ME 421 Dynamic Systems and Control
Fall 2006
Qingze Zou qzzou@iastate.edu, 294-9354, 2022 Black
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Department of Department of Mechanical Engineering Mechanical Engineering
Lab Information
Location: Black 00
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1
Last Lecture
!
9/3/15
Laplace Transform Pair
Department of
Mechanical Engineering
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Last Lecture
!
Properties of Laplace Transform
Final value theorem: if li
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Last Lecture
!
PFE for inverse Laplace Transform of
F(s)=N(s)/D(s), order of N(s)<D(s)
! Roots of of D(s) = 0
!
!
Complex conjugate roots
!
9/7/15
Distinct real roots
Repeated roots
Department of
Mechanic
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Modeling using energy method
Advantages:
2.
Elegant and simple conceptenergy conservation;
Easy to handle nonlinear dynamics;
3.
Simpler when both translational and rotational motions are involved.
1.
Bas
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Transfer Function Models
n
n
n
n
n
9/14/15
A transfer function is the ratio of the Laplace
Transform of the output to that of the input (assume
I.C.s = 0)
It is a s-domain model of the system.
A transfer f
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HW 2 B-3-17
9/22/15
Department of
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HW 2 B-4-3
x (Output)
9/22/15
Department of
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Assignment 1 Solution
Ordinary differential equations
a) Classify the following differential equations as linear/non-linear and specify the order
a. 8 + 10 + 6 = 0 Linear, 3rd-order
b. + = 0 Non-linear, 2nd -order
b) Find the general solution to the follo
LAB 3 EQUIVALENT SYSTEMS
ASSIGNMENT
To: ME 421 Student
From: Grunch and Tromby, Attorneys at Law
Subject: Contract to test Patent 7,493,601
Dear ME 421 Student,
Congratulations. Because of your outstanding work for our company in the past, y
LAB 3 EQUIVALENT SYSTEMS
PRE-LAB
Overview:
What is the objective of this lab?
List five things you will learn during this lab.
(1)
(2)
(3)
(4)
(5)
In your own words describe how, outside of this class, these things will be useful.
Electrical System:
Use t
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Announcement
!
!
!
Homework 3 is posted and due on
Thursday beginning of class
Homework 4 is posted and due next
Thursday beginning of class
Quiz 2 is Tuesday, Oct 13rd, study HW3
&4 for preparation
Depart
ME 421 Homework #5
Due via Blackboard: 6pm, Monday, October 31st, 2016
1. (25pts) Consider the liquid level system shown in the figure. Assume the outflow rate Q
(m3/s) through the outflow value is related to the liquid level H by
= 0.01
Assume also that
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Modeling of Mechanical Systems
Mechanical Elements:
Inertia elements:
Spring elements- deformable (elastic)
mass/moments of inertia resist
acceleration, store kinetic energy
Linear, nonlinear stores potenti
Automatic Controllers
Basic Idea:
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Linear systems
u(t)
If system (plant) is linear, we can use
the transfer function description to
represent the system
Plant
y(t)
U(s)
G(s)
Y(s)
Linear Time
Invariant
Syste
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Stability
Department of
Mechanical Engineering
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2
Stability (contd.)
Department of
Mechanical Engineering
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3
St
Homework 1
1. Derive the Laplace transform for the following functions.
a)
f (t) = te2t
Note that L(t) =
1
and L(f (t)eat ) = F (s + a), therefore
s2
L(f (t) =
1
(s + 2)2
b)
f (t) = et sin(2t)
Since L(sin(2t) =
s2
2
,
+4
L(f (t) =
2
2
= 2
2
(s + 1) + 4
s
ME 421 Homework #3 Solution
1. B-4-5 (20pts)
Solution:
2. B-4-11 (30 pts, please derive the analytical expression for x(t) and include printout of
your response plot x(t) in your homework submission. Label the x-axis and y-axis of
your plot. )
Solution:
3
ME 421 Homework #2
Due via Blackboard: Tuesday, September 13th, 2016 (at the beginning of the
class)
Problems with Letter B come from Ogatas book 4th edition
1. (20pts) B-3-15
Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com
2. (20pts
ME 421 Homework #6
Due via Blackboard: 8am, Tuesday, April 12th, 2016
1. (20pts) A feedback control system has a block diagram shown in Figure below. Design a
controller of minimal complexity such that the close-loop systems output y(t) can track
a unit s