MODELING OF ELECTRICAL SYSTEMS

Slides:

Advertisements

Similar presentations

AP Physics B Units.

Advertisements

X Disp. (m) x Vel. (m/s) x Acc. (m/s 2 ) m Mass (kg) k Spring cons. (N/m) c Damp. Cons. (Ns/m) f Force (N) θ Angular pos. (rad) θ Angular vel. (rad/s)

7. Modeling of Electromechanical Systems

Kirchoff’s current law Kirchoff’s voltage law 1.METHOD Current law Magnetic energy, electric energy, virtual work. Lagrange equation 2. METHOD Modeling.

Physics Lab 2008-Energy. Linear Work  The act of exerting a force through a distance in the direction of the force (constant)  W = F  x cos   F =

EE2010 Fundamentals of Electric Circuits Text Book: Introductory Circuit Analysis - Robert Boylestad.

Chapter 10: Rotation. Rotational Variables Radian Measure Angular Displacement Angular Velocity Angular Acceleration.

Newton’s 2 nd Law Of Motion By Mr. Yum. Newton’s 2 nd Law Newton’s 2 nd Law is defined as: Newton’s 2 nd Law is defined as: F = m x a Where, F = force,

A spring with a mass of 6 kg has damping constant 33 and spring constant 234. Find the damping constant that would produce critical damping

Ch. 32 Self Inductance Inductance A

Problem 1: Homework 03 Electrical Circuits: Problem 2: Problem 3: Problem 4: - + Problem 5:

Use Ohm’s Law to solve the following equations.

Ohm’s Law The most important fundamental law in electronics is Ohm’s law, which relates voltage, current, and resistance. Georg Simon Ohm ( ) studied.

1 Institute of Mechatronics and Information Systems Control and Driving Systems.

Warmup: Concept: OHM’s Law. Electrical current is a measure of the rate at which electrical charge moves in a circuit. Electrical current is measured.

System Models Mathematical Models Mechanical System Building Blocks Electrical System Building Blocks Fluid System Building Blocks Thermal Systems Building.

Physical Science Units Review

1 Chapter 4-7, Benchmark Review activity!. 2 What is the slope of a line on a distance-time graph? A. distance. B. time. C. speed. D. displacement.

Calculating Electricity

1 Institute of Mechatronics and Information Systems Electric Machines.

Electric Circuit Charges in Motion OCHS Physics Ms. Henry.

Electromagnetism I Week 8. Contents Overview Overview Coulomb’s Law Coulomb’s Law Current Current Voltage Voltage Resistance Resistance Energy and Power.

EENG 2610: Circuit Analysis Class 10: Capacitors and Inductors

ME 335 Boğaziçi University A Study on Motor Speed Control.

  Charge – coulombs (Q)  Charge of an e - & p + = 1.6 x coulombs  F e = KQ 1 Q 2 /r 2 (Coulombs Law)  Current (I) – amperes (amps) = I = Q/sec.

Electricity. Electric Current The net movement of electric charges in a single direction Electrons in a material (metal wire) are in constant motion in.

Electric Current. Electric Potential Electrons in a circuit have potential energy –The energy is related to the force exerted by an electric field –The.

L C V1V1 + -R1R1 R2R2 Example 3.1: Current in the resistor R 1 = V 1 : Input q ve q 2 : Gen. charges QqQq Q q2 L=3.4 mH, C=286 µF, R 1 =3.2 Ω, R 2 =4.5.

Session 6 - Sensor Modelling

Electricity Basics of electricity. Electricity Atoms – The smallest unit of each element Electrons – negatively charged particles in atoms Ions – charged.

Determine the mathematical models that capture the behavior of an electrical system 1.Elements making up an electrical system 2.First-principles modeling.

DC Motor Speed Modeling in Simulink

ELECTRIC CURRENTS. SIMPLE CIRCUIT What’s providing the energy? What’s “moving” in the circuit? What’s causing the movement? e.m.f. = Electromotive Force.

 Electrical circuit: a closed loop where charged particles flow  Electrical current: a flow of charged particles (e - )  Direct current (DC): a flow.

Electricity. whether two charges attract or repel depends on whether they have the same or opposite sign unit of measurement for charge is the coulomb.

Rotational Dynamics 8.3. Newton’s Second Law of Rotation Net positive torque, counterclockwise acceleration. Net negative torque, clockwise acceleration.

Lecture 3: Dynamic Models

Methods of Charging Conduction – A Charged Object comes in CONtact with a neutral object. – The neutral object takes on the same Net Charge as the Charged.

AP Equation Flash Cards. Magnetic Field due to a Current Loop.

Modeling of Electrical Circuits

7. Modeling of Electromechanical Systems

Current Electricity.

Electrical circuits, power supplies and passive circuit elements

Modeling Methods of Electric Circuits

Measurements SI base unit.

Electrical circuits, power supplies and passive circuit elements

Kinematic Analysis (position, velocity and acceleration)

Analogy Between Engineering Systems

Electricity Energy of electrons.

Emergence of Modern Science Electricity and Magnatism

Bellwork What is required for electric current to flow?

Moving conductor – eddy currents

Introduction COURSE OBJECTIVE:

Topic H: Electrical circuits

Translational-Rotational Analogues

BDU20102 Electromechanical & Control System

Current Directions and

Basic Electrical Calculations

Lecture 11 Electromagnetic Oscillations and Alternating Current Ch. 31

Electric Current.

Flash Cards – Do You Know Your Units?

Electricity Review CH

This waveform is 35.0 cm long. How long is the wavelength?

. Modeling OBJECTIVE Revision on Laplace transform

Ohm’s Law & Circuits Chapter 7.2 & 7.3.

Voltage Difference The difference in electrical potential between two places. Unit of measure = V (volts) Voltage causes current to flow through an electric.

Ch. 31 Self Inductance Inductance A

Ch. 31 Self Inductance Inductance A

ENERGY Energy J Kinetic Energy J Elastic potential energy J Ek Ee E

Presentation transcript:

MODELING OF ELECTRICAL SYSTEMS 1st METHOD Current Law (Kirchoff) Voltage Law 2nd METHOD Current Law Magnetic Energy, Electrical Energy, Virtual Work: Application of Lagrange’s Equation 2nd method is used in this course.

FUNDAMENTAL ELEMENTS OF ELECTRICAL SYSTEMS Passive Elements Active Elements - + L C R Op-Amp Analogy Between Mechanical and Electrical Systems . .. x Displacement (m) Velocity (m/s) Acceleration (m/s2) m Mass (kg) k Spring Stiffness (N/m) c Damping Constant (Ns/m) f Force (N) Generalized Coordinates q Charge (Coulomb) i Current (Amper) L Inductance (Henry) 1/C C:Capacitance (Farad) R Resistance (Ohm) V Voltage (Volt) nt Generalized Charges Lagrange’s Equation

Analogy Between Mechanical and Electrical Systems . .. x Displacement (m) Velocity (m/s) Acceleration (m/s2) m Mass (kg) k Spring Constant (N/m) c Damping Constant (Ns/m) f Force (N) . .. θ Angular Dispalement (rad) Angular Velocity (rad/s) Angular Acceleration (rad/s2) IG Mass moment of inertia (kg-m2) Kr Rotational spring constant (Nm/rad) Cr Rotational damping constant Nm/(rad/s) M Moment (Nm) q Charge (Coulomb) i Current (Amper) L Inductance (Henry) 1/C C:Capacitance (Farad) R Resistance (Ohm) V Voltage (Volt) E2 E1 E1 E2 δW δW

Modeling of Electrical Systems: Current through R1= Example 3.1: V1: Input q and q2 : Generalized charges L C V1 + - R1 R2 Qq Qq2 L=3.4 mH, C=286 µF, R1=3.2 Ω, R2=4.5 Ω D(s)=0.02618s3+26.288s2+11188.81s=0 Eigenvalues: 0, -502.06±418.70i (ξ=0.768)

No current flow through Op-Amp Example 3.2 C1 - + V1 V2 R1 R2 R3 C2 No current flow through Op-Amp Input : V1 Generalized charges: q1, q2, q3 For Op-Amp : V+=V-=0

R1=15.9 kΩ, R2=837 Ω, R3=318 kΩ, C1=C2=0.005 µF Eigenvalues: 0, -628.93±12561.76i (ξ=0.05)

V2 R2 - + V1 R1 GAIN CIRCUIT R2 - + V1 R1 V2 R V2'

INTEGRAL CIRCUIT C R V1 V2 - + Negative sign can be eliminated bu adding an extra gain circuit with gain=1

- + V1 Vc R V2 V3 R V2 V1 - + Vc

PID circuit is used frequently in Control Systems. - + R1 R4 C4 C3 R3 R V1 V2 PID Control Circuit PID circuit is used frequently in Control Systems.