Vibration Control Of Flexible Structures Based On Iterative Learning Control

Flexible structures,with agility light weight and low energy,widely occur in aerospace,marine risers,robots and so on.However,flexible structures are sensitive to external disturbances,therefore giving rise to undesired vibrations and even system paralysis.When implementing controllers,actuators and observers frequently appear saturation and backlash,which,when ignored,give rise to vibrations.This paper addresses four flexible structure systems,where a flexible string system is basic and common.The flexible string system is described second-order wave equation,where two saturation functions are used to guarantee the constrained input.By comparison,the flexible Euler-Bernoulli beam system is a fourth-order distributed parameter system,where a hyperbolic tangent function and a saturation function are used to tackle the input constraint.The flexible robotic arm system with input constraint is considered as a rotational Euler-Bernoulli beam system.The Timoshenko beam system with input backlash is a more complex system,where the transverse vibration and the rotation of the cross section of the Timoshenko beam are coupled.With the complexity of the external environment and the accuracy of the control objectives improving,a pure control methodology may not perfectly satisfy the requirement of control processes.Confronted with distributed parameter systems,nonlinear inputs,the spatiotemporally varying disturbances and time-varying disturbances,a pure boundary control scheme,a pure adaptive control law,or a pure iterative learning control(ILC)law can’t guarantee asymptotic stability or exponential stability.In order to tackle the challenge,by utilizing a dual-loop ILC methodology,dualloop boundary ILC scheme and dual-loop adaptive ILC scheme are proposed for the flexible structure systems,both of which include a D-type ILC loop aiming at the suppression of vibrations.In the dual-loop boundary ILC law,the main loop is formed to reject the distributed disturbance and the boundary disturbance.In the dual-loop adaptive ILC scheme,an adaptive loop is constructed by observer and feedbacks of system states.Based on composite energy function,the boundedness in each iteration and the convergence along the iteration axis are proved.In order to manifest the effectiveness of the proposed control schemes,this paper provides simulation through the MATLAB and robot arm experiment.In the simulation,the open-loop system without control and the closed-loop system with the designed control are compared.In the experiment,three cases are compared,including the open-loop system without control,the closed-loop system with a PD control,and the closed-loop system with the proposed control law.