# Syllabus for ME 345 — Mechatronics

Fall 2016

## Course description

This course is an introduction to the mathematical modeling and design of electrical, mechanical, and electro-mechanical systems. A system dynamical approach is used, which allows different energy domains to be modeled within a unified framework. Circuit elements covered include resistors, capacitors, inductors, diodes, transistors, and operational amplifiers. (Adopted from the course catalog.)

## General information

Instructor
Rico AR Picone, PhD
Office Hours
MWF 9–10, 11–11:40 CH 103C

Office location
CH 103C
Classroom location
Harned 115
Times
MWF 10:00–10:50 am
Website
ME 345 Website
Moodle
ME 345 Moodle

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## Textbooks

Derek Rowell and David N. Wormley. System Dynamics: An Introduction. Prentice Hall, 1997.

Paul Horowitz and Winfield Hill. The Art of Electronics. Third Edition. Cambridge University Press, 2015.

## Notes

Partial notes will be posted here.

## Schedule

The following schedule is tentative. All assignments will be set one week before the due date.

week topics introduced reading assignment due
introduction, voltage, current, resistance, signals HH 1.1–1.3
capacitors, general circuit analysis HH 1.4 Assignment #1
inductors, transformers HH 1.5, 1.6 Assignment #2
impedance, diodes, diode circuits HH 1.7, 1.8, & 1.9 Assignment #3
energy and power flow in state-determined systems RW Ch. 1 & Sec. 2.1 Assignment #4, Midterm #1
one-port elements and their generalization RW Sections 2.2–2.4, Ch. 3 Assignment #5
formulation of system models RW Ch. 4 Assignment #6
state equation formulation RW Ch. 5 Assignment #7
state equation formulation RW Ch. 5 Assignment #8
energy-transducing system elements RW Ch. 6 Assignment #9
transistors and op-amps HH 2.1, 2.2, 4.2, & 4.3 Assignment #10
operational methods for linear systems RW Ch. 7 Assignment #11
Thanksgiving week Midterm #2
system properties and solution techniques RW Ch. 8 Assignment #12
first- and second-order response RW Ch. 9 Assignment #13
finals week Final Exam

## Assignments

### Assignment #2

• Do HH Exercises 1.14, 1.15, and 1.16.
• Special Problem #1. For the RC circuit in HH Figure 1.41B, perform a complete circuit analysis to solve for $V_{out}(t)$ if $V_{in}(t) = A\ \sin{\omega t}$, where $A \in \mathbb{R}$ is a given amplitude and $\omega \in \mathbb{R}$ is a given angular frequency. Let $v_c(t)|_{t=0} = v_{c0}$, where $v_{c0} \in \mathbb{R}$ is a given initial capacitor voltage. Hint: you will need to solve a differential equation for $v_C(t)$.
• Special Problem #2. In the previous problem, find $i_C(t)$.
• Special Problem #3. For the circuit diagram below, perform a complete circuit analysis to solve for $v_o(t)$ if $V_{s}(t) = A\ \sin{\omega t}$, where $A \in \mathbb{R}$ is a given amplitude and $\omega \in \mathbb{R}$ is a given angular frequency. Let $i_L(t)|_{t=0} = 0$ be the initial inductor current. Hint: you will need to solve a differential equation for $i_L(t)$.
• Take the weekly homework quiz.

### Assignment #3

• Special Problem #1. For the circuit diagram below, solve for $v_o(t)$ if $V_{s}(t) = A\ \sin{\omega t}$, where $A=2\ V$ is the given amplitude and $\omega \in \mathbb{R}$ is a given angular frequency. Let $R = 50\ \Omega$, $L = 50\ mH$, and $C = 200\ nF$. Let the circuit have initial conditions $v_C(0) = 1\ V$ and $i_L(0) = 0\ A$. Find the steady-state ratio of the output amplitude to the input amplitude $A$ for $\omega = \{5000,10000,50000\}\ rad/s$. This circuit is called a low-pass filter—explain why this makes sense. Plot $v_o(t)$ in MATLAB for $\omega=400\ rad/s$ (you think this won’t be part of the quiz, but it will be!). Hint: either re-write your system of differential-algebraic equations and initial conditions as a single second-order differential equation with initial conditions in the differential variable or re-write it as a system of two first-order differential equations and solve that.
• Special Problem #2. For the circuit diagram below, solve for $v_o(t)$ if $V_{s}(t) = A\ \cos{\omega t}$. Let $N = n_2/n_1$, where $n_1$ and $n_2$ are the number of turns in each coil, $1$ and $2$, respectively. Also let $i_L(0) = 0$ be the initial condition.
• Take the weekly homework quiz.

### Assignment #4

• Special Problem #1. Re-do Special Problem #1 from the preceding assignment, but only consider the steady-state response. Use impedances!
• Special Problem #2. Re-do Special Problem #2 from the preceding assignment, but only consider the steady-state response. Use impedances!
• Re-read Secion 1.2.6.A of The Art of Electronics.
• HH 1.20.
• Special Problem #3: Examine the spec sheet on the real world Zener diode 1N4732A, determine its dynamic resistance $R_{dyn}$ at 4.7 V, and compute $\Delta V_{out}$ for the Zener regulator in Figure 1.16 using this diode.
• Take the weekly homework quiz.

### Assignment #10

• Special Problem #1: for the following circuit with op-amp gain $k$, develop state and output equations if the output is $v_o$. Simulate $v_o(t)$ for a step input voltage of $V_s = 5$ V, a sine wave of $V_s(t) = 5 \sin{25 t}$, and a square wave of amplitude $5$ V and frequency of $25$ rad/s. Let $R_1 = 50 \Omega$, $R_2 = 10 k\Omega$, $C = 10 \mu F$, and the op-amp open-loop gain be $k = 10^5$. Let the initial condition be $v_C(t) = 0$ V. The simulation results should be plotted to show the transient response until it reaches steady-state.
• Take the weekly homework quiz.

### Assignment #11

• Do Rowell & Wormley homework problems 7.6, 7.11, 7.12, and 7.14. Note: to find the state equations, you may use the method to the book mentions in some of the problems (going from the block diagram straight to state equations) if you like, but you are welcome to use the usual state equation formulation method we’ve discussed (linear graph, elemental equations, etc.). There is a typo in the transfer operator in problem 7.12. The numerator should be 50 (as shown in the block diagram), not 100. Also in 7.12, part c is asking for a differential equation in $\Omega$ and $v_d$.
• Take the weekly homework quiz.

## Resources

Class resources will be posted here throughout the semester.

## Slack

Everyone is required to join the messaging service called “Slack.” We’ll use it to communicate with each other during the semester. The Slack team you need to join is called ME345-2016F. You should have an invitation link in your email.

## Homework, quiz, & exam policies

### Homework & homework quiz policies

Weekly homework will be “due” on Wednesdays, but it will not be turned in for credit. However — and this is very important — each week a quiz will be given on Wednesday that will cover that week’s homework.

Quizzes will be available on moodle each Wednesday (as early as I can get them up), and must be completed by that evening (before midnight). Late quizzes will receive no credit.

Working in groups on homework is strongly encouraged, but quizzes must be completed individually.

### Exam policies

The midterm and final exams will be in-class. If you require any specific accommodations, please contact me.

Calculators will be allowed. Only ones own notes and the notes provided by the instructor will be allowed. No communication-devices will be allowed.

No exam may be taken early. Makeup exams require a doctor’s note excusing the absence during the exam.

The final exam will be cumulative.

Total grades in the course may be curved, but individual homework quizzes and exams will not be. They will be available on moodle throughout the semester.

Homework quizzes
20%
Midterm Exam #1
25%
Midterm Exam #2
25%
Final Exam
30%
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Cheating or plagiarism of any kind is not tolerated and will result in a failing grade (“F”) in the course. I take this very seriously. Engineering is an academic and professional discipline that requires integrity. I expect students to consider their integrity of conduct to be their highest consideration with regard to the course material.

## Correlation of course & program outcomes

In keeping with the standards of the Department of Mechanical Engineering, each course is evaluated in terms of its desired outcomes and how these support the desired program outcomes. The following sections document the evaluation of this course.

### Desired course outcomes

Upon completion of the course, the following course outcomes are desired:
1. students will have a clear and thorough understanding of concepts, principles, and methods of modeling mechanical, electrical, and electro-mechanical systems;
2. students will be familiar with the operation and input and output characteristics of the following electrical circuit elements:
• resistors,
• capacitors,
• inductors,
• diodes,
• transistors, and
• operational amplifiers;
3. students will understand the designs of basic circuits;
4. students will be able to model electrical and mechanical systems with a unified modeling technique;
5. students will be able to construct state-space models (including state equations) of electrical, mechanical, and electro-mechanical systems;
6. students will be able to analyze the characteristics of system models;
7. students will be able to solve for first- and second-order linear (time-invariant) system responses;
8. students will be able to solve for general linear (time-invariant) system responses;
9. students will understand the larger contexts of electro-mechanical system dynamics, especially with regard to technology development and society; and
10. students will be able to communicate what they are learning and its broader contexts.

### Desired program outcomes

The desired program outcomes are that mechanical engineering graduates have:
1. an ability to apply knowledge of mathematics, science, and engineering;
2. an ability to design and conduct experiments, as well as to analyze and interpret data;
3. an ability to design a system, component, or process to meet desired needs;
4. an ability to function on multi-disciplinary teams;
5. an ability to identify, formulate, and solve engineering problems;
6. an understanding of professional and ethical responsibility;
7. an ability to communicate effectively;
8. the broad education necessary to understanding the impact of engineering solutions in a global and social context;
9. a recognition of the need for, and an ability to engage in life-long learning;
10. a knowledge of contemporary issues; and
11. an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice

### Correlation of outcomes

The following table correlates the desired course outcomes with the desired program outcomes they support.
desired program outcomes
A B C D E F G H I J K
desired course outcomes 1