The SDF-2 was a Human built starship that was to serve as a replacement for the heavily damaged SDF-1 following the end of the First Robotech War. The SDF-2 was to serve as the flagship of the Robotech Expeditionary Force on their mission to Tirol to contact the Robotech Masters, but was destroyed during Khyron's suicide attack on the ships. That position would be filled by the SDF-3, which would lift off in 2022 after being pushed back by many factors.
According to some sources, the SDF-2 was based on the design of the SDF-1 and was built "back-to-back" with the SDF-1 in Lake Gloval. This was to assist in the transfer of material and equipment, which was to include the engines, from the SDF-1 to the new vessel (Robotech: The Macross Saga comics) Other sources suggested that the ship was not positioned there, and that the ship was not regularly seen (Macross Saga)
The SDF-2 is difficult to distinguish from the SDF-1, but there are differences. According to one source, SDF-2 did not make use of the Prometheus or Daedalus Super Carriers, and instead had ARMD platforms connected as the SDF-2's arms. (Robotech: The Macross Saga 36: To The Stars)
The SDF-2 was introduced in episode 36 of the original series. However, it was never seen on screen due to it not existing in the original Macross anime. The SDF-2 did make in an appearance in Comico's comic book adaptation of the Macross Saga.
Super Dimension Fortress Macross does have an SDF-2 in it's continuity. However, it's name is SDF-2 Megaroad and it's design differs from the SDF-1 and Robotech's SDF-2. The Robotech SDF-2 does, however, share an resemblance to the SDF-1 in the Macross film Super Dimensional Fortress Macross: Do You Remember Love as well as the pre-refit SDF-2 seen in concept art.