Fractional Order Control of A Fixed-Wing UAV

1. Fractional Order Control of A Fixed-Wing UAV Haiyang Chao, Ying Luo, Long Di Advisor: Dr. YangQuan Chen CSOIS Utah State University 2009/01/23

2. Outline • Introduction to UAV Flight Control & Fractional Order Control Techniques. • Problem Statement of UAV Flight Control. • System Identification of UAV Roll-loop Model. • Roll Loop Control of UAV Using Fractional PI Control. • Simulation of FOC Control of UAV. • Experimental Validation of FOC on a Fixed Wing Small UAV. • Future Time Line.

3. Introduction to UAV Flight Control The UAV market has grown rapidly this decade including both military and civilian applications. It is estimated that the global UAV market will reach around 7.2 billion $ for 2009 [1]. In courtesy of [1]. In courtesy of [1].

4. Introduction to UAV Flight Control • Most UAVs can be treated as flying sensors to investigate a specified area from a certain altitude. UAV flight control system plays a key role here not only for the flight stability issues but also for the sensor data interpretation part. For example, the UAV control performance can affect the georeferencing result of aerial images a lot. • There are several special requirements for UAV flight control: • Robustness Consideration. • Winds, especially gusts can affect the small UAVs a lot. • Different flight conditions including weather, altitude. • Various Payloads. • Hand-made airframes without accurate modeling. • Limited Resource Constraints • Limited accuracy for on-board inertial sensors. • Limited computational power. • Limited size weight • Anything else????

5. Introduction to Fractional Order Control Techniques • Fractional order control (FOC) is attracting lots of interests recently. • FOC introduces fractional derivative and fractional integral and provides more solution candidates for the control problem. • PI^Alpha ( ) controller is one of the simplest fractional order controllers similar to the classical proportional integral (PI) controller. • FOC can give advantages over traditional controllers because FOC has a larger memory and a wider solution selection range.

6. Contribution • Achieve more accurate trajectory tracking for our small fixed-wing UAV. • Give a more robust solution to the UAV control problem. • Test the discrete fractional order controller on a real system to show that FOC works in the real world. • Test the performance of fractional 0rder controller for a highly coupled nonlinear system.

7. Problem Statement of UAV Flight Control

8. UAV Flight Control Basics • UAV dynamics can be modeled using 12 system states: • Position: longitude, latitude, altitude . • Attitude: roll, pitch, yaw • Gyro rate: roll rate, pitch rate, yaw rate • Air speed: • Angle of attack and slide-slip angle • UAV control inputs generally include: aileron, elevator, rudder, and throttle. • So the UAV dynamics can be modeled using nonlinear equations.

9. UAV Dynamic Model • Dynamic model with 6-degree of freedom [2]. In courtesy of Austin Jensen.

10. UAV Dynamic Model • Dynamic model with 6-degree of freedom. In courtesy of Austin Jensen.

11. UAV Flight Control Basics • The nonlinear dynamic model is hard to analyze. However, it can be linearized at some trimming point and treated as a simple SISO or MIMO linear system so that linear system theories can be used. • The UAV 6 degree of freedom dynamics can be decoupled to two modes: • Longitudinal mode: pitch loop. • Lateral mode: roll loop. • The roll loop control problem or lateral dynamics is carefully studied in this paper.

12. Roll-Loop Control of UAVs • The roll loop of a UAV can be treated as a SISO (roll-aileron) system after it achieves a steady state flight. • The steady state flight means all the force and moment components in the body coordinate frame are constant or zero. It can be treated as a singular point or equilibrium point. • An intuitive controller design is classical proportional integral and derivative control (PID).

13. System Identification of UAV Roll Loop

14. System Identification of Roll-loop • Non-parametric method: transient response • Impulse response analysis • Step response analysis (FOPTD) • Square response analysis • Parametric method • Linear model • ARX • Least square parameter identification using PRBS excitations.

15. System Excitations: PRBS • PRBS stands for pesudo random binary sequence. • PRBS is good because its signal is rich in all the specified frequency. • PRBS signal length: 2^N-1, N = 1,2,3… • Example PRBS signal with the length of 255.

16. System Identification Using Square Wave Response • Steiglitz-Mcbride iteration method. • Stmcb() in matlab.

17. Roll Control of UAVs Using Fractional PI Controller

18. Fractional Order PI Controller Design for UAV 18

19. Fractional Order PI Controller Design for UAV 19

20. Fractional Order PI Controller Design for UAV • Amplitude and phase of FOPI first order model of UAV 20

21. Fractional Order PI Controller Design for UAV • Amplitude and phase of FOPI controller 21

22. Fractional Order PI Controller Design for UAV • Amplitude and phase of the open loop system 22

23. Fractional Order PI Controller Design for UAV • FOPI controller design principle 23

24. Fractional Order PI Controller Design for UAV • FOPI controller design principle 24

25. Fractional Order PI Controller Design for UAV • Numerical design process 25

26. Fractional Order PI Controller Design for UAV • Numerical design process 26

27. Simulation of Roll-loop Fractional PI Control of UAV Ref [2]. Ref [3].

28. Simulation Platform: Aerosim • Aerosim is a nonlinear 6 degree of freedom simulink model for mid-size UAV aerosonde [3]. • This tool is developed by Marius Niculescu from u-dynamics. • All the simulink blocks are achieved through dll. • Simulink minimal step: 0.02 s.

29. Simulation Platform: Aerosim

30. UAV Sys ID in Time-domain • Use time domain system identification • stmcb(y_ip(11800: 12100),x_ip(11800: 12100),0,1); • System model identified: 1.147/(s + 0.9793)

31. PID Control of Roll-loop

32. Fractional PI Control of Roll-loop

33. Controller Design • PI Controller Using Modified Ziegler-Nichols Method • Kp = 0.2601; Ki = 28.4091; Kd = 0; • Fractional Order PI^alpha controller Using Flat Phase Method • Kp = 0.5503; Ki = 28.31; alpha = 1-0.111;

34. Case 1: Wind Gust Disturbance • Wind disturbance input: [v_n,0,0];

35. K = Original 80% Case 2: Gain Margin Original

36. K = Original 120% Case 2: Gain Margin Original

37. Experimental Validation of FOC on Small Fixed UAVs

38. UAV Sys ID of 72” UAV • Use time domainsystemidentificationusing 10 hz data and data interpolationalgorithm • stmcb(y_ip(11800: 12100),x_ip(11800: 12100),0,1); • System model identified: 1.147/(s + 0.9793)

39. UAV Sys ID of 60” UAV • Use time domainsystemidentificationusing 10 hz data and data interpolationalgorithm • Stmcb();x_min = 544, x_max = 578; • data_processing_gx2_pprz_plot_interpolation_20090115.m • System model identified: 0.8887/(s + 0.7314)

40. Fractional Order PI Controller Design for UAV • IdentifiedRoll control model of our 72’’ UAV 40

41. Fractional Order PI Controller Design for UAV • Numerical curves following the designed specifications 41

42. Fractional Order PI Controller Design for UAV • Verify the numerical method by the Bode plot 42

43. Fractional Order PI Controller Design for UAV • Simulation:Implementation of the fractional operator Oustaloup Algorithm is used to realize the fractional operator approximately here: 43

44. Experimental Validation of FOC • Based on the structure under the Box Frac Der s^0.1, we are able to write it in a form as follows:

45. The continuous and discrete form of s0.1 • We need to convert this form from continuous domain to discrete form, which can be accomplished using a MATLAB function C2D • After choose the sampling time as 1/60 and the method as “tustin”, we are able to get the following form in Z domain:

46. The comparisons of s-0.9 and 1/s*s0.1 After adding a integrator, why not directly use s-0.9 instead of using 1/s*s0.1

47. Given Kp=0.5503,Ki=28.31, α=-0.111 The Plant=1/(1/13.76*s+1) Vstep=10 Some explorations

48. The continuous and discrete form of the fractional order I • The transfer function in discrete domain • The final format used for C code:

49. Problems dragging us from real flight tests • Synchronization issue, big impact on system Identification • When we convert the transfer function from continuous domain to discrete domain, some information get lost

50. Future Timeline • Solve the problem of log synchronization. • Before next Wednesday. • Haiyang & Dee. • Solve the problem of FOC discretization. • Before next Wednesday • Ying Luo & Haiyang • Write C code for FOC with parameters pre-specified. • Before next Wednesday • Haiyang & Ying Luo. • FOC flight test preparation. • Before next Thursday • Haiyang, Dee & Ying luo. • Write C code for any PI^alpha controller. • Before Feb. 4th. • Haiyang & Ying Luo. • FOC parameter online tuning. • Before Before Feb. 4th. • Haiyang & Ying Luo.