[15 17],,. [18 20], ESO, ESO,, ESO,,.,,,,.,, ;,,. 2 (Spacecraft attitude dynamics),, I, ω I b, T d, u, I ω I b + (ωb) I Iω I b = u + T d, (1)

Size: px

Start display at page:

Download "[15 17],,. [18 20], ESO, ESO,, ESO,,.,,,,.,, ;,,. 2 (Spacecraft attitude dynamics),, I, ω I b, T d, u, I ω I b + (ωb) I Iω I b = u + T d, (1)"

幻事屈
7 years ago
Views:

1 DOI: /CTA Control Theory & Applications Vol. 30 No. 12 Dec. 2013,,, (, ) :,. (ADRC) (TD) (ESO) (AFC)3.,. (ESO),. ESO,.,,.,.,. : ; ; ; ; : V : A Active disturbance rejection control of attitude for spacecraft WU Zhong, HUANG Li-ya, WEI Kong-ming, GUO Lei (School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing , China) Abstract: In order to attenuate the effects of the parameter variations and disturbances of the spacecrafts on attitude control accuracy and stability, an active disturbance rejection controller (ADRC) is designed. ADRC consists of three parts: tracking differentiator (TD), extended state observer (ESO) and attitude feedback controller (AFC). TD smoothes the process of attitude maneuver and provides differential signal of the attitude; ESO estimates the attitude and the disturbances acting on the spacecraft by taking full advantage of the information of the gyros and the attitude sensors; AFC realizes the attitude control of the spacecraft by compensating the disturbances from the ESO. Compared with the relative results, ESO has better performance by adopting the composite measurement information to correct the estimate, and ADRC has simpler structure by adopting only one loop to realize attitude control and disturbance compensation. Simulation results of a certain spacecraft demonstrate that the ADRC of this paper is feasible. Key words: spacecraft; attitude control; active disturbance rejection controller; attitude sensors; rate gyros 1 (Introduction),,.,,,,,., (active disturbance rejection controller, ADRC),,, [1 4],.,,, [5 10]. (tracking differentiator, TD) (extended state observer, ESO) (nonlinear state error feedback, NLSEF)3.,,,., [11] [12],. [13 14],.,,. : ; : [email protected]; Tel.: : ( 973 (2012CB720003); ( ).

2 [15 17],,. [18 20], ESO, ESO,, ESO,,.,,,,.,, ;,,. 2 (Spacecraft attitude dynamics),, I, ω I b, T d, u, I ω I b + (ωb) I Iω I b = u + T d, (1) 0 ω 3 ω 2 ω 1 : (ωb) I = ω 3 0 ω 1, ωb I = ω 2. ω 2 ω 1 0 ω 3 (single gimbal control moment gyroscopes, SGCMG), SGCMG h, ḣ + (ωb) I h = u. (2) (modified Rodrigues parameters, MRP), p, ω o b, ṗ = G (p) ω o b, (3) : G(p) = 1 2 {E + p + pp T [ 1 2 (1 + pt p)]e}, E. 3 (ESO design) 3.1 (ESO based on attitude sensors and rate gyros) x 1 = p, x 2 = ṗ, (1) (2), {ẋ1 = x 2, (4) ẋ 2 = f (x 1, x 2 ) + Bτ, : f(x 1, x 2 ) = 4 (1 + p T p) 2 GT (ω I b C b o ω I o) + GI 1 [ (ω I b) (Iω I b + h) + T d ] G(C b o ω I o + Ċb o ω I o), ; B = G(p)I 1, ωo I, τ = ḣ SGCMG. x 3 = f(x 1, x 2 ), ẋ 3 = a(t), (4) ẋ 1 = x 2, ẋ 2 = x 3 + Bτ, (5) ẋ 3 = a.,., y p, y p = p + n p, (6) n p. y ω, n ω. y ω = ω I b + n ω, (7) ω I b = ω o b + C b o ω I o. (8) (2),, ṗ : ṗ = G(y p )(y ω C b o ω I o), (9) C b o., (5), (6) (7). x 1 z 1, x 2 z 2, x 3 z 3, e=α(y p z 1 )+β[g(y p )(y ω C b o ω I o) z 2 ], (10) : ż 1 = z 2 + K 1 e, ż 2 = z 3 + K 2 e + Bτ, ż 3 = K 3 e, (11) : K 1, K 2 K 3, α, β (ESO analysis),, e 1 = x 1 z 1, e 2 = x 2 z 2, e 3 = x 3 z 3, e e = αe 1 + βe 2. (12)

3 12 : 1619 (5)(11) (12), : ė 1 K 1 α 1 K 1 β 0 e 1 0 ė 2 = K 2 α K 2 β 1 e (13) ė 3 K 3 α K 3 β 0 e 3 a 3,., K 1, K 2 K 3,,. : K 1 = diag{k 11, K 12, K 13 }, K 2 = diag{k 21, K 22, K 23 }, K 3 = diag{k 31, K 32, K 33 }, e 1 = [e 11 e 12 e 13 ] T, e 2 = [e 21 e 22 e 23 ] T, e 3 = [e 31 e 32 e 33 ] T, a = [a 1 a 2 a 3 ] T, (13) : ė 11 = K 11 αe 11 + (1 K 11 β)e 21, ė 12 = K 12 αe 12 + (1 K 12 β)e 22, ė 13 = K 13 αe 13 + (1 K 13 β)e 23, ė 21 = K 21 αe 11 K 21 βe 21 + e 31, ė 22 = K 22 αe 12 K 22 βe 22 + e 32, ė 23 = K 23 αe 13 K 23 βe 23 + e 33, ė 31 = K 31 αe 11 K 31 βe 21 + a 1, ė 32 = K 32 αe 12 K 32 βe 22 + a 2, ė 33 = K 33 αe 13 K 33 βe 23 + a 3. (14) (14), 3, 2. (14), 2 ė 12 K 12 α 1 K 12 β 0 ė 22 = K 22 α K 22 β 1 ė 32 K 32 α K 32 β 0 e 12 e 22 e 32 (15), s 3 + (K 12 α + K 22 β) s a 2. (15) (K 22 α + K 32 β) s + K 32 α = 0. (16), α, β, K 12, K 22 K 32 0, (K 12 α + K 22 β)(k 22 α + K 32 β) > K 32 α,,., a 2,, [13 14].,. 3.3 (ESO parameter tuning) 3.2,. 2, λ 1, λ 2, λ 3, (s + λ 1 )(s + λ 2 )(s + λ 3 ) = 0. (17), (16), : λ 1 + λ 2 + λ 3 = K 12 α + K 22 β, λ 1 λ 2 + λ 1 λ 3 + λ 2 λ 3 = K 22 α + K 32 β, (18) λ 1 λ 2 λ 3 = K 32 α.,., α, β, 3 3 K 12, K 22 K 32. α = 1, β = 0, (11), ; α=1, β =1, (11),, ; 0 < α < 1, 0 < β < 1, (11),,,.,,. 4 (ADRC design) 3,,., (TD) (attitude feedback controller, AFC),, 1. 1 Fig. 1 Schematics of ADRC for spacecraft attitude

4 , TD, SGCMG. AFC ESO, TD ESO. 4.1 (TD design) p d, SGCMG,., TD,,., TD, : { v 1 = v 2, v 2 = 2rv 2 r 2 (19) (v 1 p d ), : r TD ; v 2, p d,, SGCMG. 4.2 (AFC design), { τ 0 = k 1 (v 1 z 1 ) + k 2 (v 2 z 2 ), τ = B 1 (20) (τ 0 z 3 ), k 1 k 2. 5 (Simulation and analysis), MATLAB/Simulink., 4 SGCMG. n = rad/s, I = kg m SGCMG, σ 0 = [ ] T, SGCMG 300Nms, sin(nt) sin(2nt) T d = sin(nt) sin(2nt) N m sin(nt) sin(2nt), ω(t 0 ) = [0 0 0] T ( )/s, [φ 0 θ 0 ψ 0 ] T = [0 0 0 ] T. ω d = [0 0 0] T ( )/s, [φ d θ d ψ d ] T = [0 0 0 ] T. ESO K 1 =diag{20, 20, 20}, K 2 =diag{100, 100, 100}, K 3 = diag{800, 800, 800}. k 1 =0.3, k 2 =10. TD r = ) ESO. ESO, ESO. ESO, (11) α=1, β =0. ESO, (11) α =1, β =0.5., ESO , ESO., ESO,. 2 ESO Fig. 2 Attitude of ESO based on attitude sensors 3 ESO Fig. 3 Attitude rate of ESO based on attitude sensors 4 ESO Fig. 4 Attitude of ESO based on composite measurement information

5 12 : ESO Fig. 5 Attitude velocity of ESO based on composite measurement information 2)., ESO, ,,,,. 8 SGCMG,. 9 SGCMG, 0.02 rad/s,. 11 SGCMG, SGCMG,.,,,,,. 8 Fig. 8 Desired control torque 9 SGCMG Fig. 9 SGCMG gimbal rates 10 SGCMG Fig. 10 SGCMG gimbal angle 6 Fig. 6 Attitude angle of spacecraft 11 SGCMG Fig. 11 SGCMG singularity measure 7 Fig. 7 Attitude angular velocity of spacecraft 6 (Conclusion),

6 ,,,.,,,. (References): [1]. [J]., 1998, 13(1): (HAN Jingqing. Auto-disturbance-rejection controller and its applications [J]. Control and Decison, 1998, 13(1): ) [2]. [J]., 1989, 9(4): (HAN Jingqing. Control theory, Is it a model analysis approach or a direct control approach [J]. Journal of System Science & Mathematical Science, 1989, 9(4): ) [3],. [J]., 2002, 19(4): (HUANG Yi, ZHANG Wenge. Development of active disturbance rejection controller [J]. Control Theory & Applications, 2002, 19(4): ) [4] HAN J Q. From PID to active disturbance rejection control [J]. IEEE Transactions on Industrial Electronics, 2009, 56(3): [5] LU K F, XIA Y Q, YANG D. Controller design for rigid spacecraft attitude tracking with actuator saturation [J]. Information Sciences, 2013, 220: [6] LI S H, YANG X, YANG D. Active disturbance rejection control for high pointing accuracy and rotation speed [J]. Automatica, 2009, 45(8): [7] ZHU Z, XU D, LIU J M, et al. Missile guidance law based on extended state observer [J]. IEEE Transactions on Industrial Electronics, 2013, 60(12): [8] XIA Y Q, DAI L, FU M Y, et al. Application of active disturbance rejection control in tank gun control system [J]. Journal of The Franklin Institute, 2013, 02, 003. [9] HILLIS A J. Active motion control of fixed offshore platform using an extended state observer [J]. Proceedings of the Institution of Mechanical Engineers, 2010, 224(1): [10] LI H X, LI S H. Speed control for PMSM servo system using predictive functional control and extended state observer [J]. IEEE Transactions on Industrial Electronics, 2012, 59(2): [11] GUO B Z, ZHAO Z L. On convergence of non-linear extended state observer for multi-input multi-output system with uncertainty [J]. IET Control Theory and Applications, 2012, 6(15): [12] GUO B Z, ZHAO Z L. On the convergence of an extended state observer for nonlinear system with uncertainty [J]. Systems & Control Letters, 2011, 60(6): [13] ZHENG Q, LINDA Q, GAO Z Q. On validation of extended state observer through analysis and experimentation [J]. Journal of Dynamic Systems, Measurement and Control, 2012, 134(2), 6. [14] YOO D, YAU S T, GAO Z Q. Optimal fast tracking observer bandwidth of the linear extended state observer [J]. International Journal of Control, 2007, 80(1): [15],. [J]., 2010, 18(4): (LEI Zhongmou, L.. U Zhenduo. Nonlinear auto-disturbance rejection control for spacecraft attitude control system [J]. Aerospace Control, 2010, 18(4): ) [16],,. [J]., 2005, 22(1): (ZHU Chengyuan, YANG Di, ZHAI Kun. Active disturbance attitude controller for large flexible multi-body satellite without gyroscopes [J]. Computer Simulation, 2005, 22(1): ) [17],,. [J]., 2007, 29(12): (ZHOU Lini, TANG Guojin, LI Haiyang. Active disturbance rejection controller design for spacecraft attitude maneuver [J]. System Engineering and Electronics, 2007, 29(12): ) [18],,. [J]., 2004, 22(6): (ZHU Chengyuan, YANG Di, Yang Xu. Design of the active disturbance rejection attitude control system for large flexible multi-body satellite [J]. Aerospace Control, 2004, 22(6): ) [19],,. [J]., 2007, 28(4): (LI Shunli, LI Litao, YANG Xu. Active disturbance rejection control for flexible multi-body satellite system [J]. Journal of Astronautics, 2007, 28(4): ) [20],,. [J]., 2012, 29(3): (LAI Aifang, GUO Yu, ZHENG Lijun. Active disturbance rejection control for spacecraft attitude maneuver and stability [J]. Control Theory & Applications, 2012, 29(3): ) : (1970 ),,,,, [email protected]; (1991 ),,,, [email protected]; (1982 ),,,,, weikongming@aspe. buaa.edu.cn; (1966 ),,,,, [email protected].

(L d L q ). i d = 0,, [8].,,,,, / (maximum torque per ampere, MTPA) [9],. MTPA [9] [10],,,. MTPA, MTPA.,,,. MTPA,,,.,. 2 (Model of PMSM) d-q, :

(L d L q ). i d = 0,, [8].,,,,, / (maximum torque per ampere, MTPA) [9],. MTPA [9] [10],,,. MTPA, MTPA.,,,. MTPA,,,.,. 2 (Model of PMSM) d-q, : 32 2 2015 2 DOI: 10.7641/CTA.2015.40361 Control Theory & Applications Vol. 32 No. 2 Feb. 2015 /,,, (, 266071) : (PMSM), / (MTPA). MTPA,.., MTPA.. : ; ; ; / : TP273 : A Adaptive sliding mode maximum torque