FEA based discrete-time sliding mode control of uncertain continuum mechanics MIMO vibrational systems

Controlling uncertain nonlinear structural vibrations of moving continuum system by embedding a vibration monitoring unit to feedback algorithm

“…Control algorithm presented in Theorem 1 is constructed based on the equivalent rigid model of the system, thus calculated stability bounds are arguably accurate enough to be applicable in intense vibrations. To address this issue, one could proceed with uncertainty estimation approach to modify stability bounds following the method presented in Homaeinezhad et al 16 However, providing dynamical synchronization between system and dummy model is not always easy to achieve. To overcome this shortcoming, a more practical method is presented in Remark 4.Remark Controller inputs proximity factor is being updated in every simulation sample based on level of vibration as demonstrated in Equation 29.…”

“…Therefore, once the trajectory crosses sliding layer, that is, |s i (k)| < ρ i , control inputs should be calculated such that sliding mode regime is maintained. In such cases, is initially considered to obtain control input law instead of Equation 18 16 …”

“…Considering the fact that real mechanical systems always contain a certain level of flexibility, controller design and verification based on solely rigid model of a system may not lead to similar performance in real applications. Thus, the control problem of vibrational systems has become of great interest in recent studies 1–18 . These investigations are generally categorized into analytical and numerical approaches.…”

“…Xiuyu He et al 15 investigated control of simple end‐supported beam with mixed saturated dead zone inputs using mathematical model. In case of more complicated nonlinear problems when mode shape functions are not easily attainable, Homaeinezhad et al 16 proposed a robust algorithm to address the important problem of reference tracking in mobile multiple‐input multiple‐output vibrational systems and utilized finite element analysis (FEA) to estimate system parametric and unstructured uncertainties. Although the proposed theory did not require a precise FEA model of the plant to guarantee asymptotic stability, the synchronization task between FEA dummy model and plant is not always easily achievable.…”

Solving predictive control problem of fast‐varying multivariable systems by incorporating unknown active dynamics generated by real‐time adaptive learning machine

“…As a result, conservativeness of control algorithm becomes highly probable. This issue is further intensified when considering that successful implementation of theoretical control algorithms in real‐time mechanical systems (which are the focus of this study) often‐times requires consideration of interactions between multiple subsystems in a multi input‐multi output (MIMO) framework (Homaeinezhad, Yaqubi, & Fotoohinia, 2019; Homaeinezhad, Yaqubi, & Gholyan, 2020). In such cases, multiple worst‐case switching configurations for various subsystems have to be considered, which leads to a highly conservative design procedure.…”