Control Design For Flexible Robotic Manipulator With Input And Output Constraints

In the procedure of the development of the unknown flied for the exploitation of the deep sea and deep space detection, robotic manipulator plays a more and more important role for the terrible environment and the rigorous working requirement. With the stretching of the application of the robotic manipulator, the actual problem faced in the production and the rigorous performance index proposed in the engineering will promote the further research of the manipulator. The traditional robotic manipulator is usually composed with the rigid mechanical material and it can satisfy the demand of the production in the common engineering environment. However, the weight of the manipulator will increase inevitably and that will weaken the flexibility of the system and increase the power consumption of the robotic manipulator. In order to overcome the drawback of the traditional material, a lighter flexible material is obviously a good choice stead of the heavy rigid manipulator. In addition, it draws more and more attention for the merits such as light, good flexibility, lower power consumption and so on. The material is subjected to the external disturbance for the good flexibility of the flexible robotic manipulator. The flexible robotic manipulator will generate the vibration that will weaken the performance of the system, reduce the control accuracy, and even damage the system. It is an urgent problem how to suppress the vibration of the flexible robotic manipulator under external disturbances.In this paper, the problem of vibration suppression, angular position tracking and the dealing with the input and output constraints for the flexible robotic manipulator system are researched. Based on the Hamilton’s principle, a set of partial differential equations(PDEs) and ordinary differential equations(ODEs) are used to describe the dynamical characteristic of the flexible robotic manipulator. Two classical flexible beam models are researched in this paper, namely, Euler-Bernoulli beam and Timoshenko beam, respectively. Based on the dynamical model of the flexible beam, the active boundary controls are designed to suppress the vibration of the flexible robotic manipulator. In order to deal with the problem of the input constraints for the flexible manipulator, the active control strategy is proposed to compensate for the nonlinear characteristic. The barrier Lyapunov function is constructed to deal with the problem of output constraints and for the stability analysis of the closed-loop system. In addition, the numeral simulation is used to verify the effectiveness of the proposed boundary control by choosing appropriate parameters.