ACCURATE tracking at high speeds is required in many positioning systems， particularly in manufacturing applications. Research on discrete-time tracking controllers includes ［3］， ［10］–［12］， ［14］ which all combine feedback and feedforward controllers. The feedback controllers each include some form of disturbance compensation such as integral action， an extended state estimator， or a disturbance observer. In ［11］ a zero phase error tracking controller （ZPETC） based on approximate inversion of the closed-loop system is introduced for the feedforward compensator and this technique is used in ［3］， ［9］， ［10］， ［12］， and ［14］。 Advances have not been limited to control theory. Development and commercialization of improved electromechanical components has progressed rapidly. Particularly noteworthy from a system design viewpoint are direct-drive motors. In Manuscript received July 7， 1997; revised June 22， 1998. Recommended by Associate Editor， R. Takahashi. This work was supported in part by NSF/CGP under Grant INT-9503951. C. J. Kempf is with Kensington Laboratories， Inc.， Richmond， CA 94804 USA. S. Kobayashi is with NSK Ltd.， Precision Machinery and Parts Technology Center， Maebashi， Gunma， Japan. Publisher Item Identifier S 1063-6536（99）06446-5.

　　comparison to traditional gear-reduced systems， the technical advantages of direct-drive systems are widely known among control engineers： friction is reduced， backlash is eliminated， and the mechanical stiffness is very high. The disadvantages， on the other hand， usually do not get as much attention： electrical dynamics tend to be slow and the system is more sensitive to disturbance forces and inertia variations. To fully exploit the potential advantages of direct-drive actuators， all of these factors should be explicitly accounted for in the controller design.