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.
• PIAlpha ( ) 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 2N-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 PIalpha 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
Case 2 Gain Margin

• Original

• K Original 80

36
Case 2 Gain Margin

• Original

• K Original 120

37
Experimental Validation of FOC on Small Fixed
UAVs
38
UAV Sys ID of 72 UAV

• Use time domain system identification using 10 hz
  data and data interpolation algorithm
• 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 domain system identification using 10 hz
  data and data interpolation algorithm
• Stmcb() x_min 544, x_max 578
• data_processing_gx2_pprz_plot_interpolation_200901
  15.m
• System model identified 0.8887/(s 0.7314)

40
Fractional Order PI Controller Design for UAV

• Identified Roll 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
  s0.1, 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
After adding a integrator, why not directly use
s-0.9 instead of using 1/ss0.1

• The comparisons of s-0.9 and 1/ss0.1

47
Some explorations

• Given Kp0.5503,Ki28.31, a-0.111
• The Plant1/(1/13.76s1)
• Vstep10

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 PIalpha controller.
• Before Feb. 4th.
• Haiyang Ying Luo.
• FOC parameter online tuning.
• Before Before Feb. 4th.
• Haiyang Ying Luo.

51
Reference

• 1 http//www.defenseindustrydaily.com/a-54b-uav-
  sector-from-20062016-02592/
• 2 http//www.aerosonde.com
• 3 http//www.u-dynamics.com
• 4 Ying Luos paper.