Optimal Vibration Control of Membrane Structures with In-Plane Polyvinylidene Fluoride Actuators

Abstract

Different kinds of membrane structures have been proposed for future space exploration and earth observation. However, due to the low stiffness, high flexibility, and low damping properties, membrane structures are likely to generate large-amplitude (compared to the thickness) vibrations, which may lead to the degradation of their working performance. In this work, the governing equations are established at first, taking into account the modal control force induced by the polyvinylidene fluoride (PVDF) actuator. The optimal vibration control of the membrane structure is explored subsequently. A square PVDF actuator is attached on the membrane to achieve the vibration suppression. The influence of actuator position and control gains on the vibration control performance are studied. The optimal criteria for actuator placement and energy allocation are developed. Several case studies are numerically simulated to demonstrate the validity of the proposed optimization criteria. The analytical results in this study can serve as guidelines for optimal vibration control of membrane structures. Additionally, the proposed optimization criteria can be applied to active control of different flexible structures.

Adaptive vibration control of piezoelectric cantilever beams with uncertainties

“…) Theorem 1: For the nonlinear system with uncertainties described by (19), under the control of ASMC law (34) with switching function (28), if the adaptive updating law (35) is adopted to the active control of piezoelectric cantilever beam, then the controlled closed-loop errors and converge asymptotically to zeroes.…”

“…Considering the uncertainty of system parameters and external disturbance, ( 18) can be rewritten as (19) with uncertainties is concerned, the control objective is to design an adaptive sliding mode control law u on the basis of uncertainty estimation, which ensures system state asymptotically converge to the bounded neighborhood of zero vector, such that:…”

“…In LQR, the weighted matrixes Q and R are calculated according to the energy criterion [19]. The parameters of ASMC (34, 35) are chosen as follows: h=25, c 1 =65, k 1 =50, =30  .…”

“…The main control algorithms are used in the vibration control of smart piezoelectric cantilever beam are as followings: PD control based on optimal position feedback [12], robust control [13], adaptive control [14,15], fuzzy control [16], artificial neural network control [17], LQR control method [18][19][20][21] etc. The objective of active vibration control is to quickly suppress bending and torsional modal vibration.…”

Multi-mode Vibration Averagely Control for Cylindrical Shells by Optimally Distributed Piezoelectric Sensors and Actuators

“…In the part of piezoelectric actuators, the traditional piezoelectric ceramic is fragile, and it is hard to adhere to a curvature shell. The polyvinylidene fluoride (PVDF)s' actuation forces are low, which are usually applied for controlling the vibrations of membrane structures and thin shells made of low modulus material [18][19][20]. Macro-fiber composites (MFCs) are not only flexible, but they have relatively larger output force also.…”