Inverted Pendulum
Inverted Pendulum Operational Manual
Sheldon Logan
July 4, 2006
1
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
Sheldon Logan
July 4, 2006
1
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