Vibration Control Method For Point-to-point Motion And Trajectory Tracking Of Flexible Manipulator

Flexible robotic arms possess the advantages including dexterity,large working space,lower costs,and energy saving,thus gaining growing study and being widely used in many industries.However,such flexible manipulators confront with a common problem: vibration during operation.Solving the vibration problem is a basic and key point to realize effective manipulation and achieve a task with high quality.The existing control task and objective of flexible arm involves residual vibration suppression(VS)and steady vibration reduction(VR)of positioning and tracking control respectively,which are limited and deficient in principle methods and effectiveness of removing vibration.In this thesis,a new method to improve control of residual and steady vibration has been proposed,and for the demand of continuous vibration reduction and to deal with the deficiency using the conventional strategies,the principle and method of vibration avoidance has been investigated and presented to reduce dynamic vibration.The autonomous approach and computing algorithm of vibration control based on machine learning is further studied and explored.The main study and the innovative work are summarized as follows:1.For residual vibration of a flexible arm,the VS of point-to-point motion is studied and the impulse spectrum is proposed.The local invariance criterion for the reduction of nonlinearity of the dynamic model is introduced and studied for VR processing,and the sensitivity index associated with the criterion computation is established,with the segmented LTI pieces for control approach under the model given for computing.The calculation to verify the criterion is conducted.The existence of uniform VR of coupled multimodes and configuration variation is proved in the study,and the VR conditions and the annihilation factors are provided.The input inverse approach of VR by the impulse spectrum based on the time slicing ignition is developed and the control design procedures are discussed.The control of VR for the multimode band is investigated and the property of the impulse spectrum is analyzed for preparing the VR control over the band-wide multimodes enhancing the control robustness.The validity of the impulse spectrum control is demonstrated by numerical simulations.2.For VR of tracking control,the concept to immune vibration of a dynamic process has been investigated and the method with the rigid-to-follow-flexible(RTFF)pace is proposed for vibration avoidance(VA).The pace-following excitation is conceived by studying mechanics of materials and vibration for deformation of the neutral surface of an elastic link,and the new principle of rigid-propelling-to-follow-flexibleprecession is presented to build up the RTFF movement as the basis to constitute rigidflexible synchronization for VA.The operational task and objective of a flexible arm for VA is proposed,with the vibration avoidance defined by analyzing the avoidance behavior and essence.The mechanism of single-sided steady run of the neutral surface is examined based on the RTFF for either lead or hysteretic deformation.The property of the mechanism and the regulating law using the mechanism are analyzed and studied to provide the implementation of the controller accordingly.In regard to VA,the dynamic equilibrium of an equilibrium point and an invariant set in the defined domain of deformation is analysed in terms of the properties of the new method.The stability of the closed-loop system with the vibration control using the RTFF has been examined.Under the stable condition and property analyzed,the closed loop system with the PD controller for VA tracking is proven globally uniformly asymptotically stable for a dynamic equilibrium set and its positive limit point based on the Lyapunov and LaSalle's arguments.The numerical simulations of a single link flexible manipulator validate the proposed VA control method.3.With regard to vibration control,an approach to generate recursively a VA controller with reinforcement learning is studied.In line with the performance index derated by a discount factor,the quadratic form of infinite horizon LQT for the augmented state with possible VR commands is examined and produced;the study on the Bellman equation of optimal evaluation based on the dynamic programming of Markov chain is carried out,with the utility of tracking and VR;the computing mechanism on the policy evaluation and improvement of forward recursion on the condition of ergodicity and stationarity is studied as well,and yielding the algebraic Riccati equation is provided for the optimal policy.The online iteration algorithm based on the temporaldifference learning and the stochastic approximation of policy is studied;for policy optimality of tracking VR along a single sample trajectory,the dual efficacy of the Q function has been examined and developed,yielding the processing to convert the system knowledge based into the data based policy evaluation and improvement;the Bellman equation of the numeric Q function with possible augmented states including an input is studied,and the online forward iteration algorithm for optimal control approaching using the policy evaluation and improvement by Q learning is presented.A flexible manipulator of single link is used for simulations that validate the effectiveness of the proposed Q learning optimal tracking vibration control.