Hello everyone! Since my last blog a lot of progress has been made. While we were just starting setting up the connection to the computer in the backpack, we now have full control over a motor connected to the backpackcomputer. Although a lot of work still has to be done, the progress we have made so far was quite rewarding and has been a fun ride so far.

One of the things I have worked on is the conversion of motor phase current to required power supply current. I’ll try to explain what this exactly means, why we need it and how we went about calculating it. I think this problem is a good example of one where a mathematician was a useful addition to the team.

The motor we’re going to use in the joints are all brushless direct current (BLDC) motors. This is an electric motor, consisting of a permanent magnet rotor (turning part) and a stator (stationary part) made of different copper coils. By continuously changing the current in the coils, a suitable magnetic field is created which pushes the rotor around.

These types of motors have very high efficiency and a long lifetime, and are available in a wide variety of achievable speeds and torques. The only downside to them is that they are harder to control, since no part of the rotor (turning part) is connected to the stator (stationary part) – the stator is essentially blind to what happens to the rotor. To assess this problem, we use an ‘encoder’, essentially a digital angle measurement device. This provides the necessary information to calculate the current which makes the motor turn.

There are actually different currents going to the motors. As the magnet passes over a coil, that coil should be turned off, while the previous one should push the magnet away and the next one should attract the magnet. So most BLDC motors have three ‘phase’-wires, allowing different coils to push and pull. As the motor turns, the current over each wire cycles through a wave, each phase behind the next by two thirds of a period. Now the motor is not directly attached to the backpack computer, but to a motor controller. This motor controller receives a constant voltage and current from a power supply. The problem we had was the following: we could measure the phase current, but wanted to calculate from this the required power supply current. This is relevant because using this we can calculate the efficiency and the power being output by the motor. The power supply current turned out to be linearly related to the *amplitude* of the phase current. So from a given set of phase current values, we had to calculate the amplitude of the wave. Because we know each phase is two thirds of a period behind the next, I could derive a formula for the amplitude using some basic identities of the sine wave:

I really enjoyed working on this problem: I learned a lot about electric motors while working on it, and was also able to apply what I learned during my bachelors: look at a problem in a more abstract mathematical way and use that to derive properties.