Obviously you will want to run the panels away from the house so the supports will need to be paralell to the house. How about a 2 X 10 rafter at each end of the patio, attached to the house with a joist hanger at the 12' height and a 4 X 6 under the other end. Now, we are using only two posts.
To support the panels, you could use a 2 X 6 at 2' centers with joist hangers, except at the outer edge, the 2 X 6 should overlap the 2 X 10 and be nailed into it.
The drop from the house to the posts should be 2' for good drainage and the 10' height will still give you a well ventilated space.