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29 FLIGHT CONTROL OF A HOVERCRAFT 98 29 Flight Control of a Hovercraft You are tasked with developing simple control systems for two types of hovercraft moving in the horizontal plane. As you know, a hovercraft rests on a cushion of air, with very little ground resistance to motion in the surge (body-referenced forward), sway (body-referenced port), and yaw (taken positive counterclockwise viewed from above) degrees of freedom. The simplified dynamic equations of motion are: u ˙ = u + F u v ˙ = F v r ˙ = M, where the surge and sway velocities are u and v and the control forces in the u -and v - directions are F u and F v , respectively. The yaw rate is r and the control moment is M . There are two types of craft we will consider: 1) one where F u , F v ,and M are all commanded independently, e.g., using independent thrusters, and 2) one where F v = p v δF u and M = p φ δF u . This second case is encountered if there is a surge thruster (or set), whose exhaust pushes on a rudder with (body-referenced) angle δ . To create a lateral force or moment, you have to have some F u and some rudder action. We will use the values p v =0 . 2and p φ = 0 . 2 in this problem. Notice negative sign in p φ ; it means that a positive rudder action, counterclockwise if viewed from above, leads to a negative body torque, that is, clockwise. This is typical when the rudder is behind the thruster, and near the back of the craft. The dynamic equations are augmented with some kinematic relations to evolve the location of the craft in a fixed frame: X ˙ = u cos φ v sin φ Y ˙ = u sin φ + v cos φ φ ˙ = r, where X and Y denote the location in Cartesian coordinates, and φ is the yaw angle. See the figure below. Create a six-state model for each vehicle type from the above equations, and perform the following tasks: 1. By putting in different settings and combinations of F u , F v , M , δ , convince yourself that for each of the two cases, the behavior is like a hovercraft. In the first case, turns occur completely independently of translational motion in the X, Y plane, whereas for the second, lateral force and turning torque occur together, and they scale with both δ and F u . 2. For Case 1: From a full-zero starting condition ±s =[ u, v, r, X, Y, φ ]= [0 , 0 , 0 , 0 , 0 , 0], the ob jec t ivei s to moveto to ±s desired =[ u, v, r, X, Y, φ ] desired =[0 , 0 , 0 , 1 m,
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29 FLIGHT CONTROL OF A HOVERCRAFT 99 under closed-loop control. To
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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