24-677: Special Topics: Linear Control Systems, Fall 2020

Instructor — Prof. Ding Zhao
Teaching assistants — Peide Huang, Hongyi Zhou, Kartik Sah, John Magnus-Sharpe, Raj Kolamuri
Course linksCanvas site, Course webpage

Course description — This course offers a practical introduction to the analysis and design of model-based control for linear systems. Topics include modeling and linearization of multi-input multi-output dynamic systems using the state-variable description, fundamentals of linear algebra, analytical and numerical solutions of systems of linear time-invariant differential and difference equations, structural properties of linear dynamic physical systems (controllability, observability and stability), canonical realizations, and design of state feedforward/feedback, optimal, and stochastic controllers and observers, including pole placement, LQR, MPC, Kalman filter, adaptive control approaches. Students will learn how to design linear controllers and implement them to solve real-world problems in control and robotics

Course objectives — The objectives of this course are to develop students’ knowledge of multi-input / multi-output linear systems and their control, to enhance students’ knowledge of engineering applications of linear algebra, and to prepare students for further graduate study in control systems, robotics, machine learning, and signal processing.

Course outcomes — Upon completion of this course, the student should be able to:
  • Compare state space and transfer function approaches to the study of linear control systems and their relative advantages
  • Assess the stability of systems using various stability definitions
  • Determine the controllability and observability of a linear system
  • Design feedback controllers and observers for linear systems
  • Design optimal controller and stochastic observer for linear systems
  • Design model-based adaptive controlled for linear systems
  • Design controllers to solve real-world problems and implement them in Python and Webot

Textbook — No textbook. Lecture slides will be available on Canvas.

Lecture schedule for Fall 2020

Week Day, Date Lec# Topic
1 Tuesday, Sep 1, 2020 1 Overview, types of system, state space representation [Slide]
1 Thusrday, Sep 3, 2020 2 State space representation, examples, linearization, solution of CT LTI, expoential of matrix [Slide]
2 Tuesday, Sep 8, 2020 3 Eigen-values/vectors, determinant, linear independence [Slide]
2 Thursday, Sep 10, 2020 4 CH theorem [Slide]
3 Tuesday, Sep 15, 2020 5 Similarity transformation, matrix inverse, diagonalizability [Slide]
3 Thursday, Sep 17, 2020 6 Jordan decomposition, DT-LTI [Slide]
4 Tuesday, Sep 22, 2020 7 Controllability/observability definition, matrix test, solution of linear equations, SVD [Slide]
4 Thursday, Sep 24, 2020 8 PBH test, Jordan form test [Slide]
5 Tuesday, Sep 29, 2020 9 Laplace transformation, transfer function, ss2tf, controllable canonical forms [Slide]
5 Thursday, Oct 1, 2020 10 Observable cononical form,MIMO, kalman decomposition, minimal realization [Slide]
6 Tuesday, Oct 6, 2020 11 Lyapunov stable, stability of Linear Time-Invariant systems [Slide]
6 Thursday, Oct 8, 2020 12 LTV example, stabilizability/detectability, Lyapunov’s Indirect/direct method [Slide]
7 Tuesday, Oct 13, 2020 13 Instability, BIBO, BIBS [Slide]
7 Thursday, Oct 15, 2020 14 Description of the project, PID control, pole placement [Slide]
8 Tuesday, Oct 20, 2020 15 Luenberger observer, separation principle [Slide]
8 Thursday, Oct 22, 2020 16 Mid-term exam
9 Tuesday, Oct 27, 2020 17 Reduced order observer, MIMO poleplacement [Slide]
9 Thursday, Oct 29, 2020 18 Finite-horizon dicrete-time linear quadratic regulator [Slide]
10 Tuesday, Nov 3, 2020 19 MPC, tracking [Slide]
10 Thursday, Nov 5, 2020 20 IH DT LQR [Slide]
11 Tuesday, Nov 10, 2020 21 FH/IH CT LQR [Slide]
11 Thursday, Nov 12, 2020 22 Kalman Filter [Slide]
12 Tuesday, Nov 17, 2020 23 Extended KF, UKF, SLAM [Slide]
12 Thursday, Nov 19, 2020 24 Adaptive control [Slide]
13 Tuesday, Nov 24, 2020 25 Adaptive control [Slide]
13 Thursday, Nov 26, 2020 Thanksgiving Holiday; No Classes
14 Tuesday, Dec 1, 2020 26 Alumni events
14 Thursday, Dec 3, 2020 27 Guest Speaker
15 Tuesday, Dec 8, 2020 28 Application of model-based methods in AIML- an introduction [Slide]
15 Thursday, Dec 10, 2020 29 Review of the whole course, outraduction [Slide]

Accommodations — If you have a disability and have an accommodations letter from the Disability Resources office, I encourage you to discuss your accommodations and needs with me as early in the semester as possible. I will work with you to ensure that accommodations are provided as appropriate. If you suspect that you may have a disability and would benefit from accommodations but are not yet registered with the Office of Disability Resources, I encourage you to contact them at access@andrew.cmu.edu.

Academic Integrity Policy — Honesty and transparency are important features of a good scholarship. On the flip side, plagiarism and cheating are serious academic offenses with serious consequences. If you are discovered engaging in either behavior in this course, you will earn a failing grade on the assignment in question, and further disciplinary action may be taken. For a clear description of what counts as plagiarism, cheating, and/or the use of unauthorized sources, please see the University’s Policy on Academic Integrity.

Take Care of Yourself — Take care of yourself. Do your best to maintain a healthy lifestyle this semester by eating well, exercising, avoiding drugs and alcohol, getting enough sleep, and taking some time to relax. This will help you achieve your goals and cope with stress. All of us benefit from support during times of struggle. There are many helpful resources available on campus and an important part of the college experience is learning how to ask for help. Asking for support sooner rather than later is almost always helpful. If you or anyone you know experiences any academic stress, difficult life events, or feelings like anxiety or depression, we strongly encourage you to seek support. Counseling and Psychological Services (CaPS) is here to help: call 412-268-2922 and visit their website at http://www.cmu.edu/counseling/. Consider reaching out to a friend, faculty, or family member you trust for help getting connected to the support that can help.