This course presents an introduction to feedback control systems. Control systems have importance in all fields of engineering. The objective is to provide the student with the basic concepts of control theory as developed over the years in both frequency and time domain.


CLO-1: Understand alternative representations (Time Domain, Frequency Domain, State Space) of dynamic systems. (C2)

CLO-2: Analyze different dynamic systems for Stability, transient response, and steady-state error using mathematical models.(C4)
CLO-3: Design Linear Feedback controller using a State Space pole placement/Root Locus technique in order to meet explicit performance objectives. (C6)


  1. Basic Concepts – Two Lectures
  • Basics of control system, open-loop and closed-loop control systems, block diagram terminology and some example of systems.
  • Review of dynamic modeling, differential equations, first and second order systems, and Laplace transforms.

2. Modeling in Frequency Domain – Four Lectures

  • Transfer functions
  • Translational Mechanical System Transfer Functions
  • Rotational Mechanical System Transfer Functions
  • Transfer Functions for Systems with Gears
  • Nonlinearities and Linearization

3. Modeling in Time Domain – Four Lectures

  • State Space representation
  • Converting a Transfer Function to State Space
  • Converting from State Space to a Transfer Function

4. Time Response – Four Lectures

  • Poles, Zeros, and System Response
  • The General Second-Order System
  • System Response with Zeros and Additional Poles
  • Laplace Transform Solution of State Equations
  • Time Domain Solution of State Equations

5. Reductions of Multiple Subsystems – Four Lectures

  • Block Diagrams
  • Analysis and Design of Feedback Systems
  • Signal-Flow Graphs and Mason’ s Rule
  • Signal-Flow Graphs of State Equations

6. Stability and Steady State Error – Four Lectures

  • Routh-Hurwitz Criterion
  • Stability in State Space
  • Steady-State Error for Unity Feedback Systems
  • Sensitivity

7. Root Locus Techniques – Four Lectures

  • Use the root locus to design cascade compensators to improve the steady-state error
  • Use the root locus to design cascade compensators to improve the transient response
  • Feedback Compensation

8. Frequency Response Techniques – Three Lectures

  • Bode Plots, Stability, Gain Margin, and Phase Margin via Bode Plots
  • Introduction to the Nyquist Criterion
  • Systems with Time Delay

9. Design via Frequency Response and State Space – Three Lectures

  • Transient Response via Gain Adjustment, Lag Compensation, Lead Compensation
  • Controller Design, Controllability, Observability
  • Steady-State Error Design via Integral Control