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EEC157A – Control Systems I

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:

  1. Introduction to Control Systems
    1. Definition of Control Systems
    2. Examples of Modern Control Systems
  2. Mathematical Preliminaries
    1. Linear and Nonlinear Systems
    2. Linear Approximations of Physical Systems
    3. Differential Equations of Systems
    4. The Laplace Transform
    5. Analysis of Electrical and Mechanical Systems in the s-Domain
    6. Transfer Functions
    7. Block-Diagram Representations
  3. Mathematical Modeling and Control of Linear Feedback Systems
    1. Transfer Functions of Systems with Op-Amps
    2. Electro-mechanical Systems
    3. Modeling of DC Motors
    4. Design of a Speed Control System
    5. Design of a Position Control System
    6. Comparison of Disturbance Reduction
    7. Transient Response
    8. Steady-State Error
    9. Sensitivity to Parameter Variations in Open-Loop and Closed-Loop Control Systems
    10. The Cost of Feedback
    11. Signal Flow Graphs
    12. Mason’s Rule
  4. Stability of Linear Feedback Systems
    1. The Concept of Stability
    2. BIBO Stability
    3. Routh-Hurwitz Stability Criterion
    4. Relative Stability
    5. Location of Open-Loop and Closed-Loop Poles
    6. Design of Stable Systems
  5. Performance of Feedback Control Systems
    1. Design Requirements Based on Time-Domain Performance Specifications
    2. The Location of Poles and the Transient Response
    3. Steady-State Error
  6. The Root-Locus Method
    1. The Rules of the Root-Locus Method
    2. Analysis and Design using the Root-Locus Method
    3. Parameter Design
    4. Sensitivity and Frequency Response
  7. The Nyquist Stability Criterion
    1. Contour Mapping in the S-Plane
    2. The Nyquist Criterion
    3. Relative Stability
    4. Closed-Loop Frequency Response
    5. Design of Stable Systems using the Nyquist Criterion
    6. Stability of Systems with Time Delays
  8. Frequency Response Methods
    1. The Bode Plot
    2. Performance Specifications in the Frequency Domain
    3. Magnitude and Phase Plots
    4. Design of Feedback Systems Using Frequency Response Methods

Laboratory Projects:

  1. Stability using constant control
  2. Root-locus design
  3. Frequency domain methods
  4. Design for systems with time delay

Computer Usage:

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


  1. 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