Series PID Control With Higher-Order Derivatives for Processes Approximated by IPDT Models

The article takes up the pioneering work that led to the development of mass-used industrial controllers known by the original names of automatic-reset and hyper-reset, and generalizes them to an open family of controllers with higher-order derivatives and low-pass filters of the required order. For space limitations, the controller order is limited to the maximum degree of derivatives
$m=5$
. For the integrator plus dead time (IPDT) model, the tuning of the controller parameters and filter is performed by the method of multiple real dominant poles and using the equivalent filter delay. The proposed method is successfully tested on a limited controller output, where absolute stability can be demonstrated using the circle criterion. Compared with the SIMC design, illustrative examples verify applicability of derived controllers also by simulation of stable system with dominant first-order dynamics augmented with several shorter time constants and real-time temperature control. They confirm interesting properties of all the family members, acceleration of transients by increasing
$m$
and show that the considered maximum
$m=5$
need not be the final limit for practical application.
Note to Practitioners
—Every attempt to speed up transient responses ultimately leads to the need to respect the influence of control constraints. In connection with the use of parallel PI and PID controllers, the need arose for the use of various anti-windup circuits and conditioning techniques for their adjustment. The article offers an open family of controllers solving the problem more effectively by generalizing traditional automatic-reset controllers, also referred to in the literature as series PI and PID controllers. By expanding the automatic-reset with stabilizing controllers employing higher-order derivatives, the possibility of increasing the dynamics of the circuit even up to nearly-minimum-time control arises. The new solutions enable the achievement of higher dynamics of changes, excellent robustness and consideration of measurement noise attenuation without the need to deal additionally with special techniques eliminating negative impact of control signal limitations.