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

Proceedings of the Institution of Mechanical Engineers, Part K:

2022

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This paper proposes a new approach towards the nonlinear problem of tracking control for mobile multivariable vibrational structure featuring an Euler-Bernoulli vibrational beam. The control scheme involves obtaining interactions between flexural and rigid motions of the multivariable continuum mechanics system with actuator force limitation both regarding domain and frequency bandwidth. To this end, the boundary control inputs are selected prioritizing two tasks, satisfying actuator limitations and obtaining minimum possible tracking error. The former is employed as hard constraint in model predictive control (MPC) scheme while the latter is considered as soft constraint. The control scheme is adjusted such that when actuator limits are exceeded, the soft constraints are relaxed to maintain stability. In order to provide smooth tracking, Euler-Bernoulli transverse vibration is attenuated by incorporating Feedback Vibrational Energy Sink (FVES) method in obtaining control law. Hence, actuators are manipulated such that total vibrational energy of flexible beam is damped without using passive or conventional active dampers. The accuracy of the proposed method has been verified via FEA-based simulations.

“…The definition of continuous-time dynamical model associated with flexible system of Figure 1 is established through expressing Eqs. (9)(10)(11)(12).…”

Section: Remark 1 (Flexible Element Modal Truncation)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Proceedings of the Institution of Mechanical Engineers, Part K:

2022

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“…Hence, the control signal is calculated considering actuators' frequency bandwidth and measurement noise effects [15].…”

Section: Remark 1 (Considerations Of Measurement Noise)mentioning

confidence: 99%

“…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.…”

Section: Introduction 1overviewmentioning

confidence: 99%

FEA-based tracking control of flexible body switching dynamic structure

2021

Robotica

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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.

“…Hence, one could assign unity for either matrix and regulate the other gain accordingly. In this study, cost function gains are assigned based on acceleration synchronization technique introduced in Reference 30. The idea is briefly discussed in following remarks.Remark To proceed with acceleration synchronization, the vibration level is required to be initially detected through comparative analysis of data obtained from multiple acceleration sensors.…”

Section: Model Predictive Sliding Mode Control For Continuum Mechanicmentioning

confidence: 99%

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

Optim Control Appl Methods

Yaqubi

2020

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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.