Mixed H2/H∞ optimization approach to gap control on EDM

A robust proportional plus derivative (PD) controller of the gap between an electrode and a workpiece is designed to tolerate the bounded gain variation related to the generation of powder in the gap and the nonlinearity of the feedback signal. The robustness defined by H∞ shows that the robust PD controller can tolerate the nonlinear and time-varying feedback signals. As shown, the performance of H2, under a constraint on H∞ robustness, the proposed PD controller exhibits optimal tracking performance. The gain parameters of the PD controller that maximize fitness, as specified by the inverse of the integral of the squared error, given a step input to the system, can be determined quickly and accurately using genetic algorithms (GAs). The control performance and the rate of erosion of die-sinking electric discharge machinings are confirmed to follow from the proposed design procedure.