A Comparison of Two Sigma Point Kalman Filters for Adaptive Cross-phase Cavity Pressure Control in Injection Molding

Abstract

Injection molding is a discontinuous manufacturing process used for the automated production of plastic parts. An adaptive model-based predictive controller (MPC) for cross-phase cavity pressure control has been proposed in prior work showing good reference tracking capabilities for different processing conditions. The adaptive control topology is complemented by an Unscented Kalman Filter (UKF) estimating the system states along with a lumped model parameter mapping the system's time-variant dynamics. Previous experiments with a deterministic MPC have shown that the closed-loop performance is significantly improved when reducing the sample time. Thereby, a lower bound is given by the limited computing capacity of the controller hardware. Additionally, the closed-loop control performance correlates with the convergence rate of the parameter estimate. Both convergence behavior and computational effort are influenced by the sigma points (SP) selected within the UKF algorithm. Therefore, two different SP selection procedures, namely the standard UKF as well as the spherical simplex UKF (ssUKF) are evaluated for accuracy, computational effort and closed-loop performance. Both variations of the UKF are implemented in context of the adaptive control scheme and experimentally validated. It is shown that for both UKF designs the adaptive controller ensures good tracking of a given cross-phase cavity pressure reference. Similar closed-loop control performance is obtained if an individual tuning for each filter is performed. However, the averaged computation time of the ssUKF is approximately 34.2 (%) less compared to the UKF, which enables a significant reduction of the sampling time.