In this article, a new constrained adaptive backstepping control design is presented for vibration suppression of the quarter car suspension system equipped with a magnetorheological (MR) damper. In the controller design, parametric uncertainties related to suspension parameter and the semi-active actuator are considered. Also, the proposed controller is investigated, along with the designed road profiles based on the International Standard Organization (ISO) 8608 classification and tested under different speed conditions. The effectiveness of the proposed controller has been validated through comparisons with uncontrolled, passive, and separately designed adaptive control cases. According to the simulation and experimental results, the proposed control approach improves ride comfort and ride safety without violating suspension rattle space constraint despite the uncertainties in suspension parameters.

中文翻译：

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考虑悬架行程限制的半主动悬架约束自适应反步控制

在本文中，提出了一种新的约束自适应反步控制设计，用于抑制配备磁流变 (MR) 阻尼器的四分之一汽车悬架系统的振动。在控制器设计中，考虑了与悬架参数和半主动执行器相关的参数不确定性。此外，还研究了建议的控制器以及基于国际标准组织 (ISO) 8608 分类的设计道路剖面，并在不同速度条件下进行了测试。通过与不受控制的、被动的和单独设计的自适应控制情况进行比较，验证了所提出的控制器的有效性。根据仿真和实验结果，