63 AAS 17-656 REPETITIVE CONTROL DESIGN FOR THE POSSIBLE DIGITAL FEEDBACK CONTROL CONFIGURATIONS Tianyi Zhang * and Richard W. Longman † Digital repetitive control (RC) seeks to make a feedback control system con- verge to zero tracking error at each sample time following a periodic command. Many spacecraft sensors perform repeated periodic scanning maneuvers. Zero tracking error might best be accomplished by observing previous period error and computing the needed correction from the system inverse. Unfortunately, discrete time equivalents of continuous time models usually have zeros intro- duced outside the unit circle, making the inverse model unstable. The asymptot- ic pattern of zero locations is known in general for each pole excess. One can cancel all dynamics inside the unit circle, but one cannot cancel the zeros out- side. The authors and co-workers have developed several RC methods to design FIR filters that compensate these zeros, each making its own pattern of addition- al zeros outside. Previous literature considers many pole excesses, but normally only considers a continuous time feedback system converted to discrete time. More general applications need to handle general digital feedback control sys- tems, with digital controller, but continuous time plant, possible anti-aliasing fil- ter, possible sensor noise filter, etc. It is the purpose of this paper to examine what the possible patterns of zero locations can be for these different situations. New situations occur with repeated original zero pattern outside the unit circle, or neighboring zeros outside, or the union of zero patters for two different pole excesses. Each RC approach addresses these situations differently. Generally, the RC based on inverse frequency response tends to produce the best result, but the other approaches develop understanding of the source of observed compen- sator zero patterns. * Doctoral Candidate, Department of Mechanical Engineering, Columbia University, 500 West 120th Street, New York, New York 10027, USA. † Professor of Mechanical Engineering, and Civil Engineering and Engineering Mechanics, Columbia University, 500 West 120th Street, New York, New York 10027, USA. INTRODUCTION Spacecraft often have vibration sources such as cryo pumps, momentum wheels, control moment gyros, etc. Slight imbalance in rotating components introduces periodic disturbances to the spacecraft structure, which impair the performance of onboard fine pointing scientific instruments. Passive meth- ods have limited ability to isolate the associated sensitive equipment from these vibrations. Improved performance results when one uses feedback control for active isolation. However, feedback control systems do not perfectly cancel periodic disturbance signals. Not only is the amplitude not fully atten- uated according to the bandwidth of the control system, but the phase lag also prevents perfect cancel- lation of a periodic disturbance. Repetitive control (RC) puts an additional feedback loop around an existing feedback control system, and makes use of knowledge of the period of the disturbance. In the- ory, RC can completely eliminate the effects of the periodic disturbance.