Available online at www.sciencedirect.com

ScienceDirectProcedia Engineering00 (2014) 000–000

www.elsevier.com/locate/procedia

“APISAT2014”, 2014 Asia-Pacific International Symposium on Aerospace Technology, APISAT2014

Morphing Process Research of UAV with PID Controller

Su Haoqina, Huang Zhanb, Bao Xiaoxianga,* , Shi Hongweia, Song Jinga

aThe 11th Department of China Academy of Aerospace Aerodynamic, Beijing 100074, ChinabThe 2nd Department of China Academy of Aerospace Aerodynamic, Beijing 100074, China

Abstract

Morphing UAV (Unmanned Aerial Vehicle) change its profile to adapt for wide flight condition, and attach lots of flight tasks, so PID controller is needed to satisfy the morphing requirement of UAV. Firstly this paper shows the expression of morphing aerodynamic process. Then, characteristic values of UAV are analyzed, and PID controller is brought out to satisfy stable capacity of UAV closed system. At last, simulation is run with traditional PID controller, and the best morphing time can be got from time sets.© 2014 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).

Keywords: morphing UAV; morphing aerodynamic process; PID controller; time sets

1. introduce

Morphing UAV is the new developmental direction of UAV. Morphing wing UAV shows a complex morphing process. This phenomenon has relation with general, aerodynamic, structure disciplines, so some efficient control methods must be researched to control morphing UAV quickly and stably, and some control policy should be adopted to analyze the time chosen problem for UAV[1~5].

2. Model building

Nonlinear model of morphing UAV can be expressed as formula (1)x=f ( x , u )

(1)

* * Corresponding author. Tel.: +86-13581559863E-mail address:yuhongyan09@163.com

1877-7058 © 2014 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).

2 Su Haoqin, Huang Zhan, Bao Xiaoxiang, Shi Hongwei, Song Jing / Procedia Engineering00 (2014) 000–000

f ( x ,u ) is the nonlinear relation with states and inputs. Linear system can be got near trim points. Considering linear model of morphing UAV wing, UAV state equation at trim point can be expressed as formula (2).

{x=Ax+Buy=Cx

(2)

State vector x=[ v α ωz h ϑ ]Input vector u=[δz P ]Output vector y= [v α ωz h ϑ ]

Due to morphing UAV possessing two dynamic coefficients, linear interpolation is needed. Two main parts include parameters with time and parameters with flight speed.

Aerodynamic parameters with time such as length of wing L, area of wing S, and mean aerodynamic chord Ba, mainly are relation with time, and should be interpolated according to time. Their formulas can be expressed as (3) (4) (5). In formula (3) for example, the left formula shows the L change of morphing process from low speed to high

speed, and the right formula shows the L change of morphing process from high speed to low speed, Llow denotes

length of wing under low speed condition, and Lhigh denotes length of wing under high speed condition, Δtmorphing

denotes morphing time span, tmorphingtime denotes morphing time, t−tmorphingtime denotes time span from morphing time to now. (4)(5) are the same as (3).

L=Llow+Lhigh−LlowΔtmorphing

( t− tmorphing time) L=Lhigh+Llow−LhighΔtmorphing

( t− tmorphing time)

(3)

S=S low+Shigh−S lowΔtmorphing

( t−tmorphing time) S=Shigh+S low−ShighΔtmorphing

( t−tmorphing time)

(4)

Ba=Balow+Bahigh−BalowΔtmorphing

( t−tmorphing time) Ba=Bahigh+Balow−BahighΔtmorphing

( t−tmorphingtime )

(5)Parameters with flight speed including aerodynamic and moment coefficients, such as drag coefficient Cx, lift

coefficient Cy, side force coefficient Cz, roll moment coefficient Mx, yaw moment coefficient My, and pitch moment coefficient Mz. Their formulas can be expressed as (6) (7) (8) (9)(10)(11), In formula (6) for example, the left formula shows the Cx change of morphing process from low speed to high speed, and the right formula shows

the Cx change of morphing process from high speed to low speed, Cxlow denotes length of wing under low speed

condition, and Cxhigh denotes length of wing under high speed condition, ΔV morphing denotes morphing speed span, Vmorphing time denotes morphing speed, V−V morphingtime denotes speed span from morphing time to now. (7) (8) (9)(10)(11) are the same as (6).

Cx=Cxlow+Cxhigh−CxlowΔV morphing

(V−Vmorphing time) Cx=Cxhigh+

Cxlow−CxhighΔV morphing

(V−V morphing time)

(6)

Cy=Cylow+Cyhigh−Cy lowΔVmorphing

(V−V morphingtime) Cy=Cyhigh+

Cy low−CyhighΔV morphing

(V−Vmorphing time)

(7)

Cz=Czlow+Czhigh−CzlowΔV morphing

(V−V morphing time) Cz=Czhigh+

Czlow−CzhighΔV morphing

(V−V morphing time)

(8)

Su Haoqin, Huang Zhan, Bao Xiaoxiang, Shi Hongwei, Song Jing / Procedia Engineering 00 (2014) 000–000 3

Mx=Mx low+Mxhigh−MxlowΔV morphing

(V−V morphingtime) Mx=Mx high+

Mxlow−MxhighΔVmorphing

(V−Vmorphing time)

(9)

My=Mylow+Myhigh−MylowΔVmorphing

(V−Vmorphing time) My=Myhigh+

Mylow−My highΔV morphing

(V−V morphingtime)

(10)

Mz=Mz low+Mzhigh−MzlowΔV morphing

(V−V morphingtime) Mz=Mzhigh+

Mzlow−MzhighΔVmorphing

(V−Vmorphing time)

(11)

3. PID controller design for morphing UAV

3.1. PID control law[6,7]

Within longitudinal control system, some flight signals can be got in control loop, such as pitch rate ωz 、pitch

angle ϑ and height h, etc. So attitude control is adopted as the inner loop, and height control is adopted as outer loop for the longitude plane.

Fig.1 PID controller construction of morphing wing UAV

PID controller construction of morphing wing UAV is showed in figure 1,and Khdz

,Kϑ dz,K ω¿ separately

denote feedback gains about height, pitch and pitch rate. ϑ cand hc denote pitch angle command and height command. So longitude control law is shows as the following formula.

δz=Kϑ δz⋅[Khδz

⋅(hc−h )−ϑ ]−Kωzδz⋅ωz+δ z0

(12)

3.2. PID control law design

PID control law is designed with root locus methods, and transfer functions are analyzed in root locus drawing, and deferent feedback gains can be got to be satisfied with capacity index. Two main loops should be designed, one is pitch angle inner loop design, another is height outer loop design. Before outer loop is designed, inner loop should be designed and inner control gains must be fixed.

Transfer function from pitch rate ωz to elevator δz denote in formula (13). ωz

δz=

-0 .8991 s (s2 + 0 .4473s + 0 . 06173)(s2 + 0 .02357s + 0 .06867 )( s2 + 0 .7143s + 1 . 285)

(13)

4 Su Haoqin, Huang Zhan, Bao Xiaoxiang, Shi Hongwei, Song Jing / Procedia Engineering00 (2014) 000–000

Root locus method about ωz

δz is showed in figure 2. Damp ratio of short period ξsp can be found increase with

inner loop gain Kω¿ increasing. Due to target value of Damp ratio must satisfy 0 .6<ξsp<1 , so feedback gain Kω¿

should be selected as 1.2, then damp ratio ξω¿ of closed loop is 0.7, and satisfy the request of short period design.

When Kω¿ gain is found, Transfer function from pitch ϑ to elevator δz can be designed subsequently. Only

own integral between pitch ϑ and pitch rate ωz , so opened loop ϑδz can be got through the following way (14).

ϑδz

=ωz

δz−Kω¿ω⋅1s (14)

Root locus method about ϑδz is showed in figure 3. Due to target value of Damp ratio must satisfy 0 .6<ξ lp<1 so

feedback gain Kϑ dz should be selected as 0.6, then damp ratio ξω¿ of closed loop is 0.7, and satisfy the request of long period design.

The outer loop is from height to elevatorδz . According to experience, feedback gain Khdz can’t be larger, so Khdz can be selected as 0.1.

Fig.2 Root locus design about Transfer function from pitch rate ωz to elevator δz

Fig.3 Root locus design about Transfer function from pitch ϑ to elevator δz

4. Simulation

Nonlinear simulation of the longitudinal model of morphing UAV run with PID controller, the initial condition include flight height 1000 m and flight speed 66 m/s. the following description is control strategy about morphing UAV.

Wing shrinking time happen within 50s and 200s, and thrust force keep 150N before 50s. At the time of 50s, thrust force increase to 300N linearly without control, and speed accelerate from 0.2Ma to 0.4Ma. At the time of

Su Haoqin, Huang Zhan, Bao Xiaoxiang, Shi Hongwei, Song Jing / Procedia Engineering 00 (2014) 000–000 5

100s, wing shrinking time use 10s.Wing extending time happen within 200s and 400s, and thrust force keep 300N before 200s. At the time of 250s, thrust force decrease to 150N linearly without control, and speed decelerate from 0.4Ma to 0.2Ma. At the time of 250s, wing extending time use 10s.

(a) (b) (c) (d)

Fig.4 different morphing time simulation (a)5s (b) 10s (c) 15s (d) 20s

Four different morphing time are simulated showed in figure 4, which respectively spend time sets including 5s,10s,15s and 20s, and pitch angle (blue line), trace line (red line) and attack angle(green line) are all showed in every figure. Figure 5 shows the comparison of pitch angle varied range and figure 6 shows the comparison of attack angle varied range. Observing figure 5 and 6, too long or too short morphing time are all leaded to larger oscillation of above flight parameters. Thus 10s wing morphing time is the best selection among these times.

5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

morphing time(s)

pitc

h an

gle

varie

d ra

nge(

deg)

5 10 15 200

0.5

1

1.5

morphing time(s)

atta

ck a

ngle

var

ied

rang

e(de

g)

Fig.5 compare pitch angle varied range at different morphing time Fig.6 compare attack angle varied range at different morphing time

5. Conclusion

This paper chose the trim point of UAV within cruise time, and linear model of morphing UAV is got near the trim point. PID controller is designed for morphing UAV, and four deferent wing morphing time are simulative to select the best morphing time, the result prove that wing morphing phase can be controlled better with PID, and proper morphing time should be selected through simulation.

References

[1] C.Barbu, R.Reginatto, A.R.teel, L.Zaccarian. anti-windup design for manual fli-ght control. proceedings of the American control conference, 1999:3186-3190

[2] C.Barbu, R.Reginatto, A.R.teel Luca, Zaccurian. Anti-windup for exponentially unstable linear systems with inputs limited in magnitude and rate. proceedings of the American control conference.2000, 1230-1234.

[3] Jha A K，Kudva J N． Morphing Aircraft Concepts，Classifications，and Challenges． Industrial and Commercial Applications of Smart Structures Technologies． Bellingham: SPIE，2004，213-224

[4] Rodriguez A R． Morphing aircraft technology survey． AIAA-2007-1258， 2007．[5] Seigler T M．Dynamics and control of morphing aircraft．Blacksburg: Virginia Polytechnic Institute and State University， 2005．[6] Pierre Apkarian，Richard J Adams．Advanced Gain-Scheduling Techniques for Uncertain Systems． IEEE Trans on Control Systems

Technology， 1998，1 ( 6) : 21-32[7] Chun-Hsiung Fang, Yung-Sheng Liu, Lin Hong, et al. A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control

systems[J]. IEEE Trans. on Fuzzy systems, 2006, 14(3): 386-397.

6 Su Haoqin, Huang Zhan, Bao Xiaoxiang, Shi Hongwei, Song Jing / Procedia Engineering00 (2014) 000–000