On Active Vibration Absorption in Motion Control of a Quadrotor UAV

Conventional dynamic vibration absorbers are physical control devices designed to be coupled to flexible mechanical structures to be protected against undesirable forced vibrations. In this article, an approach to extend the capabilities of forced vibration suppression of the dynamic vibration absorbers into desired motion trajectory tracking control algorithms for a four-rotor unmanned aerial vehicle (UAV) is introduced. Nevertheless, additional physical control devices for mechanical vibration absorption are unnecessary in the proposed motion profile reference tracking control design perspective. A new dynamic control design approach for efficient tracking of desired motion profiles as well as for simultaneous active harmonic vibration absorption for a quadrotor helicopter is then proposed. In contrast to other control design methods, the presented motion tracking control scheme is based on the synthesis of multiple virtual (nonphysical) dynamic vibration absorbers. The mathematical structure of these physical mechanical devices, known as dynamic vibration absorbers, is properly exploited and extended for control synthesis for underactuated multiple-input multiple-output four-rotor nonlinear aerial dynamic systems. In this fashion, additional capabilities of active suppression of vibrating forces and torques can be achieved in specified motion directions on four-rotor helicopters. Moreover, since the dynamic vibration absorbers are designed to be virtual, these can be directly tuned for diverse operating conditions. In the present study, it is thus demonstrated that the mathematical structure of physical mechanical vibration absorbers can be extended for the design of active vibration control schemes for desired motion trajectory tracking tasks on four-rotor aerial vehicles subjected to adverse harmonic disturbances. The effectiveness of the presented novel design perspective of virtual dynamic vibration absorption schemes is proved by analytical and numerical results. Several operating case studies to stress the advantages to extend the undesirable vibration attenuation capabilities of the dynamic vibration absorbers into trajectory tracking control algorithms for nonlinear four-rotor helicopter systems are presented.

Optimization design for multiple dynamic vibration absorbers on damped structures using equivalent linearization method

The dynamic vibration absorber and tuned mass damper are widely used to suppress harmful vibration of the damped structures under external excitation. The multiple dynamic vibration absorbers have more benefit than the single dynamic vibration absorber. The multiple dynamic vibration absorbers are portability and easy to install because its size is significantly reduced compared to an individual damper. This paper proposes a design method to obtain optimal parameters of multiple dynamic vibration absorbers attached on damped primary structures by using the least squares estimation of equivalent linearization method. An explicit expression of damping ratio and tuning parameters of multiple dynamic vibration absorbers are determined for minimizing the maximum displacement of the primary structures based on the fixed-point theory. The new contribution is provided a reliable theoretical basis for optimizing parameters of the multiple dynamic vibration absorbers that are attached on the damped primary structures. The numerical results reveal the effectiveness of the proposed optimal parameters of multiple dynamic vibration absorbers in reduce vibration of damped primary structures. In the practical applications, this research results allow to divide a large dynamic vibration absorber into many equivalent small dynamic vibration absorbers, which are convenient for manufacturing and installing on the damped primary structures such as high buildings and cable-stayed bridges.

Investigation On The Optimal Tunable Bi-Stable Clustered Energy Conversion Inspired Dynamic Vibration Absorbers: A Theoretical Study

This paper introduces an energy conversion inspired vibration control methodology and presents a representative prototype of tunable bi-stable energy converters. This work is concerned on improving the vibration absorption and energy conversion performance of tunable bi-stable clustered energy conversion inspired dynamic vibration absorbers (EC-DVAs). The deterministic parametric analysis of the energy transfer performance of clustered EC-DVAs is conducted. Firstly, nonlinear vibration behaviors including transient energy transfer and snap-through motions are studied, and then effects of EC-DVA number on vibration control is investigated. Furthermore, the optimal computation based on adjusting the length ratio (namely bi-stable potential barrier height) is developed to obtain the maximum energy conversion efficiency of clustered EC-DVAs and the minimum residual kinetic energy of the primary system considering different number of clustered EC-DVAs. Moreover, the optimal calculation based on optimal EC-DVA number is also developed to achieve the most excellent vibration absorption and energy conversion performance. Finally, the optimal calculation based on optimal mass ratio is conducted. Numerical simulations show that when the total mass ratio is constant the snap-through motions of each EC-DVA depend remarkably on EC-DVA number; the energy conversion efficiency and residual kinetic energy after dynamic length ratio optimization is independent on ambient input energy and EC-DVA number; The energy conversion efficiency and vibration absorption performance based on optimal EC-DVA number maintain high efficiency and stable when the ambient input energy or the potential energy of clustered EC-DVAs varies. The optimal mass ratio is large when the system’s potential barrier is too large and the ambient input energy is small. Therefore, the presented tunable bi-stable system of clustered EC-DVAs with appropriate bi-stable potential function and proposed optimization strategies is a potential alternative for vibration control of mechanical components exposed to varying impulses.

Parameters optimization of dynamic vibration absorber based on grounded stiffness, inerter, and amplifying mechanism

In the field of dynamics and control, some typical vibration devices, including grounded stiffness, inerter and amplifying mechanism, have good vibration isolation and reduction effects, especially in dynamic vibration absorber (DVA). However, most of the current research studies only focus on the performance of a single device on the system, and those DVAs are gradually becoming difficult to meet the growth of performance demand for vibration control. On the basis of Voigt dynamic vibration absorber, a novel dynamic vibration absorber model based on the combined structure of grounded stiffness, inerter, and amplifying mechanism is presented, and the analytical solution of the optimal design formula is derived. First, the motion differential equation of the system is established, and the normalized amplitude amplification factor of the displacement is calculated. It is found that the system has three fixed points unrelated to the damping ratio. The optimal frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal grounded stiffness ratio. Accordingly, the best working range of inerter is determined. Finally, optimal grounded stiffness ratio and approximate optimal damping ratio are also obtained. The influence of inerter coefficient and magnification ratio on the response of the primary system is analyzed. The correctness of the derived analytical solution is verified by numerical simulation. Compared with other dynamic vibration absorbers, it is verified that presented model has superior vibration absorption performance and provides a theoretical basis for the design of a new type of dynamic vibration absorbers.

Vortex-Induced Vibration Suppression of Bridges by Inerter-Based Dynamic Vibration Absorbers

The vortex-induced vibration may cause fatigue of a bridge structure, affecting the safety of vehicles and the comfort of pedestrians. Inerter is a two-terminal device, which has been applied in many areas. This paper studies the problem of suppressing the vortex-induced vibration of a bridge by using an inerter-based dynamic vibration absorber (IDVA). The performances in terms of the suspension travel and the vertical displacement of the bridge with different IDVAs in suppressing vortex-induced vibration are compared, and the effect of the installation position of IDVA on the performance of suppressing vortex-induced vibration is shown. The performance indexes for the vertical displacement of six IDVA arrangements are obtained by using an iterative method, where the performance indexes for the vertical displacement are minimized by using the optimization toolbox in a commercial software. The result shows that the optimal installation positions and the number of suitable installation positions are affected by the resonant mode. Among the six arrangements, one arrangement is identified to have the best performance of suppressing vortex-induced vibration. All the six arrangements have reduced the suspension travel performance.

Optimization of the semi-active vibration absorbers

In this paper, an efficient numerical approach is proposed to maximize the minimal damping of modes in a prescribed frequency range for general viscous tuned-mass systems. Methods of decomposition and numerical synthesis are considered on the basis of the adaptive schemes. The influence of dynamic vibration absorbers and basic design elastic and damping properties is under discussion. A technique is developed to give the optimal DVA’s for the elimination of excessive vibration in sinusoidal and impact forced system. One task of this work is to analyze parameters identification of the dynamic vibration absorber and the basic structure. The questions of robustness at optimization of DVA are considered. Different types of control management for semi-active DVA’s are applied. Examples of DVA’s practical implementation are presented.