Distributed parameter modeling and model predictive control of weft insertion in air-jet weaving

In air-jet weaving, the braking of inserted weft threads plays a significant role in fabric quality and machine productivity. This contribution presents Model Predictive Control (MPC) which controls the weft tip’s position and velocity with an optimal braking force. The inserted weft thread is firstly modeled as a distributed parameter system. The relation between the braking force and the weft tip’s position is described by a Partial Differential Equation (PDE). By analyzing the PDE with Laplace transform and solving the PDE with a Galerkin method, a state-space model is presented. Subsequently, identification experiments of the constructed yarn brake are performed and the whole model is analyzed as well as reduced using balanced truncation. Based on the system states and input disturbance estimated by a dual Kalman filter, an MPC controls the weft tip’s position and velocity appropriately without any backward movement. Regarding model deviations and simulated measurement errors, the MPC performs robustly.