Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 99 (2015) 873 – 877
“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 a
The 11th Department of China Academy of Aerospace Aerodynamic, Beijing 100074, China The 2nd Department of China Academy of Aerospace Aerodynamic, Beijing 100074, China
b
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. © Published by Elsevier Ltd. This © 2015 2014The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA). 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)
* Corresponding author. Tel.: +86-13581559863 E-mail address:
[email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA)
doi:10.1016/j.proeng.2014.12.615
874
Su Haoqin et al. / Procedia Engineering 99 (2015) 873 – 877
(1) x f ( x, u) 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 ® ¯y
Ax Bu Cx
(2)
State vector x >v D Zz h - @ Input vector u >Gz P@ Output vector y >v D Zz h - @ 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, 'tmorphing denotes morphing time span, tmorphing_ time denotes morphing time, t tmorphing_ time denotes time span from morphing time to now. (4)(5) are the same as (3). L Llow L Llow high (t t morphing_ time ) 't morphing
S Ba
S low Ba low
S high S low
(t t morphing_ time )
't morphing
Ba high Ba low 't morphing
(t t morphing_ time )
L
Lhigh
S
S high
Ba
Ba high
Llow Lhigh 't morphing
(t t morphing_ time )
S low S high 't morphing
(t t morphing_ time )
Ba low Ba high 't morphing
(t t morphing_ time )
(3) (4) (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, 'Vmorphing denotes morphing speed span, Vmorphing_ time denotes morphing speed, V Vmorphing_ time denotes speed span from morphing time to now. (7) (8) (9)(10)(11) are the same as (6). Cxhigh Cxlow
Cx Cxlow
'Vmorphing Cy high Cy low
Cy
Cy low
Cz
Cz low
Mx
Mxlow
My
My low
Mz
Mzlow
'Vmorphing
Cz high Cz low 'Vmorphing
Cx Cxhigh
(V Vmorphing_ time )
Cy
Cy high
(V Vmorphing_ time )
Cz
Cz high
(V Vmorphing_ time )
Mx
Mxhigh
(V Vmorphing_ time )
My
My high
(V Vmorphing_ time )
Mz
Mz high
Mx high Mxlow 'Vmorphing My high Mylow 'Vmorphing Mz high Mzlow 'Vmorphing
Cxlow Cxhigh
(V Vmorphing_ time )
'Vmorphing Cy low Cy high 'Vmorphing
Cz low Cz high 'Vmorphing
(V Vmorphing_ time )
(6)
(V Vmorphing_ time )
(7)
(V Vmorphing_ time )
(8)
Mxlow Mxhigh 'Vmorphing Mylow My high 'Vmorphing Mzlow Mz high 'Vmorphing
(V Vmorphing_ time )
(9)
(V Vmorphing_ time )
(10)
(V Vmorphing_ time )
(11)
875
Su Haoqin et al. / Procedia Engineering 99 (2015) 873 – 877
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
Z z ǃpitch
angle - 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 K h _ dz , K- _ dz , KZz _ dz separately denote feedback gains about height, pitch and pitch rate. -c and hc denote pitch angle command and height command. So longitude control law is shows as the following formula. (12) Gz K- _ Gz >K h _ Gz hc h - @ KZz _ Gz Z z G z 0 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 Z z to elevator Gz denote in formula (13).
Zz Gz
- 0.8991 s (s 2 + 0.4473s + 0.06173) (13) (s + 0.02357s + 0.06867) (s 2 + 0.7143s + 1.285) Root locus method about Z z is showed in figure 2. Damp ratio of short period [ sp can be found increase with 2
Gz
inner loop gain
KZz _ dz
increasing. Due to target value of Damp ratio must satisfy 0.6 [ sp 1 , so feedback gain
KZ z _ dz
should be selected as 1.2, then damp ratio [Z _ dz of closed loop is 0.7, and satisfy the request of short period design. When K gain is found, Transfer function from pitch - to elevator Gz can be designed subsequently. Only z
Z z _ dz
own integral between pitch - and pitch rate
- can be got through the following way (14). Gz 1 (14)
Z z , so opened loop Gz
Zz Gz K Z
z
Z s
_ dz
Root locus method about - is showed in figure 3. Due to target value of Damp ratio must satisfy 0.6 [lp 1 so Gz feedback gain K- _ dz should be selected as 0.6, then damp ratio [Z z _ dz of closed loop is 0.7, and satisfy the request of long period design. The outer loop is from height to elevator Gz . According to experience, feedback gain K h _ dz can’t be larger, so K h _ dz can be selected as 0.1.
876
Su Haoqin et al. / Procedia Engineering 99 (2015) 873 – 877
Fig.2 Root locus design about Transfer function from pitch rate
Z z to elevator Gz
Fig.3 Root locus design about Transfer function from pitch - to elevator Gz
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 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.
877
Su Haoqin et al. / Procedia Engineering 99 (2015) 873 – 877 2
1.5
1.8
attack angle varied range(deg)
pitch angle varied range(deg)
1.6 1.4 1.2 1 0.8 0.6
1
0.5
0.4 0.2 0
5
10
15
20
morphing time(s)
Fig.5 compare pitch angle varied range at different morphing time
0
5
10
15
20
morphing time(s)
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.
