1. CS-EE 481 Spring 2003 1Founder’s Day, 2003 University of Portland School of Engineering The Inverted Pendulum Authors Jason Boyce Jen Miller Advisors Dr. Robert Albright Dr. Peter Osterberg Industry Representative Mr. Howard Voorheis

2. CS-EE 481 Spring 2003 2Founder’s Day, 2003 University of Portland School of Engineering Agenda Introduction Jen Background Jen Methods Jen & Jason Results Jason Conclusions Jason Demonstration Jen & Jason

3. CS-EE 481 Spring 2003 3Founder’s Day, 2003 University of Portland School of Engineering Introduction Special Thanks The Inverted Pendulum Problem Analog Servo Mechanism Purpose: Control System Demonstration

4. CS-EE 481 Spring 2003 4Founder’s Day, 2003 University of Portland School of Engineering Background Feedback Control Goal: Keep the pendulum from falling Functional Specifications

5. CS-EE 481 Spring 2003 5Founder’s Day, 2003 University of Portland School of Engineering Methods Research Mathematical Modeling Feedback Diagrams Transfer Functions Stability Analysis Circuit Design Construction Testing

6. CS-EE 481 Spring 2003 6Founder’s Day, 2003 University of Portland School of Engineering Research –Kent Lundberg. http://web.mit.edu/klund/www/pendulum.pdf –William McC. Siebert. Circuits, Signals, and Systems. MIT Press, Cambridge, Massachusetts, 1986.

7. CS-EE 481 Spring 2003 7Founder’s Day, 2003 University of Portland School of Engineering Mathematical Modeling Newtonian Physics –Dynamics of Pendulum Transfer Functions –Frequency Domain

8. CS-EE 481 Spring 2003 8Founder’s Day, 2003 University of Portland School of Engineering Feedback Diagram K(s) k´k´ M(s) G(s) c + + - - QcQc Q

9. CS-EE 481 Spring 2003 9Founder’s Day, 2003 University of Portland School of Engineering Transfer Functions

10. CS-EE 481 Spring 2003 10Founder’s Day, 2003 University of Portland School of Engineering Closed Loop Transfer Function

11. CS-EE 481 Spring 2003 11Founder’s Day, 2003 University of Portland School of Engineering Stability Analysis

12. CS-EE 481 Spring 2003 12Founder’s Day, 2003 University of Portland School of Engineering Circuit Design

13. CS-EE 481 Spring 2003 13Founder’s Day, 2003 University of Portland School of Engineering Cart-Track Schematic Motor V(t) 15 Ground Multi-turn potentiometer Voltage proportional to x(t) Track  (t) X(t) Hinge Cart Pendulum Belt Pulley Motor Shaft Ground Voltage proportional to  (t) 15 Potentiometer From William McC. Siebert, Circuits, Signals, and Systems, MIT Press, Cambridge, Mass., 1986

14. CS-EE 481 Spring 2003 14Founder’s Day, 2003 University of Portland School of Engineering Conclusions Analog Servo Mechanism Control System Demonstration –Aids in understanding control systems –Easy problem to conceptualize

15. CS-EE 481 Spring 2003 15Founder’s Day, 2003 University of Portland School of Engineering Demonstration