Abstract
The dynamic characteristics of the mechanical arm with a rigid-flexible structure are very complex. The reason is that it is a complex DPS (distributed parameter system) with infinite dimension and nonlinearity in essence due to the rigid-flexible coupling. So, accurately positioning and controlling the rigid-flexible mechanical arms could be difficult. Therefore, a model reduction method of rigid-flexible mechanical arms based on the approximate inertial manifold is put forward. To repress the residual vibration of the end of the mechanical arm, a feedforward control strategy is designed. The high-dimensional solution of the vibration equation of the rigid-flexible mechanical arms is projected into the complete space composed of orthogonal decomposition modes. By using Galerkin’s method, the system is simplified and the approximate solution is obtained through the interaction between high-order and low-order modes. The truncated finite mode is also used to construct a lowest-order dynamic model on the basis of approximate inertia manifold. Given the reduced-order rigid-flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. A limited number of sinusoidal signals approximately combine the input signal, by using the particle swarm optimization algorithm to optimize the input signal, and the amplitude of the sinusoidal signal is corrected. The simulation results depict the superiority of the proposed method, which greatly suppresses the end residual vibration of the mechanical arm and realizes the accurate positioning of the end of the mechanical arm. In addition, the hardware experimental device of the rigid-flexible mechanical arms is constructed, and the experimental verification of the above method is put into effect. The simulation results of angular displacement and end vibration of the reduced model are accordant which is shown by the experimental results of the hardware platform.
Highlights
A flexible mechanical arm has the advantages of a high weight ratio, low energy consumption, high efficiency, less inertia, and safe operation
Given the reduced-order rigid-flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. e input signal is approximately combined by a limited number of sinusoidal signals. e NF of the system determines the highest frequency of the sinusoidal signal, to optimize the input signal, and the amplitude of the sinusoidal signal is corrected using the particle swarm optimization (PSO) algorithm. e simulation results show that this method cannot only achieve precise positioning and effectively suppress the residual vibration generated during the movement of the rigid-flexible mechanical arms
(1) As depicted in Figure 15, the simulation conclusions of the angular velocity of the flexible mechanical arm are mainly accordant with the experimental conclusions, which demonstrate that the selection of the spectral method and the dimension reduction method of Galerkin truncation theory can accurately reflect the characteristics of the dynamic model of the flexible mechanical arm
Summary
A flexible mechanical arm has the advantages of a high weight ratio, low energy consumption, high efficiency, less inertia, and safe operation. Erefore, the residual vibration generated during the movement of the flexible mechanical arm needs to be suppressed, which is the key to achieving high-precision position control. On the basis of the above problems, the infinite-dimensional solution of the vibration equation of the rigid-flexible mechanical arms is projected into the complete space formed by the POD (proper orthogonal decomposition) mode by using the AIM [47,48,49] in this study. Given the reduced-order rigid-flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. E simulation results show that this method cannot only achieve precise positioning and effectively suppress the residual vibration generated during the movement of the rigid-flexible mechanical arms.
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