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assign4dynsoln

# assign4dynsoln - SBE 2006 Dynamics Homework Solutions...

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Unformatted text preview: SBE 2006 Dynamics Homework Solutions Preamble Imagine you are a test director at Johnson Space Center (JSC). You are interested in testing a training version of SAFER (Simplified Aid For EVA Rescue) to be used on the Precision Air Bearing Floor (PABF). The training version of the SAFER is designed to work only in one plane (i.e., the plane of motion parallel to the plane of the floor). The SAFER can be controlled in two ways: translation or rotation, depending on which jets are active at any time. Balanced jets in one direction will result in a force applied in the opposite direction. Counteracting jets on either side of the SAFER will result in a torque about the center of mass of the SAFER. The SAFER uses “bang-off-bang” control, meaning each jet is either fully on or fully off. A diagram of the training SAFER can be found below. In order to evaluate the performance of this SAFER model, you want to track the motion of a subject wearing the SAFER training unit. To collect data for your test, you have setup a small, motion tracking system. The tracking system uses magnetic markers on the SAFER and provides noisy measurements of the planar X and Y positions as well as a rotation angle, theta, of the SAFER. This problem explores the dynamics of this situation, simulates it and leads you through the development of a simple Kalman filter for tracking the position, velocity, angle and angular rate of a subject using this training version of the SAFER. 1 * e -r As s, ^gtrsn 5 1 'No "C^*lo" . NS\.\ €ral ry r J 1 . . ) l D I A p p \ r l i x p u l r I BoJ.y €orce ; l ' r l F u Y l = I l t r I To'1t T Df""*I:, (9 R"+-," b o,ty 4o"te 1^1o i^cr\$J {cane *le Jxc"{so^ l.,sr,.e r.4\.ix, 9 l c I 1 +- / ^ f- = i"*" 1'x ' t-".^ i^'rl =- 't,t' ' J .r.lno.c ! _ l c o , e "l Itt ] crs e 6.-\& Aedr L5)^ e l €-- \:z Mut""'. l"-s, r E ^ , E . I = - , i = , i , ; f r T : T i i = j 5 " * ] - * e -r As s, ^gtrsn 5 1 'No "C^*lo" . NS\.\ €ral ry r J 1 . . ) l D I A p p \ r l i x p u l r I BoJ.y €orce ; l ' r l F u Y l = I l t r I To'1t T Df""*I:, (9 R"+-," b o,ty 4o"te 1^1o i^cr\$J {cane *le Jxc"{so^ l.,sr,.e r.4\.ix, 9 l c I 1 +- / ^ f- = i"*" 1'x ' t-".^ i^'rl =- 't,t' ' J .r.lno.c ! _ l c o , e "l Itt ] crs e 6.-\& Aedr L5)^ e l €-- \:z Mut""'. l"-s, r E ^ , E . I = - , i = , i , ; f r T : T i i = j 5 " * ] - u ( u ), - ( u ); ( u ( u )] This function takes in and outputs [cos sin sin ), cos Problem 2. Simulink Model of SAFER plant dynamics Problem 2. Plots of SAFER position and rotation angle -1.8-1.6-1.4-1.2-1-0.8-0.6-0.4-0.2 0.2-3-2.5-2-1.5-1-0.5 0.5 Subject motion in X-Y plane X position (m) Y p o s i t i o n ( m ) 1 2 3 4 5 6 7 8 9 10 50 100 150 200 250 300 350 400 Subject rotation angle Time (s) R o t a t i o n a n g l e ( d e g r e e s ) 4 Problems 3-5....
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assign4dynsoln - SBE 2006 Dynamics Homework Solutions...

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