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Unformatted text preview: Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 Design Project Assignment–8 (Due date: Thu, Nov 30, 2006) 1. Our final part of the project involves the design of a controller that enables the system to track any constant commanded deviation from the runway centerline, Γ ref ( t ). Once we can do this, we can make the system track the command Γ ref ( t ) = 0 which will align the aircraft with the runway centerline. We start by finding a transfer function from the heading angle ψ to the deviation from the runway centerline Γ( t ). Note from the equation (3) in Assignment 7 that D ( s ) = 1 s ψ ( s ) (1) We now need to use equation (2) to find a transfer function from d to Γ. However, this is not straight forward since R ( t ) changes with time. For example, at t = 0, the aircraft is at an initial range R = 15000 m ,and thus Γ( t ) = d ( t ) 15000 , (2) but at t = 200 s with the aircraft travelling at U = 67 m/s , Γ( t ) = d ( t ) 1600 . (3) To circumvent this problem, we will design our compensator for a nominal value of the range ¯ R = 7000 m . Thus, we assume that Γ( t ) = d ( t ) ¯ R = d ( t ) 7000 , (4) and from (1), it follows that G Γ ψ ( s ) = Γ( t ) ψ ( s )) = U 7000 s . (5) Mechanical and Aerospace Engineering - UTA 1 of 3 Dr. Atilla DoganDr....
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- Fall '08
- Dr. Atilla Dogan