ENME 462 Assignment #12
Mitchell, Summer 2016 ver. 1
ENME 462 Vibrations, Controls, & Optimization II
Department of Mechanical Engineering
Due Date
Submission
Information
Reading Exercise
June 28th, 2016
Submit at the start of class
Include your name, stu

ENME462: Vibrations, Controls, and Optimization II (Fall 2014)
1. For the cruise control system below (with a simplified car model), design a controller so that the system responds to a step input from 0 m/s to 5 m/s in less than 3 seconds with no steady

ENME 462 Root Locus Notes
Mitchell, Fall 2016
ENME 462 Vibrations, Controls, & Optimization II
Department of Mechanical Engineering
Content: Sections 8.4 8.8 of Control Systems Engineering (7 th Edition) by Nise
Topic: Sketching the Root Locus
Root Locus

UMCP, Mitchell, Fall 2016
S. 4.4 Introduction to Second-Order Systems
S. 4.5 The General Second-Order System
S. 4.6 Underdamped Second-Order System
S. 4.7 System Response with Additional Poles
S. 4.8 System Response with Zeros
L08 - Chapters 4.4-4.8
ENME

ENME 462
HW#11
Fall 2015
Please Write Your Name and Section Number on your homework
Homework #11
Due Thursday, December 10.
Problem 1 You are given the motor whose transfer function is shown in Figure 1(a)
below.
Figure 1
(a) If this mo

ENME 462
HW#10
Fall 2015
Please Write Your Name and Section Number on your homework
Homework #10
Due Wednesday, November 25.
Problem 1 Consider the feedback system shown in Figure 1. The design specifications
are ! < 10 seconds and . . <

ENME 462
HW#9
Fall 2015
Please Write Your Name and Section Number on your homework
Homework #9
Due Wednesday, November 18.
Problem 1 Root loci are usually plotted for variations in the gain. Sometimes we are interested in
the variation

ENME 462
HW#11 Solutions
Fall 2015
Problem 1 You are given the motor whose transfer function is shown in Figure 1(a)
below.
Figure 1
(a) If this motor were the forward transfer function of a unity feedback system,
calculate the percent

g. The new root locus crosses the 0.7 damping ratio
lineSolutions
at 2.7318
ENME 462
HW#9
o
compared to 1.4171
134.427o for K = 11.075
Fall 2015
134.427 for K = 10.32 for the old root locus. Thus, the new system's settling
Problem 1 Root l

ENME 462
HW#10 Solutions
Fall 2015
Homework #10
Due Wednesday, November 25.
Problem 1 Consider the feedback system shown in Figure 1. The design specifications
are ! < 10 seconds and . . < 10%. There are three potential controllers fo

ENME 462
HW#7 Solutions
Fall 2015
Problem 1
(a) Use the Routh-Hurwitz method to tell how many poles of the following transfer function are in the
right half-plane, in the left half-plane, and on the j-axis.

ENME 462
Fall 2015
Homework #4 Solutions
Problem 1. For each pair of second-order system specications that follow, nd the location
of the second-order pair of poles.
Solution:
a. Known %OS = 12%, Ts = 0.6 s
Using formula for %OS and damping ratio, =
!" (

ENME 462
HW#5 Solutions
Fall 2015
Problem 1
The position control system for a spacecraft platform is governed by the following
equations:
The variables involved are as follows:
Sketch a block diagram of the system, identifying the component parts and thei

ENME462: Vibrations, Controls, and Optimization II (Spring 2016)
1. Transfer functions are useful because they algebraically describe the behavior of a system. A signal
input is multiplied by the transfer function to provide the signal output as seen in t

ENME462: Vibrations, Controls, and Optimization II (Fall 2016)
1. Consider the closed-loop system shown below.
1) Determine the value(s) of k such that the percent overshoot due to a unit step input is between 1%
and 10%.
2) Determine the steady state val

UMCP, Mitchell, Fall 2016
S. 5.1 Introduction
S. 5.2 Block Diagrams
S. 5.3 Analysis and Design of Feedback Systems
L10 - Chapters 5.1-5.3
ENME 462
1
Block diagrams provide a pictorial representation
of a system
Unidirectional operation blocks representing

2.4 Electrical Systems
Here we will determine transfer functions for electrical
systems
Equivalent circuits (that describe the system) consist of
three passive linear components:
Use Kirchoffs laws to formulate differential equations, then
use Laplace tra

UMCP, Mitchell, Fall 2016
S. 8.4 Sketching the Root Locus
S. 8.5 Refining the Sketch
S. 8.6 An Example
S. 8.7 Transient Response Design via Gain Adjustment
S. 8.8 Generalized Root Locus
L20 - Chapters 8.4-8.8
ENME 462
1
Recall the Definition of a Pole
Pol

UMCP, Mitchell, Fall 2016
S. 7.1 Introduction
S. 7.2 Steady-State Error for Unity Feedback Systems
S. 7.3 Static Error Constants and System Type
S. 7.4 Steady-State Error Specifications
S. 7.5 Steady-State Error for Disturbances
S 7.6 Steady-State Error f

UMCP, Mitchell, Fall 2016
S. 2.3 Transfer Functions
S. 2.5 Translational Mechanical System Transfer Functions
S. 2.6 Rotational Mechanical System Transfer Functions
L03 - Chapters 2.3, 2.5-2.6
ENME 462
1
Wrap up Laplace transforms
Transfer functions
Model

UMCP, Mitchell, Fall 2016
S. 2.1 Introduction to Modeling
S. 2.2 Laplace Transform Review
L02 - Chapters 2.1-2.2
ENME 462
1
Modeling Systems
Systems may be studied in the frequency or time
domain
Frequency-domain: how the amplitude of the signal
changes w

UMCP, Mitchell, Fall 2016
S. 4.1 Introduction to Time Response
S. 4.2 Poles, Zeros, and System Response
S. 4.3 First-Order Systems
L06 - Chapters 4.1-4.3
ENME 462
1
Transient response
Studio #2
HW #2 due Wed
In lecture or EGR 2134 dropbox by 5pm
L06 - Ch

UMCP, Mitchell, Fall 2016
S. 8.1 Introduction
S. 8.2 Defining the Root Locus
S. 8.3 Properties of the Root Locus
L18 - Chapters 8.1-8.3
ENME 462
1
Plan for the Week
Monday
Wrap up stability
Root locus
Wednesday
Mid-Semester Feedback
Review midterms
Ro

ENME462: Vibrations, Controls, and Optimization II (Fall 2016)
1. Consider the following differential equation,
Assignment #3 (Due Sept 28, 2016)
ENME462: Vibrations, Controls, and Optimization II (Fall 2016)
2. For the mechanical system at right,
Assignm

ENME462: Vibrations, Controls, and Optimization II (Fall 2016)
1.
Assignment #6 (Due Oct 19, 2016)
ENME462: Vibrations, Controls, and Optimization II (Fall 2016)
2. A machine tool is designed to follow a desired path so that
r(t) = (1-t)u(t)
where u(t) is

ENME462: Vibrations, Controls, and Optimization II (Fall 2016)
Write your section number on your homework
Problem 1 Use the Routh-Hurwitz (RH) Criterion to determine whether the systems with the
following characteristic polynomials are stable or unstable.

Due on Thursday , December 8th
9
1. Two identical pendulums, each with mass m and length l, are connected by a spring of
stiffness k at a distance d from the fixed end, as shown in Fig. 1.
a. Derive the equations of motion of the two masses.
b. Find the

ENME 462 Assignment #2
Mitchell, Summer 2017
ENME 462 Vibrations, Controls, & Optimization II: Summer 2017 Class Schedule
Department of Mechanical Engineering
Due Date
Thursday, June 1st, 2017
Submission
Information
Submit via Gradescope by 8:00 am
Includ

ENME 462 Assignment #5
Mitchell, Summer 2017
ENME 462 Vibrations, Controls, & Optimization II: Summer 2017 Class Schedule
Department of Mechanical Engineering
Due Date
8:00 am Wednesday, June 7th, 2017
Submission
Information
Submit via Gradescope by 8:00

ENME 462 Assignment #2
Mitchell, Summer 2017
ENME 462 Vibrations, Controls, & Optimization II: Summer 2017 Class Schedule
Department of Mechanical Engineering
Due Date
Thursday, June 1st, 2017
Submission
Information
Submit via Gradescope by 8:00 am
Includ

ENME 462 Assignment #3
Mitchell, Summer 2017
ENME 462 Vibrations, Controls, & Optimization II: Summer 2017 Class Schedule
Department of Mechanical Engineering
Due Date
Monday, June 5th, 2017
Submission
Information
Submit via Gradescope by 8:00 am
Include

ENME 462 Assignment #4
Mitchell, Summer 2017
ENME 462 Vibrations, Controls, & Optimization II: Summer 2017 Class Schedule
Department of Mechanical Engineering
Due Date
8:00 am Tuesday, June 6th, 2017
Submission
Information
Submit via Gradescope by 8:00 am

ENME 462 Assignment #5
Mitchell, Summer 2017
ENME 462 Vibrations, Controls, & Optimization II: Summer 2017 Class Schedule
Department of Mechanical Engineering
Due Date
8:00 am Wednesday, June 7th, 2017
Submission
Information
Submit via Gradescope by 8:00