Active predictive vibration suppression algorithm for structural stability and tracking control of nonlinear multivariable continuum-mechanics mobile systems. (English) Zbl 1469.93022

Homaeinezhad, M. R.; Fotoohinia, F.; Yaqubi, S.

Optim. Control Appl. Methods 42, No. 2, 503-525 (2021).

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.

MSC:

93B45	Model predictive control
93B12	Variable structure systems
93C10	Nonlinear systems in control theory
70L05	Random vibrations in mechanics of particles and systems
93C35	Multivariable systems, multidimensional control systems

Keywords:

active vibration suppression; continuum systems; model predictive control; robust feasibility; structural stability; tracking control

Software:

APDL; ANSYS