Stability and Stabilization Conditions for 3D Printing Control Systems with Time-Varying Delay

In the 3D printing control system (3DPCS), the control and measurement signals are transmitted through the network channel, inevitably producing time-varying delay. In this paper, the stability and stabilization problem of 3DPCS with time-varying delay are studied. First, the 3DPCS framework and state space dynamic model with time-varying delay is proposed. Second, the stability and stabilization conditions of the 3DPCS are derived by constructing the augmented Lyapunov-Krasovskii(L-K) functional and using the relaxed mixed convex combination technologies. Thus, the corresponding controller gain is further obtained. Finally, the simulation results show that the upper bound of acceptable time delay of the 3DPCS are larger, which indicates that the stability criterion in this paper is less conservative. In addition, the controller designed based on the stabilization condition can ensure the stable operation of the 3DPCS.