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Main: 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

2. Modeling Systems in State-Space Form

3. Transfer Functions

4. Introduction to Discrete Systems

5. Fundamentals of Linear Algebra

6. Linear Algebraic Equations

7. Eigenvectors and Eigenvalues

8. Similarity Transformations

9. Jordan Form

10. Functions of a Square Matrix

11. Solutions of Continuous State-Space Equations

12. Solutions of Discrete State-Space Equations

13. Solutions of Sampled-Data State-Space Equations

14. State-Space Realizations of Transfer Functions

15. Continuous-Time Bounded-Input Bounded-Output Stability

16. Discrete-Time Bounded-Input Bounded-Output Stability

17. Continuous-Time Internal Stability

18. Discrete-Time Internal Stability

19. Controllability in Continuous Time

20. Observability in Continuous Time

21. Canonical Decomposition of Controllability and Observability

22. State Feedback

23. Stabilization

24. Tracking

25. Robust Tracking with Disturbance Rejection

26. State Observers

27. Feedback from Estimated States

28. Feedback from Estimated States: MIMO Case

29. LQR Method

30. Kalman Filter (Continuous Time)

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