PID Control With Higher Order Derivative Degrees for IPDT Plant Models

In this paper, we discuss the main features of the generalized higher-order proportional-integrative-derivative control (HO-PID) based on the integral-plus-dead-time (IPDT) plant models. It was developed by extending the traditional PI-control to include $m$ th-order derivatives and $n\geq m$ th-order binomial series filters. The HO-PID control provides two additional degrees of freedom, which allow to appropriately modify the speed of the transients and the attenuation of the measurement noise, together with the closed-loop robustness. In this way, it pursues similar goals as an alternative fractional-order PID control. A broad family of the HO-PID controllers with the included low-pass filters is employed to solve a number of new problems. Their integrated suboptimal tuning, based on explicit formulas derived by the multiple real dominant pole (MRDP) method and evaluated by a novel approach that relates the speed of transients to the excessive input and output increments, has been simplified by introducing two integrated tuning procedures (ITPs). The main new finding is that HO-PID control enables faster transients by simultaneously reducing the negative effects of measurement noise and increasing the closed-loop robustness. A brief experimental evaluation using new sensitivity measures fully confirms the excellent HO-PID characteristics and shows that commissioning remains almost as simple as with the filtered PI-control.

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