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

Summary: This paper proposes a practical solution to control a problem of a class of continuum mechanics systems in which spatial equations corresponding to vibrational motions are not resolvable through conventional analytical approaches. Control scheme is constructed based on discrete sliding mode technique regarding a rigid model of a system such that control inputs are selected between Lyapunov stability bounds to manipulate the system in tracking reference values. The stability bounds and control input signal proximity to either bounds are updated in every simulation step in accordance to system vibration level using a practical acceleration synchronization method aside from evolution of rigid model states. To this end, the severity of vibrations is analyzed online using a limited number of acceleration sensors. These sensors are installed on critical nodes that are generally characterized with high level of vibrations, and the synchronization process is employed through comparative analysis with other nodes of which exhibit more rigidity within the structure. In order to highlight controller performance, virtual plant is assumed to be constructed from viscoelastic materials (VEMs) featuring time‐varying elasticity and viscosity, and Prony series parameters are involved in modeling VEMs in ANSYS® mechanical APDL student edition. Eventually, controller capability in stabilization of closed‐loop system and tracking reference values are evaluated in finite element analysis transient environment, and simulation results are compared with those of existing methods. [ABSTRACT FROM AUTHOR]