Lumped System Theory
ECE60200
Credit Hours:
3Learning Objective:
- Construct models for dynamical systems arising in various applications, such as: mechanical, electrical, pneumatic, hydraulic, economic, and biological systems
- Recognize various properties of given linear systems, such as: stability, controllability, observability, stabilizability, and detectability
- Design controllers so that a system satisfies given performance specifications
- Test and validate the controller design using simulation tools, such as MATLAB and Simulink
Description:
This course provides an introduction to the fundamentals of modern control theory for linear dynamical systems. The course adopts the state-space method that builds upon the classical transfer function methods covered in undergraduate feedback control courses. The state-space framework is used in modeling and controller design for systems arising in many engineering and non-engineering disciplines.
Topics Covered:
1. Systems and state variables2. State-space models of lumped linear systems
3. Linear algebra review
4. Functions of square matrices
5. Matrix exponential
6. Solution of linear time-invaraint systems
7. Solution of linear time-varying systems
8. Stability
9. Lumped nonlinear systems
10. Quadratic forms and singular value decomposition
11. Controllability
12. Observability
13. Minimality, BIBO stability and canonical forms
14. State feedback control
15. Output feedback observer
16. Linear quadratic regulation
17. Model order reduction