ELEC_ENG 360: Introduction to Feedback Systems

Quarter Offered

Winter : MWF 10-10:50 ; Freeman


ELEC_ENG 222 or equivalent


CATALOG DESCRIPTION: Linear feedback control systems, their physical behavior, dynamical analysis, and stability. Laplace transform, frequency spectrum, and root locus methods. System design and compensation using PID and lead-lag controllers. Digital implementations of analog controllers.

REQUIRED TEXTS: Franklin , Powell, and Emami-Naeini, Feedback Control of Dynamic Systems , Prentice Hall, 5th edition (2006)



COURSE GOALS: Students learn how the use of feedback can significantly alter the dynamic behavior of a system. They learn how to design feedback systems to meet a set of performance criteria. In the laboratory projects, they gain experience in designing controllers for a real physical system.

PREREQUISITES: ELEC_ENG 222 or equivalent


  • Transfer functions of linear time-invariant systems, poles and zeros, Laplace and Z transforms (HW Set #1)
  • Fourier transforms and Bode plots


WEEK 1: anatomy of a feedback system (plant, controller, sensors, actuators, command and reference inputs, noise and disturbance inputs), advantages of feedback (sensitivity reduction, disturbance rejection, stabilization, performance improvement) linear models of physical systems. Chapter 1

WEEK 2: linear models of physical systems, converting o.d.e.'s to transfer functions, block diagram manipulations. Chapter 3 (3.1-3.2)

WEEK 3: stability and the final value theorem, steady-state analysis, tracking error reduction via proportional control, step response of first- and second-order systems (time constant, natural and damped frequency, damping ratio). Chapter 3 (3.3)

WEEK 4: design specifications vs. pole/zero locations (overshoot, rise time, settling time). Chapter 3 (3.4-3.5)

WEEK 5: PID control, integrator windup, tracking and system type. Chapter 4

WEEK 6: Routh-Hurwitz stability criterion and root locus diagrams. Chapter 3 (3.6) and Chapter 5

WEEK 7: root locus controller design methods (proportional and lead/lag controllers). Chapter 5 (5.5)

WEEK 8: Nyquist stability criterion, Bode plots, gain/phase margins, bandwidth, crossover frequency, minimum-phase systems and Bode's gain/phase relationship. Chapter 6

WEEK 9: frequency domain controller design methods (proportional and lead/lag controllers), sensitivity/complementary sensitivity. Chapter 6 (6.7)

WEEK 10: digital implementations of analog controllers (impulse/step/ramp invariant approximations, Tustin /bilinear approximations, matched pole-zero approximations). Chapter 8 (8.3)


LABORATORY PROJECTS: seven lab sessions introduce students to control system simulation as well as the real-time control of an electro-mechanical system.

  • Lab 1: Introduction to the 366 Laboratory
  • Lab 2: Introduction to Digital Simulations
  • Lab 3: Introduction to the Control of the Torsional Disk System
  • Lab 4: PD Control
  • Lab 5: PID Control
  • Lab 6: Root Locus Design
  • Lab 7: Frequency Response of the Disk System


  • Homework - 10%
  • Labs - 30%
  • Midterm - 25%
  • Final - 35%

COURSE OBJECTIVES: When a student completes this course, s/he should be able to:

  • derive closed-loop transfer functions from block diagrams of interconnected subsystems. (HW Set #2)
  • derive time-domain response characteristics and translate time-domain design specifications into frequency-domain design objectives. (HW Sets #3 and #4)
  • analyze system stability using Routh-Hurwitz approach. (HW Set #5)
  • use root locus (HW Set #6), Nyquist, and Bode (HW Set #8) techniques to design PID (HW Set #7) and lead/lag (HW Set #9) controllers; analyze resulting closed-loop systems. controllers.

ABET CONTENT CATEGORY: 100% Engineering (Design component).