Part 1: Requirements, Preferences and Constraints – Low cost real-time closed-loop control of a consumer printer

Please make sure to read the introduction first.

In this blog post, I’ll outline the requirements, preferences and constraints for the project.

Requirements

1. The sample rate must be larger than 8 kHz.
Why? Because I intend to use this real-time platform for all future projects that I might think of, and since some of those may involve very high stiffness. With the high-frequent resonant dynamics that come with such a system, having a relatively low sample time would introduce phase-lag in frequency regions where I’d be trying to get performance. For this project, 1 kHz would probably suffice, but I’ll go as high as I can with the hardware I get.

2. The control loop must be hard real-time.
Whatever method I end up choosing to run the real-time loop, the sample time must remain constant over an experiment. I want to rely heavily on linear control theory, and this only makes sense for constant sample times.

3. Data logging must keep up with the sample rate, without dropping samples.
At 8 kHz, and two 16-bit integers per sample, this is about 256 kBit/s.

4. The PWM resolution must be at least 12 bit.
The PWM resolution indicates the number of different duty-cycles it can take on. Since the motor of my printer takes at most 24V, 12 bits corresponds to a 5 mV resolution. That sounds good enough to me.

5. The PWM frequency must keep up with the sample rate.
If the PWM frequency is larger than the sample rate, it can not complete a full period with some duty cycle before the next sample determines a new duty cycle. Let’s say that one sample must include at least two full PWM periods, to be safe. Then the PWM frequency must be at least 16 kHz. Since f_PWM = f_clock / 2^{bits_resolution} (see the previous link), I need a microcontroller with a PWM-enabled hardware timer with a resolution of >12 bits and a corresponding timer clock speed of >65 Mhz.

Preferences

1. The workflow should be user-friendly.
I’m fine with programming in C, instead of working in Simulink. However, if possible, I don’t want to need to write software in assembly to achieve the required performance.

2. The print-head should move as precisely and fast as possible.
I’m not sure yet where to put the trade-off between precision and speed, but when I have more feeling for what is physically possible, I’ll see if I can increase the print-speed while remaining the original print resolution (not that it can still print).

3. The real-time platform must be easily extendable to different projects.
My next project is likely going to be a high-speed plotter, laser-engraver or laser cutter. I want my work here to be easily applicable there.

Constraints

Since I don’t want to change any of the printer hardware (at least the driveline), I must work with what I’ve got, which poses the following constraints.

1. I must work with a 24V brushed DC motor and position measurements, coming from a photo-interrupter and a strip of about 8000 slits over 30 cm.
So the measurement resolution is about 38 μm. Printers like this that I find online typically draw at most 20W, so the power supply and motor driver need to tolerate about 1A.

2. The budget for the real-time platform is €10, for printer hardware it’s €30.
It’s a hobby. It doesn’t need to be expensive. For printer hardware, the power supply takes up about €20. I might have used the original power supply, but in this case I prefer the freedom this gives me.

If I forgot anything, I’ll add it later. The next post will cover how I selected the parts based on these requirements.