Research On Fault Tolerant Control Method Of Flexible Manipulator System Based On PDE

With the rapid development of intelligent technology and industry,robotic arms can assist or even replace human beings to complete more tasks in complex working environments.The traditional rigid manipulator has brought great help to people in the repetitive work of handling and grasping,while the flexible manipulator has attracted more and more scholars’ attention for its advantages such as fast response speed,light structural weight,low energy consumption and high load-dead weight ratio.Compared with rigid mechanical arms,flexible mechanical arms tend to produce elastic vibration in the working process due to the low flexural stiffness of their structures and materials,which increases the complexity of the motion state of flexible mechanical arms and makes the control design of flexible mechanical arms more difficult.At present,most dynamic models describing flexible manipulators are built on the basis of Ordinary Differential Equation(ODE),and ODE models tend to lead to control overflow problem because of ignoring the higher order modes.Compared with ODE model,modeling flexible manipulator based on Partial Difference Equation(PDE)and designing appropriate control law can avoid this problem.Therefore,the fault-tolerant control method of flexible manipulator with constrained PDE distributed parameter model is studied in this paper.Based on the Hamilton principle,the dynamics of single-link flexible manipulator and rigid-flexible coupled double-link manipulator are analyzed.To solve the control overflow problem caused by ignoring the higher order modes,the system model is described by the coupling form of partial differential equation and ordinary differential equation,and the finite dimensional approximation of the model is not carried out,and the control design is directly based on the infinite dimensional model.Based on the PDE model of the single-link flexible manipulator,the concurrent problems of actuator and sensor faults were considered.Aiming at the partial failure of the joint actuator,the partial failure of the angular velocity sensor and the failure of the strain sensor,an adaptive fault-tolerant control method with direct joint input was designed,which not only ensured the joint Angle position control,but also suppressed the elastic vibration of the flexible linkage.The asymptotic stability of the closed loop system is proved by using semigroup theory and La Salle invariant principle.The effectiveness of the proposed control method is verified by comparative simulation analysis.Based on the ODEs-PDE model of a rigid-flexible coupled double-link manipulator,an adaptive fault-tolerant boundary control method was designed for the multi-fault concurrency of joint torque,boundary force controller,angular velocity sensor and laser displacement sensor,considering the multi-output state constraints and multiple faults.Tangent barrier Lyapunov function and integral barrier Lyapunov function were selected to solve the multiple output constraints of joint Angle error and terminal vibration,which ensured that the multiple output state constraints of the manipulator system were limited.The asymptotic stability of the closed-loop system is proved by using semigroup theory and La Salle invariant principle.The effectiveness of the proposed control is verified by comparison and simulation.Finally,the future work is summarized and prospected for the study of fault-tolerant control of PDE flexible manipulator system.