The PID Controller – Part 2 of 4

Back to Part 1.

So, we’ve got the following equation:

,

which gives the controller output at each instant . To implement this controller, one thing to do is to consider the , i.e. the increment of the control signal from one instant to the other. So if we define:

,

we get

,

which yields

.

Grouping the addenda by the k-instant we get the almost final version of the algorithm:

,

which can be better formulated to ease implementation in code as follows:

,
,
,
,
,
.

Ok! Now that should do, it’s time to code and test; check Part 3, now!