SUMMARYThis paper addresses the tracking problem for uncertain nonlinear sandwich systems that consist of two nonlinear subsystems and saturation nonlinearity, which is sandwiched between the subsystems. The considered sandwich system is also subject to a nonsymmetric input saturation constraint. Due to the nonsmooth characteristics of sandwiched saturation nonlinearity and also the input saturation function, the design procedure deals with hard challenges. To overcome these difficulties, a recursive approach is suggested that consists of two phases. For the implementation of the proposed approach, a tracking problem is solved in each phase. In the first phase, the second subsystem with sandwiched saturation nonlinearity is considered and the output tracking problem of the desired time-varying reference signal is solved using backstepping method. The outcome of the first phase is the desired reference signal that should be tracked by the first subsystem in the next phase. In the second phase, the robust control input is designed for the first subsystem by employing adaptive sliding mode technique such that, despite the nonsymmetric input saturation constraint, model uncertainty and external disturbances, the output of the first subsystem follows the desired signal that is obtained in the previous phase. The simulation results for a mechanical sandwich system are illustrated to verify the effectiveness of the proposed control method.

中文翻译：

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受饱和非线性影响的非线性夹心系统的自适应鲁棒跟踪器设计

摘要本文解决了由两个非线性子系统和夹在子系统之间的饱和非线性组成的不确定非线性夹层系统的跟踪问题。所考虑的三明治系统也受到非对称输入饱和约束。由于夹层饱和非线性的非光滑特性以及输入饱和函数，设计过程面临着严峻的挑战。为了克服这些困难，提出了一种包括两个阶段的递归方法。为了实现所提出的方法，在每个阶段都解决了一个跟踪问题。在第一阶段，考虑具有夹层饱和非线性的第二子系统，并使用反步法解决所需时变参考信号的输出跟踪问题。第一阶段的结果是所需的参考信号，应该由下一阶段的第一个子系统跟踪。在第二阶段，通过采用自适应滑模技术为第一个子系统设计鲁棒控制输入，使得尽管存在非对称输入饱和约束、模型不确定性和外部干扰，第一个子系统的输出遵循获得的期望信号在前一个阶段。对机械夹层系统的仿真结果进行了说明，以验证所提出的控制方法的有效性。通过采用自适应滑模技术为第一个子系统设计鲁棒控制输入，这样，尽管存在非对称输入饱和约束、模型不确定性和外部干扰，第一个子系统的输出仍遵循前一阶段获得的所需信号。对机械夹层系统的仿真结果进行了说明，以验证所提出的控制方法的有效性。通过采用自适应滑模技术为第一个子系统设计鲁棒控制输入，这样，尽管存在非对称输入饱和约束、模型不确定性和外部干扰，第一个子系统的输出仍遵循前一阶段获得的所需信号。对机械夹层系统的仿真结果进行了说明，以验证所提出的控制方法的有效性。