Reliable and straightforward PID tuning rules for highly underdamped systems

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