AAE 364L Lab 6 - AAE364L Lab6 TA:NathanHoutz EricVandeRiet...

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State Space Control for the Two Degrees of Freedom Helicopter AAE 364L Lab 6 TA: Nathan Houtz Eric Van de Riet 11/30/16 1
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Introduction Objective This lab consisted of three parts, and had three objectives.  The first objective was to test  the error feedback controller designed for the pre-lab, and to improve upon it experimentally, if  necessary.  The second objective was to test the state-space feedback controller designed for the  pre-lab and improve it as necessary. The third objective was to test the best feedback controller  by flying the helicopter by hand.  It should be noted that the third objective provided no data and  was merely meant as a fun diversion. Intended Methods All lab equipment was provided and set up before the students entered the lab.  All that  was required of the students was to ensure the equipment was properly set up and to run the  experiment.  Running the experiment involved using the MATLAB command window to ensure  parameters were correctly set up.  Simulink was used to conduct the experiment and observe the  response in real-time.  Inputs for the experiment included voltage supplied by Simulink to one or both of the pitch and yaw motors.  For parts (i) and (ii), the inputs included sine waves for both  pitch and yaw that the helicopter was supposed to follow for optimal response.  Outputs for both  parts (i) and (ii) were pitch and yaw angles, as well as the voltages supplied to both motors. For  part (iii), the input was a voltage for which the signal originated from the joystick.  Part (iii) as  attempted, but no useful data was obtained, as the helicopter was impossible to control. Procedure Definition of Variables Symbol Description c p pitchaxis viscousfrictioncoefficient c y yawaxisviscous frictioncoefficient h verticaldistance of center of mass ¿ pivot point g accelerationdue ¿ gravity k pp gain ¿ pitchmotor ¿ pitchangle k py gain ¿ yaw motor ¿ pitchangle k yp gain ¿ pitchmotor ¿ yawangle 2
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k yy gain ¿ yawmotor ¿ yawangle J p moment of inertia relative ¿ pitchaxis J p ' newmoment of inertia relative ¿ pitchaxis J shaft moment of ineriaof metal shaft about yaw axis J y moment of inertia relative ¿ yawaxis L total length of helicopter l distance from front propeller axis to pivot point m total mass of helicopter m b mass moving about pitch axis m h mass of helicopter without small mass m motors mass of pitch and yaw propellers, shields, and motors m s small mass added to helicopter n number of cycles p 0 adjusted initial pitch angle R c longitudinal position of center of mass of helicopter v p input pitch motor voltage v y input yaw motor voltage v pe
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