An additive manufacturing system is disclosed for use in fabricating a structure. The additive manufacturing system may include a print head, and a support configured to move the print head. The support may include a first link, a second link rotationally connected to the first link at a joint, and an encoder-less motor rigidly mounted to the first link and configured to drive rotation of the second link relative to the first link. The support may also include a sole encoder associated with the joint and configured to generate a signal indicative of an angular position of the first link relative to the second link. The additive manufacturing system may further include a controller in communication with the sole encoder and the encoder-less motor. The controller may be configured to selectively trim operation of the encoder-less motor based only on the signal.