Inverted Pendulum

Topics: Control theory, Rotary encoder, Circuit diagram Pages: 13 (2789 words) Published: July 1, 2013
Inverted Pendulum Operational Manual
Sheldon Logan
July 4, 2006

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1 Table of Contents
1 2 3 Table of Contents........................................................................................................ 2 Table of Figures .......................................................................................................... 3 Introduction................................................................................................................. 4 3.1 Equations of Motion ........................................................................................... 4 3.2 Inverted Pendulum Control System .................................................................... 6 3.2.1 Linearization and Linear Control................................................................ 7 3.2.2 Non Linear / swing up Control ................................................................... 7 3.2.3 Motor System.............................................................................................. 7 Inverted Pendulum Control Hardware ........................................................................ 9 4.1 Harris Board 2.0.................................................................................................. 9 4.2 PIC 18F452 Microcontroller............................................................................... 9 4.3 Xilinx Spartan 3 FPGA....................................................................................... 9 4.4 Freescale H-Bridge MC33886 ............................................................................ 9 4.5 AD 7233 D/A Converters ................................................................................. 10 4.6 4N35-M Opto-Isolators..................................................................................... 10 4.7 US Digital H3-2048-HS Ball Bearing Optical Shaft Encoder.......................... 10 4.8 National Instruments DAQ-6036E PCMCIA Card .......................................... 10 4.9 LOKO DPS-5050 Power Supply ...................................................................... 10 4.10 HP 6236B 5V 3A Power Supply ...................................................................... 11 4.11 Reliance Brush Type DC Servo Motor............................................................. 11 MATLAB Control .................................................................................................... 12 Microprocessor Control ............................................................................................ 17 Appendix A: Electrical Circuit Diagrams................................................................. 18 Appendix B: Inverted Pendulum Mechanical Drawings .......................................... 20

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5 6 7 8

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2 Table of Figures
Figure 1: Inverted Pendulum System.................................................................................. 4 Figure 2: Angle Definitions ................................................................................................ 5 Figure 3: Wiring D/A Bread Board .................................................................................. 12 Figure 4: Wiring D/A outputs to NI box........................................................................... 13 Figure 5: Powering D/A Bread Board .............................................................................. 13 Figure 6: Motor Drive Circuit........................................................................................... 14 Figure 7: Connecting Motor to H-Bridge ......................................................................... 14 Figure 8: Opened Switch 1 ............................................................................................... 15 Figure 9: StateSpaceRT Model......................................................................................... 16 Figure 10: D/A Breadboard Circuit Diagram...
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