# Lumped System Theory

## ECE60200

3

### Learning 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 variables
2. 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
17. Model order reduction

### Prerequisites:

It's highly recommended that you are familiar with Laplace transform and ordinary differential equations. Knowledge of undergraduate feedback control is not strictly needed for most topics but will definitely increase your appreciation of some of the topics covered in this course. Knowledge of linear algebra is needed. Although officially Purdue's MATH 511 is listed as a co-prerequisite of this course, in practice, students who took MATH 511 and this course in the same semester often found it challenging as the pace of the two courses may not be fully synchronized. Some references that can help you freshen up on linear algebra include 1) Linear Algebra and Its Applications, 4th ed., G. Strang, 2006 and 2) Introduction to Linear Algebra, 4th ed., G. Strang, Wellesley-Cambridge Press, 2009.

20 / 80

### Homework:

Approximately 7 homework assignments

No

### Exams:

Two midterm exams; one final exam

### Textbooks:

None; a list of recommended reading is provided in the course.

### Computer Requirements:

ProEd minimum computer requirements; student edition of MATLAB or its equivalent (e.g., Mathematica).

MATLAB

view