This article presents novel schemes using which a robustly stable and feasible optimal controller can be obtained for uncertain vibrational systems. Furthermore, the aforementioned objectives are satisfied solely employing a rigid approximation of continuum mechanics systems. Simultaneously, significant reductions in control complexity and computation burden are attained. On this basis, a new model predictive sliding mode control method for general class of continuum mechanics systems is developed. The control scheme is constructed based on a mathematical model corresponding to equivalent rigid representation of nonlinear flexible mechanism, considering that the partial differential equations (PDE) for original system may not be solvable using analytical approaches. The proposed method features a model predictive control (MPC) based on minimization of an optimization cost constituting predicted sliding functions over a finite prediction horizon. In order to mitigate undesired vibrational effects, control input weighting factor considered in calculation of cost is updated in every sample in accordance with intensity of vibrations observed through a limited number of acceleration sensors. Robust feasibility and stability of control algorithm in presence of modeling uncertainty are guaranteed based on investigation of a Lyapunov‐based terminal cost function within the assigned constraints. The performance of closed‐loop system in control of a flexible mechanism is evaluated for a multitude of reference signals. Simulations are conducted in Finite Element Analysis (FEA) environment utilizing ANSYS Mechanical APDL. Obtained results indicate superior performance in terms of tracking quality, closed‐loop stability, and mitigation of undesired vibrational effects in comparison with existing control schemes.

中文翻译：

---

主动预测振动抑制算法，用于非线性多变量连续体力学移动系统的结构稳定性和跟踪控制

本文提出了新颖的方案，通过该方案可以为不确定的振动系统获得鲁棒稳定且可行的最优控制器。此外，仅使用连续体力学系统的刚性逼近就可以满足上述目的。同时，大大降低了控制复杂度和计算负担。在此基础上，为通用力学系统的通用类开发了一种新的模型预测滑模控制方法。考虑到原始系统的偏微分方程（PDE）可能无法使用解析方法求解，因此基于与非线性柔性机械的等效刚性表示相对应的数学模型构造控制方案。所提出的方法的特征在于模型预测控制（MPC），该模型基于构成有限滑动预测范围内的预测滑动函数的最优化成本的最小化。为了减轻不希望的振动影响，根据通过有限数量的加速度传感器观察到的振动强度，在每个样本中更新在成本计算中考虑的控制输入加权因子。通过研究在分配的约束内基于Lyapunov的终端成本函数，可以保证存在模型不确定性时控制算法的鲁棒可行性和稳定性。针对大量参考信号评估了闭环系统在柔性机构控制中的性能。利用ANSYS Mechanical APDL在有限元分析（FEA）环境中进行仿真。与现有的控制方案相比，获得的结果表明，在跟踪质量，闭环稳定性以及减轻不良的振动影响方面，其性能均优越。