Dynamic optimization of first-order systems via static parametric programming: application to electrical discharge machining

In this paper, it is shown that dynamic optimization problems of first-order systems can be transformed into a static parametric programming problem, where the state plays the role of the parameter. Thus, an optimal feedback law is obtained. This concept is applied to the die-sinking electrical discharge machining, a highly time varying industrial process which necessitates adaptation of machining settings during operation. It is shown that the minimum-time operation of this process is equivalent to choosing the manipulated variables that maximizes the speed of machining at every position.