Approximate Inertial Manifold-based Dimension Reduction Modeling And Vibration Suppression For Rigid-flexible Manipulators

A rigid-flexible coupling manipulator has the characteristics of a rigid and flexible arm.It has the advantages of a high self-weight ratio,low energy consumption,small inertia and safe operation.It has been widely used in aerospace,medicine,robots and other fields.The rigid-flexible coupling manipulators not only have nonparametric uncertainty but also include complex factors such as dynamic/static friction,joint flexibility,structural resonance and actuator dynamics.In addition,a complex coupling relationship exists between the state variables of the rigid-flexible coupling manipulators,which greatly increase the difficulty of modeling and vibration suppression.The studies on its dynamic modeling,dimension reduction and vibration suppression have important theoretical value and high practical application value.In this dessertation,the theory and method of dynamic modeling,dimension reduction and vibration suppression of rigid-flexible coupling manipulators are studied and verified by experiments.A rigid-flexible dynamic model reduction method based on an approximate inertial manifold is proposed for a rigid-flexible coupling manipulator.The dynamic equation of infinite-dimensional rigid-flexible coupling manipulators is evolved into a lower-order nonlinear approximate model which uses low modes to capture high mode behavior,in order to reduce the loss of model accuracy caused by direct truncation and dimensionality reduction.The simulation and experiments verify the rationality of the proposed dimensionality reduction modeling method.An open-loop control method of residual vibration at the end of a rigid-flexible coupling manipulator is developed.Based on the lowest order dynamic approximation model of the rigid-flexible coupling manipulator,and according to the dynamic response of the manipulator end,the particle swarm optimization algorithm is used to optimize the input signal.In addition,the open-loop suppression of the residual vibration at the end of the rigid-flexible coupling manipulators is performed.This aims at the minimum error of the manipulator reaching the target position and the minimum residual vibration displacement at its end.The simulation verifies the effect of the optimized input signal.Compared with the original input signal before optimization,the maximum amplitude of residual vibration at the end of the rigid-flexible coupling manipulator is reduced by 70%.Aiming at the direct truncation and dimensionality reduction nonlinear model of the dynamic equation of infinite-dimensional rigidflexible manipulators,a fuzzy supertwist nonsingular terminal sliding mode control strategy is proposed.The sliding mode surface coefficient is dynamically adjusted in real-time using the fuzzy method,which improves the convergence speed and control performance of the system.The stability of the closed-loop system is proved by the Lyapunov method.The results of the simulation demonstrate that the input torque chattering is reduced by 65% and the maximum amplitude of the end when the tracking process is disturbed is reduced by nearly 59%,which efficiently improves the robustness and vibration suppression effect of the control system.Aiming at the lowest order nonlinear approximate model of rigid-flexible coupling manipulators based on the approximate inertial manifold,the residual vibration control performance of rigid-flexible coupling manipulators is studied using fuzzy supertwist nonsingular terminal sliding mode control strategy.The controller parameter selection conditions used to ensure the stability of the closed-loop system is obtained by the Lyapunov method.The results show that the dynamic performance of the fuzzy supertwist nonsingular terminal sliding mode controller designed based on the lowest order nonlinear approximate model is greatly improved.Moreover,there is no steady-state error and overshoot.The input torque chattering is reduced by 65%,and the maximum terminal amplitude is reduced by 77.8%,which not only ensures the high control quality but also reduces the difficulty and complexity of the controller design.On the experimental platform of rigid-flexible coupling manipulators,the dimension reduction model based on an approximate inertial manifold is experimentally verified,and the vibration suppression experiment of rigid-flexible coupling manipulators is performed.The experimental results verify the vibration suppression effect of the fuzzy supertwist nonsingular terminal sliding mode control.They also verify the superiority of the proposed method in suppressing the end residual vibration of rigid-flexible coupling manipulators.