Constrained Series PI, PID and PIDA Controller Design Inspired by Ziegler–Nichols

Abstract

The present paper complements the results of several recent papers on higher-order (HO) controllers with automatic-reset. A modification of the two-step tuning of the constrained second-order derivative controllers based on integrator-plus-dead-time (IPDT) models is proposed. In the first step, the linear controller is designed using the multiple real dominant poles (MRDPs) method to avoid the slowdown of the closed-loop dynamics due to the presence of slow poles. In the second step, the smallest time constant of the numerator of the MRDP-optimal controller transfer function is selected as the automatic-reset time constant. The derived control method was tested on a thermal system for the filament disc dryer to demonstrate the deployment, tuning, use and impact of controllers with increasing derivative degree in practical applications. It is shown that the use of HO controllers is similar to the traditional hyper-reset controllers (i.e. series proportional-integral-derivative [PID] controllers) from the user’s point of view. However, the advantages are faster transient responses while maintaining sufficiently smooth input and output shapes of the process with a minimum number of monotonic intervals. The overall design can be seen as a generalisation and discretisation of the Ziegler and Nichols graphical tuning method. One of the main new features is the consideration of a constrained control signal, as is typical for a pulse width modulated (PWM) actuator. Such actuators are often used in speed-controlled electric drives and in power electronics, among other applications.