Sinfin Community School was placed into special measures by Ofsted in February and a follow-up report last month said inadequate progress had been made.
It has faced consistent opposition from campaigners, including the Sinfin, Spondon and All Against Incineration (SSAIN), but finally got the go-ahead in September after a public inquiry.
Simon Bacon, chairman of Sinfin, Spondon and all Against Incineration (SSAIN), said the judge will rule on whether the plant is mainly a disposal facility or a recovery facility.