果园货运链索横向振动非线性控制

为有效抑制果园货运链索行进过程中的横向振动,提出采用一种非线性边界控制方法进行链索横向减振主动控制。考虑到多边形效应对链索振动造成的影响,基于Hamilton原理建立了复杂工况下轴向行进链索和边界作动器的动力学耦合模型。通过构建广义能量函数作为系统的Lyapunov函数,设计了受控链索的控制规律,进行了链索横向振动闭环系统的渐近稳定性证明推导。仿真与试验结果表明,通过作动器引入控制力,链索横向振动在主动控制率的作用下能够在5个周期内被有效抑制。该文为货运行进链索的振动控制研究提供了理论参考。

Nonlinear transverse vibration control of orchard conveying chain system

Abstract: Vibrations associated with motion can degrade the performance of transport systems in orchards. It is important to suppress vibrations which are subjected to varying parameter and boundary disturbance. Early research on the vibration reduction in continuously moving systems wasfocused on the passive control methods by changing the mass or stiffness to absorb vibrational energy. To improve the effectiveness of vibration controller, many active control methods have been proposed with actuating mechanisms to compute the control effect. The application of conveying chain system was proved to be labor-saving and high efficientin mountainous orchards. Unlike a moving string system, the conveying chain system in the orchard is more complicated in the structure and boundary excitation. When the chain link engages a sprocket tooth,there is an impact caused bypolygonal action.The polygonal actionresults from the chain-support engagement and its resulting vibrations are the source of most of the noise. Moreover, it is inconvenient to mount actuators on the conveying chain system. Since the boundary control technique requires relatively few sensors and actuators, a particularactuator as the control mechanism was attached and coupled to the boundary of the moving chain.The control forcewas applied by the actuatorwith negligible dynamics, which was used to reduce the energy of the moving chain while dissipating the energy of a short length of the chain. An image acquisition device was used to measure the transverse displacement of the observation point. The actuator was activated when the vision sensor indicated that the chain vibration has occurred. The behaviorof transverse vibration could be predicted by a two-dimensional model in a vertical plane. Then the mathematical model of the coupled chain system including the actuator dynamics was derived by using Hamilton''s principle, which could be represented by the nonlinear partial differential equations after the constraints had been applied. The Lyapunov method illustrates that the states of the system will ultimately travel to an equilibrium point if the total energy is dissipating. The energy dissipation strategy was extended to the chain model considering the polygon effect. In the controlled span part, the Lyapunov method was proposed to design the force control law for ensuring the vibration reduction in one span. Based on the total vibration energy of the moving chain, an energy-based Lyapunov function candidate was defined, which assured the dissipation of the vibration energy. To assure the asymptotical stability of the closed-loop system, a force control law was analyzed to determine the control force under the conditions of unknown disturbance and known disturbance. The proposed control force aimed to enforce this span part to be stationary or vibrate with a small amplitude. The comparison of the vibration amplitude at mid-span point under the controlled condition and uncontrolled condition clearly demonstrated that the vibration of chain part decreased much faster with the controller. The asymptotic exponential stability of moving chain system is proved by using the boundary force controller. The performance of the chain control systemdepends on force control law with guaranteed stability as well as actuator placement. Both simulation and experimental results confirm the feasibility of vibration suppression.