Automatic Control Systems

This page describes the EEGR4933 Automatic Control Systems class that was taught in the spring of 2019 at LeTourneau University. This is an undergraduate class that introduces some of the most important methods used for the design of control systems, with an emphasis on state-based methods. The class does not go very deep into mathematical details, but emphasizes the essential concepts and computer-aided controller design. Simulation is carried out in MATLAB and Simulink. The related EEGR3523 Mechatronics, which includes an introduction to control systems, is normally taken before this class.

Textbook: Many of the topics covered in this class appear in Feedback Control Systems, 5th edition, by Phillips and Parr, Prentice-Hall, 2010.

Homework: Weekly homework sets were assigned.

Lectures: The class had 42 lectures of 55 minutes each. The first 23 lectures were focused on continous-time systems; the discrete-time case was also considered, but briefly. The remaining 19 lectures focused on the discrete-time case. The material was structured as follows:

1. Introduction to the state-variable model. Contniuous-time and discrete-time examples.
2. The state-variable model. The relation to the transfer function model. Controllable and observable canonical forms.
3. The state-variable model. The relation to the transfer function model. Controllable and observable canonical forms.
4. Stability in continuous-time systems. Examples. Equilibrium points.
5. Stability in discrete-time systems. Controllability.
6. Controllability. Observability. Examples.
7. Linear state feedback.
8. Linear state feedback. Examples.
9. State estimation. State feedback with state estimation.
10. State feedback with state estimation. Examples.
11. Integral control. LQR control.
12. LQR control. Examples. Kalman estimation.
13. Kalman estimation. LQG.
14. LQG examples.
15. LQG example. Discrete-time integral control.
16. Discrete-time LQR and Kalman estimation. Systems with delay. The Smith predictor.
17. The Smith predictor. Linearization.
18. Linearization. Examples.
19. Equilibrium points. Asymptotic stability. The relation to the stability of the linearized models.
20. Gain scheduling.
21. Gain scheduling. Examples.
22. Fuzzy control. Examples.
23. Fuzzy control. Examples.
24. Comparison of continuous and discrete-time systems. The Z-transform.
25. The Z-transform.
26. Sampled data systems.
27. The starred transform. Examples.
28. The starred transform. Examples. Block diagrams.
29. More examples.
30. Converting continous-time state-variable models to discrete time.
31. Conversions from continuous-time to discrete-time.
32. State-variable methods for discrete-time systems. Dead-beat control. Integral control.
33. LQR. Kalman estimation.
34. Transfer-function based methods. The bilinear transformation. Jury's test of stability.
35. Jury's test of stability.