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EHA反馈线性化最优滑模面双模糊滑模控制

1. 海军航空工程学院兵器科学与技术系, 烟台 264001;
2. 空军勤务学院 航空弹药系, 徐州 221000

Double fuzzy sliding mode control for EHA based on feedback linearization optimal sliding surface
ZHANG Zhen1 , LI Haijun1 , ZHU Defang2
1. Department of Ordnance Science and Technology, Naval Aeronautical and Astronautical University, Yantai 264001, China ;
2. Department of Aerial Ammunition, Air Force Logistics College, Xuzhou 221000, China
Received: 2015-07-07; Accepted: 2015-09-11; Published online: 2015-10-14 16:22
Corresponding author. Tel.: 13081617309E-mail: li_haijun@sohu.com
Abstract: In order to improve the control performance for electro-hydrostatic actuator(EHA), double fuzzy sliding mode control based on feedback linearization optimal sliding surface was proposed. The nonlinear model of EHA was linearized based on the feedback linearization by establishing linear switching function and adopting optimal control theory. Fuzzy control was introduced into sliding mode control to reduce the chattering, and a fuzzy controller was adopted to estimate the switching control gain based on the characteristics of optimal sliding mode switching function; another fuzzy controller was adopted to adjust the corrective controller based on the principle of the sliding mode control. The simulation results show that the proposed control scheme is effective.
Key words: electro-hydrostatic actuator (EHA)     feedback linearization     sliding mode control     optimal control     fuzzy control

1 EHA非线性建模 1.1 系统描述

EHA系统组成原理如图 1所示，该系统执行元件为对称双作用液压缸，液压泵为双向定排量泵，动力源为永磁同步电机。EHA控制器通过比较指令位移与实际位移的大小，来改变电机的转速和转向，从而达到控制作动器位移的目的。

 图 1 EHA系统组成原理 Fig. 1 Composition principle of EHA system
1.2 系统的非线性模型

1.2.1 永磁同步电机模型

 (1)

 (2)

 (3)

1.2.2 泵控缸模型

 (4)

 (5)

 (6)

 (7)

1.3 系统的非线性模型状态空间描述

q轴定子电压uq作为模型输入量。此时令u=uqx1=iqx2=wrmx3=P1P2x4=xtx5=dxt/dt，通过式(1)～式(7)，可得EHA非线性模型状态空间描述为

 (8)

2 非线性模型反馈线性化

EHA非线性模型状态空间描述形式所对应的仿射非线性系统的标准形式为

 (9)

 (10)

2.1 反馈线性化条件

2.2 反馈线性化求解

 (11)

 (12)
 (13)

 (14)
3 模糊滑模控制器设计 3.1 最优滑模面的滑模控制

3.1.1 滑模面函数及其参数确定

EHA的控制目标是使作动器状态向量z跟踪期望状态向量zr，因此定义跟踪误差向量为

 (15)

 (16)

 (17)

 (18)

 (19)

 (20)

 (21)

 (22)

H=Q22-1Q21e1′+e2′，则式(22)可表示为

 (23)

 (24)

 (25)

 (26)

 (27)

3.1.2 滑模控制器设计

 (28)

 (29)

 (30)

 (31)

 (32)

 (33)

3.2 模糊控制器设计

3.2.1 切换控制增益的模糊控制

 (34)

1)当r≤－γ时，系统满足指定滑模发生条件，无需改变K的大小，即ΔK=0。

2)当－γ < r < 0时，系统满足滑模发生条件，但不满足指定滑模发生条件，需要K有较小的改变。ΔK的正负与LdLf4h(x)和s有关，不失一般性，设LdLf4h(x)>0，此时系统已趋向滑模面，则s>0时，应有ΔK>0，以使向－∞移动，从而r趋向于更小；则s < 0时，应有ΔK < 0，以使向+∞移动，从而r趋向于更小。

3)当r=0时，系统不满足滑模发生条件，需要K有较大的改变。ΔK的正负分析同上。

4)当r>0时，系统不满足滑模发生条件，且远离滑模面运动，需要K有很大的改变。ΔK的正负分析同上。

r={NB, NM, NS, ZO, P}

ΔK={ZO, VS, S, M, B}

1)规则1。若r为NB，则|ΔK|为ZO。

2)规则2。若r为NM，则|ΔK|为VS。

3)规则3。若r为NS，则|ΔK|为S。

4)规则4。若r为ZO，则|ΔK|为M。

5)规则5。若r为P，则|ΔK|为B。

 (35)

 (36)

 (37)

3.2.2 切换项的模糊控制

s={N, ZO, P}

μ={N, ZO, P}

1)规则1。若s为N，则μ为P。

2)规则2。若s为ZO，则μ为ZO。

3)规则3。若s为P，则μ为P。

 (38)

4 仿真验证

EHA理想跟踪轨迹设置为yd=sin(2πt)，初始位置设置为0.8，外界干扰主要考虑外负载力，其采用高斯函数表示为FL=aexp[－(tc)2/2b2]，a决定负载力大小，b表示负载力作用时间范围，c表示负载力的中心，a=10 kN，b=0.5，c=1.5。同时由于作动器工作频宽为0～3 Hz，故本文所设计控制器对跟踪轨迹为yd=sin(4πt)和yd=sin(6πt)信号进行了仿真。

 图 2 反馈线性化控制仿真结果 Fig. 2 Simulation results of feedback linearization control
 图 3 反馈线性化滑模控制仿真结果 Fig. 3 Simulation results of sliding mode control based on feedback linearization
 图 4 反馈线性化模糊滑模控制仿真结果 Fig. 4 Simulation results of fuzzy sliding mode control based on feedback linearization
 图 5 反馈线性化最优滑模面双模糊滑模控制仿真结果 Fig. 5 Simulation results of double fuzzy sliding mode control with optimal sliding surface based on feedback linearization
 图 6 4种控制方法跟踪误差的对比 Fig. 6 Tracking errors of four control schemes
 图 7 不同频率跟踪信号下的跟踪误差的对比 Fig. 7 Tracking errors under different frequency tracking signals

5 结论

1)本文所提控制算法与反馈线性化控制相比具有较好鲁棒性，与传统的滑模和模糊滑模控制相比进一步削弱了抖振且提高了响应速度。

2)在EHA工作频宽范围内，可以满足其控制精度要求。

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#### 文章信息

ZHANG Zhen, LI Haijun, ZHU Defang
EHA反馈线性化最优滑模面双模糊滑模控制
Double fuzzy sliding mode control for EHA based on feedback linearization optimal sliding surface

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(7): 1398-1405
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0454