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State-Space Control Systems

(ME EN 5210/6210 & CH EN 5203/6203)

In State-Space Control Systems, we will learn how to analyze and design systems expressed as coupled linear first-order differential equations. As an alternative to Classical Control Systems (ME EN 5200/6200), which makes use of the Laplace transform to analyze and design single-input/single-output systems, state-space methods enable us to analyze and design multi-input/multi-output systems in time domain. We will consider both continuous-time and discrete-time equations. Control systems are used to regulate the temperature in a room, to command a robot arm along a desired trajectory, to autopilot an airplane, and to ensure that manufacturing processes stay within specifications. A course in control systems provides a student with a common language with which to qualitatively and quantitatively discuss system performance and specifications. In addition, state-space methods are used to analyze a variety of systems that, at first, seem quite distinct from engineering systems, including economic and social models.

This is not a course about forming state-space models, but rather, analyzing and controlling systems that are already described in state-space form. Other courses exist, at the undergraduate and graduate level, that focus on the topic of forming state-space models for physical systems.

This course is offered every Spring semester.

A course syllabus from the Spring 2016 offering can be found here, which provides the structure of the course and the topics that are covered.

Video Tutorials

1. Introduction to Linear Systems
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2. Modeling Systems in State-Space Form
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3. Transfer Functions
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4. Introduction to Discrete Systems
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5. Fundamentals of Linear Algebra
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6. Linear Algebraic Equations
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7. Eigenvectors and Eigenvalues
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8. Similarity Transformations
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9. Jordan Form
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10. Functions of a Square Matrix
⚠ (:youtube 1Cpne5xpG60 loop=0 fs=1 scale=1.2:)

11. Solutions of Continuous State-Space Equations
⚠ (:youtube KG7PY1iKDGw loop=0 fs=1 scale=1.2:)

12. Solutions of Discrete State-Space Equations
⚠ (:youtube FGAOequUUe8 loop=0 fs=1 scale=1.2:)

13. Solutions of Sampled-Data State-Space Equations
⚠ (:youtube O1gnwcJEW7w loop=0 fs=1 scale=1.2:)

14. State-Space Realizations of Transfer Functions
⚠ (:youtube cnbY2AUtGAY loop=0 fs=1 scale=1.2:)

15. Continuous-Time Bounded-Input Bounded-Output Stability
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16. Discrete-Time Bounded-Input Bounded-Output Stability
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17. Continuous-Time Internal Stability
⚠ (:youtube hszc-koueB8 loop=0 fs=1 scale=1.2:)

18. Discrete-Time Internal Stability
⚠ (:youtube 6w3hZxVOBYw loop=0 fs=1 scale=1.2:)

19. Controllability in Continuous Time
⚠ (:youtube qsfd80lqt4w loop=0 fs=1 scale=1.2:)

20. Observability in Continuous Time
⚠ (:youtube SmOJSlFKP-g loop=0 fs=1 scale=1.2:)

21. Canonical Decomposition of Controllability and Observability
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22. Controllability and Observability in the Jordan Form
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23. Controllability of Sampled-data Systems
⚠ (:youtube teZMg1sHy00 loop=0 fs=1 scale=1.2:)

24. State Feedback
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25. Stabilization
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26. Tracking
⚠ (:youtube URBvoe7IKKs loop=0 fs=1 scale=1.2:)

27. Robust Tracking with Disturbance Rejection
⚠ (:youtube rruA2GGu6uU loop=0 fs=1 scale=1.2:)

28. State Observers
⚠ (:youtube Jn9ZTxl1vdY loop=0 fs=1 scale=1.2:)

29. Feedback from Estimated States
⚠ (:youtube LXav9w_EBOY loop=0 fs=1 scale=1.2:)

30. Feedback from Estimated States: MIMO Case
⚠ (:youtube RFbF__Q7mxw loop=0 fs=1 scale=1.2:)

31. LQR Method
⚠ (:youtube St5L-ekOKGA loop=0 fs=1 scale=1.2:)

32. Kalman Filter (Continuous Time)
⚠ (:youtube 4Ef1RO06DnY loop=0 fs=1 scale=1.2:)