Balancing the mobile inverted pendulum.
"A practical approach"

Mechatronics lecture by Keith Colson

Why build a mobile inverted pendulum?

• After being introduced to Joe Le Pendule 1.. 2.. 3.. by Felix Grasser of the Swiss Federal Insitute of Technology I was fascinated. They constructed Joe before the Segway was release showing it to be quite original.

• The mobile pendulum is obviously a good practical challenge in dynamic control theory

• The project covers mechatronics very well as it includes electronics, mechanics, software and little luck..

Where do you start?

• The mechanics

• Big motor = big motor controller, heavier batteries and vice versa.

• Find some motors first.

What motors should I use?

• On a servoing (q) system a low backlash (q) motor is going to make life easier and smoother on this task (q).

• Gearing: Scratch or integrated. Time and cost.

• Motor size (what's easy to get your hands on) or pendulum size?

• Faulhaber motor: They dont get much nicer than Swiss designed core-less motors. High efficiency, geared, zero-backlash, expensive.

What about the wheels?

• Wheel circumference * n revs per second = meters per second.

• Set by top speed

• The kids K'nex wheels.

• Hubbing with lathe.

• Home brew encoder. (unfinished)

The Chassis

• Height = pendulum frequency. (about 1 second or 1 Hz in my case) / 2 due to CG.

• Short = faster response needed.

• CG: Center of gravity.

• Battery weight and location. Battery count.

• Practical pendulum height = wheel diameter * 3, ascetically pleasing too, proportionate.

• Chassis Drawn in Protel, parts added as component footprints.

• Acrylic looks nice, fairly light, machines easily.

• Finished mechanics using only 3 screws. Learn to bypass screws.

• Motor mounting with bulldog clip, fast easy, flexible. lets not waste time machining stuff we don't need to..

The Motor driver

• H-bridge motor controller, small, simple.

• Fet driver, cheap.

• Board can fit on back of small motors

• Don't forget your electrolytic capacitor to filter the power supply.

The Power supply

• 4 x 1.5V AA batteries = 5.2 to 6 volts working range.

• 12 volts out from 5 to 6 volts in using boost regulator.

• UC2577 boost regulator simple solution.

• Press'n peel board (one afternoon)

• Mark both male and female connectors with nail polish so polarity is maintained.

• Nail polish stops smoke leaks.
  

The Microprocessors

• 2 x Silabs 8051 variant 25 mips, C8051F330

• Serial for coms between micros

• Crystal-less operation

• 2 wire Jag

• Keil compiler (fast floating point)

• 5 volt and 3.3 volt power-supply

• 2 x 8 bit PWM for motors

• Wire wrap is fast, easy to change configuration.

• SIP and vero (strip) board = fast assembly
  

Simple Balance

• Balance with potentiometer.

• Simplifies problem

• Tune motor PID control loop.

• Integral limit added to aviod integrator wind up. (saturation)

• Add IMU when confident with performance.
  

The Inertial Measurment Unit (IMU).

• Analog devices Gyroscope - ADXRS300 32 pin BGA

• Analog devices 2 axis accelerometer - ADXL202

• 2 boards SIP design. Press'N'Peel board.

• BGA soldered in $50 toaster oven.

• Gyroscope = high frequency rate of rotation (relative)

• Accelerometer = low frequency gravity vector (absolute)

The Kalman Filter.

• Kalman filter removes gyro DC bias and drift..

• Kalman filter low pass filters accelerometer.

• Kalman filter fuses high frequency and low frequncy signals to give absolute gravity vector.
  

Version 2 of the Inertial Measurement unit.

• For future projects, I2C, serial support

• Very small 50x20x9mm, Kalman filter built in.

Final touches

• Added a hat to stop it smashing into the floor when it falls over. (Kids toy ball)

• Turn off the motors when fallen.

• Video of the pendulum balancing. Yes, it is programmed to turn in circles.

• Balancing Video

• Battling Video
  

Conclusion

• The inverted pendulum in its simplest form proves to be a challenge. While it did balance many improvements could be made.
• A radio control for testing purposes
• A way to get back up after falling over.
• Motor/wheel encoders for more stable control.
• "Smart" closed loop motors each with their own processor and PID control loop.
• Smart motors can then be used in other projects.
• Motors and IMU set up as I2C slave devices with one master microprocessor.
• I2C has only 4 wires. 5V, 0V, Clock, Data. Tidy design with a daisy chain cable.
• Autonomous operation via sensors.

Questions ?