# Unbalanced motors, Rate PID & Bandwidth

For a multirotor to fly, the thrust of each motor has to be equal, within certain tolerances. These tolerances depend on the bandwidth of the multirotor which are usually reflected in (well tuned) rate PIDs.

Let me explain:

The rate PIDs are usually tuned to reach the best impulse response which depends on the moment of inertia (radius, mass and mass distribution) and thrust inertia (prop weight, motor power, ESC, etc etc).
Unbalanced motors result in a steady-state error for the rate PID which it has to compensate for using the P and the I terms. Going too high with either term – higher than the multirotor bandwidth can allow – will cause oscillations and instability.

It might seem obvious that unbalanced motors are bad. In the end all motors – even high end ones – tend to have slight Kv differences which results in different thrust for the same PWM input. It happened to me when I last tested my quad – it kept flipping over at launch and I didn’t understand why the PIDs cannot compensate for this. All other quads work and surely they have their own unbalanced motors.

So when I got home I measured the Kv of each motor and I found that one of them is lazier – around 90% thrust compared to the others.

So I fired up the simulator and added some randomness to each motor thrust (between 80% and 120%) and yes – the quad wouldn’t fly. The rate PID was unable to compensate for the difference in thrust. Increasing a lot the P term or a bit the I term stabilized the quad.

So Success!!

But what if I couldn’t increase the P or I because of oscillations? What if my PID was at its limit, stability wise? Then the quad would not be able to fly with this particular combination of motors and moment of inertia.

Seems like a silly conclusion – if the motors are bad the quad will not fly – but I felt like I had some sort of epiphany that the thing responsible to compensate for bad motors is the same thing responsible for fully using the quad bandwidth – so unbalanced motors need some bandwidth margin to allow the PID to compensate for them.

# Testing rig

I built a custom testing rig out of some plywood sticks and these kind of elastic cords:

There is just enough clearance for 7 inch props and the quad is free to rotate around one axis (Y or roll in the video). I can easily change the free axis as the cords connect to the arms with metal hooks.

The issue I’m debugging now is related to a tendency of the motors to generate different thrust for the same throttle input. I think it’s because the ESCs have different settings on them as I couldn’t find any issue with my code so far. If I send 50% throttle to all motors the quad spins a lot.

# RC Case

I finished designing the case that will fit the silkopter RC system.

Here’s how it looks like:

Components:

1. Raspberry Pi3
2. Official Raspberry Pi 7″ touchscreen
3. A 3 axis gimbal stick for the yaw/pitch/roll
5. A motorized 10K fader for the throttle
6. A brushed Pololu motor controller. Pololu modules are awesome btw
7. 2 clickable rotary encoders to tune custom parameters like PIDS
8. 2 switches to save/restore the custom parameters
9. 7 push buttons to change flight modes, RTH and other cool things

The case is pretty big due to the screen. It’s 22.3 cm tall, 19.5 cm wide and 4.4 cm deep – so I couldn’t print it in one piece on my Prusa I3 printer. So I had to split in in a few pieces, print each one and them glue them together.

After a few failed prints, here’s the end result:

I’m painting it now with matte black paint and tomorrow I will put all the components together.

The only problem I’m having now is that I broke my touchscreen while fitting it in the case so I need to order another one.

# Binary Releases

I decided to start making binary releases available for everyone to download.

Here’s the first one – the GS and the brain binaries:

https://bintray.com/jeanleflambeur/silkopter/gs_brain/d779ff73ee330c82acc82171ddfdbb03701da784

I’ll write a new post later today or tomorrow about the install steps and how to get it working.

Note this is not finishes for flying, it’s an experimental release of the new version of Silkopter that can be used to debug sensors and test most of the nodes.

# Silkopter FC

Finally, after some DHL delivery trouble the boards arrived:

After watching a few tutorials I immediately tried soldering the most difficult part – the MPU9250 chip. Turns out – if you don’t have the right flux type it’s impossible. I managed to ruin 2 boards in the process and broken 1 chip…

Notice the PCB changing color next to the IMU I2C pins and the ‘dry’ look. The pin header holes are also darker than the others due to the heat.

2 days later my new flux came: Chip Quick SMD291 ordered from farnell. This time it went much better as I was able to solder 2 chips in 5 minutes, from the first try. The trick is that tacky solder flux doesn’t evaporate from the hot air and keeps the chip floating while the solder melts (and prevents oxidation). When the solder flows, the chip kinda snaps into place and that’s it. In my first tries I used a flux pen that dried immediately and the friction between the chip and the PCB was greater than the solder surface tension – preventing the chip from snapping into place.

So this is the board almost complete, except for the ADS1115 ADC that didn’t arrive still:

The last few days I spent trying to get the RF4463 chip to respond on SPI1. I expected surprises and I got them:

• first of all, activating SPI1 on a RPI3B results in boot times of 2 minutes due to an interrupt issue with the UART driver. Solution: disable the bluetooth and use ttyAMA0 instead of ttyS0
• next I simply couldn’t get the chip to respond at all. 2 days I spent on this until I went back to the schematic thinking the wiring is not ok. Then I realized that the chip select is connected to CS2 which is GPIO 16 but the SPI1 overlay I used uses GPIO 18 as CS. Duh! Solved by adding dtoverlay=spi1-1cs,cs0_pin=16 in /boot/config.txt
• that’s it – it works now 🙂

In the last moment I added 3 WS2812B RGB LEDs thinking that I will be able to drive them with PIGPIO. I didn’t check the datasheet closely enough to see that they need PWM impulses in the order of 0.5ns whichare way below the resolution of the library.

So today after soldering the LEDs I realized that I cannot drive them. Desperate, I turned to the schematic and saw that by sheer luck I connected the LEDs to GPIO 13 – which happens to be the hardware PWM channel 1. Yaay – exactly what this library needs.

So I downloaded the lib, configured it on DMA channel 4 and PWM channel 1 and ran it and voila! It works with <1% CPU usage:

So now I have almost all the hardware working – the dual IMUs, the Baros, the RF chip and most importantly – vital for a 2016 multirotor – the LEDs.

I have 6 unpopulated left to give away (for free of course, shipping covered by you) if someone is interested!

So now – back to software. The RC is coming along nicely.

# Classic TX

I thought to give my Flysky TH9x TX a change to use it with silkopter so I made a new node called “CPPM Receiver”. This samples a CPPM stream on a GPIO and outputs the PWM streams that can be fed into the main node.

It uses the PIGPIO setAlertFunc which calls a user provided function for all level transitions on a certain gpio pin. The resolution is 5 microseconds which is waay more than needed for a standard CPPM stream. The gap between channels is 400 microseconds so way bigger than the minimum resolution of the library.

It started more of a proof of concept but in the end I think it’s perfectly usable.

Here’s a video with it in action, connected to a D8R-II receiver:

# Schematic & PCB #2

I finally finished the schematic and PCB and will send them to DirtyPCB today.

It is in HAT format ready to be used with the new (when it’s released) Raspberry PI A3.

It supports either a RF4463F30 or a RFM22B (on the back side) connected to SPI2, a MPU9250 IMU and MS5611 baro connected to SPI1 and/or another set of MPU9250 & MS5611 connected to I2C.

On the same I2C there is an ADS1115 for current/voltage sensing and 2 extra ADC pins broken out on a separate controller.

PIGPIO is connected to 6 PWM pins – 4 for motors and 2 for a gimbal.

In the end I also had sufficient space to include 3 NeoPixels (or WS2812b) RGB LEDs to show various status info. They are all driven by only one GPIO using a serial-like protocol and I think I can make this work with the PIGPIO wave functions.

In a future revision I might add a buzzer for alerting comm errors – like link lost – and expose 2 more PWM outputs.

First I have to check if the PCB will be manufactured ok.

Some screenshots:

Update July 14th:

I made some tweaks to the SCH and PCB to include a diode for the leds, according to Adafruit.

In the previous version I was powering the LEDs from 3.3V which is below their minimum voltage. Datasheet here.

To fix this I routed the led VCC to 5V but through a diode.
The WS2812b leds expect the high input voltage to be within 0.7 VCC. With a 5V VCC this results in a 3.5V high level. The raspberry pi provides a reliable 3.3V on the GPIO and there was the risk of the leds failing to understand the PI. There are 2 solutions – a level converter to increase the high level of the PI to 5v or lowering the VCC of the leds a bit. I choose the second ’cause it’s way simpler. A diode drops the voltage from 5V to ~4.3V which in turn drops the expected high level to a convenient ~3V.

Two other changes that I did are:

• Fixed some signal traces that were running parallel on the top and bottom sides – like the I2C and some PWM outputs. Not sure how important it is but just to avoid any nasty coupling
• Broken out the I2C to a pin header to eventually connect a PX4Flow.

The board is in production now and I really hope it gets here by Friday.

In the meantime I’m investigating a PPM input solution in case I want to use a standard RC system with this board.

# Schematic & PCB

The Silk FC schematic is finished and the PCB is 70% done.

Here are some screenshots:

There is a bit of wiring acrobatics with the PWM connector as I couldn’t find an eagle 6×3 header so I improvised one from 3 2×3 headers… Ugly but it works.

As soon as they are done I will put them on github.

The board is 2 layers only and has the specs from my last post.

I intend to add a footprint for a RFM22B as well as the RF4463F30 so I can choose which to use, in case one of them has issues.

The board should work in both single-imu-baro more and also in dual-imu-baro.

I got 2 MPU9250 and MS5611 from my previous Drotek 10 DOF boards with a bit of hot air.

I’m really curious how it will end up as this is my first SMD board and especially my first QFN package. The MPU is really really tiny – like 2 square millimeters.