Large amplitude vibrations are often associated with geometric nonlinearity. These nonlinear systems are usually controlled using linear controllers, such as positive position feedback (PPF). Nonlinear control has also often been limited to single-input single-output (SISO) architectures. The present study develops a nonlinear PPF controller implemented with both a SISO and a multiple-input multiple-output (MIMO) architecture on a real experimental set-up, consisting of a clamped composite sandwich beam. The controller aimed to reduce the vibration amplitude observed when the structure was subject to a stepped-sine excitation in the frequency neighborhood of the first natural frequency for different force excitation levels. The developed nonlinear controller is based on a linear PPF controller to which a cubic term was added since the system under study is of hardening type. The control parameters were selected by optimization of the reduction of the vibration at low excitation amplitude. The nonlinear MIMO and SISO versions of the controller were compared to linear MIMO and SISO versions, which omitted the cubic term but maintained the other parameters. The nonlinear controllers were found to outperform the linear ones, and the MIMO versions of each controller also outperformed the SISO ones. Overall, the experimental evidence shows that a nonlinear MIMO PPF controller should be preferred for the application under study.

中文翻译：

---

夹层梁多输入多输出非线性主动振动控制实验方法


大振幅振动通常与几何非线性相关。这些非线性系统通常使用线性控制器进行控制，例如正位置反馈（PPF）。非线性控制通常也仅限于单输入单输出 (SISO) 架构。本研究开发了一种非线性 PPF 控制器，在真实的实验装置上实现了 SISO 和多输入多输出 (MIMO) 架构，该装置由钳位复合夹层梁组成。该控制器的目的是减少当结构在不同力激励水平的第一固有频率的频率邻域内受到步进正弦激励时观察到的振动幅度。所开发的非线性控制器基于线性 PPF 控制器，由于所研究的系统是硬化型系统，因此添加了三次项。通过优化低激励振幅下的振动减少来选择控制参数。将控制器的非线性 MIMO 和 SISO 版本与线性 MIMO 和 SISO 版本进行了比较，线性 MIMO 和 SISO 版本省略了三次项，但保留了其他参数。研究发现非线性控制器的性能优于线性控制器，并且每个控制器的 MIMO 版本也优于 SISO 版本。总体而言，实验证据表明非线性 MIMO PPF 控制器应优先用于所研究的应用。