Lumped Modeling with Circuit Elements, Ch. 5, Text

Lumped Modeling with Circuit Elements, Ch. 5, Text

Lumped Modeling with Circuit Elements, Ch. 5, Text Ideal elements represent real physical systems. Resistor, spring, capacitor, mass, dashpot,

inductor To model a dynamic system, we must figure out how to put the elements from different domains together. Alternatives include numerical modeling of the

whole system. Lumped element modeling offers more physical insight and may be necessary for timely solutions. Example. Electrical: ResistorInductor-Capacitor (RLC) system.

C No power source, transient response depends on initial conditions

R i L B1, B2 depend on initial conditions

Example. Mechanical: Spring-MassDashpot system. x k

m No power source, transient response depends on initial conditions

b B1, B2 depend on initial conditions Equations are the same if:

1/k k b

m . I <-> x b

. x m

or C 1/C


R Goal: Simulate the entire system. Usual practice: Write all elements as electrical circuit elements.

Represent the intradomain transducers (Ch. 6) Use the powerful techniques developed for circuit analysis, linear systems (if linear), and feedback control on the whole MEMS system.

Senturia generalizes these ideas. Introduce conjugate power variables, effort, e(t), and flow, f(t). Then, generalized displacement, q(t) And generalized momentum, p(t)

e . f has units of power e . q has units of energy p . f has units of energy Variable Assignment Conventions

Senturia uses e -> V, that is, effort is linked with voltage in the electrical equivalent circuit. He explains the reasons (for example potential energy is always associated with energy storage in capacitors).

Following Senturias e -> V convention: For effort source, e is independent of f For flow source, f is

independent of e For the generalized resistor, e=e(f) or f=f(e) Linear resistor e=Rf

Electrical, V=RI Mechanical, F=bv For the generalized capacitor (potential energy):

For a linear electrical capacitor: permitivity A area G Gap

The mechanical equivalent is the linear spring. (Check in table.)

Cspring = 1/k, F=kx Generalized Inductor or inertance (kinetic energy?)

p1 Linear inertance: momentum flow

m mass v velocity p momentum momentum?

Electrical? But what is this??? ???

v Reluctance

q=Ce, e=(1/C)q, Electrical Q=CV (Fmm in example!) (Senturia, not necessary to approximate)

Recently Viewed Presentations

  • Think About It - Pc&#92;|Mac

    Think About It - Pc\|Mac

    THINK ABOUT IT What's the smallest part of any living thing that still counts as being "alive?" Can we just keep dividing living things into smaller and smaller parts, or is there a point at which what's left is no...
  •  H R M C O N S U

    H R M C O N S U

    HR Projects Outsourcing برون سپاری پروژه های منابع انسانی. آدرس: تهران - ابتدای جاده مخصوص - خیابان شهید عموئیان (بیمه پنجم) - نبش کوچه صلح پرور - پلاک 2 - طبقه سوم شرقی Tel: 44667408 - 44667409 Fax:44667384 Website:
  • Gerunds and Gerund Phrases - Mrs. White&#x27;s English Website

    Gerunds and Gerund Phrases - Mrs. White's English Website

    Gerunds and Gerund Phrases 8th Grade English Clauses and Verbals Unit Who has my subject? What is the subject of these sentences? Dancing is the love of Tiffany's life? Playing chess is Steve's secret passion! Gerunds In the previous lesson,...
  • TRICARE Overseas Program Briefing

    TRICARE Overseas Program Briefing

    TRICARE. Overseas Program, or TOP, briefing. TOP is the Department of Defense health care program for geographical areas and territorial waters outside the U.S. ... sight or safety. In the event of an emergency, go to the nearest emergency care...
  • Energy Star® Multifamily New Construction

    Energy Star® Multifamily New Construction

    Energy neutral systems do not need to be explicitly listed in the ERP Tables. Example: Non-ENERGY STAR / DLC LED lighting is the most common measure that does not meet MPS. Non-qualifying LED lighting cannot contribute toward savings. Measures Eligible...
  • Mapping Toolbox - Weebly

    Mapping Toolbox - Weebly

    Mapping Toolbox: Basic mapping skills Recap of BOLTSS; identifying major features on a map; being able to demonstrate urban spread on a map. 1. What goes on a map? Have you heard of BOLTSS before? Do you know what it...
  • Honors Chemistry Lab

    Honors Chemistry Lab

    Honors Chemistry Lab From Notebook to Report. Guidelines. Setting Up Your Lab Notebook. Table of contents pages 1 and 2. Rubric tape onto pages 3 and 4. ... a numerical setup, work and solution. Solutions must have a unit and...
  • Chapter 7

    Chapter 7

    Theory of Computation: Chapter 7 Reductions Definition : We write L ₁ ≤ L ₂ if there is a way to solve x ∈ L ₁ by making 'calls' to L ₂ as an oracle, and say L ₁ is...