A universal map of three-dominant-pole assignment for PID controller tuning

Abstract

A novel dimensionless parameterisation of the three-pole assignment for control plants with delay is presented. A second-order model with input delay is chosen as an approximation of the plant properties. The prescribed trio of poles is considered in form of one pair of complex conjugates and a real pole and it is shown that this option is not a matter of choice but necessary constraint for control design with delay in the loop. The prescribed poles are determined by the damping and root ratios with a natural frequency derived from the ultimate frequency of the plant. The three-pole assignments are determined by two similarity numbers λ1,λ2 considered as coordinates of the map. The limitation of admissible damping ratio due to the dominance condition is one of the original results presented in the paper. Furthermore, the influence of the root ratio is evaluated and final design recommendations are presented.