CATALOG DESCRIPTION: Discrete dynamics systems; discrete models of continuous systems feedback and digital controllers; analog-digital conversion; digital control design including PID, lead-lag, deadbeat, and model matching controllers.

REQUIRED TEXTBOOK : None.

REFERENCE TEXTBOOKS: Phillips & Nagle, "Digital Control System Analysis and Design," 3rd ed., Prentice Hall, '95.

COURSE COORDINATOR: Randy Freeman

COURSE GOALS: Students learn two techniques for designing digital controllers for analog systems. The first is simply to derive a digital approximation to an analog controller designed using the methods taught in EECS 366. Students learn why this method may fail when the sample time is not small enough. The second technique, which is the focus of the course, is to derive an exact discrete-time equivalent of the analog plant and then perform the design entirely in the discrete domain. Students learn how this second technique can be used to achieve performance objectives (e.g. deadbeat control) not possible with linear analog controllers.

PREREQUISITES: EECS 360 or equivalent

DETAILED COURSE TOPICS:

  • Week 1: introduction; brief review of discrete-time systems and Z-transforms
  • Week 2: time/frequency response, mappings between s- and z-planes
  • Week 3: digitizations of analog designs, limitations on sampling period
  • Week 4: sampled-data systems, ideal sampler, starred transform, a/d and d/a conversion
  • Week 5: pulse transfer function and block diagrams
  • Week 6: discrete-time stability and root locus diagrams
  • Week 7: discrete-time Nyquist and Bode plots
  • Week 8: digital controller design; lead-lag and PID controllers
  • Week 9: introduction to algebraic design; deadbeat control
  • Week 10: model matching and exploitation of free design choices for performance improvement

COMPUTER USAGE:

Matlab and Simulink projects assigned on a regular basis

HOMEWORK ASSIGNMENTS:

Five homework assignments to test and reinforce concepts taught in class.

LABORATORY PROJECTS: pilot lab projects (4 labs total)

GRADES:

Homework--- 30% 
Midterm--- 30% 
Final--- 40%

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

  • ITEM 1: derive discrete-time transfer functions from difference equations via the z-transform; derive discrete-time transfer functions for approximate integrators and differentiators; perform inverse z-transforms to obtain time sequences; Matlab implementation of difference equations
  • ITEM 2: derive digital approximations to analog controller designs; compare resulting analog and digital controllers in time and frequency domains using Matlab and Simulink; determine effects of sampling period on quality of approximations
  • ITEM 3: derive pulse transfer functions from block diagrams of sampled-data systems; derive zero-order hold equivalents of analog plants; determine time-domain properties (rise time, settling time, overshoot, etc.) from z-plane pole locations; analyze stability and steady-state behavior of sampled-data systems
  • ITEM 4: design sampled-data controllers in discrete domain using root locus, Nyquist, and Bode plot techniques; design discrete-time lead/lag controllers; analyze closed-loop stability and performance using gain and phase margins
  • ITEM 5: design sampled-data controllers in discrete domain using algebraic techniques; design deadbeat and model matching controllers; compare performance of deadbeat designs and lead/lag designs using Matlab and Simulink (performance criteria include settling time, rise time, overshoot, disturbance attenuation, control effort, noise response); use engineering judgment to select appropriate design trade-offs