Optimal tuning of PID controllers for integrating processes via the symmetrical optimum criterion

Revisiting the Magnitude Optimum criterion for robust tuning of PID type-I control loops

“…Comments 1 and 3: In similar fashion with the revision of the Magnitude Optimum criterion presented in this work, in [27,28] it is shown that the principle of the Symmetrical Optimum criterion which can be regarded as an extension of the Magnitude Optimum criterion, can be extended to the design of type-II, III and type-p control loops, see [26]. Therefore this comment has to be revised.…”

On PID Controller Design by Combining Pole Placement Technique with Symmetrical Optimum Criterion

“…In this paper, the conditions for choosing the pole value refer to the symmetrical optimum criterion, which simplify the expressions of PID parameters. The goal is to find that pole value of the CLTF, which satisfies the assumptions of symmetrical optimum criterion around natural frequency 0 , for the transfer function of open-loop system given in (16). Using this value, the expressions of PID parameters given in (22a), (22b), (22c), and (22d) are simplified.…”

“…There is only one admissible value for the pole ( = − ) of CLTF given in (10), so that the corresponding OLTF given in (16) has symmetrical characteristics around 0 , and this value is as follows:…”

“…Pole placement technique (PPT) [12][13][14] and symmetrical optimum criterion (SOC) [15][16][17][18] were intensively studied as separated methods on both types of reduced plant models mentioned above.…”