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The boundary limits of the controller gain parameters for each loop that were applied in MATLAB/Simulink environment were obtained by trial and error.
Table 3 Boundary limits of the controller gain parameters Gain parameters Minimum value Maximum value Kp 1 4 5 Kd 1 3 4 Ki 1 0.4 0.8 Kp 2 4 5 Kd 2 3 4 Ki 2 1 1.3 Kp 3 10 13 Kd 3 15 20 Ki 3 2 3.
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The ultimate gain (upper limit) of the controller has been specified properly via root locus plot before starting the optimization process to avoid falling in instability region.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com