A head-mounted device may have display projectors that provide images. Waveguides may be used in conveying the images to eye boxes. Optical couplers such as prisms may be used to couple the images from the projectors into the waveguides. The waveguides may guide the images to output couplers that couple the images toward eye boxes for viewing by a user. During operation of the head-mounted device, sensor circuitry may be used to measure for potential misalignment between optical components such as projectors, couplers, and waveguides. Control circuitry may provide control commands to zero hold power piezoelectric actuators or other positioners based on the sensor measurements, thereby tilting and otherwise repositioning the optical components relative to each other to correct for optical component misalignment.