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)
REFERENCE TEXTS: None
COURSE COORDINATOR: Randy Freeman
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: EECS 222 or equivalent
PREREQUISITES BY TOPIC :
- Transfer functions of linear time-invariant systems, poles and zeros, Laplace and Z transforms (HW Set #1)
- Fourier transforms and Bode plots
DETAILED COURSE TOPICS
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)
COMPUTER USAGE: Matlab
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).