Introduction Aircraft control systems serve several purposes in modern day aircraft from managing the control systems to ensure that they are behaving in a way that makes the aircraft easier to control to being activated to bring aircraft out of serious situations. These systems will only get more prevalent as the world pivots towards fly by wire aircraft
Aircraft control systems Non linear systems
Control systems come in several different varieties. There are open loop systems where there is only one input which receives no influence from the rest of the process, feedback control systems where the output feeds back to the input and compares the desired output to the current output and the closed loop system which involves feeding data back into the input but the key difference between closed and feedback loops is that there is no error calculated and therefore there is no desired value to reach.
This section got me to work with a non linear system of the Quanser aero2
F-16 deep stall recovery The final part of my ORIS was engineering a control system that can recover an f-16 from a deep stall. A deep stall is when an aircraft is pitched up at an angle of 60 degrees to the horizontal and the aircraft is travelling towards the earth which isn’t the direction of the earth. This is mainly because of slow speed. The method to get out of a deep stall involves rocking the nose back and forward in order to create enough momentum to get the nose down so that the aircraft can build up speed. To make this happen I used 2 different control systems, one is a sine wave input of values of 20 degrees elevator pitch up and down and the other system was a closed loop system feeding back pitch rate into the model. Alpha is pitch angle, v is speed and q is pitch rate.
Linear systems The purpose of this task working with linear systems is to recreate wind tunnel data with the equation kωn
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(𝑠2 +2ω n cs+ω2 n ) +9.4
The purpose of this is to find the values for k(stiffness) c(spring constant) and ωn (the natural frequency of the drone). In order to find these values I used the following code to create for loops(a loop that subs in a bunch of values into a function) to understand how each of these variables effects the output of the function.
This showed that k changes the end value of the function, c changes the position of the x intercept and ωn change the damping force .After matching the response to the wind tunnel data I got the values as c=+-0.29, k=+-9.4 and ωn=+-10. The pluses and minuses are due to the fact that the values for the step up response need to be negative in order to properly model the step down response. The response for these values are seen above with the yellow line being the real values and the red and blue lines being the recreated data.
Quanser aero2 This system’s non linearity is because of the electrical nature of this drone. This means that this drone is powered by voltage and the relationship between output pitch angle(a measure of force) and voltage is non linear. In order to regulate this system I used a proportional, integral, derivative(PID) controller. The Proportional control works by producing a value that is proportional to the current error found by subtracting the desired value from the current value. The integral control works by adding the errors over time and then multiplying it by a value so that the total error eventually reaches 0. The derivative control produces a damping effect by multiplying a value and the error’s derivative. The value does change with the error’s change. In the control system the input was the desired pitch angle. This then gets fed into the PID controller which then goes into the system of the Quanser Aero2. The output then creates a feedback control loop due to the subtract block.
Sine wave system
Closed loop system The sine wave system works by isolating the system to an unstable section where the oscillations diverge to infinity. This means that the nose of the aircraft will be able to get down. The graphs for each system is below.
I then used the feedback control system in figure 4 in order to smooth out the pitch response so that there are no oscillations when the drone reaches the desired pitch angle. The pitch angle is shown in the top graph and the elevator response is shown in the bottom graph. The results are shown in figure 3. closed loop system
Bibliography Dividing the output by the desired input would the pitch of the drone between 0 and 1. As seen in figure
Figure 3
Dr Duc Nguyen, M. H. (2022). Analysing dynamic deep stall recovery using a nonlinear. Bristol: Nonliner Dynamics Journal. Duc Nguyen, M. H. (2023). Derivation of control inputs for deep stall recovery using. Bristol: Royal Aeronautical Journal. Instruments, N. (2024, July 8). google. Retrieved from National instruments: https://www.ni.com/en/shop/labview/pid-theoryexplained.html?srsltid=AfmBOooo-A9CqokQjaz3QGsiaI8dVqF04ItLb62kVyF8boT2YVuQ9Fpe Prechtl, R. (2017). Youtube. Retrieved from Youtube: https://www.youtube.com/watch?v=qg1Ojydzv8U