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"impose a cap on" is a correct and usable phrase in written English.
You can use it when you are referring to the setting of a limit or restriction on something. For example, "The mayor proposed to impose a cap on the number of cars allowed on the main street".
Exact(57)
The proposal hammered out today would for the first time impose a cap on the amount of debt that the state can carry at one time.
But they provided few details beyond saying that the plan would impose a cap on the amount of debt the state could carry at any one time.
There are also questions over how it would impose a cap on each company's profits.
Patten says he could not reasonably impose a cap on the amount to be spent.
Q: Why did you not impose a cap on the amount people would have to spend on hotel costs?
He said that Cameron's plan to impose a cap on immigrants from eastern Europe was probably illegal and certainly counterproductive.
The stalemate over rent has stalled movement toward a final vote on Mr. Cuomo's deal with legislative leaders to impose a cap on local property taxes.
He is already seeking to impose a cap on local property taxes, a priority that teachers fiercely oppose because it could deprive schools of revenue.
Similar(3)
A full-blown crisis was averted only when America, which contributes 22% of the UN's budget, and other big donors abandoned their bid to re-impose a cap on UN spending just before funds ran out in June.
In Florida this year, legislators imposed a cap on the state's pay for public university presidents.
The Swiss National Bank seemed to be protecting the downside by imposing a cap on the franc's level against the euro.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com