Modeling and control of die-sinking EDM

This paper explores the mathematical model for electrically discharged machining (EDM) machine. Conventionally, it is known that the machining efficiency of EDM is closed related to the so-called ignition delay time. Here, it can be observed that the ignition delay time is the RC time-constant of the circuit model of Diesinking EDM. Then, it can be shown that ignition delay time is closed related to the gap resistance. According to electromagnetic theory, it can be shown that in the first and middle stages of machining process, the overall control system becomes a nonlinear Lur'e system. As for the final stage of machining process, the overall control system becomes a linear system. For the Lur'e problem of Die-sinking EDM, we applied the SPR (Strict Positive Real) condition for the control of EDM. A differential-PID controller is proposed in the beginning and middle stage of machining process. In the final stage of machining process, A PID controller can applied to the final stage of machining process. An adaptive controller switch from Differential-PID (DPID) controller and PID controller is proposed in this paper. Experimental results will be verified. Especially, the machining efficiency can be enhanced up to 33% compared to the conventional optimal PID controller.