Adaptive modal vibration control for smart flexible beam with two piezoelectric actuators by multivariable self-tuning control

Abstract

It has been popular for decades that the vibrations of space structures are suppressed with smart actuators. However, the higher mode vibrations are often motivated when a control strategy is applied to attenuate the vibration for the smart structures. Moreover, if the multi-mode vibration of a smart structure is suppressed with multi-actuators, a proper multivariable control law will be adopted to solve the coupling problem caused by the multi-actuators of the smart structure. Therefore, in the paper, a decoupling technique for two modal vibrations of a smart flexible beam with two piezoelectric patches is adopted by adaptive control. The proposed control law is designed with a multivariable minimum variance self-tuning control. Considering the first two orders of modal vibrations, two piezoelectric patches are configured on the flexible beam according to the strain of the first two orders of modal vibrations along the longitudinal direction of the beam. A dynamical model for the flexible beam with two piezoelectric actuators is constructed by the mode superposition method. With the dynamical model, simulations are implemented to suppress the free vibration of the flexible beam. Moreover, experiments are carried out to verify the effectiveness of the multivariable minimum variance self-tuning control for vibration suppression of the flexible structure. The control results clearly show that the free vibration amplitude of the cantilevered beam with two control voltages applied to the two piezoelectric patches is less than that with one control voltage applied to the first piezoelectric actuator. Thus, multivariable minimum variance self-tuning control is a more efficient approach for suppressing multimodal vibration for a smart flexible beam with two piezoelectric actuators compared with the conventional velocity feedback control.

A state-of-the-art on smart materials actuators over the last decade: control aspects for diverse applications

“…From the above discussion, controllers for the piezo actuator are also identified in the application, along with classical forms to modern forms. A summarization of the control for the piezo devices are shown in figure 8 including optimal control [36, 37], LQR control [38,39], switching control [40], fuzzy control [41][42][43][44][45], fuzzy sliding mode control [42], adaptive sliding mode control [46][47][48][49], force control [50], predictive sliding mode control [51][52][53][54], proportional differential (PD) control [41,55,56], PID control [57], H-infinity technique [58], feed-forward control [59], neural networks [60,61], active control [61][62][63][64][65], and identification/delayed feedback/genetic/adaptive models [65][66][67][68][69][70].…”

Modelling and Control of Longitudinal Vibrations in a Radio Frequency Cavity

“…In this paper, we propose a novel approach to examine the flexural free vibrations of uniform beams, building upon previous research conducted by various scholars [23][24][25][26][27][28][29]. The organization of this paper is as follows.…”

Multiple-input multiple-output robust vibration control for constrained gyroelastic solar panel considering parametric and un-modeled dynamic uncertainties

“…With an increasing complexity of space missions and expectation of reducing launch costs reduction, the spacecraft is becoming larger, more lightweight and flexible, and prone to vibration, which leads to the problem of spatial pointing accuracy and shape (Lewis and Inman, 2001; Guo et al, 2020). For solving vibration problems above, active vibration suppression methods are more effective in practical engineering (Fanson, 1987; Williams, et al, 2019; Zhang and Li, 2020). Angular momentum exchange devices, which can provide sufficient, continuous, and precise control torques under the condition of occupying only a small internal space, are a kind of control actuators widely used for active vibration suppression (Guo et al, 2018; Gupta et al, 2011; Hu et al, 2013a, 2020, Wang et al, 2017).…”