Dynamic Observer Modeling and Minimum-Variance Self-Tuning Control of EDM Interelectrode Gap

Abstract

The electric discharge machining (EDM) interelectrode gap directly determines the discharge state, which affects the machining efficiency, workpiece surface quality, and the tool wear rate. The measurement of the real-time varying interelectrode gap during machining is extremely difficult, and so obtaining an accurate mathematical model of the dynamic interelectrode gap will make EDM gap control possible. Based on p-type single-crystal silicon EDM, a flat-plate capacitance model is introduced to analyze the time-domain characteristics of the inter-electrode voltage in the breakdown delay phase. Further, we theoretically established a physical model of the interelectrode spacing d and the charging time constant τ of the plate capacitor. The least-squares fitting of the experimental data was used to determine the model coefficients, and in combination with the actual machining process, a minimum-variance self-tuning controller was designed to control the interelectrode gap in real time. The experimental verification results show that the established physical model can correctly predict the interelectrode gap in the actual machining process. The minimum-variance self-tuning controller improves machining stability, and eliminates the occurrence of the short-circuit state.