Premium Essay

Fundamentals of Systems - Iii

In: Science

Submitted By nareshshah139
Words 1412
Pages 6
Homework 1 - ECES 513 Fundamentals of Systems - III
Naresh Shah, Pranav Ram Kamarajugadda May 2, 2014
Problem 1. A serial robot can be described as a set of n coupled links parameterized by a vector of co-ordinates x = (x1 , x2 ...., xn ), with n µ(x)ij j=1 d2 xj dt2

n

= F (x, x, x)i + ˙ ¨ n j=1 n

Kij (xj − xj,0 ) Kij (xj − xj,0 )

τij xj = ¨ j=1 j=1

where µ(x) is a mass matrix, τ is an inertia matrix, F (x, x, x) is a vector of generalized ˙ ¨ resultant forces, x0 = (x1,0 , x2,0 ....xn,0 ) is a reference configuration and K is a matrix of joint stiffnesses. Select state variables for the system and write down the state equations. Under what conditions is the system linear? Proof. Assuming a two-link system: Let y1 = x1 , y2 = x1 , y3 = x1,0 , y4 = x1,0 be the state ˙ ˙ variables of the manipulator. Then, y 1 = x1 y2 = −µ−1 (x1 )[F (x1 , x1,0 ) + K(x1 − x1,0 )] y3 = x1,0 y4 = τ −1 K(x1 − x1,0 ) + τ −1 u where u is the input vector.

1

Problem 2. Analyze the following equations graphically. In each case sketch the vector on the phase plane, find all the fixed points, classify their stability, and sketch the graph for different initial conditions.Attempt to obtain the analytical solution for x(t). • x = − sin(x) ˙ • x = x − x3 ˙ • x = e−x sin(x) ˙ Proof. .... 1. x = − sin(x) ˙

1 sin x sin x − sin x = − sin x2 = − 1−cos x2

⇒ Let u = cos x ⇒ du = − sin xdx ⇒ du 1−u2

→ −0.5 ln |u − 1| + 0.5 ln |u + 1|

Analytical Solution is ⇒ t = −0.5 ln | cos x − 1| + 0.5 ln | cos x + 1| Fixed points for this differential equation are the points where x = 0 are at x0 = nπ. ˙ Intuitively, when n = even, the solution is ‘stable’. When n=odd, the pendulum is inverted, and hence ‘unstable’.

2

2. x = x − x3 ˙

1 x−x3 1 ⇒ (x + x ) 1−x2

=

1 x(1−x2 )

=

1 x

+

x 1−x2

= ln |x| + 0.5 ln |1 − x| − 0.5 ln |1 + x|

The analytical

Similar Documents

Premium Essay

Organization Behaviour

...1. Define OB 2. Goal of OB 3. List the fundamental concept of OB 4. What are the key forces of OB 5. Explain how the study of the fundamental concept of organizational behavior can help better manage their people at work 6. Name the different models of organizational behavior with a description of any one. 7. Why managers need to study OB 1. Define OB * Organisational behavior is the systematic study and careful application of knowledge about how people-as individual and as groups –act within organsiastions. * OB is a field of study that investigates the impact that individuals, groups and structure have on behavior within organisations for the purpose of applying such knowledge towards improving an orgnasiation’s effectiveness. 2. Goal of OB Leaders must be able to: i. Describe ii. Understand iii. Predict iv. Control individual behavior in the organisation * Describe: * OB is a science that analyses as to how people behave in different situations in the organisation. A manager should be able to describe the behavior of each individuals under his command. 3. List the fundamental concept of OB Fundamental concepts of OB The nature of people i) Individual differences ii) Perception Iii) A whole person Iv) Motivated behavior V) Desire for involvement Vi) Value of the person The nature of organisation i) Social systems ii) Mutual interest iii) Ethics i) Individual differences : * People have much in common (excitement in any achievement) but each person...

Words: 985 - Pages: 4

Free Essay

Software

...JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD M. TECH (REAL TIME SYSTEMS) COURSE STRUCTURE AND SYLLABUS I YEAR I SEMESTER Code Group Subject L P Credits Advanced Computer Architecture 3 0 3 Advanced Micro Controllers 3 0 3 Fundamentals of Real Time Systems 3 0 3 Design & Development of Real Time Systems 3 0 3 Elective -I Digital Control Systems Distributed Operating Systems Cloud Computing 3 0 3 Elective -II Digital Systems Design Fault Tolerant Systems Advanced Computer Networks 3 0 3 Lab Micro Processors and Programming Languages Lab 0 3 2 Seminar - - 2 Total Credits (6 Theory + 1 Lab.) 22 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD MASTER OF TECHNOLOGY (REAL TIME SYSTEMS) I SEMESTER ADVANCED COMPUTER ARCHITECTURE UNIT I Concept of instruction format and instruction set of a computer, types of operands and operations; addressing modes; processor organization, register organization and stack organization; instruction cycle; basic details of Pentium processor and power PC processor, RISC and CISC instruction set. UNIT II Memory devices; Semiconductor and ferrite core memory, main memory, cache memory, associative memory organization; concept of virtual memory; memory organization and mapping; partitioning, demand paging, segmentation; magnetic disk organization, introduction to magnetic tape and CDROM. UNIT III IO Devices, Programmed IO, interrupt driver IO, DMA IO modules, IO addressing; IO channel...

Words: 3183 - Pages: 13

Free Essay

Mumbai University

...Science of University of Mumbai | Ist Year IInd Year IIIrd Year | Syllabus of Ist Year - Bachelor of Science (BSc) of University of Mumbai | Ist Year | Paper I Section 1 - Computer Organisation Section 2 - Ms-Windows and Ms-office Paper II Section 1 - Programming techniques and Algorithms through C Section 2 - Networking and Internet fundamentals | | Syllabus of IInd Year - Bachelor of Science (BSc) of University of Mumbai | Paper I Section 1 - Data structures with advanced C Section 2 - Event drive programming using Visual Basic Paper II Section 1 - Numerical Analysis with "C" Section 2 - Introduction to Java Paper III Section 1 - Introduction to file and Database Management Systems Section 2 - Principles of Rational Database Management System | Syllabus of IIIrd Year - Bachelor of Science (BSc) of University of Mumbai | Paper I Section 1 - System Software Section 2 - Data Communication and Networking Paper II Section 1 - Advanced Java 1 Section 2 - Advanced Java 2 Paper III Section 1 - Operating Systems Section 2 - The Linux OS Paper IV Section 1 - Structured System Analysis and Design Section 2 - Object Oriented Analysis and Design and Software Engineering Concepts Applied Components: Web Design and Applications Paper I - Principles of Web Design Paper II - Web Technologies | BSC-IT Syllabus (http://eduvark.com/bsc-syllabus-mumbai-university-31903.html) #2 April 5th, 2013, 09:53 AM | Rohit Barla Super...

Words: 502 - Pages: 3

Free Essay

Syllabus

...SCHEME OF EXAMINATION FOR MASTER OF COMPUTER APPLICATIONS (MCA) (SIX-SEMESTER Programme) |Semester – I | |Paper |Title of the Paper |Duration |Maximum Marks |Total | |No. | |Of Exam | | | | | | |Theory |Sessional* | | |MCA-101 |Computer Fundamentals and Problem Solving Using C |3 Hours |80 |20 |100 | |MCA-102 |Computer Organisation |3 Hours |80 |20 |100 | |MCA-103 |Discrete Mathematical Structures |3 Hours |80 |20 |100 | |MCA-104 |Software Engineering |3 Hours |80 |20 |100 | |MCA-105 |Computer Oriented Numerical and Statistical Methods |3 Hours |80 |20 |100 | |MCA-106 |Software Laboratory - I |3 Hours | | |100 | | |C (Based on MCA-101) |...

Words: 13848 - Pages: 56

Premium Essay

Cma Syllabus 2012

...the institute of cost accountants of india(ICAI) (A Statutory body under an act of parliament) SYLLABUS 2012 STRUCTURE & contents  Evaluation  Synthesis  ANALYSIS  ANALYSIS  APPLICATION  APPLICATION  COMPREHENSION  COMPREHENSION  COMPREHENSION  KNOWLEDGE  KNOWLEDGE  KNOWLEDGE LEVEL A LEVEL B LEVEL C FOUNDATION COURSE - Syllabus 2012 the institute of cost accountants of india(ICAI) (A Statutory body under an act of parliament) SYLLABUS 2012 STRUCTURE & contents The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 1 FOUNDATION COURSE - Syllabus 2012 The Following table lists the learning objectives and the verbs that appear in the syllabus learning aims and examination question. Learning objectives Level A COMPREHENSION What you are expected to understand List Make a list of. State Express, fully or clearly , the details/ facts of. Define Give the exact meaning of. Communicate the key features of. Distinguish Highlight the differences between. Explain Make clear or intangible/state the meaning or purpose of. Identify Recognise, establish or select after consideration. Illustrate What you are expected to know Definition Describe KNOWLEDGE Verbs used Use an example to describe or explain something. The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) ...

Words: 18528 - Pages: 75

Premium Essay

Data Communication and Networking

...SEMESTER III |SL. |COURSE CODE |COURSE TITLE |L |T |P |C | |NO | | | | | | | |THEORY | |1 |MC9231 |Computer Networks |3 |0 |0 |3 | |2 |MC9232 |Microprocessors and its |3 |0 |0 |3 | | | |Applications | | | | | |3 |MC9233 |Software Engineering |3 |0 |0 |3 | |4 |MC9234 |Computer Graphics |3 |0 |0 |3 | |5 |MC9235 |Web Programming |3 |0 |0 |3 | |PRACTICAL | |6 |MC9237 |Graphics Lab |0 |0 |3 |2 | |7 |MC9238 |Microprocessor Lab |0 |0 |3 ...

Words: 1592 - Pages: 7

Premium Essay

My Essay

...CECS 6605 Advanced Database Systems Assignment 1 Deadline: September 8, 2013 Part I. Entity Relationship Diagrams (ERD) Database Design Using Entity-Relationship Diagrams (2003) by Sikha Bagui and Richard Earp Auerbach Publications ISBN:0849315484 Chapter 1 (Database Design Using Entity-Relationship Diagrams) * Checkpoint 1.1, Problem 1; pp. 13-14 * Checkpoint 1.3, Problem 1, 3; pp. 25 Chapter 2 (Database Design Using Entity-Relationship Diagrams) * Checkpoint 2.1, Problems 1, 3, 5, 7; pp. 39 * Checkpoint 2.3, Problems 1, 3; pp. 61 Chapter 3 (Database Design Using Entity-Relationship Diagrams) * Checkpoint 3.1, Problems 1, 3, 5; pp. 78 Chapter 4 (Database Design Using Entity-Relationship Diagrams) * Checkpoint 4.1, Problems 1, 3, 5; pp. 99 * Checkpoint 4.3, Problems 1, 3; pp. 117 Part II. SQL A Guide to SQL (2008) by Philip J. Pratt and Mary Z. Last Use only Oracle for this part. Please show the complete question, query used, and print the query results. Do the exercises from the Henry Books Database. Chapter 1 (A Guide to SQL, Henry Books) * Exercises - odd numbers Chapter 2 (A Guide to SQL, Henry Books) * Exercises - odd numbers Chapter 3 (A Guide to SQL, Henry Books) * Exercises - odd numbers Chapter 4 (A Guide to SQL, Henry Books) * Exercises - odd numbers Part III. Database System Fundamentals Fundamentals of Database Systems (2011) by Ramez Elmasri; Shamkant B. Navathe ...

Words: 352 - Pages: 2

Free Essay

India

...India is often hailed as the world’s largest democracy.1 At the core of that democracy is a thriving, independent judicial system that has been an important engine of social change and development.2 Yet, despite possessing a well-developed system of law inherited from British colonial rule,3 for the first fifty years following independence * Milan Dalal is the Executive Note Editor for the Boston College International & Comparative Law Review. 1 See, e.g., Ramachandra Guha, India After Gandhi: The History of the World’s Largest Democracy (2004) (discussing history of India and its democratic nature). 2 Justices of the Indian Supreme Court are chosen on the basis of seniority and free of political considerations at the behest of the President with consultation from the Chief Justice. The Chief Justice is appointed by the President. 3 See Cent. Intelligence Agency, World Fact Book: India, https://www.cia.gov/library/ publications/the-world-factbook/geos/in.html#Govt (last visited May 15, 2008) (noting India’s legal system is “based on English common law”); see also Rahul Mehrotra & Sharada Dwivedi, The Bombay High Court: The Story of the Building—1978–2003, at 15 (2004) (“[F]irst official British Court of Justice [of Bombay] was inaugurated . . . on 8 August 1672.”). India has possessed an organized system of appellate review since at least 1861, when British Parliament passed the India High Courts Act, allowing appeal from regional high courts to the...

Words: 1497 - Pages: 6

Premium Essay

Paper

... and y be Boolean variables where the value of x is 1. For each of the following Boolean expressions, determine, if possible, the value of the expression. If you cannot determine the value of the expression, then find the number of assignments of values for w and y that will result in the value 1 for the expression. a) x + xy + w b) xy + w * c) xy + xw d) xy + w * 4. a) Find the fundamental conjunction made up from the variables w, x, y, z, or their complements, where the value of the conjunction is 1 precisely when i) w = x = 0, y=_ z = 1. ii) w = 0, x = 1, y = 1, z = 0. iii) w = 0, x = y = z = 1. iv) w = x = y = z = 0. b) Answer part (a) this time for fundamental disjunctions, instead of fundamental conjunctions, where the value of each fundamental disjunction is 0 precisely for the stated values of w, x, y, z. 5. Suppose that f : B3 →B is defined by f (x, y, z) = (x + y) + (xz). a) Determine the d.n.f. and c.n.f. for f . b) Write f as a sum of minterms and as a product of maxterms (utilizing binary labels). * 9. Let Bn →B. If the d.n.f. of f has m fundamental conjunctions and its...

Words: 523 - Pages: 3

Premium Essay

Senior Systrem Engineer

...College of Information Systems & Technology Bachelor of Science in Information Technology with a Concentration in Information Management The Bachelor of Science in Information Technology (BSIT) degree program is focused on the acquisition of theory and the application of technical competencies associated with the information technology profession. The courses prepare students with fundamental knowledge in core technologies, such as systems analysis and design; programming; database design; network architecture and administration; web technologies; and application development, implementation, and maintenance. This undergraduate degree program includes 45 credits in the required course of study and 15 credits in the concentration. Some courses have prerequisites. In addition, students must satisfy general education and elective requirements to meet the 120-credit minimum, including a minimum of 48 upper-division credits required for completion of the degree. At the time of enrollment, students must choose a concentration. The Information Management concentration is designed to provide coverage of the collection, architecture, modeling, retrieval and management of data for meaningful presentation to the organization. This concentration prepares students to develop, deploy, manage, and integrate data and information systems to support the organization. Note: The diploma awarded for this program will read: Bachelor of Science in Information Technology and will not reflect the concentration...

Words: 1892 - Pages: 8

Premium Essay

Tech Analysis

...1. System Construction         A. Profile:               i. State and explain your investing/trading strategy, philosophy and theory underpinning your system. (It is essential that this is consistent with the scenario selected). First of all, the scenario we choose is being individual investor. Generally, our investing strategy combines both fundamental analysis and technical analysis. For example, we plan to use high share price relative strength, volume and MACD as well as low P/E ratio, Earning persistency, low P/B ratio indicators since the mixing growth and value strategies could not only reducing the volatility of strategies based on growth alone but also increasing the capital appreciation potential of strategies. Therefore, we believe the mixing strategies could help us to make fewer mistakes, increase probability to maximize our absolute returns through the years and also outperform buy and hold after expenses. Moreover, we will use fundamental methods to calculate an accurate proportion for the amount of money we put in each stock in order to well diversify risks and max net profit. For the philosophy, we believe that markets are efficient, prices move in trends and history repeats itself from technical analysis aspect. Moreover, even though fundamental analysis is worthless somehow, low P/B, P/E, P/CF and high yield show otherwise.             ii. What is your approximate expected time horizon/holding period per trade? The holding period per trade...

Words: 2109 - Pages: 9

Premium Essay

Director

...Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition III. Valuation of Future Cash Flows 8. Stock Valuation © The McGraw−Hill Companies, 2002 273 CHAPTER Stock Valuation 8 When the stock market closed on July 3, 2001, the common stock of McGrawHill, publisher of fine-quality college textbooks, was going for $67.40 per share. On that same day, stock in General Motors (GM), the world’s largest automaker, closed at $64.72, while eBay, the on-line auction company, closed at $69.16. Since the stock prices of these three companies were so similar, you might expect that the three companies would be offering similar dividends to their stockholders, but you would be wrong. In fact, GM’s annual dividend was $2.00 per share, McGraw-Hill’s was $0.98 per share, and eBay was paying no dividends at all! As we will see in this chapter, the dividends currently being paid are one of the primary factors we look at when attempting to value common stocks. However, it is obvious from looking at eBay that current dividends are not the end of the story, so this chapter explores dividends, stock values, and the connection between the two. I n our previous chapter, we introduced you to bonds and bond valuation. In this chapter, we turn to the other major source of financing for corporations, common and preferred stock. We first describe the cash flows associated with a share of stock and then go on to develop a very famous result, the dividend growth...

Words: 12686 - Pages: 51

Premium Essay

Saloni

...FUNDAMENTAL DUTIES Fundamental Duties of India are guaranteed by the constitution of India in Part IV. These duties are identified as the moral obligations and help in promoting the spirit of patriotism and to uphold the unity of the country. These duties are designed concerning the individuals and the nation. However, these fundamental duties are not legally enforceable. Furthermore, the citizens are morally obligated by the constitution to perform these duties. The Fundamental Duties were added by the 42nd Amendment Act in 1976. Article 51-A of the constitution provides ten Fundamental Duties of the citizen. These duties can be classified accordingly as concerning the environment, duties towards the State and duties towards the nation and also duties towards self. However, these are non-justiciable, incorporated only with the purpose of promoting patriotism among citizens. The international instruments such as the Universal Declaration of Human Rights and International Covenant on Civil and Political Rights include reference of such duties. These Fundamental Duties are such obligations that extend not only to the citizens, but also to the State. According to the Fundamental Duties all citizens should respect the national symbols of India and also the constitution. The fundamental duties of the land also aim to promote the equality of all individuals, protect the environment and public property, to develop scientific temper, to abjure violence, to strive towards excellence...

Words: 1929 - Pages: 8

Premium Essay

Mba Syllabus

...Subject: Principles of Management Semester-I Unit I Introduction - Nature, function, definition and importance of management, Definition, nature, purpose and scope of management, Functions of a manager, an overview of planning, organizing, staffing leading and controlling. Is management a science or art? Unit II Development of Management Thought - Scientific management; Contribution of Taylor, Fayol, Mary Follet, Elton Mayo; Hawthorne experiments, Contingency approach, Indian heritage in production and consumption. Management and administration, Management as a profession, Professionalism of management in India, Management ethics and management culture, Skills required of manager, Classification of skills, Methods of skills development. Unit III Management Planning - Concept of planning, objectives, Nature, Types of plan, Stages involved in planning, Characteristics of a good plan, Importance, Limitations of planning, Making planning effective, Strategic planning in Indian Industry, MBO. Decision Making - Concept, characteristics of decisions, Types of decisions, Steps Involved in decision making, Importance of decision making, Methods of decision making, Committee Decision Making. Unit IV Organisation - Concepts, Principle of organization, Importance, Features of good organization structure, Types of...

Words: 3209 - Pages: 13

Free Essay

Customer Satisfaction

...authoritative source for information on the College’s policies, programmes and services. Programme information in this catalogue is effective from September 2010. Students who commenced studies at the College prior to this date, are to be guided by programme requirements as stipulated by the relevant department. Updates on the schedule of classes and changes in academic policies, degree requirements, fees, new course offerings, and other information will be issued by the Office of the Registrar. Students are advised to consult with their departmental academic advisors at least once per semester, regarding their course of study. The policies, rules and regulations of the College are informed by the laws of the Republic of Trinidad and Tobago. iii Table of Contents PG 9 PG 9 PG 10 PG 11 PG 11 PG 12 PG 12 PG 13 PG 14 PG 14 PG 14 PG 14 PG 15 PG 17 PG 18 PG 20 PG 20 PG 20 PG 21 PG 22 PG 22 PG 22 PG 23 PG 23 PG 23 PG 23 PG 24 PG 24 PG 24 PG 24 PG 25 PG 25 PG 25 PG 26 PG 26 PG 26 PG 26 PG 26 PG 26 PG 27 PG 27 PG 27 PG 27 PG 27 PG 27 PG 28 PG 28 PG 28 PG 28 PG 28 PG 33 PG 37 Vision Mission President’s Welcome Institutional Profile Management Structure Registered Status and Accreditation Candidacy Commitment to Quality and Continuous Improvement Core Values General Information Equal Opportunity Disability Right to Privacy Campus Safety and Security How to Use this Catalogue List of Programmes Admissions Four-tiered Admissions Process Prior Learning and Assessment (PLA) How to Apply...

Words: 108220 - Pages: 433