525.629.81 - Discrete-Time Control Systems

Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on the course menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

• Introduction to the Course (Review of Continuous-Time Control System concepts)
• Introduction to Discrete-Time Control: Signal Conversion and Processing
• Difference Equations, the z- and Inverse z-Transform, and s- versus z-Plane Mapping
• Discrete-time Transfer Functions, Block Diagrams and Introduction to Discrete-time Stability Analysis
• Time-Domain Analysis of Discrete-Time Systems: Time Domain Metrics, Steady-Steady State Error, Root Locus
• Frequency-Domain Analysis of Discrete-Time Systems: Frequency Domain Metrics, Polar Plot, Nyquist Criterion, Bode Plot via the w-Transformation
• Discrete-Time Control Design Using Analog Design Emulation (Indirect Digital Design) via Numerical Integration, Pole-Zero Mapping, Hold Equivalents
• Direct Digital Design in the Frequency Domain Using Transform Techniques
• Direct Digital Design via Root Locus Techniques
• Introduction to Discrete-Time State-Space Control Systems Design

Course Goals

As a follow-on to the Continuous Control Systems (EN.525.609) course, the primary goal of this course is to present a comprehensive introduction to the theory and design of discrete-time control systems. The emphasis of this course is the representation, modeling, analysis and synthesis of discrete-time / sampled-data systems via classical time- and frequency-domain methodologies.  Control design / synthesis introduces both digital design emulation methods (e.g., emulating a continuous-time compensator via zero-pole mapping, hold equivalents, etc.) and direct design (z- and w-transform) methods using root locus and frequency domain synthesis techniques (e.g., Bode, Nyquist).  This “classical” approach to discrete-time control representation, analysis and synthesis is followed by a discussion of the “modern” approach which includes discrete-time state-space representation of dynamic systems, controllability, observability, similarity transforms, and pole placement via full state feedback methods.  Moreover, each student must review the open literature for relevant (applications-based) discrete-time control publications (conference proceedings, journal articles, textbook sections/ chapters) and select, review, implement (in Matlab, or similar programming platform), and present a discrete-time control systems design project that reflects / emphasizes one or more of the key topics introduced in this course.  

Course Learning Outcomes (CLOs)

• Describe, mathematically, dynamic systems in transfer function (input/output) and state space forms and convert from one form to the other.
• Apply sampled-data theory, z-transform methods, and related analytical tools to describe and analyze digital control systems.
• Assess the stability of discrete-time systems.
• Apply time- and frequency-domain analysis methods to analyze and design discrete-time systems.
• Design discrete-time control systems using emulation methods and transform techniques (direct digital design).
• Conduct a technical literature review of digital control systems applications to implement / replicate in MATLAB a control concept from a selected technical paper / journal article.
• Explain the key issues arising in digital controller implementation.

Textbooks

Phillips, C. L., Nagle, H. T., & Chakrabortty, A. (2014). Digital control system analysis and design (4th ed.). Pearson. ISBN-10: ‎ 0132938316

Other Useful References

• Automatic Control Systems, by B.C. Kuo, Prentice Hall Publishers, ISBN: 0-13-304759-8
• Digital Control of Dynamic Systems, by Franklin, Powell and Workman, Addison Wesley Publishers, ISBN: 0-201-82054-4
• Digital Control Systems, by B.C. Kuo, Saunders College Publishing; ISBN: 0-03-012884-6

Required Software

You will need access to a recent version of MATLAB. The MATLAB Total Academic Headcount (TAH) license is now in effect. This license is provided at no cost to you. Send an email to software@jhu.edu to request your license file/code. Please indicate that you need a standalone file/code. You will need to provide your first and last name, as well as your Johns Hopkins email address. You will receive an email from Mathworks with instructions to create a Mathworks account. The MATLAB software will be available for download from the Mathworks site.

Student Coursework Requirements

Preparation and Participation (10% of Final Grade Calculation)

You are responsible for carefully reading all assigned material and being prepared for discussion. The majority of readings are from the course text. Additional reading may be assigned to supplement text readings.

Post your initial response to the Discussion questions by the evening of day 3 for that module week. Posting a response to the discussion question is part one of your grade for module discussions (i.e., Timeliness).

Part two of your grade for module Discussion is your interaction (i.e., responding to classmate postings with thoughtful responses) with at least two classmates (i.e., Critical Thinking). Just posting your response to a discussion question is not sufficient; we want you to interact with your classmates. Be detailed in your postings and in your responses to your classmates' postings. Feel free to agree or disagree with your classmates. Please ensure that your postings are civil and constructive.

I will monitor module Discussions and may respond to some of the discussions as discussions are posted. In some instances, I might  summarize the overall discussions and post the summary for the module.

Evaluation of preparation and participation is based on contribution to discussions.

Preparation and participation is evaluated by the following grading elements:

1. Timeliness (50%)
2. Critical Thinking (50%)

Preparation and participation is graded as follows:

• 100–90 = A—Timeliness [regularly participates; all required postings; early in discussion; throughout the discussion]; Critical Thinking [rich in content; full of thoughts, insight, and analysis].
• 89–80 = B—Timeliness [frequently participates; all required postings; some not in time for others to read and respond]; Critical Thinking [substantial information; thought, insight, and analysis has taken place].
• 79–70 = C—Timeliness [infrequently participates; all required postings; most at the last minute without allowing for response time]; Critical Thinking [generally competent; information is thin and commonplace].
• <70 = F—Timeliness [rarely participates; some, or all required postings missing]; Critical Thinking [rudimentary and superficial; no analysis or insight is displayed].

Assignments (40% of Final Grade Calculation)

Assignments will include a mix of qualitative assignments (e.g. literature reviews, model summaries), quantitative problem sets, and case study updates. Include a cover sheet with your name and assignment identifier. Also include your name and a page number indicator (i.e., page x of y) on each page of your submissions. Each problem should have the problem statement, assumptions, computations, and conclusions/discussion delineated. All Figures and Tables should be captioned and labeled appropriately.

All assignments are due according to the dates in the Calendar.

Late submissions will be reduced by one letter grade for each week late (no exceptions without prior coordination with the instructors).

If, after submitting a written assignment you are not satisfied with the grade received, you are encouraged to redo the assignment and resubmit it. If the resubmission results in a better grade, that grade will be substituted for the previous grade.

Qualitative assignments are evaluated by the following grading elements:

1. Each part of question is answered (20%)
2. Writing quality and technical accuracy (30%) (Writing is expected to meet or exceed accepted graduate-level English and scholarship standards. That is, all assignments will be graded on grammar and style as well as content.)
3. Rationale for answer is provided (20%)
4. Examples are included to illustrate rationale (15%) (If you do not have direct experience related to a particular question, then you are to provide analogies versus examples.)
5. Outside references are included (15%)

Qualitative assignments are graded as follows:

• 100–90 = A—All parts of question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [rich in content; full of thought, insight, and analysis].
• 89–80 = B—All parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [substantial information; thought, insight, and analysis has taken place].
• 79–70=C—Majority of parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [generally competent; information is thin and commonplace].
• <70=F—Some parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [rudimentary and superficial; no analysis or insight displayed].

Quantitative assignments are evaluated by the following grading elements:

1. Each part of question is answered (20%)
2. Assumptions are clearly stated (20%)
3. Intermediate derivations and calculations are provided (25%)
4. Answer is technically correct and is clearly indicated (25%)
5. Answer precision and units are appropriate (10%)

Quantitative assignments are graded as follows:

• 100–90 = A—All parts of question are addressed; All assumptions are clearly stated; All intermediate derivations and calculations are provided; Answer is technically correct and is clearly indicated; Answer precision and units are appropriate.
• 89–80 = B—All parts of question are addressed; All assumptions are clearly stated; Some intermediate derivations and calculations are provided; Answer is technically correct and is indicated; Answer precision and units are appropriate.
• 79–70=C—Most parts of question are addressed; Assumptions are partially stated; Few intermediate derivations and calculations are provided; Answer is not technically correct but is indicated; Answer precision and units are indicated but inappropriate.
• <70=F—Some parts of the question are addressed; Assumptions are not stated; Intermediate derivations and calculations are not provided; The answer is incorrect or missing; The answer precision and units are inappropriate or missing.

Course Project (30% of Final Grade Calculation)

As part of this course, the student will research and select (pending instructor approval) a conference / journal article or textbook section / chapter discussing applications-based discrete-time control system concept and / or analysis or design process in an area of particular interest to the student. The paper / article should reflect and emphasize one or more of the key topics introduced in this course.  Example application areas include: discrete-time stability analysis of an aerodynamic vehicle (airplane, guided missile, etc.), discrete-time proportional-integral-derivative (PID) control design for a specific application (e.g., aircraft or missile flight control, space telescope pointing, etc.), application of the Nyquist stability criterion to discrete-time stability analysis and/or controller design of a discrete-time compensator for a specific application, etc.  Purely theoretical papers are allowed if directly relevant to and expound upon the course topics but are not preferred.

At the start of the semester, you should begin to think about selecting a topic for your project. To ensure the idea aligns with the overall goals of the course, the instructor must approve your project proposal before you begin further developing your idea. Project topic selection and accompanying candidate published papers / textbook sections must be submitted in PDF form to the instructor by the end of Module 6. During Module 13, you will submit your completed project presentation charts (PDF form) and presentation video (MP4 only) of your project to the class.

Student final presentations should include the following sections: 

• Overview of the presentation.
• Motivation and problem description / setup.
• Summary of author’s approach to solving the problem.
• Summary of author’s published results and compared / contrasted with your results (if applicable).
• Summary and (your) closing remarks / conclusions.

 Additional information and detailed instructions about the course project can be found in the “Course Project Description” document located within the Course Information folder of the course site.

The course project is evaluated by the following grading elements:

1. Student preparation and organization (40%).
2. Student technical understanding of the course project topic (40%).
3. Technical preparation and correspond results (e.g., computer simulation work to replicate results) (20%)

Course Project is graded as follows:

• 100–90 = A—Student Preparation, presentation organization and technical results are clear, well defined and understood [rich in content; full of thought, insight, and analysis].
• 89–80 = B— Student Preparation, presentation organization and technical results are clear, well defined and understood [substantial information; thought, insight, and analysis has taken place].
• 79–70 = C— Student Preparation, presentation organization and technical results are clear and reasonably defined and understood [generally competent; information is thin and commonplace].
• <70 = F— Student Preparation, presentation organization and technical results are not clear or well defined and understood [rudimentary and superficial; no analysis or insight displayed].

Exams (20% of Final Grade Calculation is from the Midterm Exam)

The midterm exam will be available at the start of Module 7. You can take the exams at any time during the week they are released.  However, the exams are self-timed and you will have 75-minutes to complete the midterm exam once you have viewed / downloaded them.  Once you have completed the exam, scan the exam with your solutions into PDF form (make sure the scan is oriented correctly and is readable) and upload the result to the assignment area.  Do not discuss the exam with anyone, including your classmates until the exams are graded.  You may refer to a 1-sided sheet of your notes / equations, and you may not open the textbook or search the internet for answers.

The exams are evaluated by the following grading elements:

6. Each part of question is answered (20%)
7. Writing quality and technical accuracy (30%) (Writing is expected to meet or exceed accepted graduate-level English and scholarship standards. That is, all assignments will be graded on grammar and style as well as content.)
8. Rationale for answer is provided (20%)
9. Examples are included to illustrate rationale (15%) (If a student does not have direct experience related to a particular question, then the student is to provide analogies versus examples.)
10. Outside references are included (15%)

Exams are graded as follows:

• 100–90 = A—All parts of question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [rich in content; full of thought, insight, and analysis].
• 89–80 = B—All parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [substantial information; thought, insight, and analysis has taken place].
• 79–70 = C—Majority of parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [generally competent; information is thin and commonplace].

Grading Policy

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students. This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University is committed to providing welcoming, equitable, and accessible educational experiences for all students. If disability accommodations are needed for this course, students should request accommodations through Student Disability Services (SDS) as early as possible to provide time for effective communication and arrangements.  For further information about this process, please refer to the SDS Website.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.  For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.    If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.