11.4.1 The Problem

The feedback and set point are both in units of ``ticks per PID period'' up to this point. This is okay for most cases, assuming the encoding has sufficient resolution. However, for robots with low resolution encoders, and also for low-speed situations, just counting ticks between PID invocations produces coarse and quantized results.

Let us assume the PID control loop is invoked at 20Hz (20 times per second). Let us also assume the encoder disk has 1000 transitions per revolution. At a very low speed, such as 0.1 revolutions per second, we only get 100 ticks per second. This is divided by 20 because the sampling frequency is 20Hz. As a result, we only have, on the average, 5 ticks per period.

The error term is going to be even more quantized because it is the difference between the set point and the feedback. As a result, the control signal has very poor resolution because it depends on the error term.