The second-order systems can capture the dynamics of a vast majority of industrial processes. However, the existence of uncertainty in second-order approximation of such processes is inevitable because the approximation may not be accurate or the operating condition changes, resulting in performance degradation or even instability. This article aims at designing a novel robust proportional–integral–derivative controller for the uncertain second-order delay-free and time-delay systems in an optimal manner. The method is simple, effective, and can efficiently improve the performance of the uncertain systems. The approach is based on the linear quadratic theory, in which by adding a new matrix in the quadratic cost function regarding the uncertainties, the stability of the perturbed system is guaranteed and proven for both time-delay and delay-free second-order cases. The comparison with the recent works in the literature supports the effectiveness of the proposed methodology.

二阶系统可以捕获绝大多数工业过程的动态。但是，不可避免地存在这种过程的二阶近似，因为近似可能不准确或操作条件发生变化，从而导致性能下降甚至不稳定。本文旨在为最优的不确定二阶无延迟和时滞系统设计一种新颖的鲁棒比例积分微分控制器。该方法简单，有效，可以有效地提高不确定系统的性能。该方法基于线性二次理论，其中通过在关于不确定性的二次成本函数中添加新矩阵，对于时滞和无延迟的二阶情况，扰动系统的稳定性得到了保证和证明。与文献中最新著作的比较证明了所提出方法的有效性。