Vibration is an intrinsic phenomenon in many mechanical and mechatronic applied devices and undesirable vibration can either degrade the performance of the system or lead to unpredictable outputs. The main purpose of this article is to introduce a novel second-order proportional–integral–derivative sliding mode control methodology to suppress the undesirable vibrations of a class of applied dynamical systems with applications to mechatronic and mechanical devices. After designing a nonlinear proportional–integral–derivative terminal sliding manifold, rigorous mathematics are provided to guarantee that the origin is a practical finite time stable equilibrium point. Consequently, two efficient control laws are proposed to ensure the occurrence of the sliding motion with and/or without system unknown parameters. Motivated by situations encountered in practice, unknown lumped uncertainties are also added to the system and their impacts are tackled using adaptive control techniques. Furthermore, a hard nonlinear dead-band function is utilized in the control input and its effects such as lags and delays appeared on the control signals as well as on the system outputs are dealt with by the proposed proportional–integral–derivative variable structure controller. The proposed second-order variable structure controller not only utilizes the simple effective design approach of the proportional–integral–derivative controllers to ensure a reasonable transient performance, but also displays fast convergence properties demonstrated in non-singular terminal sliding modes. Finally, through simulation studies, it is confirmed that the proposed control strategy is effective in vibration attenuation of microelectromechanical resonators.

振动是许多机械和机电应用设备中的固有现象，不希望的振动会降低系统性能或导致不可预测的输出。本文的主要目的是介绍一种新颖的二阶比例-积分-导数滑模控制方法，以抑制机电系统和机械设备中一类应用动力学系统的不良振动。在设计了非线性比例-积分-微分终端滑动流形之后，提供了严格的数学方法来保证原点是一个切实可行的有限时间稳定的平衡点。因此，提出了两种有效的控制律，以确保在有和/或没有系统未知参数的情况下发生滑动运动。受实际情况的启发，未知的集总不确定性也被添加到系统中，并且使用自适应控制技术解决了它们的影响。此外，在控制输入中使用了硬的非线性死区功能，并通过提出的比例积分微分变量结构控制器来处理其滞后和延迟等在控制信号以及系统输出上的影响。所提出的二阶变结构控制器不仅利用比例积分微分控制器的简单有效设计方法来确保合理的瞬态性能，而且还显示出在非奇异终端滑模下的快速收敛性。最后，通过模拟研究，