A new control concept for instrument pointing, tracking, and vibration suppression is introduced based on zero annihilation periodic (ZAP) control. In ZAP control, the control gains vary periodically in time, in sharp contrast to conventional controllers whose control gains are fixed in time. The main advantage is that perfect "deadbeat" pointing, tracking, and vibration suppression can be achieved-even in the presence of flexible structural elements and noncolocated actuator and sensor hardware. The deadbeat response has clear advantages for optical instruments that must be held steady and precisely pointed during imaging. The ability of ZAP designs to effectively control noncolocated and nonminimum phase configurations opens up many new possibilities for high-performance instrument pointing, vibration damping, target tracking, and other advanced optics control applications.