Nonlinear Systems and Control Lecture # 9 Lyapunov Stability
Example: Pendulum equation with friction x˙1 = x2 x˙2 = − asinx1 − bx2 V (x) = a(1− cosx1)+ 1 2 x2 2 V˙ (x) = ax˙1 sinx1 +x2x˙2 = − bx2 2 The origin is stable V˙ (x) is not negative definite because V˙ (x) = 0 for x2 = 0 irrespective of the value of x1 – p. 13/15
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
Documents from same domain
Using Microsoft Visual Studio to Create a Graphical User ...
www.egr.msu.eduUsing Microsoft Visual Studio to Create a Graphical User Interface ECE 480: Design Team 11 Application Note Joshua Folks April 3, 2015 Abstract: Software Application programming involves the concept of human-computer interaction and in this area of the program, a graphical user interface is very important. Visual widgets such as
Using, Microsoft, Visual, Studio, Create, Using microsoft visual studio to create
Effects of temperature dependence of electrical and ...
www.egr.msu.eduEffects of temperature dependence of electrical and thermal conductivities on the Joule heating of a one dimensional conductor F. Antoulinakis,1 D. Chernin,2 Peng Zhang,1,a) and Y. Y. Lau1 1Department of Nuclear Engineering and Radiological Sciences, The University of …
ECE 410: VLSI Design Course Lecture Notes - egr.msu.edu
www.egr.msu.eduECE 410: VLSI Design Course Lecture Notes (Uyemura textbook) Professor Andrew Mason Michigan State University. ECE 410, Prof. A. Mason Lecture Notes Page 2.2 CMOS Circuit Basics nMOS gate gate drain source source drain pMOS
Power!Supply,!Arduino!MEGA!2560,! and!Stepper!Motors ...
www.egr.msu.edu• 12V 10Amp power supply • Stepper motors o Datasheet • Wires ! 3! Getting Started The Arduino board is the link between the power supply and stepper motors. Thus, it is important to understand the input/output pins of the microcontroller. As shown
no capabilities for “online” memory Write operations ...
www.egr.msu.eduECE 410, Prof. A. Mason Lecture Notes 13.7 Multi-Port SRAM • Allows multiple access to the same SRAM cell simultaneously. – Provide high data bandwidth.
Chapter 2. Design of Beams – Flexure and Shear
www.egr.msu.eduCE 405: Design of Steel Structures – Prof. Dr. A. Varma Chapter 2. Design of Beams – Flexure and Shear 2.1 Section force-deformation response & Plastic Moment (Mp) • A beam is a structural member that is subjected primarily to transverse loads and negligible
Design, Chapter, Beam, Chapter 2, Flexure, Design of beams flexure and
Introduction to Wireless Communications and Networks
www.egr.msu.edurepeater stations are placed along the path of a digital system at distances short enough to ensure that noise and distortion remain within a limit. The viability of regenerative repeaters is the main reason for the superiority of ... Base station receives the request and sends it to the MSC.
Combustion Examples - Michigan State University
www.egr.msu.eduCombustion Examples Example: Combustion of Butane with Specified Air to Fuel Ratio Butane is burned with air with 130% theoretical air. Balance the chemical reaction equation and determine the air to fuel ratio of the combustion process. Solution: We begin by writing our unbalanced theoretical chemical reaction equation for butane.
SHEET METALWORKING - Michigan State University
www.egr.msu.eduSheet-metal Operation . 7. Bending of Tube Stock. 2. Introduction • Cutting and forming thin sheets of metal usually performed as cold working • Sheet metal = 0.4 (1/64) to 6 mm (1/4in) thick • Plate stock > 6 mm thick • Advantage - High strength, good dimensional accuracy, good surface finish, economical mass
Sheet, Plate, Metal, Bending, Metalworking, Sheet metal, Sheet metalworking
Design a simple DC power supply - Michigan State University
www.egr.msu.eduThe power supply that has been designed provides a good alternative to a more expensive power supply. The power supply has few components, covers a small area, and is very simple in design. Figure 5: Final Design. Works Cited “Dc Power Supply.” Test Equity. 2 Apr. 2009
Related documents
IGCSE PHYSICS - ENERGY, WORK AND POWER (6)
igcsestudybank.weebly.comaction of a pendulum, where at each end of its swing the pendulum has a maximum amount of gravitational potential energy, and at the middle of ... due to friction between the stone and the air. the = mgh gh x 2 10 x 6 x 2 120 120 - 10.95 bite down the formula:
Pavement Distress and Evaluation
pavement.engineering.asu.edu•Coefficient of friction: •Wet condition is more critical W F f W F . Measurement Equipment Locked wheel skid Mu meter British Pendulum Tester Others . Mu Meter . AND THIS WHAT THEY WANT ! Title: PowerPoint Presentation Author: ETS Created Date:
13 Lyapunov functions
www.ndsu.eduNow I will include friction in my problem: x¨ +sx˙ +sinx = 0, s > 0. I can rewrite my equation as the system x˙ = y, y˙ = −sy +sinx, which has the same equilibria as the conservative pendulum equation. Here, however, I can use the standard linearization approach to conclude that the origin is locally asymptotically stable (do this).
Chapter 4 – Homework Problems - Rose–Hulman Institute ...
www.rose-hulman.edufriction between the disks is Pk = 0.15. Bearing friction can be neglected. Determine: a) the angular acceleration of each disk, b) the final angular velocity of each disk. Problem 4.8 A gear reduction system consists of three gears A, B, and C. Gear A starts from rest at time t = 0 and rotates clockwise with constant angular acceleration.
Chapter, Problem, Homework, Friction, Chapter 4 homework problems
Classical Mechanics - University of Texas at Austin
farside.ph.utexas.edu(e.g., the motion of a pendulum in a grandfather clock). Circular motionŠmotion by which a body executes a circular orbit about another xed body [e.g., the (approximate) motion of the Earth about the Sun]. Of course, these different types of motion can be combined: for instance, the
Simple Harmonic Motion - University of Oklahoma
www.nhn.ou.edufriction so that the spring oscillates with SHM how much energy is kinetic and potential when the spring is at (a) x = .10 m, (b) x = .0 m Let’s suppose that the spring is not horizontal, but is instead in a vertical position. The motion is basically the same as a horizontal spring except for where the equilibrium position is located.
Worked Examples from Introductory Physics (Algebra–Based ...
www2.tntech.eduWorked Examples from Introductory Physics (Algebra–Based) Vol. I: Basic Mechanics David Murdock, TTU October 3, 2012