing
Information: Drawings are not to scale.
Description
Downloads
VALUES AT NOMINAL VOLTAGE
Nominal voltage
12 V
No load speed
12500 rpm
No load current
11 mA
Nominal speed
3890 rpm
Nominal torque (max. continuous torque)
0.904 mNm
Nominal current (max. continuous current)
0.114 A
Stall torque
1.37 mNm
Stall current
0.16 A
Max. efficiency
56 %
CHARACTERISTICS
Terminal resistance
74.9 ?
Terminal inductance
0.868 mH
Torque constant
8.53 mNm/A
Speed constant
1120 rpm/V
Speed / torque gradient
9830 rpm/mNm
Mechanical time constant
7.26 ms
Rotor inertia
0.0706 gcm?
THERMAL DATA
Thermal resistance housing-ambient
37.6 K/W
Thermal resistance winding-housing
22 K/W
Thermal time constant winding
4.05 s
Thermal time constant motor
156 s
Ambient temperature
-40…+85 ?C
Max. winding temperature
+100 ?C
MECHANICAL DATA
Bearing type
ball bearings
Max. speed
14300 rpm
Axial play
0 – 0.1 mm
Radial play
0.015 mm
Max. axial load (dynamic)
0.5 N
Max. force for press fits (static)
8.8 N
(static, shaft supported)
120 N
Max. radial load
1.5 N, 5 mm from flange
OTHER SPECIFICATIONS
Number of pole pairs
1
Number of commutator segments
7
Number of autoclave cycles
0
PRODUCT
Weight
6g
OPERATING RANGE
n [rpm]
11440
8580
5720
2860
0
0
0.01
0.3
0.04
0.5
0.07
0.8
0.10
1.1
0.13
M [mNm]
I [A]
Continuous operation range
Short term operation range
Description
maxon DCX motors feature unrivaled power density (torque per volume) and absolutely quiet running. The robust
engineering, combined with the globally patented ironless winding, makes the DCX motors a highly dynamic drive for
almost every application scenario.
The DCX 10 S is available as a small drive with preloaded ball bearings or sintered bearings. The optional spark
suppression (CLL) turns this DC motor with precious metal brushes into a real long-distance runner.
Downloads
CATALOG PAGE
??? (chinesisch, PDF 1 MB)
Version 2020
Katalogseiten (deutsch, PDF 123 KB)
Version 2020
Catalog page (english, PDF 121 KB)
Version 2020
Cat?logo Pagina (espa?ol, PDF 134 KB)
Version 2020
Page de catalogue (fran?aise, PDF 133 KB)
Version 2020
??????? (???, PDF 399 KB)
Version 2020
Videos
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