With the # III platform, I
checked the actuator drive performance in a similar way that I used on
platform # II as well.
The
gearing is now done with V-belts, and pulley radius ratios are slightly different.
Based on the pulley ratios (big one 75mm and small ones 25mm) and motor torque spec (0.24Nm/A) , I calculated the following belt pulling force: 28.8N per Ampere motor current.
I verified this by measuring the belt pulling force with a handy scale, while driving the motor with a constant current supply:
As can be seen from the measurements, I come out somewhat lower than the
calculated force, probably due to V-belt friction.
Below, the actuator performance under platform load is calculated and tested.
In this case I have checked the heave function of the platform, as this
action requires most power from the servo system. I used very basic
formula's to determine the heave properties.
The force needed to accelerate a mass. In my case, the complete platform
including the pilot weighs around 130kg. Note that the platform is balanced
by the bungee cords, so the actuators don't need to overcome gravity when
pushing upwards, they just need to accelerate the mass.
To achieve an acceleration of 1G (9.8m/s2) I would need 1274N of
force, or 425N per actuator in case each of them pushes 1/3 of the total
weight. Using my measured Force-Drive Current graph, I would need about
19Amps of drive current per motor.
The actual acceleration depends on the servo characteristics.
The easiest way to examine the platform servo performance is by applying a
step signal to the platform drive. The servo will try to respond as fast as
it can. Limitations due to servo power supply, signal gain and bandwidth can
be derived from the platform position waveform.
The above graph shows the input step and platform position output together,
for both positive heave (going up) and negative heave (going down). The
response of one actuator is shown, but all three behave quite similar. I
applied a heave step of 10cm, in the middle of the servo range.
The rising and falling slopes show similar response, which means that the
platform is well balanced.
There is some overshoot (~15%) in the platform position output. This could
be reduced by lowering the servo gain, but this would then also reduce the
acceleration properties. The overshoot does not show excessive ringing, so
the system is not unstable. The overshoot is not noticed during flight.
To be able to measure the velocities and acceleration, the zoomed-in step
response is shown below.
When examining the step response, you can see that the platform will first
accelerate, then move with constant speed (straight line) and then
decelerate with some overshoot.
The speed of the platform can be derived from the angle of the straight
line.
S = 0.1m, t = 0.16sec, so v = 0.62m/s
To achieve this velocity takes about 0.135sec (the acceleration part)
With this formula the acceleration can be calculated: 4.6m/s2
which is almost 0.5G. This is not such a bad value for heave.
Calculating back from this measured acceleration, the required total force
is 598N. Each actuator needs to push 199N, and this would require 8.9A motor
current per actuator.
I measured the servo amp input current of one actuator during the step
response. It shows an actual peak current of about 12.5Amps during the
initial acceleration phase. The difference is probably again caused by
friction losses.
I measured the motor drive voltage during the heave step, see above graph.
It shows that the H-bridge is fully switched on during the step. This means
that the motor current is basically determined by the H-bridge supply
voltage and the motor resistance. (+ some series resistance of the drive
circuit). This means that the only way to increase dynamic servo speed is to
increase the supply voltage, or lower the motor DC resistance.
Finally I did a quick efficiency check:
To get the platform mass moving with a certain speed requires energy
according below formula.
With the measured velocity of 0.62m/s, the kinetic energy is 25J
The electric energy supplied during the acceleration period is
The power during acceleration is 12.5A*38V=475W per motor. Total input
power is about 1425W.
The electrical energy during the 0.135msec = 192J
This shows that there is a lot of loss in the system. efficiency is only 13%.
A quick calculation shows that at 12.5A motor current, the voltage drop
across the MOSFET's is about 1.9V
(2* Rdson * 12.5A)
Measurements showed that the voltage drop is much higher, about 7Volts. The
total power loss in the drive circuit during heave is therefore about 260W.
(to be investigated further)
The same check has also been done for slow speed heave motion.
(Asymmetrical cosine sweep).
At 0.35m/s step over a 28cm range, the current draw is about 3Amps. Power is
about 84W per motor. Total is about 250W. There is hardly any acceleration
spike during this run, so all the power here is basically due to friction
loss.
The graph also shows some distortion: This is due to the error amp loading
on the position potmeter voltage. The actual run is quite smooth.
Video showing sine-wave drive with platform position and battery current consumption.
~ To be continued ~