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 first-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 different 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-off 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.

当应用自动控制时，比例-积分-微分 (PID) 控制器占绝对优势。文献中对这些控制器有大量的调整规则。然而，对于高度振荡（或高度欠阻尼）的系统，例如在石油生产和聚合反应器中发现的系统，可用的方法提供较差的闭环性能和稳健性。此外，这些调整规则中的大多数是为基于具有纯时间延迟 (FOPTD) 传递函数的一阶系统和并行形式的 PID 控制器开发的。因此，本文的重点是通过不取消主极点和易于调节的鲁棒性能为高度欠阻尼系统开发适当的调谐规则，使其适用于串联和并联 PID 控制器，因为建议的调整只将控制器零点放在实轴上。新的调整规则是为这些系统开发的，并在 15,000 个不同的传递函数上进行了测试，这些传递函数由具有纯时间延迟 (SOPTD) 表达式的二阶描述。此外，还提供了一个推荐间隔，其中控制器增益可以在线或通过模拟变化，以实现性能和鲁棒性之间的所需权衡。提议的规则也通过两个案例研究得到验证：石油生产中的段塞抑制和工业气相聚乙烯反应器的温度控制。此外，还提供了一个推荐间隔，其中控制器增益可以在线或通过模拟变化，以实现性能和鲁棒性之间的所需权衡。提议的规则也通过两个案例研究得到验证：石油生产中的段塞抑制和工业气相聚乙烯反应器的温度控制。此外，还提供了一个推荐间隔，其中控制器增益可以在线或通过模拟变化，以实现性能和鲁棒性之间的所需权衡。提议的规则也通过两个案例研究得到验证：石油生产中的段塞抑制和工业气相聚乙烯反应器的温度控制。