Readings

The readings listed below are from three textbooks:

VdV: Amazon logo Van De Vegte, J. Feedback Control Systems. Prentice Hall PTR, 1993. ISBN: 0-13-016379-1.

RMS: Amazon logo Rohrs, C. E., J. L. Melsa, and D. G. Schultz. Linear Control Systems. McGraw Hill, 1993. ISBN: 0-07-041525-0.

G&VV
: Gelb, A., and W. E. Vander Velde. Multiple-Input Describing Functions and Nonlinear System Design. McGraw Hill, 1968.

The entire G&VV book is also downloadable below.

LEC # TOPICS READINGS
1 Introduction VdV: Chapter 7, S 1-4
2 Frequency Response Bode Plot Rules VdV: Chapter 7, S 5
3 Frequency Response (cont.) Gain / Phase Margins VdV: Chapter 7, S 6
4 Bode Plot Exercises VdV: Chapter 7, S 7-8
5 Bode Plots for Unstable Open - Loop Systems  
6 Root - Locus Review VdV: Chapter 6, S 1-3
7 Root - Locus Examples VdV: Chapter 6, S 4-6
8 Compensation Design Principles RMS: Chapter 8, S 1-2
9 Compensation Design Principles (cont.) RMS: Chapter 8, S 1-2
10 Proportional Control + Extra Handout RMS: Chapter 8, S 1-2
11 Lag and PID Compensation RMS: Chapter 8, S 4
12 Lead and PID Compensation RMS: Chapter 8, S 5
13 Examples RMS: Chapter 8, S 1-5
14 High Frequency Roll-off Notch and Plant Inversion RMS: Chapter 8, S 6
15 Design Example Lead-Lag Compensation + Extra Handout RMS: Chapter 8, S 7
16 Examples (cont.) RMS: Chapter 8, S 7
17 More Examples RMS: Chapter 8, S 8
18 Control of Unstable Plants RMS: Chapter 8, S 9
19 Control of Unstable Plants (cont.) RMS: Chapter 8, S 9-10 + RMS: 6.6
20 Quiz  
21 Models of Nonlinearities Introduction (PDF) (Courtesy of D. B. DeBra. Used with permission.)

Chapter 1 (PDF)
Chapter 2 (PDF)
22 Common Effects of Nonlinearities G&VV: 1.0-1.3 (PDF - 2.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)
23 Prof. David Trumper's Lecture  
24 Describing Functions Introduction and Motivation G&VV: 1.4-1.6 (PDF - 2.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)
25 Describing Function Analysis G&VV: 3.0-3.1 (PDF - 4.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)
26 Computing DFs G&VV: Chapter 2 (PDF - 2.6 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)
27 DF Analysis: Example 1, Stability of Boat Autopiloot Notes
28 DF Analysis: Example 1 (cont.) Notes
29 DF Analysis: Limit Cycling G&VV: 3.2 (PDF - 4.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)
30 DF Analysis: Jump Resonance G&VV: 3.3 (PDF - 4.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)
31 DF-based Compensation Design G&VV: 3.5 (PDF - 4.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)
32 DF-based Compensation Design (cont.) G&VV: 3.5 and 3.7 (PDF - 4.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)
33 Phase-Plane Analysis Introduction and Motivation Chapter 3 (PDF)
34 Phase Plane Drawing Rules Chapter 3 (PDF)
35 Phase - Plane Example I Carry-on Suitcase  
36 Phase - Plane Example II Satellite System Chapter 3 Extra (PDF)
Chapter 4 (PDF)
Chapter 5 (PDF)
37 Phase - Plane Example III Satellite System Chapter 3 Extra (PDF)
Chapter 4 (PDF)
Chapter 5 (PDF)
38 Phase - Plane and Parameter Dependence of System Dynamics Chapter 6 (PDF)
39 Phase - Plane and Parameter Dependence of System Dynamics (cont.) Chapter 6 (PDF)
  Final Exam (3 hours)  


 

Downloadable Textbook

The complete G&VV text (Gelb, A., and W. E. Vander Velde. Multiple-Input Describing Functions and Nonlinear System Design. McGraw Hill, 1968) is provided below.

Chapter 1. Table of Contents, Nonlinear Systems and Describing Functions (PDF - 2.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Chapter 2. Sinusoidal Input Describing Function (PDF - 2.6 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Chapter 3. Steady-state Oscillations in Nonlinear Systems (PDF - 4.3 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Chapter 4. Transient Oscellations in Nonlinear Systems (PDF - 1.7 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Chapter 5. Two-sinusoid-input Describing Function (PDF - 1.9 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Chapter 6. Dual-input Describing Function (PDF - 2.8 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Chapter 7. Random and Other Signals in Nonlinear Systems (PDF - 3.1 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Chapter 8. Nonoscillatory Transients in Nonlinear Systems (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Chapter 9. Oscillations in Nonlinear Sampled-data Systems (PDF - 2.4 MB) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Appendix A. Amplitude-ratio-Decibel Conversion Tables (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Appendix B. Table of Sinusoidal-Input Describing Functions (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Appendix C. Table of Dual-input Describing Functions (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Appendix D. Table of Two-sinusoid-input Describing Functions (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Appendix E. Table of Random-input Describing Functions (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Appendix F. Table of Sampled Describing Functions (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Appendix G. Analytical Justification for the Filter Hypothesis (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Appendix H. Introduction to Probability and Random Process (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)

Index (PDF) (Courtesy of Authur Gelb and Wallace Vander Velde. Used with permission.)