Error Compensation Using Inverse Actuator Dynamics

Abstract

The use of Non-Rotationally Symmetric (NRS) optical surfaces has increased significantly in recent years. These surfaces can be quickly machined using a diamond turning lathe and a Fast Tool Servo (FTS). However, the dynamic response of the actuator influences the output tool motion resulting in form errors. This dissertation describes an open-loop command modification technique, also know as a deconvolution operation, that can significantly reduce tool motion errors. The technique uses knowledge of the gain and phase response of the dynamic system and the information content of the driving command to modify the amplitude, phase and shape of the input command signal. The modified command signal creates the desired tool motion.

The research made use of a commercial FTS to demonstrate the error compensation technique and implemented a system identification method using Digital Signal Processing (DSP) to determine the closed-loop transfer function of the actuator. This measurements exposed the physical limits of the FTS which constrained the tool speed to 140 mm/s and the nonlinear dynamic behavior of the FTS as a function of the command amplitude. Initial validation of the inverse dynamics technique for a fixed amplitude tool trajectory employed a single transfer function to modify the entire input command signal. The experiments showed that the excursion of the actuator was identical to the desired path after a start up period.

The tool trajectory of an FTS is dependent on the spindle speed and the cross-feed rate which may drift over a long fabrication time and an NRS feature can contain varying amplitude. To address these issues, two adaptive modification schemes using the Short-Time Fourier Transform (STFT) and an equivalent inverse dynamics filter were proposed. These schemes can account for the changing frequency and amplitude content of the driving command using the most recent machining conditions and the appropriate transfer function.

The experimental confirmation of the error compensation scheme involved the fabrications of two off-axis features: a sphere and a cosine groove. The adaptive schemes were used to create an off-line modified input command. Measurements of the machined surfaces using a laser interferometer experimentally validated that the deconvolution operation can extend the usable bandwidth of the FTS to produce the proposed surfaces. The measurements across the machined parts indicated that the form fidelity of the deconvoluted features was improved by 2 orders of magnitude over that of the features produced using the unmodified input command signals.