This course focuses on the analysis and design of systems control. This course will introduce time-domain systems dynamic control fundamentals and their design issues for electrical engineering applications. Emphasis will be on linear, time-invariant, multi-input multi-output continuous time systems. Topics include open and closed-loop state-space representations, analytical solutions, computer simulations, stability, controllability, observability, pole-placement controller/observer design, and brief introduction to optimal control. ECE 301 (Linear Systems) or equivalent is the pre-requisite for this course. A strong background in linear algebra and differential equations is not required but is highly recommended. The MATLAB/SIMULINK computer software package will be used extensively to assist in the understanding of concepts and fundamentals of system dynamics and control, and also to analyze and design control systems. 3 credit hours

Prerequisite Courses
ECE 301 Linear Systems

Recommended Background Courses
ECE 435 Elements Control                        ECE 436 Digital Control System

Recommended Co-Requisite Courses
ECE 513 Digital Signal Processing            ECE 514 Random Processes
ECE 556/456 Mechatronics

The course materials can be classified into basic material (95%), recommended materials (4%), and optional materials (1%). Exams and homework will be based mainly on the basic material. Recommended materials will be presented once a while for your entertainment, and optional materials will be presented once a long while for your imaginations.

A.  Homework (approximately 6 – 9 assignments):                          20%

B.  1st Exam:                                                                                      25%

C.  2nd Exam:                                                                                     25%

D.  Final Exam:                                                                                  30%

The problems of exams will be based mainly on lecture materials and the textbook.

Your Class Grade = MAX {Relative standing, Absolute standing}, where
(a) Relative standing
The whole class grade will be “curved” and your grade will be based on your relative standing in the class.
(b) Absolute standing (AS – average score)

MATLAB Student Version, latest version, Mathworks. (Recommended)

References (Optional):

A. Chi-Tsong Chen, Linear System Theory and Design, HRW. (Advanced)
B. Thomas Kailath, Linear Systems, Prentice Hall. (Intermediate)
C. Katsuhiko Ogata, Modern Control Engineering, Prentice Hall. (Basic)

A.    General description of Systems and System Dynamics (Basic)

1.   The Concepts of Systems, System Dynamics and Classifications

2.   Control Theory

Systems Performance

Goal: After these lectures and studies, students should have a general concept and meaning of “dynamic” systems. Hopefully, you will be fascinated with “systems and control” and are interested to find more.

B.  State Variables and State Space Description of Dynamic Systems (Basic)

1.   The Concept of State           

2.   State Space Representation of Dynamic Systems

3.   State Equation for Dynamic Systems

4.   Obtaining State Equations from Input-Output Differential Equations

Goal: After these lectures, students should know how use state-space description to model simple linear electric circuits, dc motor dynamics, transfer functions, and high-order differential equations.

C.  Analysis of the Equation of (Linear Time Invariant) Dynamical Systems (Basic)

1.   Solution of State Equations — Time domain solutions

2.   Solution of Nonlinear Equations

Goal: After these lectures, students should know how to apply some basic linear algebra such as matrix operations and eigenvalues to solve linear system and control problems directly in time domain – Yes! We do not need to go to frequency domain to find the solutions.

D.  Controllability and Observability (Basic)

1.   Concepts and Definitions

2.   Time-Invariant Systems with Distinct Eigenvalues

3.   Time-Invariant Systems with Arbitrary Eigenvalues (optional)

Goal: After these lectures, students should understand under what circumstance that they could solve the control problem. If so, how can they solve the problem in a professional manner.

E.  Nonlinear Equations and Perturbation Theory (Basic)

1.   Taylor Series

2.   Linearization of Nonlinear Equations

Goal: After these lectures, students should know that most systems in the real-world are nonlinear, yet in most cases, we can linearize the nonlinear system and apply the linear control system design techniques learned in the class to a system to obtain good performance.

F.   Stability for Linear and Nonlinear Systems (Basic)

1.   Equilibrium Points

2.   Stability Definitions

3.   Linear Time-Invariant Stability

4.   Nonlinear Time-Invariant Stability (Recommend)

5.   Direct Method of Lyapunov (Optional)

Goal: After these lectures, students should feel comfortable and confident in using the word stability for control applications. They should also be able to use the techniques to test if the system is stable.

G.   Design of Linear Feedback Systems (Basic)

1.   Observer Design

2.   Controller Design

Goal: After these lectures, students should be able to synthesize all the concepts and techniques learned in previous lectures to perform design work for applications.

H.   Nonlinear Control Systems (Basic-Recommended)

1.   Linearization

2.   Dynamic Linearization Using State Feedback

Goal: This session has a strong tie with Topic E. Actually; they are in the same chapter of the text. After these lectures, students should be able to apply the techniques learned for linear system to a class of nonlinear system control.

I.    Brief Introduction to Optimal Control (Basic)

Goal: The session will provide the class with basic concept of optimal control, which often used along with state-space description.

NCSU has recommended minimum specifications for computers used for classes. Depending on your computer needs, we recommend your computer meet or exceed the following minimum specifications below.

PCs must have an Intel-compatible 1 GHz processor, 512 MB RAM, 60 GB hard drive with 1 GB free space available, 256 Color Display, CD-ROM drive, 1024x768 (min.) video adapter, sound card, and speakers. The operating system should be Windows XP Pro. Real One Player Basic (available free online) and high speed Internet connection such as cable, DSL, T1 or LAN will be required for EOL courses.

MAC users must have a G4 processor with firewire and USB factory built-in, 512 MB RAM, 60 GB with 1GB free space available, 256 Color Display, CD-ROM drive, 1024x768 (min) video adapter, sound card, and speakers. The operating system must be MacOS 10.4 (minimum) along with the above RealOne and Internet specifications above.

For more detailed information on computer specifications and recommendations, please refer to our website at: http://engineeringonline.ncsu.edu/currentstudents/computeraccess.htm