Piezoelectric actuators are increasing used in high precision and high speed position control applications because of their high stiffness,nanometer displacement resolution and fast frequency response.Like many other materials,piezoelectric stacks posses hysteresis,a form of nonlinearity which considerably degrades a systems performance,especially in cases requiring precision positioning,such as atomic force microscopes.Recently,piezoelectric stacks have found new applications in a fast tool servo (FTS) system that is to move the tool small distance into and out of the workpiece several times per revolution of the pan,thus generating nonaxisymmetric surfaces or correcting for errors.