The union representing faculty at Minnesota's 30 community colleges settled a long-running dispute with the Minnesota State system that could grant its members nearly $2 million in back pay.

The Minnesota State College Faculty union has argued since 2010 that the system's two-year institutions do not properly pay faculty who take on special assignments such as overseeing independent studies, labs and internships or chairing their departments. The agreement signed Wednesday settles a lawsuit the union filed two years ago. The system admitted no wrongdoing in the settlement but agreed to revisit faculty pay for the 2016-17 and 2017-18 academic years.

"We just wanted to make sure faculty are paid fairly and accurately," said Matt Williams, the incoming union president. "That's what we have been pushing for this entire process."

The two sides will jointly pick a referee to go over additional pay claims that professors submit by the end of October. The union estimates the settlement will affect between 180 and 700 instructors — a wide range because leaders are unsure how many campuses used the approach to calculate pay under contention.

"We are pleased that we have reached this agreement with the faculty union at our state colleges, and we look forward to continuing our work together providing a quality, affordable education for our students and meeting the workforce needs of Minnesota," Eric Davis, the system's vice chancellor for human resources, said in a statement.

In 2010, the union first charged that system campuses were underpaying some of its members for work they did in addition to giving course lectures. At issue is a complicated method of calculating faculty pay in the union's 171-page contract with the system.

"If the only thing we did was teach lectures, that would be easy to calculate," Williams said. "We have such a wide diversity of work we do as faculty that it defies easy ways to measure our workloads."

The system disputed the union's claim, but in 2016 an arbitrator sided with faculty in that disagreement. The following year, the union filed an unfair labor practices lawsuit in Ramsey County District Court alleging that the system had not fully complied with the arbitrator's ruling.

Wednesday's settlement caps the amount of back pay faculty can receive at $1.9 million, so if overall claims exceed that amount, they will be adjusted down to meet the threshold. The agreement also caps salary for the referee at $50,000, paid by the system, and says the system will take steps to ensure it calculates faculty pay following the arbitrator's guidance in the future. It is not clear what the long-term financial impact on the system will be.