MTH 425 Study Guide - Fall 2018, Comprehensive Midterm Notes - Transfer Function, Block Diagram, System Of Linear Equations
12 Oct 2018
School
Department
Course
Professor
MTH 425
MIDTERM EXAM
STUDY GUIDE
Fall 2018
MTH 425 CH 1
Modeling
Chapter 1
Objectives
• To be able to apply Laplace and inverse Laplace transform to time domain
equations
• To be able to derive transfer function (model) of the electrical and
mechanical systems (translational, rotational).
2
Laplace Transform Review
(sec 2.2 of textbook)
• Why?
• – Many engineering systems are represented mathematically
by differential equations.
• – Differential equations are difficult to model as a block diagram.
• – But we prefer system representation by block diagram where there
are distinct inputs-outputs and separate parts.
Input
R(s)
output
C(s)
Laplace Transform
find more resources at oneclass.com
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3
System G(s)
Laplace Transform Review
• ExampleofModeling(accelerometerwithinrocket-propelledsled, 6345 mph,
- US Air Force)
y+
b
y+
k
y=−Mx MM
4
Laplace Transform Review • When?
– When coefficients of differential equations (model parameters) are
LINEAR, TIME-INVARIANT (LTI).
– Many systems are not LTI but can be simplified to LTI systems.
– InthiscoursewewillfocusonLTIsystems.
output Input
5
Laplace Transform Review • TheLaplaceTransformisdefinedas:
where:
6
Laplace Transform Review
• Wecanderiveatablefor conventional functions:
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Objectives: to be able to apply laplace and inverse laplace transform to time domain equations, to be able to derive transfer function (model) of the electrical and mechanical systems (translational, rotational). Us air force) b k y+ y+ y= mx mm. When coefficients of differential equations (model parameters) are. Many systems are not lti but can be simplified to lti systems. 1 f 1 (0 ) df dt t=0 . Based on table 2. 1, the inverse of the laplace transfer s function f(s)=l(f(t))= is. From table 2. 2 we know the inverse transform of. Convert complicated functions into a sum of simpler terms for which we know the laplace transform. Always make sure the order of nominator is less than denominator. L(g (t)+g (t)+g (t))=g(s)+g (s)+g (s) 123123: for example: f(s)=g(s)+g (s)+g (s) Laplace transform review: case 1: roots of the denominator of f(s) are real and distinct: 12n12mn find each coefficient k by multiplying both sides by m m m.
