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Category > Programming Posted 05 May 2017 My Price 8.00

A schematic for the satellite and scientific probe

 

A schematic for the satellite and scientific probe for the Gravity Probe-B (GP-B) experiment that was launched on April 30, 2004 is sketched in Fig. 7.83. Assume that the mass of the spacecraft plus helium tank, m1, is 2000 kg and the mass of the probe, m2, is 1000 kg. A rotor will float inside the probe and will be forced to follow the probe with a capacitive forcing mechanism. The spring constant of the coupling k is 3.2 × 10 6 . The viscous damping b is 4.6 × 10 3 .

(a) Write the equations of motion for the system consisting of masses m 1 and m 2 using the inertial position variables, y1 and y2.

(b) The actual disturbance u is a micrometeorite, and the resulting motion is very small. Therefore, rewrite your equations with the scaled variables Z1= 10 6y1, Z2 = 10 6y2, and v = 1000u.

(c) Put the equations in state-variable form using the state , the output y = Z2 , and the input an impulse, u = 10 -3 δ(t) N-sec on mass m1 .

(d) Using the numerical values, enter the equations of motion into MATLAB in the form

And define the MATLAB system: sysGPB = ss(F,G,H,J). Plot the response of y caused by the impulse with the MATLAB command impulse(sysGPB). This is the signal the rotor must follow. (e) Use the MATLAB commands p = eig(F) to find the poles (or roots) of the system and z = tzero(F,G,H, J) to ind the zeros of the system.

 

 

 
 

Answers

Alpha Geek
(8)
Status NEW Posted 05 May 2017 11:05 AM My Price 8.00

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file 1493982251-Answer.docx preview (299 words )
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