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Lumped System Theory

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.

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.

Spring 2024 Syllabus

Topics Covered:

Weeks Module Assignments and Exams
1 & 2

Welcome and Introduction

1. Systems
2. State Variables
3. State-Space Models
4. State-Space Models vs. Transfer Functions
FunWork 1
3 & 4
1. Linear Algebra Review
2. Function of Square Matrices
3. Matrix Exponential
4. Solutions of Continuous-Time Autonomous LTI Systems
FunWork 2
5 & 6
1. Solutions of Discrete-Time Autonomous LTI Systems
2. Solutions of Autonomous LTV Systems
3. Stability of Continuous-Time Linear Systems
4. Stability of Discrete-Time Linear Systems
FunWork 3
7 & 8
1. Stability of Nonlinear Systems Around Equilibrium Points
2. Solutions of Controlled Continuous-Time LTI Systems
3. Solutions of Controlled Discrete-Time LTI Systems
Midterm 1
9 & 10
1. Solving Continuous-Time Dynamical Systems Numerically
3. Lyapunov Stability Theory
4. Reachability and Controllability of Discrete-Time LTI Systems
FunWork 4
11 & 12
1. Controllability of Continuous-Time LTI Systems
2. Separating the Controllable Part from the Uncontrollable Part of a Given System
3. Observability of Continuous-Time LTI Systems
4. State-Space Realizations of Transfer Functions

Funwork 5

Midterm 2

13 & 14
1. Bounded-Input Bounded-Output (BIBO) Stability
2. Canonical Forms of Single-Input-Single-Output (SISO) Systems
3. State Feedback Control

FunWork 6

15
1. State Observer Design
2. Observer-Based Feedback Controller
3. Linear Quadratic Regulation (LQR) Problems (additional module for your knowledge, but material not covered on Final Exam)

FunWork 7

Final Exam Week

Final Exam

Prerequisites:

• It is expected that you are familiar with the 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 MA 511 is listed as a co-prerequisite of this course, in practice, students who took MA 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:
• Linear Algebra and Its Applications, 4th ed., G. Strang, 2006
• Introduction to Linear Algebra, 4th ed., G. Strand, Wellesley-Cambridge Press, 2009

Applied / Theory:

10/90

Homework:

Homework is assigned biweekly and may involve MATLAB programming.
Exams:
Two midterm exams; one final exam

Textbooks:

No required textbooks for this course. The lectures are mostly based on instructor's own notes. However, the following may be useful references:
• C.T. Chen, "Linear Systme Theory and Design", Oxford University Press, Fourth edition, 2013
• S.H. Zak, "Systems and Control", Oxford University Press, 2003
• P.J. Antsaklis and A.N. Michel, "A Linear Systems Primer", Birkhauser Boston 2007
• T. Kailath, "Linear Systems", Prentice Hall, 1980
• W.J. Rugh, "Linear System Theory", Pearson, Second edition, 1995

Computer Requirements:

A computer capable of running Matlab is required for solving some homework problems

MATLAB