Lectures: MW 10--11:20, F 10:00--10:50 in HRC 145 for in-person attendees, on Panopto for remote students.

Instructor: Prof. Sawyer Fuller (home page), minster@uw.edu

Office Hours: After class session and Fridays 12:30--2:00p in MEB321 on Zoom at https://washington.zoom.us/my/blinkminster

Teaching Assistant:  John James,  jmjames@uw.edu

Office Hours:   (All sections) Tues. 2:30--3:30pm & Thurs. 2:30--4:00pm in MEB251

                         (Edge students) Wed. 6:30-8:00pm  zoom room

Course online resources: lecture slides, videos, and files

Prerequisites: An undergraduate semester/quarter in linear systems (e.g. ME374) and a semester/quarter in classical continuous-time control systems (e.g. ME471 or AA/EE447, which covers linear frequency-domain transfer function description of systems through the Laplace Transform, the root locus, and feedback control including Nyquist stability criterion and gain and phase margins).

Required Textbook:  Digital Control Engineering Analysis and Design, 3rd. Ed. by M. Sami Fadali & Antonio Visioli. 

Grade Weights are given on Canvas (and are subject to change by up to 10%).

Midterm Quiz: Acceptable resources to use during exam: 1 sheet of letter-sized paper, both sides, of your own notes, an on-paper copy of the textbook, your homework solutions, lecture slides and other resources provided on the canvas website including your own notes on them, pencil and scratch paper to work out solutions, and a scientific or graphing calculator. No other resources are permitted including computers or mobile phones.

Homework: Weekly homework assignments. Solutions are due in PDF format on canvas at the assigned time. 

Design Labs: Several projects will be assigned that entail designing a digital control system using MATLAB and Simulink or the Python Control Systems Library. Each project will require a brief report. The report will be due, in PDF format on the assigned due date.

Grading:

• Projects and exams: your score will be based upon the extent that your solution demonstrates understanding of the subject matter of this course. Please box answers, specify units, and label all graphs if applicable. Solutions submitted with parts not entirely legible will be ignored.
• Homeworks will be self-graded, with oversight from the instructional staff regarding accuracy of your self-assessment. This provides additional training and feedback that helps cultivate self-reflection. Guidelines are provided in this .pdf, but it is important to be aware that it is not possible to receive full credit for a problem unless it is attempted.
• Grace periods: You have three "grace periods" that allow you to turn in an assignment late by up to two weekdays for any reason -- no instructor approval necessary -- but you may have no more than one grace period per assignment. Additional delay incurs a 10% grade penalty per weekday. Grace periods cannot be used for the Midterm or final project.

Collaboration, plagiarism, and academic integrity: Collaboration on homework and lab projects with your fellow students is encouraged, but each homework solution or project report you turn in must be solely your creation. Plagiarism (copying other people's work without acknowledgement) will not be tolerated. Please see the University of Washington's Policy on Academic Misconduct for more information. If the instructors find any evidence of plagiarism or cheating, the student may be subject to disciplinary action. Please contact the instructor(s) with questions.

Computing: You will have two options as far as software for computer-aided design of control systems. Option 1 is to use MATLAB (along with its included Simulink, Simscape, and the Control System Toolbox). New this year is Option 2, to complete all exercises exclusively using the open-source Python Control Systems Library. It is experimentally possible to use option 2 using online Jupyter notebooks such as google collab. For MATLAB, you will need a computer with the software installed (which is free for students; please download from uware).

Disability Accommodations: If you have already established accommodations with Disability Resources for Students (DRS), please communicate your approved accommodations to the instructors at your earliest convenience so we can discuss your needs in this course.

If you have not yet established services through DRS, but have a temporary health condition or permanent disability that requires accommodations (conditions include but not limited to; mental health, attention-related, learning, vision, hearing, physical or health impacts), you are welcome to contact DRS at 206-543-8924 or uwdrs@uw.edu or disability.uw.edu. DRS offers resources and coordinates reasonable accommodations for students with disabilities and/or temporary health conditions.  Reasonable accommodations are established through an interactive process between you, your instructor(s) and DRS.

Course Description

This course provides an introduction to how digital control systems are designed. A digital control system typically consists of a physical system that is continuous-time in nature, or "analog," that must be controlled by a digital computer. The computer performs sensor measurements and computes outputs at fixed time intervals, that is, in "discrete-time." This course is about designing controllers, and avoiding the pitfalls, of such (very common) systems. It is complementary to a course concerned with how a controller is executed on computer hardware, such as ME477: Embedded Computing in Mechanical Systems.

We start by introducing difference equations and the z-transform, which are the discrete-time counterparts of differential equations and the Laplace transform for continuous-time systems. We use them to compute the time and frequency responses of discrete-time systems. Next we describe how to model digital control systems and the components that comprise them, including analog-to-digital converters, digital to analog converters, zero-order hold circuits, and computation/time delays.  Information loss due to sampling and its consequences are also covered.  

Topics related to the stability of digital control systems, including Bounded-Input Bounded-Output (BIBO) stability, internal stability, and gain and phase margins, are covered next.  

The determination of digital control laws by the classical methods is the next topic.  Here we'll cover design by discrete equivalents, e.g., using the Tustin's mapping, direct z-plane root locus design, and the loop-shaping method (shaping the loop transfer function's frequency response).

Lastly, we will introduce state-space-based methods for determining digital control laws, e.g., pole placement with state or output feedback.  And we will discuss the linear quadratic (LQR state feedback + LQG state estimator) control design methods.

In addition to reading assignments in our textbook (Digital Control Engineering Analysis and Design by M. Sami Fadali and Antonio Visioli), and assigned homework problems, several projects will be assigned that entail designing control systems that function within a realistic simulation in Simulink or Python-Control. The simulations are designed to reproduce, to the extent that it is possible, designing a feedback controller for a real system.

Topics:

1. (chapter 1)
   Introduction
   Why digital control?
   Examples of digital control systems
   
   
2. (chapter 2)
   Discrete-Time Systems
   Difference equations
   The z-transform
   z-transform solution of difference equations
   Time response of discrete-time systems
   Frequency response of discrete-time systems
   The sampling theorem
   
   
3. (chapter 3)
   Modeling Digital Control Systems
   ADC model
   DAC model
   Transfer function of a ZOH
   Transfer function of DAC, analog system, and ADC combination
   Systems with transport lag
   The closed-loop transfer function
   Steady-state error and error constants
   
   
4. (chapter 4)
   Stability of Digital Control Systems
   BIBO, asymptotic and internal stability
   Nyquist stability criterion
   Phase and gain margins
   
   
5. (chapter 6)
   Digital Control System Design
   Digital implementation of analog controllers
   Direct z-plane root locus design
   Loop shaping (frequency response) design
   
   
6. (chapters 7 and 10)
   Optimal Control
   Optimal linear quadratic regulator design
   Kalman filter design
   LQG optimal control