PDE Based Adaptive Control of Flexible Riser System With Input Backlash and State Constraints

In this paper, a class of flexible riser systems modeled by partial differential equations (PDEs) with the backlash is considered. The backlash is formulated as the addition of a linear input and a interference-like term, then an new auxiliary item is introduced to compensate for the impact of this backlash. In addition, the constraint problem for the position and the velocity is also taken into consideration. To solve this constrain problem, the logarithmic barrier Lyapunov function is employed. For the flexible riser system, two kinds of adaptive controllers are proposed under the following two cases. One controller is designed when only the parameter of backlash is unknown. On the basis of this result, the other controller is presented when some system parameters cannot be measured through actual measurement. Then, combing the theory of Lyapunov stability, the two controllers can guarantee the boundedness of all signals in the closed-loop flexible riser system. Further, both the position and the velocity satisfy their corresponding constraint condition. Finally, the simulation example verifies that the proposed control method is effective.