Graduation Speech -- Graduation Speech, Commencement Address

Today is both an end, and a start. In the wake of thirteen difficult years we have at long last finished up our Kutztown training. It’s been a rough street, loaded up with thrashings, triumphs, and shocks. We’ve took in a ton en route, and not simply science and math and English, in spite of the fact that our instructors have ensured we gotten a lot of that as well. Seeing similar individuals for quite a while has shown us what fellowship isâ€and isn’t, and we’ve discovered that life isn't in every case reasonable. We’ve additionally built up some fascinating aptitudes, similar to how to avoid bucketsâ€or freshmanâ€in a jam-packed passage on a stormy day. Or on the other hand how to fend off warmth stir in the boiling science wing and hypothermia in the over cooled English homerooms. All things considered, we despite everything figured out how to shout the most intense of any class at each pre-game event since our first year. We’ve e ndure social shows and state administered tests and finals. Furthermore, presently, after all the schoolwork and the late evenings considering and the 14,580 hours of sitting in class, yes I crunched the numbers, we’re here to commend the way that we’ve made it. At the point when we began kindergarten this second appeared to be so awfully far away. We were just five years of age ourselves, and thirteen years should have been an unfathomable length of time. When we arrived at middle school we were excessively bustling stressing over whether we would have the option to open our storage spaces or recall where our classes were to really think about the progression of time. By ninth grade there was the disgrace of being green beans, and afterward in a matter of moments three years had passed and our senior year had snuck up on us. Out of nowhere all that we did was an achievement; our last show, our last gathering, our last test, even our last day of classes. By this point senoritis had set in, and we were prepared to leave and... ... not to tune in. Without your commitment we would not be the place we are today, and I don’t think I’m alone in saying that I consider a large number of you companions, and not simply instructors. To the band and the stage group, a debt of gratitude is in order for assisting on our exceptional night. What's more, to the class of 2004: sail. Sail from this spot into the huge and unchartered future, yet don’t neglect to think back each every so often and recollect where you originated from. Secondary school is finished, yet you can take the recollections made here with you any place you go. Pack them away in your heart, and when you’re feeling apprehensive or debilitated recollect the excitement of dominating that football match, or the glow of your best friend’s grin, or the security of more straightforward occasions. In any case, don't choose not to move on everlastingly, for the time has come to proceed onward. Follow your heart, go after your f antasies. The world anticipates us, and it’s time to make it our own.

The process of growth and thus there is no optimum size of firm Essay

The procedure of development and therefore there is no ideal size of firm - Essay Example The monetary hypothesis has confidence in the reason that an association would exponentially increment fit as a fiddle if its development and improvement systems are in accordance with its prerequisites and wants over the long haul. This infers the discussion that the procedure of development is basically connected with its prosperity, both inside the transient condition just as over the long haul plan of things (Napach 1998). It is effectively deducible from the said point of view that there is no ideal size of the firm yet it is a relative issue in any case. The attention must stay on the way in which the firm if developing to make it sound as large as opposed to passing by the sheer size. The worldwide and provincial settings of the firm are imperative to comprehend in light of the fact that this is an indication of extension and development which are truly apparent inside the main part of things. In this way the contention that the procedure of development is connected with the firm as far as its extension and improvement appears to be substantial yet without its ideal size simultaneously. This is on the grounds that organizations like to connect their own selves with the developing requests of the business as opposed to opening up workplaces which are neither sensible nor controllable. There is a critical need to appreciate that a firm will possibly develop on the off chance that it needs to develop from its own underlying foundations, instead of counts on domains which are unnecessary for its own premise. Size is in this manner a side-effect of a firm’s development and is simply an issue of the measurements which are available inside the setting of the firm itself. These are hailed as minor and have no job at all in its development and advancement systems (Penrose 1995). The contention appears to be consistent in light of the fact that a firm would just rely upon its assets to get it to a position where it was never a piece of, as opposed to relying a lot upon the perspectives which would expand its size, which is not yet clear as a significant power to deal with in the evolving

Filipino Psychology essays

Filipino Psychology papers We have talked about creation an examination on the brain science of the Filipinos, and the field I picked is on Personality. Much has been composed and many research contemplates directed on Filipino character. Be that as it may, past written works have examined related subjects on values, character attributes, conduct, and standards of direct of the Filipino in the light utilized by Western techniques, utilizing Western language not indigenous to the Filipino culture. By the by, there have been considers directed that attempted to utilize Filipino phrasings that have typefied social worth qualities as got from Malay roots, and Chinese, Indian, Spanish, and American impacts (Andres,1981). Ongoing investigations via Landa Jocano show that underneath these social assorted varieties of the Filipino, fundamental likenesses despite everything exist in institutional conduct and worth direction. The explanation hence in making this investigation is to comprehend the Filipino worth framework in light of the fact that to comprehend it is to acknowledge Filipino conduct. This paper tries to discover what is the mentality of the fourth year Psychology Students of Xavier University as a vital aspect for understanding Filipino conduct and character. 1. To show the structure of Filipino measures of greatness (pamantayan) 2. To recognize the ideas of attractive attributes. 3. To count the standards individuals need to accomplish. 4. To assess the demeanor of fourth year Psychology understudies of Xavier University in the light of the gauges as a worth model. 1. Identify the objective populace in yr this case the fourth year brain science understudies of Xavier University. 2. See them by and by before leading the real examination to clarify that they are one of the subjects under investigation. 3. Write a proper letter and cause them to resolve to answer the survey as really as could be expected under the circumstances. ... <! filipino brain research expositions We have talked about creation an examination on the brain research of the Filipinos, and the field I picked is on Personality. Much has been composed and many research contemplates directed on Filipino character. However, past written works have talked about related subjects on values, character characteristics, conduct, and standards of lead of the Filipino in the light utilized by Western strategies, utilizing Western language not indigenous to the Filipino culture. By and by, there have been examines directed that attempted to utilize Filipino phrasings that have typefied social worth characteristics as got from Malay roots, and Chinese, Indian, Spanish, and American impacts (Andres,1981). Ongoing examinations via Landa Jocano show that underneath these social assorted varieties of the Filipino, essential similitudes despite everything exist in institutional conduct and worth direction. The explanation thusly in making this investigation is to comprehend the Filipino worth framework on the grounds that to comprehend it is to acknowledge Filipino conduct. This paper looks to discover what is the demeanor of the fourth year Psychology Students of Xavier University as a vital aspect for understanding Filipino conduct and character. 1. To show the structure of Filipino gauges of greatness (pamantayan) 2. To distinguish the ideas of attractive qualities. 3. To list the standards individuals need to accomplish. 4. To assess the disposition of fourth year Psychology understudies of Xavier University in the light of the principles as a worth model. 1. Identify the objective populace in yr this case the fourth year brain science understudies of Xavier University. 2. See them by and by before leading the genuine investigation to clarify that they are one of the subjects under examination. 3. Write a proper letter and cause them to resolve to answer the survey as actually as could be expected under the circumstances. ... <!

The Argumentative Essay Topics about Athletes Cover Up

The Argumentative Essay Topics about Athletes Cover Up An essay introduces claims about either side of an issue. I am sure this will assist you in future and you'll have the ability to compose an impressive essay. The thesis provides you with a guideline about how to go about with writing the essay. Your thesis needs to be relevant so the report can use a structure that's flexible in order to fit in the shoes of the readers. Virtually all the teachers follow this pattern whilst checking your essays. These are the sorts of things you'll be exploring when you compose a parenting argumentative essay. There are some who are great in writing essays about realities and not about abstracts while some are somewhat more proficient in finding works of fiction. The introduction should offer general information which will be included in the post. If you read the rest of this blog carefully and follow all the instructions and tips then it isn't impossible to become great grades in your essay, as you are able to get all the needed essay writing guide here. You may continue to keep your argumentative essays for your upcoming job portfolio in case they're highly graded. Now, if you would like to perfect your argumentative essay writing skills, then you should participate in extracurricular essay writing practice. This sort of essay focuses on proving your stance is valid, therefore it turns theory into fact. Having selected a superior topic to argue about, at this point you will need to make an argumentative essay outline. Do not neglect to develop an efficient outline to be successful! Read and analyze some persuasive essay examples to find out more regarding the structure and vocabulary employed within this kind of essay. This list of easy argumentative essay topics can help you to practice and find the essential writing abilities. Recent argumentative essay topics that are related to society is going to do. Without these 3 standard components, your essay is going to be considered incomplete. An argumentative essay requires you to choose a topic and have a position on it. Read the list and stay in mind that interesting topics are an appropriate way for an intriguing assignment. This informative article won't only show you just how to choose argumentative essay topics, but it is going to also teach you just how to compose the undertaking, also! When you have decided on the topic through our guide, we'll also supply you with article writing samples and templates which will also steer you through the writing. Take a look at how to think of an essay topic! The above-mentioned topic selection may give you a crystal clear comprehension of what things to write about. You should also think of the quantity of information readily available to you about this issue you're rushing towards. Picking an emotional topic is also a superb idea. No matter this issue, you could always rely on their help! Spam mail ought to be outlawed. When you are requested to pick a great topic for your argument, start with something you're acquainted with. It's possible to also restate the ideas which you have discussed in the body paragraphs in order to make your point valid. They don't know how to make certain that their points are persuasive enough. The trick to scoring well with these kinds of topics is that the writer knows the health care facts. Use transition words in order to connect the paragraphs and create the point flow. However, according to numerous scholars and activists there's still a very long way to go. The problem of athletic fitness ought to be dealt which much more strictness. The topic has to be interesting, the topic has to be essential and finally the topic has to be informative. Naturally, it's the topics you may have a tiny laugh about!

The Need for Quality After School Programs in American...

The Need for Quality After School Programs in American Schools Since the fall of 1997 America has experienced a rapid increase in the number of school shootings. These crimes have been completely non-discriminate towards either social status or ethnicity. What these incidents do have in common is the fact that students between the ages of 10 to 16 committed them. When later interviewed, most of the students who instigated these crimes reported feeling like â€Å"loners† or â€Å"outcasts† within their student body and communities. It has been the direct effect of these violent acts that people across America are looking towards permanent solutions for these problems and the need for quality after-school programs has come into the national†¦show more content†¦Children, families and communities can all benefit greatly from quality after-school programs. The majority of the time spent by unsupervised children and youth is either watching television or with peers in unsupervised activities. Quality after-school programs p rovide a safe, supervised environment for these young people and children. After-school programs also provide structured supervised activities, which improves the overall learning process. The students involved in quality after-school programs create more positive relationships with their peers and also with caring responsible adults with whom these students can foster lasting bonds. This in turn helps to harvest students with a higher level of self-esteem. Students that perform better in academics as well as develop stronger social skills. In his speech on the issue of childcare President Clinton said the following: â€Å"Improving after-school care is integral to improving child care across our country†¦ Through after-school programs we can bring parents the peace of mind that comes with knowing their children are safe. We can teach our children to say no to drugs and yes to reading, sports and computers.† (The White House at Work 1/26/99) The president also mentioned his plan to provide these services to parents who could not otherwise affordShow MoreRelatedCommunity After School Program Essay1455 Words   |  6 PagesMontgomery County After School Program caters to children ages 5-11 years of age. The Mid County Center After School Program receives children from Bel Pre and Strathmore Elementary Schools. Both schools are considered Title I, which means that the school has a majority of children from low-income families. The school provides free breakfast and lunch to all students. Bel Pre and Strathmo re Elementary School receive funding from Elementary and Secondary Education Act to assist the schools in meeting theRead MoreTitle Viii Nursing Workforce Development1537 Words   |  7 Pagesindustry is in need of a strong nursing workforce that can provide quality care. The present nursing shortage is only predicted to worsen as the baby boomers retire and health care needs expand. The shortage is projected to reach more than one million nurses, and reform is needed to increase the interest in nursing therefore funding is needed for this transformation ((American Association of College of Nursing, n.d.). Prevention is essential to quality care therefore public health nurses need to be trainedRead MoreHigh Quality Universal Pre K Can Reduce Achievement Gaps For Minority And Low Income Children1045 Words   |  5 PagesBrannan High-Quality Universal Pre-K can reduce achievement gaps for minority and low-income children To: Barbara Boxer From: Erin Brannan Date: May 1, 2016 Re: High-Quality Universal Pre-K can reduce achievement gaps for minority and low-income children Statement of Issue: Many minority children and children from low-income families enter kindergarten without the academic skills they need to succeed. Math and reading abilities at kindergarten entry are powerful predictors of later school success.Read MoreNational Debt Is Necessary For The Funding Of Federal Programs1210 Words   |  5 Pagesnecessary for the funding of federal programs. Government spending is not only a focus of the United State’s political system, but it affects one’s personal choices and lifestyle. There is a concern with where and why money is spent. A key aspect of government spending is allocated to education. Education is fundamental in how one benefits society and the economy. The United States education program is not only necessary for the success of the country, but it is in need of a more efficient system withRead MoreThe Importance Of Physical Education On American Schools1412 Words   |  6 Pages The Importance of Physical Education in American Schools Review Hommes, Tiffany J., Bemidji State University, USA Background Many children in America do not receive the needed amount of physical activity needed to maintain a healthy weight. Approximately17% of children are obese (Robert Wood Johnson Foundation, 2016) and 1 in 3 children are overweight or obese (American Heart Association, 2016). This is a local and national emergency that needs to be addressed to keep children healthy, preventRead MoreThe Significance Of Physical Education Essay1212 Words   |  5 PagesThe Significance of Physical Education in American Schools Review Hommes, Tiffany J., Bemidji State University, USA Background Many children in America do not receive the needed amount of physical activity needed to maintain a healthy weight. Approximately17% of children are obese (Robert Wood Johnson Foundation, 2016) and one in three children are overweight or obese (American Heart Association, 2016). This is a local and national emergency that needs to be addressed to keep children healthyRead MoreThe Public Educational System Of The University Of Alabama955 Words   |  4 Pagesstudents come from privileged backgrounds which hinders them from understanding the educational restraints that low income public schools face every day. Being able to talk with people who may or may not share similar views as myself has always been essential for my continuing success. Being part of a minority, I am continuously searching for professional development programs that challenge my analytical thinking on sociopolitical issues affecting this country, such as the educational system and howRead More Special Education I mplementation For Native American Girls Essay1712 Words   |  7 PagesNative American Girls Quality education for children has been an ongoing issue for todays society. There has also been an increasing concern for the education of students with special needs. The effect of these concerns has been noted in many communities, such as the Native American community. The population of special education students in the Native American communities is not necessarily higher than others, however, their community is effected, therefore also in need of qualityRead MoreEssay about Social Injustice1119 Words   |  5 Pageshousing, and medical care and necessary social services,† states Article 25.1 of the Universal Declaration of Human Rights. Unfortunately today, American citizens do not have equal access to health care, as they should be given. Federal programs and health care companies know that they don’t all have the same health status nor do they have the same access to quality health care services. Even though the Universal Declaration of Human Rights states that all humans are legally to have fair and equal accessRead MoreOrganizational Impact On Nursing And Nursing Education1602 Words   |  7 Pagesinfluenced the practice of providing quality care to the public and propelled Nursing to the profession that it is today. Among these groups are the Quality and Safety Education for Nurses (QSEN), American Association of Colleges of Nursing (AACN), and Institute of Medicine (IOM). We will discuss how these three organizations have impacted nursing and the nursing education. The Quality and Safety Education for Nurses (QSEN) looks to educate nurses in improving the quality and safety of patient care in the

Essay on The Handmaids Tale as a Warning to Society

The Handmaids Tale as a Warning to Society nbsp; Margaret Atwoods renowned science fiction novel, The Handmaids Tale, was written in 1986 during the rise of the opposition to the feminist movement. Atwood, a Native American, was a vigorous supporter of this movement. The battle that existed between both sides of the womens rights issue inspired her to write this work. Because it was not clear just what the end result of the feminist movement would be, the author begins at the outset to prod her reader to consider where the story will end. Her purpose in writing this serious satire is to warn women of what the female gender stands to lose if the feminist movement were to fail. Atwood envisions a society of extreme changes in†¦show more content†¦In the previous world this would refer to God and His omnipresence as he watches over his people. However, now the name symbolizes the eyes of a totalitarian government watching to see that no one breaks the rules. This especially applies to the women of the society. nbsp; In Gilead the social relationship that once existed between men and women is a thing of the past. In the former society women had value and felt good about themselves and how they looked. However, in the new society the men have stripped the women of their freedom and equality and lowered them to varying degrees of status. The young healthy women are labeled handmaids and are issued (24) by the government to various high-ranking officials in order to offer them the opportunity to create offspring. Getting pregnant is their only hope of survival. Females who are not of childbearing age are called Marthas because their purpose is to work and serve the men. A third category of women is labeled Unwomen because of their worthlessness in this male dominated society. All three categories are divided into colonies to prevent their rebelling against the system. Also, within each colony communication is limited and higher education is denied. In order to enforce this kind of oppressive social structure, the government uses various forms of intimidation. nbsp; ToShow MoreRelatedThe Handmaid s Tale By Margaret Atwood1249 Words   |  5 PagesDystopian Research Essay: The Handmaid’s Tale by Margaret Atwood In the words of Erika Gottlieb With control of the past comes domination of the future. A dystopia reflects and discusses major tendencies in contemporary society. The Handmaid s Tale is a dystopian novel written by Margaret Atwood in 1985. The novel follows its protagonist Offred as she lives in a society focused on physical and spiritual oppression of the female identity. Within The Handmaid s Tale it is evident that through theRead MoreTotalitarianism, Violence, and the Color Red in the Handmaid’s Tale1863 Words   |  8 PagesTotalitarianism, Violence, and the Color Red in The Handmaid’s Tale In literature, the color red symbolizes many things, each with its own emotional impact. Red can be associated with violence and bloodshed, or it can be associated with love and intense emotions. In The Handmaid’s Tale, Offred, chosen to be a â€Å"baby-maker† for a couple she was assigned to, desires to escape the dystopian society that she lives in. Thus, Margaret creates a fictional government that uses totalitarianism, violenceRead MoreAnalyse and Compare the Significance and Effectiveness of the Ways the Author of the Novels Choose to Open and End their Narratives1934 Words   |  8 PagesGo ends in uncertainty as Kathy drives away still looking for Hailsham yet for the reader there is no uncertainty; we know Kathy will die and it is the inevitability of this that leaves readers dissatisfied. The disordered opening of the Handmaids Tale, however, emphasises the confusion and fear which characterises a totalitarian state. The uncertainty of the narrative c reates a morbid curiosity within the reader that over the course of the novel is never really satisfied. Atwood’s presentation ofRead MoreThe Importance of Memory in Margaret Atwoods Handmaids Tale.2058 Words   |  9 PagesFor this essay I aim to show the importance of memory and of remembering the past in The Handmaid’s Tale by Margaret Atwood. The Handmaid’s Tale is a ‘speculative fiction’ first published in 1985 but set in the early 2000s. The novel was in response to changes in US politics with the emergence of Christian fundamentalism, the New Right. Atwood believed that society was going wrong and wrote this savage satire, similar to Jonathan Swift’s ‘A Modest Proposal’, depicting a dystopia which she uses asRead MoreThe Importance of Memory in Margaret Atwoods Handmaids Tale.2065 Words   |  9 PagesFor this essay I aim to show the importance of memory and of remembering the past in The Handmaid’s Tale by Margar et Atwood. The Handmaid’s Tale is a ‘speculative fiction’ first published in 1985 but set in the early 2000s. The novel was in response to changes in US politics with the emergence of Christian fundamentalism, the New Right. Atwood believed that society was going wrong and wrote this savage satire, similar to Jonathan Swift’s ‘A Modest Proposal’, depicting a dystopia which she uses asRead MoreEssay on Silent Spring - Rachel Carson30092 Words   |  121 Pagesoffprint from Gales For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare Contrast, What Do I Read Next?, For Further Study, and Sources.  ©1998-2002;  ©2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale a nd Design ® and

Quadcopter free essay sample

The Quad Copter presented in this project, is a type of quad rotor helicopter or quadrocopter that is lifted and propelled by four rotors. Early designs in the 1920s and 1930s suffered from poor performance and lack of stability due to limited controls and system integrations. Today with advanced electronics, accurate sensors and control system technology these limitations are becoming more a thing of the past, technology today has allowed these systems to grow more and more appealing due to increased stability and payload capacities. To overcome these obstacles, complex integration of various sensors would have to be incorporated to allow this configuration of flight to be successful, the quad copter. The overall goals of this project are the following: 1. Achieve Autonomous Take off and Landing. 2. Streamline Mechanical Construction/ Weight. 1 3. Attain a workable design that can be improved over time. The points presented above will be discussed thoroughly within this paper. 1. 2 History [1] The concept of a quad-rotor aircraft has existed since early in the 20th entury. Throughout the 20th century not many unique rotor-craft designs have been developed. The earliest workable designs for a quad-rotor were developed by George DeBothezat and Etienne Oemichen. The Oemichen‘s quad-rotor design is the earliest mention of a complete four-rotor hovering vehicle in past history. Oemichen‘s first design in 1920 failed in the initial attempt to become airborne, thereby requiring Oemichen to add additional lifting power and stability of a heliumfilled balloon. After a number of recalculations and redesigns, Oemichen was able to come up with a design that actually was capable of lift off and even established world helicopter flight records of the time, remaining airborne for up to 14 minutes at a time by 1923. Figure 1. 1 DeBothezats Quad-Rotor Design, 1922. The DeBothezat‘s design was created for a 1921 contract with the United States Air Corps as seen in Figure 1. 1. After working on his design for over 2 years, he was able to develop a fairly capable helicopter, which was able to take on a payload of up to 3 people in addition to the pilot. His design was deemed underpowered, unresponsive and susceptible to reliability issues. In 2 addition, instead of the calculated 100 meters cruising altitude, his craft was only capable of reaching a height of roughly 5meters. The early designs were propelled by additional rotors located somewhere on the rear or the front of the craft, perpendicular to the main rotors. Thus, they are not true quad-rotor designs. It was not until the mid-1950s that a true quad-rotor helicopter flew, which was designed by Marc Adam Kaplan. The prototype first flew in 1956, and did so with great success. The 2200 pounds craft was able to hover and maneuver using its two 90 horsepower motors, each capable of driving all four rotors in backup mode. Control in this case did not call for additional rotors on the sides of the craft, but was obtained by varying the thrust between rotors. This also was the first quad-rotor design that was able to fly successfully forward. Despite these early proofs-of-concepts, people saw little practical use for quad-rotors. They simply were not competitive with the performance specifications (speed, payload, range, etc. ) of more conventional aircrafts. No production contracts were awarded and interest in quad-rotors diminished. 3 1. 3 Prospective Applications [1] [6] Quad Copter designs are constantly progressing as the years go on. It wasnt too long ago that designs were limited and constrained, those days are history. The number of projects being undertaken regarding the topic has considerably increased, most of which are for commercial payload, human transport and military use. Currently Bell Helicopter Textron and Boeing Integrated Defense Systems are doing joint research and development of the Bell Boeing Quad Tilt Rotor, as depicted in Figure 1. 2. The initial design consists of four 50-foot rotors powered by V-22 engines. The main role of the Bell Boeing Quad Tilt Rotor will be that of a cargo helicopter with the ability to deliver pallets of supplies or also deploy paratroopers. The first wind tunnel tests were completed in 2006 and the first prototype is expected to be built in 2012,with great anticipation. Figure 1. 2 Bell Boeing Quad Tilt Rotor. 4 Chapter 2. Quad Copter Dynamics and Theory 2. 1 Concepts of Quad Copter Flight [3] [4] [5] Copters are one of the most complex flying machines due to versatility and maneuverability to perform a number of tasks. Classical helicopters are usually equipped with a main rotor and a tail rotor. However the UAV (Unmanned Air Vehicle) presented in this paper is known as a quad copter. Quad rotors are symmetrical vehicles with four equally sized rotors at the end of four equal length rods. By making use of multiple rotors it allows for greater thrust and maneuverability. Each of the rotors on the quad-rotor helicopter produces both thrust and torque. Given that the front and rear motors both rotate counter-clockwise and the other two rotate clockwise , resulting in a net orque of zero due to the rotational axis. Lastly, the quad rotors symmetrical design allows for easier control of the overall stability of the aircraft. Figure 2. 1 Quad Copter Torque Pattern and Movement Generality. 5 The principle for maintaining an equal rate of change for the two opposing rotors is how the translation of the craft is determined, as shown in Figure 2. 1. Due to either a pitch or a roll, the lift force is displace d in the x and y axes, resulting in a horizontal force component that will direct the craft. The altitude of the quad-rotor is altered by changing the rate of all rotors by the same amount. The UAV representation is obtained by representing the quad copter as a solid body evolving in 3D to one force with three moments (Figure 2. 2). The general coordinates of this craft are: q=(x, y, z, , ) [2. 1] Where ( x, y, z) denotes the position of the center of the mass of the craft in relation to the frame base and ( , ) denotes the three angles yaw, pitch and roll (Euler angles) and represent the orientation of the copter. Figure 2. 2 Quad Copter General Inertial Frame Coordinates. 6 2. Dynamics of a Quad Rotor The kinematic relations relate the movements and rotations in the earth-fixed inertial reference to the body-fixed reference frame. The derivatives with respect to time of the angles ( , [ in which N( , ]T = N ( , , ) , ) can be expressed in the form: [2. 2] = [p q r]T are the angular velocities with respect to the body reference frame and , ) is the 33 matrix given by: N( , , )= [2. 3] This matrix depends only on ( , singularity hold. , ) and is invertible if the boundaries on ( , , ) for non Similarly, the derivative with respect to time of the position (x, y, z) is given by: [ ]T = V0 [2. ] where V0 = [u0 v0 w0]T is the absolute velocity of the quad rotor with respect to an earth-fixed inertial reference frame. Let V = [u v w]T be the absolute velocity of the quad rotor expressed in a body-fixed reference frame. V and V0 are related by: V0 = R( , , )V [2. 5] 7 where R( , R( , , )= , ) is the rotation matrix given by: [2. 6] After the rotation matrix has been applied, the translational equations of motion with respect to an inertial frame are given by: m( ) = m( )= ) [2. 7] m( ) = Following the Euler-Lagrange equations, the rotational dynamics include torques and Coriolis terms. The coriolis term, C( , ) , defines the gyroscopic effects on the system when the craft yaws. represents the vector of torques applied to the system. = ( C( , ) ( T ) [2. 8] + C( , ) = = J + C( , ) It follows that =[ , , ]T= [2. 9] Combined with [2. 7] the translational and rotational dynamics can be summarized as = = = [2. 10] 8 Where x and y are the coordinates in the horizontal plane, and z is the vertical position and are the yaw, pitch and roll angles respectively. 2. 3 Assumptions It is not possible to create a model that conforms to reality completely. Some assumptions need to be made, in this model the following is assumed: †¢ The quad rotor structure is rigid and its deformation characteristics will be disregarded. †¢ The quad rotor structure is symmetrical and material inconsistencies will be disregarded. †¢ The propellers are rigid and deflections will be ignored. †¢ The cross products of the inertia matrix can be neglected. †¢ The ground effect is neglected. 9 Chapter 3. Control Theory 3. 1 Closed-Loop Control Systems In closed-loop control systems the difference between the actual output and the desired output is fed back to the controller to meet desired system output. Often this difference, known as the error signal is amplified and fed into the controller. The general structure of a closed-loop feedback control system is seen in Figure 3. 1. A few examples of feedback control systems are elevators, thermostats, and cruise control in automobiles. Figure 3. 1 Typical Closed Loop Control. 10 3. 2 Classical Control using PID Method [2] [15] The PID (Proportional Integral Derivative) control is one of the earlier control methods implemented. Early on its execution was in pneumatic devices in the 1940s, followed by vacuum and solid state analog electronics, before arriving at today’s digital use of microprocessors. It offered a simple control structure that was understood by operators and was relatively easy to work with. The quad rotor will use a PID system, which will be tuned to determine the optimum response and settling time, illustrated in Figure 3. 2. The PID controller equation is a closed-loop feedback system which will output a control signal u and receive feedback from the sensors. The controller will calculate the difference between the desired position and current position, adjusting u accordingly. The equation for a PID controller is as follows: = + + [3. 1] e(t) = ed(t) ea(t) Where ed denotes the desired condition, ea the actual condition, and e(t) denotes the actual difference, error, the two at each individual time step. A PID controller has proportional, integral and derivative terms that can be represented in transfer function form as K(s) = Kp + + Kds [3. 2] Where Kp represents the proportional gain, Ki represents the integral gain, and Kd represents the derivative gain, respectively. By tuning these PID controller gains, the controller can provide control actions designed for specific process requirements. The integral term Ki is proportional to both, magnitude of the error and the duration of the error. It (when added to the proportional term) accelerates the movement of the process towards the set 11 point and often eliminates the remaining steady-state error that may occur with a proportional only controller. The rate of change of the process error is calculated by determining the differential slope of the error over time (i. e. , its first derivative with respect to time). This rate of change in the error is multiplied by the derivative gain Kd. Figure 3. 2 Typical PID Control Logic. Feed-forward control plus feedback control can considerably improve performance over a simple feedback control done whenever there is a major disturbance affecting the system. In idyllic situations, feed-forward control can entirely neutralize the effect of the measured disturbance. Feed-forward control is used along with feedback control as necessary to track set point changes and to curb unmeasured disturbances that are always present in any real process. For this project, feed-forward control accounts for the behavioral dynamics of the quad copter, such as its momentum and motor response time. The integral term determines the magnitude of the accumulated error by summing the instantaneous error over time. The integral control equation is: I= Ki [3. 3] Note that t is replaced with , which denotes the past time. 12 The derivative term accounts for the rate at which the error is varying. In addition, by decreasing the rate of change close to the set point reduces overshoot and increases settling time. D = Kd P = Kp e(t) [3. 4] [3. 5] 3. Control Tuning [16] For tuning of the PID controllers, several tuning algorithms have been developed, such as Ziegler-Nichols and Lambda tuning. The Zeigler-Nichols tuning method is a heuristic method of tuning a PID controller. It was developed by John G. Zeigler and Nathaniel B. Nichols. This tuning process is the response of a plant to unit-step input. If the response results in an S-shaped curve, both time constant and delay time are determined by a differential slope line at the inflection point of the curve. When iterative tuning is used, the following algorithm can be used to et the desired overall response: 1. Investigate the step response. 2. Add gain KP to reduce the rise time tr if necessary. 3. Add gain KD to improve the maximum overshoot Mp if necessary. 4. Add gain KI to eliminate steady state error ess if necessary. 5. Adjust gains till desired overall response is obtained. 13 The transfer function of this method equals: = [3. 6] The values of Kp, Ti, and Td are determined by the factors in Table 3. 1. This method demonstrates improvement in contrast to traditional manual tuning, but still is difficult to set exact values to critical gain. Table 3. Values Set by Zeigler-Nichol Tuning Method. Type of Controller P PI PID Kp T/L 0. 9 T/L 1. 2 T/L Ti ? L/0. 3 2L Td 0 0 0. 5 L 3. 31 Vertical Position Control When operating above the ground effect, the control output U1 is approximately proportional to the vertical acceleration in the body reference frame. To remain at constant height, a large value of U1 is required to counteract gravity, additionally a PID controller is added to stabilize the motion in the z direction (Figure 3. 3). The control law can be described by: r1 = U1 = zp (z zd) KZI ) [3. 7] Figure 3. 3 Vertical Position Controller [1]. 14 3. 2 Horizontal Position Control The horizontal position (x, y) of the quad rotor is controlled by adjusting the roll and pitch. The total thrust produces a lift acceleration approximately equal to the gravity (g) in a direction normal to the plane of the rotors (Figure 3. 4). A small angle of roll acceleration ? g. results therefore in a lateral The commands in x and y direction are described by: Ux = Uy = P( d) KxI KyI ) ) [3. 8] yP (y yd) Corrected for the yaw angle they give the commands for the desired roll and pitch angle: d= d= Ux + Ux + Uy Uy [3. 9] Figure 3. 4 Horizontal Position Controller [1]. 3. 3 Roll and Pitch Position Control Because the quad rotors layout is symmetrical the roll and pitch control can be assumed independent for small attitude angles (Figure 3. 5). Relative to the yaw control a higher bandwidth is required, since the value has a direct relationship to the lateral acceleration in x and y direction. U2 = P( d) ) 15 U3 = P( d) ) [3. 10] Figure 3. 5 Roll Position Controller [1]. 3. 34 Yaw Position Control The yaw is the least critical of the controls since it has no direct effect on the quad rotors motion. It can be independently tested and tuned, while having manual control in the remaining channels (Figure 3. ). The PID control law for yaw is described by the following equation: U4 = P( d) I ) [3. 11] Figure 3. 6 Yaw Position Controller [1]. 3. 4 Rotor Theory Unlike other helicopters which require complex mechanical rotor mechanisms to control the pitch of the blades, a quad-rotor relies solely on differential torque and thrust, and thus uses fixed-pitch blades. One of the goals of the project is to increase total thrust; increasing thrust is accomplished by increasing the velocity of the air being moved by the rotor, or by increasing the amount of air being moved by the rotors. 3. 12] 16 Where T is the thrust, is the mass airflow, and u9 and u0 are the outgoing and incoming velocities, respectively. From a simple physics perspective, using the kinetic energy equation: [3. 13] Doubling the thrust by double m would lead to double the energy required. Doubling the thrust from doubling differential velocity would require four times the energy. The design of propellers is a complex subject, and as there were already dozens of readily available propellers on the market, it was both cost and time e ffective to select a commercial blade. The propellers are designed for radio control applications, and their airfoils are highly proprietary. The standard measure of propellers is diameter x pitch, where pitch refers to the angle of incidence at ? of the radius. Using this angle, the pitch is converted to inches by how far the propeller would move after one revolution if it were â€Å"screwed† into a solid substance. 17 Chapter 4. Electrical Control Systems 4. 1 The Microcontroller Arduino ATMega 2560 [8] The microcontroller we decided to utilize in our project was the Arduino Mega 2560, after careful review of several models. Considering that this single part is the heart of the project we selected with special care to characteristics like connectivity, available I/O and broad power integration. The microcontroller offered all the features we needed to develop the quad copter, with the characteristics we desired. It is based on Atmels ATMega 2560 microcontroller. The board comes with 54 digital input/output pins, 16 analog inputs, 4 UARTs (hardware serial ports), a 16 MHz crystal oscillator, a USB connector, and a power jack. The operating voltage of the microcontroller is 5V, with an input voltage of 7 to 12V. The ATMega 2560 has a flash memory of 256 KB, of which 8 KB are reserved for the boot loader. 8 KB of SRAM, 4 KB of EEPROM, and a clock speed of 16 MHz. The Arduino Mega 2560 can be powered through a USB connection or with an external power supply. Additionally, the Arduino platform was particularly attractive because of its open-source physical computing platform based on a simple i/o board and a development environment that implements the Processing/Wiring and language, seen below in Figure 4. 1. Figure 4. 1 Arduino Mega 2560 Microcontroller Board. 18 The ATMega 2560 comes with an Atmel AVR core which combines a wide instruction set with 32 general purpose working registers. All 32 registers are directly coupled to the ALU (Arithmetic Logic Unit), allowing two independent registers to be accessed in one single execution of the instruction per clock cycle. In order to maximize parallelism, the AVR uses a Harvard architecture – with separate memories and buses for program and data. Figure 4. 2 shows the block diagram of the AVR architecture. Figure 4. 2 Arduino Mega 2560 Microcontroller Block Diagram. 19 . 2 Electronic Speed Controllers An electronic speed control or ESC is a circuit with the purpose to control an electric motors speed, its direction and possibly also to act as a dynamic brake in some cases. ESCs are often used on electrically powered brushless motors essentially providing an electronically-generated three phase electric power, with a low voltage source. An ESC interprets control information in a way that var ies the switching rate of a network of field effect transistors (FETs), not as mechanical motion as would be the case of a servo. The quick switching of the transistors is what causes the motor itself to emanate its characteristic highpitched whine, which is especially noticeable at lower speeds. It also allows much smoother and more precise variation of motor speeds in a far more efficient manner than the mechanical type with a resistive coil and moving arm once in common use. The ESC generally accepts a nominal 50 Hz Pulse Width Modulation (PWM) servo input signal whose pulse width varies from 1ms to 2ms. When supplied with a 1ms width pulse at 50 Hz, the ESC responds by turning off the DC motor attached to its output. A 1. 5ms pulse-width input signal results in a 50% duty cycle output signal that drives the motor at approximately 50% speed. When presented with 2. 0ms input signal, the motor runs at full speed due to the 100% duty cycle (on constantly) output. The correct phase varies with the motor rotation, controlled and monitored by the ESC. The orientation of the motor is determined by the back EMF (Electromotive Force). The back EMF is the voltage induced in a motor wire by the magnet spinning past its internal coils. Finally, a PID algorithm in the controller adjusts the PWM to maintain a constant RPM. Reversing the motors direction may also be accomplished by switching any two of the three leads from the ESC to the motor. 20 4. 21 Turnigy Plush 18A ESC Modules [13] [14] The ESC controller chosen for this project was the Turnigy Plush 18A series, shown in Figure 4. 3. Many considerations had to be made in making the appropriate selection. Ideally the ESC controller should be paired to the motor and rotor craft with the following considerations. 1. Temperature and thermal characteristics. 2. Max Current output and Impendence. 3. Needs to be Equipped with a BEC (Battery Eliminator Circuit) to eliminate the need of a second battery. 4. Size and Weight properties. 5. Magnet Rating. The Plush series Turnigy ESCs offered several outstanding performance features that fulfilled our needs, fast sync timing, a generous current rating and a small size to weight footprint (Table 4. 1). Specifications as follows: Table 4. 1 Turnigy Plush18A Specifications. Continuous Current Rating Burst Current Rating BEC Mode BEC LiPo Cells Weight Size 18 Amp 22 Amp Linear 5V/ 2 Amp 2-4 Cells 19 grams 24x45x11mm Additionally, the speed controller has fixed throttle settings so that the stop and full throttle points of all the various modes which can be cut through cleanly. The controller produces audible beeps to assist in navigating through the program modes and troubleshooting logs. 21 Figure 4. 3 Turnigy Plush18A ESC Packs. 4. 3 The Battery Pack Selecting the proper battery for our rotor copter was a challenging task. Nickel Cadmium (NiCd), Nickel Metal Hydride (NiMH), and Lithium Polymer (LiPo) were common choices with the advantages and disadvantages of each battery pack. NiCd batteries are reasonably inexpensive, but they have a number of negatives. NiCd batteries need to be fully discharged after each use. If they aren’t, they will not discharge to their full potential (capacity) on following discharge cycles, causing the cell to develop what’s commonly referred to as a memory. Additionally, the capacity per weight (energy density) of NiCd cells is commonly less than NiMH or LiPo cell types as well. Finally, the Cadmium that is used in the cell is quite destructive to the environment, making disposal of NiCd cells an issue. NiMH cells have many advantages over their NiCd counterparts. NiMH cell manufacturers are able to offer significantly higher capacities in cells approximately the same size and weight of equivalent NiCd cells. NiMH cells have an advantage when it comes to cell memory as well, as they do not develop the same issues as a result of inappropriate discharge care. Lithium Polymer (LiPo) cells are one of the newest and most revolutionary battery cells available. LiPo cells maintain a more consistent voltage over the discharge curve when compared to NiCd or NiMH cells. The higher nominal voltage of a single LiPo cell (3. 7V vs 1. 2V for a typically NiCd or NiMH cell), making it possible to have an equivalent or even higher total 22 nominal voltage in a much smaller package. LiPo cells typically offer very high capacity for their weight, delivering upwards of twice the capacity for ? the weight of comparable NiMH cells. Lastly, a LiPo cell battery needs to be carefully monitored during charging since overcharging and the charging of a physically damaged or discharged cell can be a potential fire hazard and possibly even fatal. LiPo Pros: ? ? Highest power/weight ratio. Very low self-discharge. Less affected by low temperatures than some. LiPo Cons: ? ? ? Intolerant of over-charging. Intolerant of over-discharging. Battery. Significant fire risk. Figure 4. 4 Zippy 4000 mAh 4. 31 Zippy 4000mAh Battery Pack Module [17] Considering our copters weight, current load and predicted discharge rates, the Zippy 4000mAh battery pack seemed to fit the bill (Figu re 4. 4). The Zippy 4000mAh battery pack offered the following characteristics seen in Table 4. 2: Table 4. 2 Zippy 4000 mAh Battery Specifications Table. Capacity Voltage Discharge Weight Dimensions Balance Plug Discharge Plug Max Charge Rate 4000 mAh 3 Cell 11. 1 V 20C Constant 30C Burst 306 grams 146x51x22mm JST-XH Bullet Connector 2C 23 To approximately calculate the run time, the following equation was used: Run Time (Mins) = Battery mAh Rating [4. 1] Considering the average hovering current consumed by the motors is 12Amps per motor. We were able to calculate a min run time of 5 minutes and a max run time of 10 minutes, which was sufficient in our case, since we would be running at reduced speeds for testing with spare batteries. . 4 The Gyroscope Transducer A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. A MEMS gyroscope takes the idea of the Foucault pendulum and uses a vibrating element, known as a MEMS (Micro Electro-Mechanical System). These typically are packaged similarly to other integrated circuits and provide either analog or digital outputs. In addition, they are inexpensive and have become widely available today. They provide accurate 3 axis positioning of a craft and are highly reliable over the years with no internal moving parts. 4. 1 ITG3200 Gyro Module [11] The Gyro Sensor chosen for this project was the ITG 3200 by Invensense (Figure 4. 5). The ITG3200 featured a three 16-bit analog-to-digital converters (ADCs) for digitizing the gyro outputs, a user-selectable internal low-pass filter bandwidth, and a Fast-Mode I2C (400kHz) interface as shown in the block diagram below (Figure 4. 6). In addition it included a embedded temperature se nsor and a 2% accurate internal oscillator. 24 The ITG-3200 had a wide power supply range of anywhere between 2. 1 and 3. 6V with a low operating current of 6. 5mA. The sensor also featured a interrupt output, and an optional clock input. Figure 4. 5 ITG 3200 Gyro Board. Figure 4. 6 ITG 3200 Gyro Functional Block Diagram. The ITG-3200 detects the rotational rate of the x, y, and z axes for roll, pitch, and yaw respectively. This is achieved through its three independent vibratory MEMS gyroscopes. When 25 the gyros are rotated about any of the sense axes, it causes a deflection that is detected by a capacitive pickoff. 4. 5 The Accelerometer Sensor An accelerometer is a device that measures proper acceleration by measuring weight per unit of mass, a quantity of force, or g-force (although it is not a force). Consequently, by measuring weight, an accelerometer measures the acceleration of the free-fall reference frame (inertial reference frame) relative to itself (the accelerometer). Single- and multi-axis models of accelerometers are available to detect magnitude and direction of the proper acceleration (or g-force), as a vector quantity, and can be used to sense orientation, coordinate acceleration (so long as it produces g-force or a change in g-force), vibration, shock, and falling (a case where the proper acceleration changes, since it tends toward zero). Micro machined accelerometers are increasingly present in modern electronic devices, to detect the position of the device or provide for the game system input. Pairs of accelerometers extended over a region of space can be used to detect differences in the proper accelerations of frames of references associated with those points. 4. 51 BMA180 Accelerometer Module [12] The Accelerometer Sensor chosen for this project was the BMA180 by Bosch (Figure 4. 8). The Bosch BMA180 three-axis, high performance digital accelerometer was chosen because of its superior variable characteristics. The BMA180 provides a digital 14-bit output signal via a 4-wire SPI or I2C interface. The full-scale measurement range can be set to A ±1g, 1. 5g, 2g, 3g, 4g, 8g or 16g. 26 The sensor also has two operating modes consisting of low-noise and low-power. The input power supply voltage should be between 1. 62 and 3. 6V for VDD and 1. 2 to 3. 6V for VDDIO. The sensor will typically only consume 650uA in standard mode. Figure 4. 7 BMA180 Accelerometer Block Diagram. As seen in Figure 4. 7 the BMA180 diagram shows: 1. The micromechanical g-sensors elements which measure acceleration in the x,y and z directions. . The front end circuit including pre amplifiers and multipelxers. 3. The 14 bit Analog to digital controller. 4. The Interrupt generator and output interface. Figure 4. 8 BMA180 Accelerometer Board. 27 4. 6 The Barometer Transducer Bosch BMP085 [9] A barometer is a scientific instrument used to measure atmospheric pressure (Figure 4. 9). We chose Bosch’s BMP085 Digital Bar ometric Pressure sensor for this project. The ultra-low power and low voltage electronics of the BMP085 are ideal for navigation devices. With a low altitude noise of merely 0. 5m at fast conversion time, the BMP085 offers superior performance for an application such as ours. It comes equipped with I2C capabilities for easy system integration with microcontrollers and offers a measuring range of 300 to 1100 hPa with an absolute accuracy of down to 0. 03 hPa. This sensor supports a voltage supply between 1. 8 and 3. 6VDC. Figure 4. 9 BMP085 Barometer Board. 4. 61 Barometric Pressure in Altimetry Barometric pressure has a measurable relationship with altitude, meaning you can use the BMP085 to deduce how high the quad copter has climbed. At sea level the air pressure is on average 1013hPa. The measuring limits of the BMP085 should allow us to measure pressure at elevations anywhere between -1640 to about 29,000 ft above sea level. 28 Figure 4. 10 BMP085 Barometer and Altitude Relationship. With the measured pressure p and the pressure at sea level p0, the altitude in meters can be calculated with the international barometric formula. p0 is the average pressure at sea level (1013hPa), and p is the pressure that we measured. This relationship is observed in Figure 4. 10. Note that this equation gives you altitude in units of meters. Altitude (meters) = 44330 [4. 2] 4. 7 The Brushless Motors Each of the four rotors comprises of a Brushless DC Motor attached to a propeller. The Brushless motor differs from the conventional Brushed DC Motors in their concept essentially in that the commutation of the input voltage applied to the armatures circuit is done electronically, whereas in the latter, by a mechanical brush. As any rotating mechanical device, it suffers wear during operation, and as a consequence it has a shorter nominal life time than the newer Brushless motors. In spite of the extra complexity in its electronic switching circuit, the brushless design offers several advantages over its counterpart, to name a few: higher torque/weight ratio, less operational noise, longer lifetime, less generation of electromagnetic interference and much more 29 power per volume. Virtually limited only by its inherent heat generation, whose transfer to the outer environment usually occurs by conduction. 4. 71 KDA20-22L Brushless Motors [10] The KDA Brushless motors were chosen for our copter because of their superior specifications (Table 4. ), weight, power output and availability (Figure 4. 11) . Additionally, this motor offered a wide variety of securing provisions which was extra helpful in its mounting and use. Table 4. 3 KDA 20-22L Brushless Motor Specifications. Kv (rpm/v) Weight Max Current Max Voltage Motor Length Motor Diameter Total Length 924 56 grams 17 Amps 11V 32mm 28mm 46mm Figure 4. 11 KDA 20-22L Brushless Motor. 30 Figure 4. 12 Quad Copter H ardware Block Diagram. Figure 4. 13 Quad Copter As Constructed. 31 4. Software Development General Concepts All of the electrical hardware components previously mentioned provide the necessary ground work for the software subsystems to allow the copter to function as desired, as depicted in block diagram Figure 4. 12. The software plays one of the most important roles controlling and facilitating the features of the device discussed in this paper. All of the inputs from the various sensors gyroscope, accelerometer and barometric sensor are to be taken and evaluated by the microcontroller to facilitate flight (Figure 4. 13). The goal of this project is to successfully achieve unmanned flight by simply hovering and landing. The quad copter must be able to take off from a stationary position to a hovering state and then land once again using the following organization illustrated in Figure 4. 14. Figure 4. 14 Software Architecture Organization. 4. 81 Operating Modes of Flight The quad copter has three main operating states known as, take off, hover and land. These states together form what is known as VTOL (Vertical Takeoff Landing) with characteristics shown in Figure 4. 5. 32 The Take Off stage involves several procedures, which include motor/ESC initializations, data acquisition of the attached sensors and any human input. If after evaluating this data the quad copter senses that it has not met the necessary criteria it will slowly ramp up the necessary motor thrust until it reaches the desired set point while the microcontroller is verifying the sensor data. When the actual altitude equals the desired position, the quad copter can now go to hovering mode. Hovering is the most challenging component of flying any copter. While in the hovering stage, the copter must take into account many factors that assist the craft in steady flight. Among the most common causes for a quad copter to not perform sufficiently is drifting in the horizontal plane. Movements in all four directions such as forward, back, right, and left, are consequences of drifting, accumulation of small errors in various values leading to uncontrollable oscillations which have to be accounted for. Landing is the final stage of flight, the landing process is the opposite of the take off phase. The system checks for x and y levels; if they are leveled, the altitude is checked. At this point, the acquired value is checked with the ground level. If the acquired values are not at ground level, thrust from all motors are decreased and decelerated until the ground level is reached, only then will the system halt activity. 33 Figure 4. 15 Quad Copter Operating Modes Of Flight. 4. 2 Position Flight Control Position control is currently implemented using a PID controller design which actuates the vehicle’s roll and pitch as control inputs. Tilting the vehicle in any direction causes a component of the thrust vector to point in that direction, so commanding pitch and roll is directly analogous to commanding accelerations in the X-Y plane. However, the current control implementation has little ability to reject 34 disturbances from wind and translational velocity effects. For this scale aircraft, even mild winds can cause large disturbances. A key weakness of this and similar position controllers used is the assumption that the velocity of the free stream and attitude control are decoupled. This is in fact only true for very small velocities. 4. 83 Kalman Filter Design[7] A Kalman filter is used to reduce the error in tracking. The Kalman filter operates by predicting the next value from the current value and the previous value. This is then corrected once the next measurement is taken to be between the measurement and the predicted value. This reduces the influence of noise on the measurement of the position. Over time errors in measurements tend to accumulate causing the sensors inefficiencies for long term measurements and thus they tend to drift. The ideal solution to the problem described above would be combining both, gyroscope and accelerometer data values resulting in the offset of the deficiencies of each with the strengths provided by the two sensors. Kalman filtering is an iterative approach that requires two varying input values. At every iteration, the Kalman filter will change the variables in the linear model, so the output of the model will be closer to the second input (Figure 4. 16). For the project, two inputs will consist of the gyroscope and accelerometer data, the model using the gyroscope data looks like: ) [4. 3] Since individual applications are favored and computed, equations for the filter in one dimension are required. Equations [4. 3] are reduced for the latter two dimensions. Where, K is the Kalman gain, P 35 s the estimation error covariance, measurement. is the filtered value, S is the sensor noise, and z is the The process noise p is reduced gradually, when tuning the filter for optimal performance. Concurrently, sensor noise S is increased until a satisfactory speed/noise level is achieved. Figure 4. 16 Kalman Filter Recursive Algorithm. 36 Chapter 5. Structural and Mechanical Approaches 5. 1 The Frame of the Quad Copter Typical quad-rotors utilize a four-spar method, with each spar anch ored to the central hub like the spokes on a wheel. The frame of the quad copter is composed of a combination of materials chosen for their strength, weight and flexibility. When designing an autonomous quad-rotor, there are several material options which must be considered. When designing a machine capable of flight, weight must be greatly well thought-out. The materials considered for our project aluminum, plastic, and carbon fiber. Historically, aluminum historically, has been the material of choice for RC helicopters. Aluminum is light and strong, dissipates heat well, and is relatively inexpensive compared to the other