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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

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