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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 timevarying 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.

In this paper, robust stabilization and predictive tracking control for a class of nonlinear uncertain multivariable systems is presented. The control scheme is built by incorporating nonlinear model predictive control in discrete sliding mode control to obtain optimal results while satisfying hard constraints and closed-loop robustness in the presence of external disturbance (matched or unmatched) and parametric uncertainty. Additionally, the control input domain limitation is involved in construction of the model predictive control scheme by employing sliding functions admissible bounds. The problem of cost minimization is solved through optimal selection of terminal cost gain and allocation of system dynamics with respect to sliding surfaces while robust stabilization and feasibility are ensured through the prediction horizon.

Summary 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.

In dynamically switched systems with unknown switching signal, the control system is conventionally designed based on the worst switching scenario to ensure system stability. Such conservative design demands excessive control effort in less critical switching configurations. In the case of continuum mechanics systems, such excessive control inputs result in increased structural deformations and resultant modeling uncertainties. These deformations alter differential equations of motion which cripple the task of control. In this paper, a new approach for tracking control of uncertain continuum mechanics multivariable systems undergoing switching dynamics and unknown time delay has been proposed. Control algorithm is constructed based on the mathematical rigid model of the plant and a Common Lyapunov Function (CLF) is proposed upon sliding hyperplane regarding all switching configurations. Considering the model-based nature of sliding mode control (SMC) and inevitable uncertainties induced from modeling simplifications of continuum system or parameter evaluation errors, Finite Element Analysis (FEA) is utilized to approximate total model uncertainties. To obtain robust stability, instead of conventional switching functions in the construction of control law, the control inputs are selected such that system dynamics reside within stability bounds which are calculated based on the Lyapunov asymptotic stability criterion. Therefore, the unwanted chattering issue caused by continuous switching is not observed in control input signals. Eventually, the accuracy of the proposed method has been verified through the student version of ANSYS® mechanical APDL-based simulations and its effectiveness has been demonstrated in multiple operating conditions.