The Air Force said yesterday that it has awarded McDonnell DouglasCorp. a $3.39 billion contract to develop the controversial C-17military cargo plane at its Douglas Aircraft plant. The contract award, which was made Tuesday, has been anxiously awaited by McDonnell Douglas, which eventually will add 13,000 people to the payroll. It also represented a rejection of critics who wanted the Air Force to use older and presumably cheaper alternatives, such as the existing C-5 made by Lockheed or a military version of Boeing's 747.