INVESTIGATION OF CONTROL THEORY ON SPAARO UAV MODEL

# INVESTIGATION OF CONTROL THEORY ON SPAARO UAV MODEL -...

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INVESTIGATION OF CONTROL THEORY ON SPAARO UAV MODEL Aero Engineering Laboratory AOE 4154 Lab Instructor: Dr. Roger Simpson Lab TA: Scott Burger Lab Section: Friday 3:55 – 5:20 Date Performed: September 18, 2009 Student Name: Craig Sossi Student Number: 904512344 Honor Pledge: By submitting this document I pledge that I have neither given nor received unauthorized aid. Craig Sossi Page | 1

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The purpose of this experiment is to investigate how proportional gain control affects the stability of a SPAARO wind tunnel model in pitch control response. An open jet wind tunnel and roughly 1/8 scale model of a SPAARO UAV are used in conjunction with LabVIEW to obtain data used to compute coefficients for the third order response model, and stability is then analyzed. The results show that as gain increases, the aircraft takes longer and longer to return to steady state until a critical value when the aircraft becomes unstable and oscillations grow instead of decaying. INTRODUCTION Control theory is the study of the response of dynamic systems, either through the use of open-loop or closed-loop controllers. For an open-loop controller, outputs created by the system are not monitored so the controller has no way of knowing if the desired outputs have been achieved. An example of this type of controller is an electrical outlet timer. If a lamp is connected to the timer in a dark room, the lamp will turn on at a specific time and provide light to the room. If another lamp is brought into the room and turned on, the timer lamp will continue to turn on at its specified time because it does not first check to see if the task of lighting the room is already completed. A closed-loop controller on the other hand introduces feedback into the system, which compares the outputs of the system to the desired output and corrects for any error. For this experiment it can be seen that by adjusting the ratio of elevator deflection to angle of attack through the use of gain control, the dynamic response of an aircraft can be controlled. Since the aircraft is fixed about it pitch axis, the pitch angle of the aircraft and angle of attack are equivalent. This system can then be modeled as a second order dynamic model, shown in equation 1. [1] (1) This equation is a linear time-invariant ordinary differential equation with a characteristic equation of: (2) Stability for this system can be evaluated through the signs of constants a and b . If both are greater than zero, the system is stable. Since a proportional controller is used in this experiment, the change in elevator deflection can be replaced with the gain control times the change in pitch angle, modeled in equation 3. Page | 2
(3) Compared with equation 1, it can be seen that only the constant b is changed, and if the correct sign is chosen for the gain control K , the system will never go unstable for any value of K . However, we must model the aircraft system with a slightly more complex third order model.

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