Observer theory is applied to design an active controller for a machine tool such as a lathe to reduce the chatter tendency and forced vibration effects that can be detrimental to a workpiece surface finish. An observer is used to estimate difficult to measure relative motion between the cutting tool and workpiece. The estimated motion is used in conjunction with measured states in a second application of observer theory to design a control system that causes the cutting tool to track the workpiece, negating relative vibratory motion. Hence, the entire control system with the cutting tool position as an output is an observer of workpiece motion. Stability of the controlled system as a function of mismeasurements of dynamical parameters and its ability to reduce forced vibration effects are discussed. Performance calculations are based on a second order machine tool-workpiece dynamical model; however, the presented methods of design and analysis can be extended to higher order systems.

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