UAV: Design to Flight Report

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1 UAV: Design to Flight Report Team Members Abhishek Verma, Bin Li, Monique Hladun, Topher Sikorra, and Julio Varesio. Introduction In the start of the course we were to design a situation for our UAV's mission. We chose for our mission to be a search and rescue type. In this case, instead of searching for injured people we wanted to search for missing payloads. We planned on working with the University of Minnesota High-Altitude Ballooning and Rocket teams. In the situation, where a payload would have gone missing from one of their flights we would have our UAV go out to hunt for them. We would search and transmit the coordinates to the home base (people on the ground). We would also take pictures of the surrounding area. If the missing payload is in a dense wooded area for example, these pictures would help share valuable information. This mission would involve a bit of work in terms of deciding the UAV's path around the particular search area, consideration for battery usage, and incorporating the different types of equipment (radios/cameras) that have to be placed in the UAV's body. We would have needed a transmitter to transmit the pictures (live or not live) and the missing payload's signal back to the people at ground base. The types of transmitters were shown in the second assignment. We had to make sure that whatever the transmitter used in our aircraft would not have any incorrect influences on the equipment inside the UAV already. We had to also consider how much mass these items could be as well. We modeled this initial mission in terms of the UAV's maneuvering capabilities. We designed our UAV model to reflect the dimensions of the Ultra Stick 25e. The airframe physical properties were used in determining the load factor for this aircraft. The remainder of this paper shows the results from our analysis of this aircraft including the equations of motion, control laws, and data received from flight.

2 Figure : Ultra Stick 25e UAV.

3 2. Flight Envelope Figure 2: Flight Envelope We also determined the steady maneuvering envelope. We found certain values for the turning performance, maximum climb rate (with values for speed, turn-rate, and climb-rate), and the maximum descent rate. These were the values that our aircraft had to stay within these limits to be considered a safe aircraft. These are indicated on the following graphs. As shown in figure 2, the maximum steady rate of climb is 276.7ft/min, which is equivalent to 3.75 m/sec at following flight conditions: load factor (n) =.2, velocity (v) =3.85 m/sec, and flight path angle = 83. degree. The maximum steady rate of descent is 378 ft/min, which is equivalent to 7 m/sec at following flight conditions: load factor (n) =.96, velocity (v) =25 m/sec, flight path angle = -6.3 degree. These results are verified by available power versus speed plot in figure 3. The green curve represents the maximum power available via thrust and the red curve is the power consumed via drag. Figure 4 is a plot that represents the turn rate within feasible maneuvering envelope. The maximum turn rate occurs at load factor (n) = 4.4 and velocity (v) =2

4 m/sec. The maximum turn rate is 2 rad/s, which corresponds to minimum turn radius of.5 m for the aircraft. Figure 3: Available power versus speed

5 Figure 4: Turn rate (rad/sec) 3. Model simplification (Linearization and Decoupling) The linear model for Ultra Stick 25e UAV is given as decoupled longitudinal dynamics and lateral-directional dynamics. These were modeled in a state-space form. Longitudinal dynamics is given with the following: A lon =.8 B lon = 4.57 The lateral-directional dynamics is given with the following: ' A lat =.3 M lat ' B lat = = With these matrices, we can build the UAV linear model in Simulink, which is shown as below.

6 Figure 5: Linear model of UAV The first basic analysis we did with the Simulink models including incorporating a doublet elevator input. The following response is shown below:.8.6 Elevator Aileron Rudder 5 u v w.4 Input (a) Input Velocity [m/s] (b) Velocity.8.6 p q r 4 3 Phi Theta Psi.4 2 Rate of Angle (c) Rate of angle Angle (d) Angle Figure 6: Response with elevator input

7 The second analysis was incorporating a doublet aileron input in to this model. The following response is shown below: Elevator Aileron Rudder 5 5 u v w Input Velocity [m/s] (a) Input (b) Velocity.8.6 p q r 5 Phi Theta Psi.4 Rate of Angle (c) Rate of angle Angle (d) Angle Figure 7: Response with aileron input

8 We also analyzed this model with giving a step input for the rudder in the Simulink model. The following is the response shown below:.5 4 Elevator Aileron Rudder 3 u v w 2 Input.5 Velocity [m/s] (a) Input (b) Velocity.5 p q r 25 2 Phi Theta Psi Rate of Angle.5 Angle (c) Rate of angle 5 5 (d) Angle Figure 8: Response with rudder input

9 4. Heading Control Design Figure 9: The heading control system The heading control system consists of three main components: the inner loop, the course angle controller, and the anti-windup. The course angle controller is designed as a proportional-integrator (PI) controller, so as to take the bias and noise in the consideration. Its structure is shown in the figure below: Figure : Course angle controller (PI) The anti-windup system is shown in the figure below. The logic of the antiwindup is that if absolute the roll error exceeds the threshold, exceeds the deflection, and the roll error is of different sign, then the anti-windup will be activated. Figure : Anti-windup

10 The inner loop of heading control system is a roll control system, which is shown in the figure below. It is consist of two parts: the model of UAV and the inner loop proportional-derivative (PD) controller. Figure 2: The inner loop To facilitate the control design of the system, we first simply the transfer function from aileron input to roll rate, which is inherently a fourth-order system. At first from the state space matrix, we neglected all the other states and inputs. We included the roll rate and aileron deflection input, which will gave us p = Alat ( 2,2) p+ Blat (2,)ς where, a φ 2 = B lat (2,) = , a φ = A lat (2,2) = The comparison between the simplified model and full-state model is given in both frequency domain and time domain, as shown in figures below. 3 2 Bode Diagram From: xi To: p 5 Aileron Input Simplified Full-state Magnitude (db) - 5 Phase (deg) Simplified Full-state Frequency (rad/s) (a) Frequency domain (b) Time domain Figure 3: The comparison between the simplified model and full-state model

11 As can be seen from above, the two models has some discrepancy on the low frequency part that simplified model has some steady state error. But the simplified model has fast response. We analyzed the inner loop system as well. The desired transfer function is φ( s) φ ( s) ref 2 = ωn φ 2 s + 2ζω s + ω [] nφ 2 nφ where, ω n φ = K p, φ aφ2 and K d, φ 2ζω nφ aφ =. a φ2 From here we designed the inner loop PD control gains. Note that the proportional gain should not be too large so that the saturation of the elevator actuator needs to be considered. With these constraints, we designed the inner loop controller as K pφ =. 5 and K dφ =. 62 by setting the damping ratio to be.7, and then the natural frequency becomes ω n φ = The comparison between the inner loop system with the simplified model and that with full-state model is given in both frequency domain and time domain, as shown in figures below. 2 Bode Diagram Gm = Inf db (at Inf rad/s), Pm = 64 deg (at.66 rad/s).4.2 Reference Simplified Full-state Magnitude (db) Phase (deg) Inner-loop Roll [rad/s] Frequency (rad/s) (a) Frequency domain (b) Time domain Figure 4: The comparison between the inner loop with simplified model and fullstate model As can be seen from above, the two models give almost the same inner loop response. Besides, the Bode plot shows that the gain margin is infinity and the phase margin is 64 degree, indicating that the system is quite robust.

12 For the outer loop, we assume the inner loop system is perfectly fast in response that it will not affect the outer loop control design. Therefore, its transfer function is seen to be. However, when designing the controller, we should set the bandwidth to be 3~5 times smaller than that of the inner loop. Besides, to eliminate the steady state error due the bias, PI controller is adopted for outer loop. The derived control gains are K pκ =2. 5 and K iκ =.. Under the above controller, when given a step course angle input with a magnitude of, the response is as below: Reference Response..5 Original Saturated Course Angle [rad] Aileron Input [rad] (a) Course angle (b) Aileron deflection Roll rate [rad/s].5 Roll [rad] (c) Roll rate (d) Roll Figure 5: Time History for course angle, aileron deflection, roll rate and roll angle for step input of degree for course angle. The comparison between the outer loop system with the simplified model and that with full-state model is given in both frequency domain and time domain, as shown in figures below.

13 5 Bode Diagram Gm = 2.7 db (at 8.3 rad/s), Pm = 7 deg (at.7 rad/s).8.7 Reference Simplified Full-state Magnitude (db) Outer-loop Course Angle [rad] Phase (deg) Frequency (rad/s) (a) Frequency domain (b) Time domain Figure 6: The comparison between the outer loop with simplified model and fullstate model As can be seen from above, the two models give almost the same outer loop response. Besides, the Bode plot shows that the gain margin is 2.7dB (larger than 6dB) and the phase margin is 7 degree, indicating that the system is enough robust. 5. Altitude Control Design Altitude control system is in the form as shown in the figure below. Figure 7: Altitude Control system. The altitude control system consists of three main components: the inner loop (pitch attitude controller), the outer loop (altitude controller) and the anti-windup. The altitude controller is designed as a PI controller so as to take the bias and noise in the

14 consideration. This structure is shown in the figure 7. The anti-windup system is already shown in the figure. The inner loop is a pitch attitude control system, which is shown in the figure below. It is consist of two parts: the model of UAV and the inner loop PD controller. Figure 8: The inner loop for altitude control system To facilitate the control design of the system, we first simply the transfer function from elevator input to pitch rate. From the state space matrix, we neglected all the other states and inputs. We included only the pitch rate, pitch, and elevator deflection input. This gave us the following: ᄋ q = A (3,3) q + A (3, 4) θ + B (3,) η lon lon lon where, aθ 3 = B lon (3,) = 4.57, aθ 2 = A lon (3, 4) =, aθ = A lon (3,3) = 6.55 The comparison between the simplified model and full-state model is given in both frequency domain and time domain, as shown in figures below.

15 (c) Frequency domain (d) Time domain Figure 9: The comparison between the simplified model and full-state model As can be seen from above, the two models has some discrepancy on the low frequency part. The simplified model has fast response. The inner loop system was designed with the desired transfer function as θ ( s) ω c θ ζω ω 2 nθ = 2 2 ref ( s) s + 2 nθ s + nθ where, ω nθ = K p, θaθ 3 + aθ 2 and K [2] 2ζωn θ aθ d, θ =. aθ 3 We designed the inner loop PD control gains. Note that the proportional gain should not be too large that the saturation of the elevator actuator needs to be considered. With these constraints, we designed the inner loop controller as K p θ =.5 and K θ =.337 by setting the damping ratio to be.7, and then the natural frequency resulted in ω = The comparison between the inner loop system with the simplified model nθ and that with full-state model is given in both frequency domain and time domain, is shown in figures below. The time histories for pitch angle, pitch rate, and elevator deflection for step input of degrees for the pitch attitude is also shown. d

16 (c) Frequency domain (d) Time domain Figure 2: The comparison between the inner loop with simplified model and fullstate model Figure 2: Time history pitch angle, pitch rate and elevator deflection for step input of degrees for pitch attitude.

17 As can be seen from above, the Bode plot shows that the gain margin is infinity and the phase margin is 64 degree, indicating that the system is enough robust. The inner-loop bandwidth is 9 rad/sec. For the outer loop, we assumed the inner loop system is perfectly fast in response that it will not affect the outer loop control design. However, when designing the controller, we should set the bandwidth to be 3~5 times smaller than that of the inner loop. Besides, to eliminate the steady state error due to the bias, PI controller is adopted for outer loop. The derived control gains are K ph =.2282 and K =.. The comparison between the outer loop system with the simplified model and that with full-state model is given in both frequency domain and time domain (for step input of 2 meters), as shown in figure 2. In figure 2, the two models gave almost the same outer loop response. Besides, the Bode plot shows that the gain margin is infinite and the phase margin is 8 degree, indicating that the system is enough robust. The time histories for altitude, pitch rate, pitch angle, and elevator deflection for step input of 2 meters for altitude is also shown. ih (c) Frequency domain (d) Time domain Figure 22: The comparison between the outer loop with simplified model and fullstate mode

18 Figure 23: Time history for altitude, pitch rate, pitch angle and elevator deflection for step input of 2 meters for altitude. 6. Controller Validation and Flight Test Two steps are crucial in order to ensure that the controller is suitable for real flight, which are simulation in the loop and hardware in the loop. Simulation in the loop is to convert the controller from a Simulink block to a flight code written by C language. This is to check whether our controller is properly designed. Hardware in the loop is to use the flight computer to input control signal by analyzing the states information from Simulink. This is to check whether signals are well transmitted. Both of these two steps will greatly reduce the material and time cost of the control design process. After applying these two steps, we can proceed to flight test for the final check of the designed controller. The result of the flight test is given below. Three runs of the schedule are taken. For each run, the UAV first does a climb of meters and then make a 8 degree turn several seconds later.

19 5 φ (rad) θ (rad) ψ (rad) h (m) time (s) 6. Results of the heading control Figure 24: The result of the flight test The result of inner loop of heading control system is shown in the figure below Command Simulation SIL Flight test φ (rad) time (s) Figure 25: The result of heading control inner loop As can be seen in the above figure, given the same roll reference command (a doublet with 25 degree of magnitude), all the three steps (pure simulation with the simplified

20 model, simulation in the loop and flight test) have quite similar result. Since the simulation adopts the simplified model, its result is the most optimistic that it has the fastest response and no steady state error. Another phenomenon is that it takes more time to turn right since the step is larger. The result of outer loop of heading control system is shown in the figure below Command Simulation SIL Flight test ψ (rad) time (s) Figure 26: The result of heading control outer loop As can be seen in the above figure, given the same course angle reference command (a step with 8 degree of magnitude), all the three steps (pure simulation with the simplified model, simulation in the loop and flight test) have quite similar result, and they have no overshoot. Since the simulation adopts the simplified model, its result is the most optimistic that it has the fastest response, while simulation in the loop gives the worse response. Below shows the response of the roll angle given a course angle input. The blue line is the roll reference given by the outer loop controller (before saturation), which will exceed the physical limit of the UAV. The result is in accordance with the course angle response that simulation gives the best result while SIL is the worst.

21 Command Simulation SIL Flight test 2 φ (rad) time (s) Figure 27: The roll angle response of the heading control 6.2 Results of the Altitude control The result of inner loop of altitude control system is shown in the figure below Command Simulation SIL Flight test.5 θ (rad) time (s) Figure 28: The result of altitude control inner loop (pitch attitude) As can be seen in the above figure, given the same pitch reference command (a doublet with degree of magnitude), all the three steps (pure simulation with the simplified model, simulation in the loop and flight test) have quite similar result. Since the simulation adopts the simplified model, its result is the most optimistic that it has the fastest response with no steady state error.

22 The result of outer loop of altitude control system is shown in the figure below h (m) Command Simulation SIL Flight test time (s) Figure 29: The result of altitude control outer loop (altitude) As can be seen in the above figure, given the same altitude reference command (a step with meters of climb), the pure simulation with the simplified model gives nice data even while the simulation in the loop and flight test are noisy. Since the simulation adopts the simplified model, its result is the most optimistic that it has the fastest response. Below shows the response of the pitch angle given an altitude input Command Simulation SIL Flight test.5 θ (rad) time (s) Figure 3: The pitch response of the altitude control

23 7. Frequency Analysis of Flight Test Data 7. Frequency response for pitch controller (Inner loop of altitude controller) Figure 3: Selection of doublet responses for pitch from flight data Figure 32: Transfer function (Closed Loop) for pitch based on cross spectrum for pitch response

24 Figure 33: Open loop transfer function for pitch computed using closed loop transfer function which itself is extracted from flight data Figure 34: Open loop transfer function for pitch via flight data VS original second degree open loop transfer function for pitch controller (equation [2])

25 Figure 35: Coherence for pitch response 7. Frequency response for roll attitude controller (Inner loop of heading controller) Figure 36: Selection of doublet responses for roll from flight data

26 Figure 37: Transfer function based on cross spectrum for roll response Figure 38: Open loop transfer function for roll computed using closed loop transfer function which itself is extracted from flight data

27 Figure 39: Open loop transfer function for roll via flight data VS original second degree open loop transfer function for roll controller (equation []) Figure 4: Coherence for roll response

28 8. Flight Trajectory The following figure shows the flight trajectory. The red section highlights the time when course angle is commanded. The aircrafts responds well to the reference command. Figure 4: Flight Trajectory: top view. The red section shows the nonzero heading commands.

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