Two types of delay-dependent stability analysis and stabilization design conditions: Application to 3D printing control systems with time-varying delay

3D printing forming quality control is a research hotspot and difficulty. The traditional approach is either to optimize the printing material properties, to optimize the printing device structure, or to control the printing process, for achieving the purpose of precision printing. In fact, in the 3D printing control system (3DPCS), control and measurement signals are transmitted through open communication network, inevitably leads to communication and transmission delays, which can adversely affect the 3DPCS dynamics and even cause instability, not to mention guarantee precision printing. For such a time-delay system, this paper presents an open issue, i.e. the stability analysis and stabilization control problem of the 3DPCS, in order to serve the improvement of the printing accuracy. First, the 3DPCS framework and dynamic model with time-varying delay are proposed. Second, the delay-dependent stability and stabilization conditions of the 3DPCS are derived by constructing the augmented Lyapunov–Krasovskii functional (LKF) and by using the relaxed mixed convex combination technologies, after which less conservative conditions are obtained by introducing a free weighting matrix to improve the accuracy. Thus, the corresponding controller gain is further obtained. Finally, the 3DPCS example and a well-known numerical example are carried out. Simulation results show that the upper bound of acceptable time delay of systems are larger, and the controller designed based on the stabilization condition can ensure the stable operation of the 3DPCS. Both aspects demonstrate the advantages of the proposed approach.