Control of Vibration in Mechanical Systems Using Shaped Reference Inputs

Dynamic systems which undergo rapid motion can excite natural frequencies that lead to residual vibration at the end of motion. This work presents a method to shape force profiles that reduce excitation energy at the natural frequencies in order to reduce residual vibration for fast moves. Such profiles are developed using a ramped sinusoid function and its harmonics, choosing coefficients to reduce spectral energy at the natural frequencies of the system. To improve robustness with respect to parameter uncertainty, spectral energy is reduced for a range of frequencies surrounding the nominal natural frequency. An additional set of versine profiles are also constructed to permit motion at constant speed for velocity-limited systems. These shaped force profiles are incorporated into a simple closed-loop system with position and velocity feedback. The force input is doubly integrated to generate a shaped position reference for the controller to follow. This control scheme is evaluated on the MIT Cartesian Robot. The shaped inputs generate motions with minimum residual vibration when actuator saturation is avoided. Feedback control compensates for the effect of friction Using only a knowledge of the natural frequencies of the system to shape the force inputs, vibration can also be attenuated in modes which vibrate in directions other than the motion direction. When moving several axes, the use of shaped inputs allows minimum residual vibration even when the natural frequencies are dynamically changing by a limited amount.

Reflectance Map Techniques for Analyzing Surface Defects in Metal Castings

This report explores the relation between image intensity and object shape. It is shown that image intensity is related to surface orientation and that a variation in image intensity is related to surface curvature. Computational methods are developed which use the measured intensity variation across surfaces of smooth objects to determine surface orientation. In general, surface orientation is not determined locally by the intensity value recorded at each image point. Tools are needed to explore the problem of determining surface orientation from image intensity. The notion of gradient space , popularized by Huffman and Mackworth, is used to represent surface orientation. The notion of a reflectance map, originated by Horn, is used to represent the relation between surface orientation image intensity. The image Hessian is defined and used to represent surface curvature. Properties of surface curvature are expressed as constraints on possible surface orientations corresponding to a given image point. Methods are presented which embed assumptions about surface curvature in algorithms for determining surface orientation from the intensities recorded in a single view. If additional images of the same object are obtained by varying the direction of incident illumination, then surface orientation is determined locally by the intensity values recorded at each image point. This fact is exploited in a new technique called photometric stereo. The visual inspection of surface defects in metal castings is considered. Two casting applications are discussed. The first is the precision investment casting of turbine blades and vanes for aircraft jet engines. In this application, grain size is an important process variable. The existing industry standard for estimating the average grain size of metals is implemented and demonstrated on a sample turbine vane. Grain size can be computed form the measurements obtained in an image, once the foreshortening effects of surface curvature are accounted for. The second is the green sand mold casting of shuttle eyes for textile looms. Here, physical constraints inherent to the casting process translate into these constraints, it is necessary to interpret features of intensity as features of object shape. Both applications demonstrate that successful visual inspection requires the ability to interpret observed changes in intensity in the context of surface topography. The theoretical tools developed in this report provide a framework for this interpretation.