Yeah, University of Wisconsin Madison does provide scholarships based on merit. Here are some of them:

Kemper K. Knapp Merit Scholarships
Total Worth: Up to $7,500
Eligibility: Up to $7,500
Minimum Criteria: High academic merit as demonstrated on the admissions application
Separate application needed: No
Application deadline: February 1

National Merit Finalist Scholarship
Total Worth: Up to $8,000
Eligibility: Up to $8,000
Minimum Criteria: National Merit Finalist who has selected UW-Madison as their “first choice” institution with the National Merit Scholarship Corporation
Separate application needed: No
Application deadline: February 1

William F. Vilas Merit Scholarship
Total Worth: Up to $1,600
Eligibility: Up to $1,600
Minimum Criteria: Based upon the highest academic achievement as evidenced in their admission application
Separate application needed: No
Application deadline: February 1

University of Wisconsin Madison provides aids at an average of 16644 per student meeting 80% of students need. 96% of students with need receive financial aid at an average of 5265 need-based grant. They also provide other scholarships including Applied Math, Engineering & Physics (AMEP) Leadership Prize.