Design calculations

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Maximum speed

Motor has 5600 RPM at 6V no load. Gearing is 9.68:1 Wheel diameter is 6cm.

This gives a max speed of 5600/60/9.68*0.06*Pi = 1.8m/s

(with a maximum motor voltage of 9V should - for short periods - allow up to 2.7m/s).

Encoder calculations

The encoder has 48 ticks per revolution. This gives 48*9.68 = 464.64 ticks per wheel revolution, or Distance per tick = pi*0.06/464.64 = 0.40568 mm/tick

Speed calculation

Speed is calculated based on time between encoder ticks

At max speed there should be approx 4.48 encoder ticks per ms, or 223 us between tics. If there is more than one encoder tick within 1ms, then the velocity is averaged over 1 ms. At lower speed the velocity gets updated at every tick time (fewer than one encoder tick in 1 ms). If time between encoder pulses is more than 0.5 sec, then speed is set to 0. If time since last encoder tick is longer than last encoder tick period, then velocity is based on time since last tick (up to 0.5 sec, where the speed is set to 0). I.e. the minimum speed measured is 2*0.0041 m/s = 0.81cm/sec.

Sample time is (pt.) 1ms.

At low speed the time between encoder ticks make the calculated wheel velocity delayed, resulting in poor controller performance (or even instability). A velocity estimator is implemented based on anchor voltage and current velocity. This is then high-pass filtered and added to the encoder based velocity. This function currently disabled - gave problems while balancing.

The motor big controller has problems with low (and high) PWM values at the used 20kHz switch rate. This gives almost no motor power if PWM is less than 7-10%. Lower switch frequency may give problems with audio noise and high peak current in anchor coils. The tiny motor controller has much higher BW, but noise from switching can give false encoder pulses, and thus there is mounted 1-4.7nF filter capacitors on the encoder lines.

Parameter estimation

Pololu say that at 6V stall current is 2.2A, or R_A = 2.7 Ohm

On this robot the total anchor resistance is estimated to about 3.3 Ohm (including H-bridge and wires) based on current step response.