Tuning of PID Control for the Double Integrator Plus Dead Time Model by Modified Real Dominant Pole and Performance Portrait Methods

The paper discusses the proportional-integral-derivative (PID) controller from the viewpoint of (a) the analytical tuning of the PID controller for the double integrator plus dead time (DIPDT) model and (b) the numerical tuning using the performance portrait method (PPM). In the first case, the already published tuning with multiple real dominant pole, extended by integrated tuning procedures, which incorporate the inevitable low-pass filters by delay equivalences, is elaborated for modified sets of real poles. By considering several such modified sets of real poles, resulting in several new sets of controller parameters, the design can be better adapted to the requirements of the control tasks solved and to the limitations of the existing control loop hardware. In a noisy and uncertain environment, the balance between speed of setpoint and disturbance responses and acceptable excessive controller effort can thus be improved. The effectiveness of the analytical design can be evaluated using the numerical performance portrait method (PPM). For an already generated performance portrait (PP), it can offer a broad spectrum of controller settings that satisfy various design constraints. However, the results of the analytical design are still important as they facilitate the initial steps in the elaboration of the PPM and in explaining the nature of PID control. The developed controller tuning are compared using a new interpretation of PID controller as an extension of the stabilising PD controller by disturbance observer (DOB). The input disturbances reconstructed by DOB by evaluating the controller output of an integral process model in steady-state, can be estimated by a low-pass filter with a sufficiently long (integral) time constant. All analysed results are in full agreement with the proposed DOB interpretation, which furthermore contributes significantly to the explanation of the problems related to the optimal design of PID controllers.