Project Phase 1

Introduction

This project requires you to apply the dynamic modelling approach used in the course to obtain

the nonlinear and linearized equations of motion for the Quanser 3 degree-of-freedom (DOF)

helicopter, shown in Figure 1. You will also do some preliminary controller design (for the pitch

and roll dynamics). This is an important prerequisite to phase 2 of the project, which will require

you to develop and test controllers for the full system.

This project is based (in part) on lab 1 from MIT OCW 16.30 Lab 1. Please refer to that lab, in

particular, read the Introduction and Physical Model sections and note the angle definitions in the

figure on page 1 and the data table on page 2. The remainder of this set of project instructions

assumes you have read those two sections.

Summary of Equations and Numerical Parameters

Nonlinear equations of motion:

????????¨= ??????????h – ????????sin?? – ??????? – ????????????????(???cos?? + ???sin??) (1)

????????¨= ????????????????????cos?? – ???????? sin(?? – ??????????) – ????????????sin?? + ??????????????????? – ??????? (2)

????????¨= ????????????????????sin?? – ????????????cos?? (3)

where

?? = ??????? (4)

?????????? = ?????????????? – ??????? (5)

???????? = ???????????? – ??????? (6)

and

????????? + 6???????? = 780???????? (7)

??????????? + 6?????????? = 540?????????? (8)

The required numerical parameters are given in Table 1.

Table 1 – Physical parameters of the 3-DOF unit MIT OCW 16.30 Lab 1

Parameter Value Units Description

?? 1.15 kg mass of rotor assembly

?? 3.57 kg mass of whole setup

?????????? 0.66 m length from pivot point to heli body

???? 0.004 m length of pendulum for roll axis

???? 0.014 m length of pendulum for pitch axis

??h 0.177 m length from pivot point to the rotor

?????? 0.036 Nms2 moment of inertia about x-axis

?????? 0.93 Nms2 moment of inertia about y-axis

???? 4.25 × 10-3 Ns coefficient of thrust

?????????? -25 deg. theta rest value

?? 9.81 m/s

2

acceleration due to gravity

???? [0.02, 0.2] Nms roll damping coefficient

????

[0.1, 0.9] Nms pitch damping coefficient

Figure 1 – 3 DOF Helicopter – adapted from Quanser website

Project Assignment

Items 1-3 can be completed after Lecture State-space model features (2/2).

- Explain the physical source and meaning of each term in the nonlinear equations of motion

for the Quanser 3 DOF helicopter (equations 1-3). - Linearize the equations of motion about a steady hover equilibrium. At this condition ???

0 =

???

0 = ???

0 = 0, ??0 = ??0 = ??0 = 0 (because the “reference” travel angle can be set

arbitrarily), ?????????,0 = 0, ???????????,0 = 0, ??0 = 0 (flight path angle), and ??0 = 0 (velocity).

Note that the linear model does not perfectly represent the dynamics of the actual Quanser

due not only to the approximations inherent in linearization, but due to variations in pitch

and roll damping from one Quanser unit to another. This is why ranges are given in the MIT

OCW document for these quantities. ???? and ???? could be anywhere in the ranges given.

– Express your results for this problem in symbolic form. - Ignoring the dynamics in travel (??), obtain state space models for the pitch and roll

dynamics.

– Express your results in symbolic form.

– Use the numerical values provided in the MIT OCW document to check the

following for the full range of ???? and ???? values:

• stability

• controllability

• observability

• stabilizability

• detectability

Reporting Requirements:

Your project report MUST be submitted electronically via Blackboard as a single zip file, with

the following naming convention: LASTNAME_Firstname_MECH_4672_I_YYYY.zip where

YYYY is the year for the course. For example, RAHIMI_Afshin_MECH_4672_I_2019.zip.

• This is an individual project.

• The style of the document should be in APA version 6 format. Make sure you follow the

instructions provided in the resource at the end of this document and look at the sample

APA paper to get an idea of what the guidelines are. If you have questions, always ask!

• The report should be maximum 10 pages in length including figures. Be as concise as

possible while clearly communicating your thought process and findings. Appendices do

not count towards this length constraint.

• Your report must detail your design process, the results, and explain why you think your

design is the best one you could come up with, e.g. justify all design choices and the

adequacy of the performance obtained.

• Ensure all figures are of sufficient size and clarity to be easily read. Outputs from

MATLAB/Simulink should be generated as vector files rather than using screenshots (see

the documentation for details). Free PostScript to vector formats such as .svg, .emf, and .eps

is available online, look for Inkscape software; if you have difficulty finding one, come to

see me at office hours and I will help you. Screen captures from MATLAB/Simulonk are

not acceptable in your report.

• Observe standard technical writing conventions – label all figures, put data in tables, etc.

• Use three significant figures for all results and comparisons between numbers.

• Your report should (if applicable) contain:

– Title page Following instructions for APA version 6 cover page

– Table of contents

– List of figures and/or tables

– Abstract The purpose for an abstract is to present the gist of the study/work in the

shortest way possible where problem is introduced, methods are clear, and outcome

is communicated. Therefore, if you read an abstract section of the report you would

know whether it is related to what you are searching for and would not have to go

through the complete report.

– Introduction This introduction should be designed to interest your reader in your

topic and provide some historical context for your project. You need to identify the

problem you are trying to solve and its significance. At the end of this section, you

need to transition to problem statement. Remember that at this point you have

completed the project so all the material in this section should now represent the

work done and there should be no ambiguity.

– Problem Definition In this section quickly provide the summary of the problem you

are required to solve and all the available information about your system dynamics,

required tasks, etc.

– Theory In this section, you need to provide theory on what you are solving and

required equations, assumptions, etc. goes here. This is the section you need to use

your in-text citations the most and must have an appealing flow in the context. Make

sure you adhere to the citation style required.

– Methodology In this section, you should discuss the methods and sources you have

used to conduct your project and solve the problem using the theory and tools. Try

to connect your theory section to here using the equations you have introduced

earlier with equation numbers, etc.

– Results and Discussions This section is the place where you need to showcase the

hard work you put in to complete the project. In this section, using the methods you

suggested to solve the problem on the data you have used to analyze, you need to

clearly show through, graphs, plots, tables, and other appropriate presentation means

what you have learned, and through the process helped solve the problem you

intended to solve. Each result needs to be accompanied by a reasonable discussion

on the outcomes. The discussion needs to incorporate the intentions of the study as

well as the outcomes so that one can understand clearly how the presented results

match with the solution you are proposing for the problem at hand. It is also

important to make sure that all plots and tables are discussed in your discussion as

otherwise they would have been presented for no reason. This section should

transition to your conclusion section where you conclude the study by summarizing

your learning outcome of the project.

– Conclusion In your conclusion, now that you have completed the project, you need

to clarify what you did and what you learned from it. It needs to briefly reflect on

the problem, mention the methods used to solve it, draw on the important results

obtained through the study and provide some suggestion for the future directions of

the study in case someone else is interested to continue your work and improve it

further because there is always room for improvement!

– References You need to have credible sources. Using Mendeley is strongly

recommended as it can save you tons of time and make sure you are doing your

citations correctly and efficiently. Citations in APA 6 format. Any in-text citations

should also follow APA 6 guidelines.

– Appendices This section needs to include any additional material that is needed for

the report to be self-sustainable but cannot fit in the page limit of the paper. Your

MATLAB/Simulink files would go here. If you have extensive derivations, lookup tables, code, supplementary equations, etc. they all go here in their respective

subsection numbered either numerically “Appendix 1, 2, 3…” or alphabetically

“Appendix A, B, C…”.

Submission file:

• Submit your project as a single ZIP file. This file should contain

– Your reports original file (Word document, etc.)

– All supporting plots, figures, tables, that are required for the original report

– PDF version of your report that should run on any computer and look the same

– All you MATLAB/Simulink files with instructions (instruction.txt) for someone to

be able to run and get the same results. All in structured folders under (MATLAB

folder). Use the figure below as a guideline to structure your zip file.

Figure 1. Structure of the .zip file to be submitted

Penalties

You will be penalized for the following:

Page overage

For each page over the page limit you will be deducted 10% of the total grade. This is to ensure

all are evaluated on a fair basis. Please note that your line spacing needs to adhere to the style

requested and page limit will be checked in that format.

Late submissions

The penalty for late submission is 10% for the total mark deduction for each day, up to 3 days,

after which the mark for this component of the course will be ZERO. Note that partial marks are

not awarded for hours and minutes during late submission.

.Zip file

report folder

report.PDF report.Doc(x)

Sample Solution

Translation process is an artistic communication between the author, the translator and the reader and the words used by the translator constitutes the major part in the process of communicating ideas or feelings of the author. “Literature is both the condition and the place of artistic communication between senders and addressees or the public” (Basnett,2002) The translator is the first one who must comprehend, read and interpret the source text then to render it in a different medium. Literary translation includes fiction,poetry, drama and the language arts must be taken into consideration by the translator. The purposes of the translator are to transfer the information but also to create an equivalent form of art. The beauty of the translators’ work is that they bring a great contribution to the creative process being recognized as part of the literary world. The literary translator must therefore possess a great knowledge of both the TL culture and language and the SL culture being able to command to>

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