Analysis of equivalent control structures for positioning systems

This paper analyses how to obtain an equivalent behavior of a positioning system using three different control structures, all based on cascaded loops: a PID controller on the position loop without the speed loop closed; a P controller on the position loop combined with a PI controller on the speed loop (P+PI); a PI controller on the position loop combined with a P controller on speed loop (PI+P). Equivalence formulas for converting a PID into a P+PI or PI+P and vice-versa are derived. The analysis covers extended PI/D controllers with proportional and derivative weighting and presence of filters at controllers' output. The experimental results included, prove that the equivalence formulas deduced analytically are correct.