Multidelayed Repetitive Control of Fast Tool Servo for Diamond Turning of Functional Surfaces

This article presents a multidelayed repetitive control (MDRC) scheme to achieve the ultra-precision tracking control of the fast tool servo (FTS) for diamond turning of functional surfaces. A general time-domain analysis of the FTS toolpath is conducted by using the Taylor expansion, which reveals that the maximal deviation between two adjacent toolpath cycles is approximately several hundreds of nanometers and thus indicates that the FTS toolpath presents quasi-periodic. Consequently, an extra time delay term is induced in the MDRC scheme to compensate this deviation and thus results in the enormous accuracy improvement for tracking the quasi-periodic toolpaths than the conventional RC scheme. The stability analysis of the MDRC scheme is provided based on the small gain theorem, following by the detailed design procedure. Moreover, comprehensive toolpath tracking experiments of three typical functional surfaces and machining experiments of the microlens array are carried out on a self-developed FTS system and a commercial ultra-precision lathe. Experimental results show that the proposed MDRC scheme can achieve the ultra-precision tracking for the FTS toolpath with the root-mean-square errors less than 30 nm and has potential to track quasi-periodic trajectories with the slowly varying amplitude in other ultra-precision machining and measurement fields.