Jigsaw Team Estrogen Stephanie Wilson Amanda Newman Jessica Raymond

Slides:

Advertisements

Similar presentations

Dynamic Behavior of Closed-Loop Control Systems

Advertisements

LAPLACE TRANSFORMS.

Dynamic Behavior of Closed-Loop Control Systems

Lecture 131 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001.

1 Section 2 SECTION 2 Partial Fractions. 2 We need to split the following into separate terms: Roots of the denominator D(s): Case I – unrepeated factor.

Transforming C(s) into c(t): Negative Feedback Control with Proportional Only Controller Jigsaw Team Estrogen Stephanie Wilson Amanda Newman Jessica Raymond.

Voltage Control System: Proportional Integral (PI) Controllers Team Purple: John Pangle Jessica Raymond Justin Whitt ENGR 329 November 30, 2005.

FLOW RATE CONTROL SYSTEM

Red Team Amanda Newman Ankit Patel Bryan Cuervo UTC ENGR 329 Sept. 14, 2005.

Ch 6.2: Solution of Initial Value Problems

Laplace Transforms 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for.

Bogazici University Dept. Of ME. Laplace Transforms Very useful in the analysis and design of LTI systems. Operations of differentiation and integration.

Green Team Speed System Proportional Only Controller Design and Experimental Dustin Fraley DeAndre Strong Stephanie Wilson.

CHAPTER III LAPLACE TRANSFORM

Chapter 4 Laplace Transforms.

ORDINARY DIFFERENTIAL EQUATION (ODE) LAPLACE TRANSFORM.

Lesson 6-4 Example Example 3 Determine if the triangle is a right triangle using Pythagorean Theorem. 1.Determine which side is the largest.

Chapter 9 Laplace Transform §9.1 Definition of Laplace Transform §9.2 Properties of Laplace Transform §9.3 Convolution §9.4 Inverse Laplace Transform §9.5.

EXAMPLE 2 Rationalize denominators of fractions Simplify

Quadratic Formula Standard Form of a Quadratic Equation ax 2 + bx + c = 0  example  x 2 + 6x + 8 = 0  we learned to solve this by:  factoring  completing.

Laplace Transforms 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for.

(e.g., deviation variables!)

Laplace Transforms 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for.

Continuing with Integrals of the Form: & Partial Fractions Chapter 7.3 & 7.4.

Basic Concepts  Block diagram representation of control systems  Transfer functions  Analysis of block diagrams  P, PI and PID controllers ( Continuous.

Solving Proportions. 2 ways to solve proportions 1. Equivalent fractions (Old) Cross Products (New)

Integrating Rational Functions by Partial Fractions Objective: To make a difficult/impossible integration problem easier.

To add fractions, you need a common denominator. Remember!

Chapter 3 Dynamic Response The Block Diagram Block diagram is a graphical tool to visualize the model of a system and evaluate the mathematical relationships.

Using Partial Fraction Expansion

Subsea Control and Communications Systems

SECTION 8-5 Partial Fraction. Rational Expressions: Find a common denominator 1.

Inverse Laplace Transforms (ILT)

Continuing with Integrals of the Form: & Partial Fractions Chapter 7.3 & 7.4.

Martin-Gay, Beginning Algebra, 5ed

ABE425 Engineering Measurement Systems ABE425 Engineering Measurement Systems PID Control Dr. Tony E. Grift Dept. of Agricultural & Biological Engineering.

case study on Laplace transform

University of Warwick: AMR Summer School 4 th -6 th July, 2016 Structural Identifiability Analysis Dr Mike Chappell, School of Engineering, University.

Lesson 11: Solving Mechanical System Dynamics Using Laplace Transforms

Lesson 12: Transfer Functions In The Laplace Domain

Laplace Transforms Chapter 3 Standard notation in dynamics and control

CHAPTER III LAPLACE TRANSFORM

Chapter 6 Laplace Transform

Chap2. Modeling in the Frequency Domain

Youngjune, Han Chapter 4 Time Response Youngjune, Han

Completing the Square 8

Solving Radical Equations

Chapter 0 Review of Algebra.

EQUATIONS & INEQUALITIES

12.1 Operations with Radicals

2.2 Limits Involving Infinity, p. 70

LAPLACE TRANSFORMS PART-A UNIT-V.

Operations on Functions

Laplace Transforms: Special Cases Derivative Rule, Shift Rule, Gamma Function & f(ct) Rule MAT 275.

Sec. 2.2: Limits Involving Infinity

2.2 Limits Involving Infinity

Three times a number minus 35 is 79. 9n – (6/n) n or 4n (11 + n) or 3(n + 11) 4n2 + 5n n or 7n + 23 Three times a number.

Finding Equilibrium Concentrations When Given K and Initial Concentrations or Pressures

7B-1b Solving Radical Equations

UNIVERSITI MALAYSIA PERLIS SCHOOL OF ELECTRICAL SYSTEM ENGINEERING

Unit 3 Practice Test.

Solution of ODEs by Laplace Transforms

Chapter 4 THE LAPLACE TRANSFORM.

Completing the Square Algebra Review.

Example 1: Find the magnitude and phase angle of

Unit 1.3 Part A Learning Goal:

2.5 Limits Involving Infinity

Exercise 1 For the unit step response shown in the following figure, find the transfer function of the system. Also find rise time and settling time. Solution.

Limits Involving Infinity

Algebra with Fractions 2

Presentation transcript:

Jigsaw Team Estrogen Stephanie Wilson Amanda Newman Jessica Raymond Transforming C(s) into C(t): Negative Feedback Control with Proportional Only Controller Jigsaw Team Estrogen Stephanie Wilson Amanda Newman Jessica Raymond (We Laplace Transforms)

Goal: Advantages and disadvantages of different t0 (dead time) values System: Any FOPDT system in a negative feedback loop with a Proportional-Only Controller

From Block Diagram Algebra… Negative feedback control loop for FOPDT system with P-only controller CLTF:

With Pade’s Approximation… CLTF:

This Reduces to… CLTF: Therefore…

Final Value Theorem In Laplace Domain

Now for C(t)… CE: First we must simplify the denominator… for partial fraction decomposition CE:

Substitute for Easier Math… CE: m p q

Now Complete the Square

Distribute the left side Simplify the last term Distribute the left side Factor the right

Solve for C

Solve for A

Solve for B

Substitute for m, p, q m p q

Separate the terms

Manipulate… to Fit Page 15 Formulas…

Inverse LaPlace Transform

Substitute A, B, C, m, p, q back into C(t)

Final Value Theorem In Time Domain

CONCLUSION Advantages of Increased t0 Disadvantages of Increased t0 Reaches steady state faster Larger values of stable operating gain Bigger gain is better Disadvantages of Increased t0 Increase in t0 results in a decrease in the ultimate 0 0gain of the loop (Kcu) Poor performance Limited values of stable operating gain