Instructor:

Asst. Prof. OÄŸuzhan Çifdalöz

Office: N – B12

Lecture Hours:

Thursday, 12.20 – 15.10, Location: M102

Course Description:

This course introduces state-space methods for the analysis and control design of linear time invariant systems. The objective of the course is to introduce state-space methods for the analysis and control design of linear time invariant systems.  Following topics will be covered: state-space representation of dynamical systems, basic properties of state-space models, modal analysis, state-space arithmetic, block diagram representation, state transition matrix, introduction to controllability, observability, state feedback, state observers, LQR design.

Learning Outcomes

Students will

1. understand the concept of state-space and its utility in analyzing and designing linear systems
2. understand the physical meaning of an eigenvalue/eigenvector
3. understand concept of stability, controllability, stabilazibility, observability, and reachability
4. learn how to design control systems using state-space via methods such as the model based compensator and linear quadratic regulator
5. Students have a practical working knowledge of state-space modeling and control systems design using computer aided design software packages (e.g. MATLAB/SIMULINK)

References:

1. Bernard Friedland, "Control System Design: An Introduction to State-Space Methods", Dover Publications, Inc., 2005, ISBN: 0-486-44278-0.
2. Paul M. DeRusso, Rob Jay Roy, Charles M. Close, Alan A. Desrochers, "State Variables for Engineers", Wiley Interscience, 1998, ISBN: 0471577952.
3. Kemin Zhou, John C. Doyle, "Essentials of Robust Control", Pearson, 1997, ISBN: 978-0135258330.

Grading Policy

Midterm Exam, 35%, Final 65%.

Course Outline

Week

Topic(s)

1

Big Picture: Systems, models, definition of states, linear vs. nonlinear systems, continuous vs. discrete systems.

2

Solving ODEs using Laplace transform, Transfer Function from State Space Description.

3

Block Diagram representation of State-Space Equations, Poles, Zeros, Eigenvalues, Eigenvectors.

4

State Transition Matrix

5

State Transition Matrix

6

Modeling Dynamical Systems, Lagrangian, Descriptor State-Space, Inverted Pendulum Example

7

Modal Analysis, Right/Left Eigenvalues and Eigenvectors, Modal Decomposition

8

State – Space Descriptions: Canonical Forms

9

MIDTERM

10

State-Space Arithmetic

11

Controllability and State Feedback

12

Observability and State Observer

13

Separation Principle and Model Based Compensators

14

Introduction to Linear Quadratic Regulators