Active predictive vibration suppression algorithm for structural stability and tracking control of nonlinear multivariable continuum‐mechanics mobile systems

Abstract

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.

Model predictive tracking control of uncertain moving structures with nonaffine saturated actuation: Rotating control force

“…The reader is referred to the existing works in the field of nonlinear MPC. 25,40 The terminal cost satisfying Assumptions 1-8, associate feasible set, and corresponding control law will be obtained in Theorem 2.…”

Tracking control of moving flexible system by incorporation of feedback-based vibrational energy sink in model predictive control algorithm

“…MPC scheme implementation is not readily conductible in mechanical APDL environment. Nevertheless, a procedure proposed and implemented in authors previous framework 29 such that feasible solutions are calculable in more straightforward manner. FEVS algorithm is schematically described in Figure 2 in block-diagram format.…”

“…(14). The procedure is thoroughly discussed in 29 with the exception that in this study, forthcoming siding functions now include dynamical terms associated with continuum system vibrations. …”

“…The MPC incorporation with SMC is generally employed to benefit from both SMC inherent robustness in dealing with uncertainties associated with nonlinear problems and MPC capability for addressing system constraints. 29–31 The main issue emerges when optimal solution is not available due to necessary satisfaction of hard constraints such as actuator limitations. In this study, a new technique is utilized such that tracking performance is considered as soft constraints.…”

FEA-based tracking control of flexible body switching dynamic structure

“…Zhang et al [14] used adaptive sliding mode in control of parallel mechanism with flexible links. The other groups are conducted prioritizing stabilization and tracking problems of flexible mechanisms with or without vibration attenuation [15,16] which is also the approach the current paper adapts. Franco et al [17] discussed balancing control of an inverted pendulum using an energy-shaping controller with adaptive disturbance-compensation.…”