Su Haoqin, Huang Zhan, Bao Xiaoxiang, Shi Hongwei, Song Jing/ Procedia Engineering 00 (2014) 000–000 1
“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, China
bThe 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
- introduce
Morphing UAV is the new developmental direction of UAV. Morphing wing UAV shows a complex morphing process. This phenomenonhas 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].
- Model building
Nonlinear model of morphing UAV can be expressed as formula (1)
(1)
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).
(2)
State vector
Input vector
Output vector
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, denotes length of wing under low speed condition, and denotes length of wing under high speed condition, denotes morphing time span,denotes morphing time,denotes time span from morphing time to now. (4)(5) are the same as (3).
(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, denotes length of wing under low speed condition, and denotes length of wing under high speed condition, denotes morphing speed span, denotes morphing speed, denotes speed span from morphing time to now. (7) (8) (9)(10)(11) are the same as (6).
(6)
(7)
(8)
(9)
(10)
(11)
- PID controller design for morphing UAV
- PID control law[6,7]
Within longitudinal control system, some flight signals can be got in control loop, such as pitch rate 、pitch angleand heighth, 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,andseparately denote feedback gains about height,pitch and pitch rate. and denote pitch angle command and height command. So longitude control law is shows as the following formula.
(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 to elevatordenote in formula (13).
(13)
Root locus method about is showed in figure 2. Damp ratio of short period can be found increase with inner loop gain increasing. Due to target value of Damp ratio must satisfy, so feedback gainshould be selected as 1.2, then damp ratio of closed loop is 0.7, and satisfy the request of short period design.
Whengain is found, Transfer function from pitchto elevator can be designed subsequently. Only own integral between pitchand pitch rate , so opened loopcan be got through the following way (14).
(14)
Root locus method about is showed in figure 3. Due to target value of Damp ratio must satisfy so feedback gain should be selected as 0.6, then damp ratioof closed loop is 0.7, and satisfy the request of long period design.
The outer loop is from height to elevator. According to experience, feedback gain can’t be larger, socan be selected as 0.1.
Fig.2 Root locus design about Transfer function from pitch rate to elevator
Fig.3 Root locus design about Transfer functionfrom pitch to elevator
- 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 strategyabout 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.
Fig.5 compare pitch angle varied range at different morphing time Fig.6 compare attack angle varied range at different morphing time
- 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.
* Corresponding author. Tel.: +86-13581559863
E-mail address: