Repetitive control and its application to linear servo unit for CNC machining of elliptical pistons

In this paper, the basic theory of repetitive control are summarized and modified repetitive controllers are introduced. The steady-state error and asymptotic stability condition are presented. A CNC precision lathe implemented with the repetitive control system for machining elliptical pistons is constructed, which consists of a precision linear servomechanism, computer controlled repetitive controller and machine-tool. The cutting tool driven directly by the linear servomechanism in radial direction of the piston tracks the section curve of the piston. Compared with the machining results performed by a traditional piston CNC machine-tools with PID regular, the tracking error given by the proposed control method was reduced by 40%.