PID controllers
Variants

Although the later controller is not an exact equivalent of analogue PID controller, it is able to replace or even supersede it in most applications. It is sometimes called a PSD controller (proportional-summation-difference). In this text, we will call the digital implementation a PID as well. Output of the program is the control variable uk (e.g. a position of actuated mechanic part, a valve displacement). Corresponding algorithm is called positional or absolute. In theory, various coefficients are used to define controller adjustment, here we will use simply P, I, D standing for gains of particular components.

The program, implementing this algorithm, computes control variable u at each step of execution. The term positional or absolute is used to distinguish it from another PID algorithm derivative, which computes increments of control variable Δu, instead. The later one is called a velocity or incremental algorithm. It can be regarded as the absolute algorithm followed by a differentiator. The actual value of u can be summed inherently by the actuator, e.g. in case of stepper motor, fed by number of steps Δu.