There is a system. It is based on a 6 year cycle and basically goes like this:
Every team is paired with a team from the other division, supposed to be based on competitive criteria. For 2016-2021, we have the following pairings:
PSU-Iowa
Michigan-Wisconsin
Ohio St-Nebraska
Michigan St-Northwestern
Rutgers-Illinois
Maryland-Minnesota
Indiana-Purdue (this inter-division one is always set)
These teams play for 6 straight years, rotating home and away (at the East school in even years, at the west school in odd years). As an aside, this is why the East teams will always be 5 home/4 away conference games in even years and 4 home/5 away conference games in odd years.
The remaining 2 inter-conference games each season rotate every year. Basically, it is Team A and @Team B in Year 1, Team C and @ Team D in year 2, Team E and @ Team F in year 3, then @Team A and Team B in year 4, @ Team C and Team D in year 5, @ Team E and Team F in year 6. So, over a 6 year cycle, you play each of those teams home and away each 1 time. They do the rotation that way so that you play each team at least once in a 3 year period meaning every player/student should experience playing each conference team during a normal college career.
So, for PSU they played Minnesota home and Purdue away in 2016. They will play Minnesota away and Purdue home in 2019. Nebraska and Northwestern are in 2017 and 2020. Wisconsin and Illinois are in 2018 and 2021.
The Big Ten hasn't officially announced schedules for 2020 and 2021 but we know which teams we'll be playing those seasons because of the pattern.
Assuming no changes to the conference and if they keep the same system in place, then in 2022-2027, we'd get a different paired team from the other division -- likely Nebraska or Wisconsin if they tried to keep the "stronger" teams playing each other more. All the pairings would shift to different teams, except Indiana/Purdue.