AAE 364L Lab 5 - PID Control of the Two Degrees of Freedom...

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PID Control of the Two Degrees of Freedom Helicopter AAE 364L Lab 5 TA: Nathan Houtz Eric Van de Riet 11/10/16 1
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Introduction Objective This lab consisted of three parts, but due to unforeseen circumstances, was reduced to two parts. The first part had the experimenter’s testing the best gains that were found from the pre-lab in order to test the helicopter’s response. From this, new gains were implemented to attempt to improve the helicopter’s response. The second part of the lab involved closed loop flight testing using a joystick to observe the response of the helicopter using the controller from the first part. 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 part (i), the inputs included sine waves for both pitch and yaw that the helicopter was supposed to follow for optimal response. For part (ii), inputs also included signals from the joystick that coincided with helicopter pitch and yaw if all went as planned. Outputs for both parts (i) and (ii) were pitch and yaw angles, as well as the voltages supplied to both motors. Procedure Definition of Variables Symbol Description c p pitchaxis viscousfrictioncoefficient c y yawaxisviscous frictioncoefficient h verticaldistance of center of mass ¿ pivot p g accelerationdue ¿ gravity k pp gain ¿ pitchmotor ¿ pitchangle k py gain ¿ yawmotor ¿ pitchangle k yp gain ¿ pitchmotor ¿ yawangle k yy gain ¿ yawmotor ¿ yawangle J p moment of inertia relative ¿ pitchaxis 2
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J p ' newmoment of inertia relative ¿ pitchaxis J shaft moment of ineriaof metal shaft about yaw 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 input pitch motor voltage for equilibrium v ye input yaw motor voltage for equilibrium x distance from small mass to pivot point x 1 adjusted distance from small mass to pivot point θ pitch angle ´ θ pitch rate ´ θ pitch angle acceleration σ decay rate ψ yaw angle ´ ψ yaw rate ´ ψ yaw angle acceleration ω damped angular frequency 3
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Schematic Description of Apparatus Figure 1 : Helicopter model Above in Figure 1 is the helicopter model that was used in this lab. The front motor, henceforth referred to as the pitch motor, controls the pitch angle of the model.
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