4 units – Fall Quarter

**Lecture:** 3 hours

**Laboratory:** 3 hours

**Prerequisite:** EEC 100

**Grading:** Letter.

**Catalog Description: **

Analysis and design of feedback control systems. Examples are drawn from electrical and mechanical systems as well as other engineering fields. Mathematical modeling of systems, stability criteria, root-locus and frequency domain design methods.

**Expanded Course Description:**

- Introduction to Control Systems
- Definition of Control Systems
- Examples of Modern Control Systems

- Mathematical Preliminaries
- Linear and Nonlinear Systems
- Linear Approximations of Physical Systems
- Differential Equations of Systems
- The Laplace Transform
- Analysis of Electrical and Mechanical Systems in the s-Domain
- Transfer Functions
- Block-Diagram Representations

- Mathematical Modeling and Control of Linear Feedback Systems
- Transfer Functions of Systems with Op-Amps
- Electro-mechanical Systems
- Modeling of DC Motors
- Design of a Speed Control System
- Design of a Position Control System
- Comparison of Disturbance Reduction
- Transient Response
- Steady-State Error
- Sensitivity to Parameter Variations in Open-Loop and Closed-Loop Control Systems
- The Cost of Feedback
- Signal Flow Graphs
- Mason’s Rule

- Stability of Linear Feedback Systems
- The Concept of Stability
- BIBO Stability
- Routh-Hurwitz Stability Criterion
- Relative Stability
- Location of Open-Loop and Closed-Loop Poles
- Design of Stable Systems

- Performance of Feedback Control Systems
- Design Requirements Based on Time-Domain Performance Specifications
- The Location of Poles and the Transient Response
- Steady-State Error

- The Root-Locus Method
- The Rules of the Root-Locus Method
- Analysis and Design using the Root-Locus Method
- Parameter Design
- Sensitivity and Frequency Response

- The Nyquist Stability Criterion
- Contour Mapping in the S-Plane
- The Nyquist Criterion
- Relative Stability
- Closed-Loop Frequency Response
- Design of Stable Systems using the Nyquist Criterion
- Stability of Systems with Time Delays

- Frequency Response Methods
- The Bode Plot
- Performance Specifications in the Frequency Domain
- Magnitude and Phase Plots
- Design of Feedback Systems Using Frequency Response Methods

**Laboratory Projects:**

- Stability using constant control
- Root-locus design
- Frequency domain methods
- Design for systems with time delay

**Computer Usage:**

Use MATLAB (with Control Systems Toolbox) for analysis and design.

**Textbook/reading: **

- R. Dorf,
*Modern Control Systems*, Addison-Wesley.

**Engineering Design Statement:**

The lectures devote considerable time to design issues and design methods. Early in the course (Section III), a simple design problem (design of a position control system) is discussed to highlight design issues. Stability and performance (Sections IV and V) are discussed in terms of design requirements. The root-locus and frequency response methods (Sections VI – VIII) are presented as design tools, and their use is illustrated by several examples.

The design material introduced in the lectures is supported by a computer-aided design laboratory. Students employ MATLAB and the associated Control Systems Toolbox to carry out a series of design exercises which effectively illustrate the use of root-locus and frequency response methods for control system design. The laboratory work culminates in four open-ended design projects which are allocated 35% of the final grade. Approximately 50% of the homework is design related. The midterm and the final examination have several questions on the design of control systems to satisfy given performance objectives.

**Relationship to Outcomes:**

Students who have successfully completed this course should have achieved:

Course Outcomes | ABET Outcomes |

An ability to apply knowledge of mathematics, science, and engineering | A |

An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | C |

An ability to identify, formulate, and solve engineering problems | E |

An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. | K |

**Professional Component:**

Engineering Depth, Laboratory

Engineering Science: 2 credits

Engineering Design: 2 credits