Parameter Identification And Control Study Of Two Types Of Rod Equations

Robots are widely used in technology development as an essential tool for transforming and upgrading the manufacturing industry.Rigid robots,represented by robotic arms,have played an essential role in repetitive industrial operations such as handling and painting because of their high efficiency and ease of control.However,rigid robots are generally difficult to be applied in small and complex environments due to the influence of working space,etc.Therefore,flexible robots,represented by continuum robots,are born.In applying these two typical robots,the urgent problems to be solved are their modeling,parameter identification,and stability control.To address the above problems,the following research work is carried out in this paper with the robotic arm dynamics equation describing the rigid link and the Euler-Bernoulli beam equation(two types of rod equations)that mainly describe the flexible link:1.For the Lagrange and Newton-Euler methods,after a brief analysis of their advantages and disadvantages,the dynamics of the robotic arm are modeled using the Lagrange method.Based on the model,the relevant physical parameters are identified using a particle swarm algorithm.Using the identification results,the adaptive non-singular robust integral sliding mode controller and the improved adaptive non-singular terminal sliding mode controller are used to track the joint trajectory of the robot arm,and the jitter phenomenon of the sliding mode controller is weakened by optimizing the switching function.Through simulation comparison,the two sliding-mode controllers designed in this paper can achieve accurate trajectory tracking with less jitter in the controller output;using adaptive law and robust term improves the anti-interference capability of the robotic arm,and the system is more robust.2.There exists a fundamental master equation in Euler-Bernoulli beam theory,and the general modeling is simplified,extended,or expanded based on this master equation to meet the actual robot’s physical system.In order to better fit the flexible robot system,the fundamental Euler-Bernoulli beam with a cantilever beam structure and unknown flexural stiffness(product of second moment of inertia and Young’s modulus)is used as the object of study for parameter identification in this paper.Since the Euler-Bernoulli beam is a system of partial differential equations,the general parameter identification method will no longer be applicable.In this paper,we use the finite difference method to discretize the Euler-Bernoulli beam in space and time,then transform it into a discrete expression of the system of ordinary differential equations system through a series of transformations and collations.Based on the expression form of the discrete system,the analytical expression of the flexural stiffness is obtained after fitting using the least squares method and a series of iterations.Applying the identification idea and method from the simulation results can finally obtain the expression of flexural stiffness close to the ideal one.3.In order to solve the control problem of the Euler-Bernoulli beam under disturbance,the system of underlying master equations of the Euler-Bernoulli beam is simplified in this paper,and disturbances such as external disturbances and internal uncertainties are introduced.A disturbance observer is designed to estimate the above disturbances in real-time,and Riesz basis theory is used to prove the effectiveness of the observer to equate the disturbance estimates as part of the controller inputs;the system is stabilized by designing an integrated feedback controller by combining the disturbance observer output values.The simulation results show that the disturbance observer can effectively estimate the disturbance;the integrated feedback controller enables the stabilization control of the system.