Reliable and straightforward PID tuning rules for highly underdamped systems

Abstract

Proportional-Integral-Derivative (PID) controllers reign absolute when automatic control is applied. There is an expressive number of tuning rules for these controllers in literature. However, for highly oscillatory (or highly underdamped) systems, such as the ones found in oil production and polymerization reactors, the available methods provide poor closed-loop performance and robustness. Besides, most of these tuning rules are developed for systems based on a frst-order with pure time delay (FOPTD) transfer function and for parallel form PID controllers. Therefore, the focus of this paper is the development of appropriate tuning rules for highly underdamped systems through non-cancellation of dominant poles and easily adjustable robust performance, making them applicable for both series and parallel PID controllers, since the proposed tuning only places the controller zeros at the real axis. The new tuning rules were developed for these systems and were tested on 15,000 diferent transfer functions described by a second-order with pure time delay (SOPTD) expression. Additionally, a recommendation interval is also provided in which the controller gain can be varied online or by simulations to achieve the desired trade-of between performance and robustness. The proposed rules are also validated using two case studies: the suppression of slugging in oil production and the temperature control of an industrial gas phase polyethylene reactor.