0. Some Notes Bruce D. Kothmann 26 Oct 2009
MechaMiniSegway
Some Notes
Bruce D. Kothmann
26 Oct 2009

1. Simplified Model Weight Q=Motor Torque Pin Shear Force F= Friction
Normal Force
FBD of Body
Sum Center of Wheel (Ignore Wheel Inertia!)
Forces Whose Line of Action Goes Through Pin Don’t Show Up!
Sum Pin in Body
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2. Simple Model (Continued)
Sum Forces Parallel to Slop on Both Bodies (Ignore Mass of Wheel!)
Substitute Acceleration into Body Moment Equation & Assume Small-Angles
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3. Now Include Motor Equations
Voltages in Motor
Motor Torque
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4. Parameters Not Difficult to Measure
Motor Constants
R from Current & Voltage with No Rotation
K from Voltage When Known Speed
Radius (r) Measured Directly
Use Total Mass for m
Balance Body on Fulcrum to Find CG Length (l)
Inertia About Hinge From Pendulum Experiment
Hold Wheels with Body Hanging Upside-Down
Measure Frequency of Body Swinging Freely [rad / sec]
I = (m*g*l) / (frequency)2
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5. Some Insights From Equations
Steady-State Stuff Easy to Calculate & Useful
d/dt0 in Trim
Also Need Zero Acceleration (a=0Q=mgrg)
Note That in Steady State on a Slope: q =(r/l)g ! Need to “Lean Into the Hill” to Counter Steady Torque, Because Total System CG Needs to Be Centered Over Contact Point! Simple Integral Feedback on q Won’t Work!
Equations Easily Sort out “Torque versus Speed” Perspectives on Motor Voltage Effect
Minimum Gain for Static Stability Easily Calculated
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6. MechaMiniSegway Notes
More Insights…
Equations Too Simple—Motor Torque Response Won’t Be Instantaneous  Proportional Feedback on Angle Will Be Dynamically Destabilizing  Need Derivative Feedback
How to Prevent Slow Drift & Deal with Slope? It Looks Like PD Feedback on q & Integral Feedback on Speed (W) Might Work?
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7. MechaMiniSegway Notes
Other Random Thoughts
Scaling of accelerometer voltage into A/D: you really only care about +/- 5 deg, so make sure that is +/- 5 volts (requires simple op-amp?)
If you want to do low-pass or high-pass filtering, the very high processor speed may cause problems, because digital filter coefficients may require very high precision. Also, digital filters are easiest to design with a fixed frame rate. MATLAB has a very convenient “C2D” function for converting analog filters to digital.
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