机载光电跟踪系统的自抗扰与快速非奇异终端滑模组合控制方法

doi:10.12382/bgxb.2022.0890

摘要/Abstract

摘要：

机载目标跟踪系统由于受到外部干扰、内部参数摄动和未建模动态等扰动的影响,使跟踪控制分系统设计面临巨大的挑战。以两轴四框架的光电稳定平台为对象研究抗扰动控制方法,针对自抗扰控制的扰动补偿一般留有扰动残差和滑模控制会引入较大抖振的问题,设计一种自抗扰与快速非奇异终端滑模组合控制的方法。利用线性扩张状态观测器来估计总扰动量并在控制端进行补偿,从而允许设计滑模控制的控制率时采用较小的滑模切换增益,并通过设计快速非奇异终端滑模面得到控制率,加快系统收敛的同时避免非奇异现象。数值仿真结果表明,该组合控制方法在外部扰动和模型不确定性的影响下,可以实现快速收敛与高跟踪精度的同时引入较小的抖振,并且实现了机载目标跟踪系统需求的快速响应性能,验证了这个组合控制方法的有效性。

关键词: 两轴四框架, 光电跟踪系统, 自抗扰控制, 滑模控制, 组合控制

Abstract:

Due to the influence of external disturbances, internal parameter perturbations and unmodeled dynamics, the design of the tracking control subsystem of the airborne object tracking system is faced with great challenges. A disturbance rejection control method is studied based on the optoelectronic stabilized two-axis four-gimbal platform. To solve the problems that the disturbance compensation of active disturbance rejection control (ADRC) is generally accompanied by disturbance residuals and that sliding mode control will introduce large chattering, a compound control method of ADRC and fast non-singular terminal sliding mode (FNTSM) control is designed. The linear extended state observer is employed to estimate the total disturbance and compensate it, thus allowing a smaller switching gain for the sliding mode when designing the control rate of sliding mode control, and fast non-singular terminal sliding surface is designed to obtain the control rate, which accelerates system convergence and avoids non-singular phenomena. The simulation results show that the proposed method can achieve high stability accuracy and introduce small chattering despite the influence of external disturbances and model uncertainties, which verifies the effectiveness of the compound control method.

Key words: two-axis four-gimbal structure, optoelectronic tracking system, active disturbance rejection control, sliding mode control, compound control

高雨轩, 侯远龙, 高强, 侯润民. 机载光电跟踪系统的自抗扰与快速非奇异终端滑模组合控制方法[J]. 兵工学报, 2023, 44(4): 1071-1085.

GAO Yuxuan, HOU Yuanlong, GAO Qiang, HOU Runmin. Compound Control Method of ADRC and FNTSM for Airborne Object Tracking System[J]. Acta Armamentarii, 2023, 44(4): 1071-1085.

图/表 26

图1 机载光电跟踪系统

Fig.1 Airborne optoelectronic tracking system

图2 两轴四框架的平台结构

Fig.2 Two-axis four-gimbal platform structure

图3 载体坐标系v到外方位坐标系A的变换

Fig.3 Transformation from coordinate system v to A

图4 外方位坐标系A到外俯仰坐标系E的变换

Fig.4 Transformation from coordinate system A to E

图5 外方位坐标系E到内方位坐标系a的变换

Fig.5 Transformation from coordinate system E to a

图6 内方位坐标系a到内俯仰坐标系e的变换

Fig.6 Transformation from coordinate system a to e

图7 内外框架控制系统结构框图

Fig.7 Diagram of control system of inner and outer gimbals

图8 内框架控制系统的结构框图

Fig.8 Diagram of inner gimbal control system

图9 直流力矩电机等效模型

Fig.9 Equivalent model of DC torque motor

图10 内框架控制系统数学模型

Fig.10 Mathematical model of inner gimbal control system

图11 带有脱靶量滞后的系统模型

Fig.11 Time-delay system model with miss distance

图12 基于自抗扰与滑模的组合控制器结构图

Fig.12 Structure of compound controller based on ADRC and sliding mode control

图13 FCADRNTSM的仿真实验模型

Fig.13 Simulation model of FCADRNTSM

图14 阶跃响应的跟踪仿真

Fig.14 Tracking simulation of step response

图15 阶跃响应的跟踪误差曲线

Fig.15 Tracking error curve of step response

表1 阶跃响应仿真结果

Table 1 Simulation results of step response

控制器	到达时间/s	最大误差/rad	RMSE/rad
FCADRNTSM	0.305	0.025	0.0053
LADRC	0.728	0.026	0.0061
SMC	1.028	0.017	0.0040

图16 正弦输入的跟踪仿真

Fig.16 Tracking simulation with sinusoidal input

图17 正弦输入的跟踪误差曲线

Fig.17 Tracking error curve with sinusoidal input

表2 正弦仿真结果

Table 2 Simulation results with sinusoidal input

控制器	到达时间/s	最大误差/rad	RMSE/rad
FCADRNTSM	0.168	0.026	0.0049
LADRC	5.165	0.115	0.0741
SMC	0.961	0.016	0.0021

图18 组合控制方法的控制量u

Fig.18 Controller input u of compound control method

图19 滑模控制的控制量u

Fig.19 Controller input u of sliding mode control

图20 输入信号为5sin 2 π 20 t的跟踪误差比较

Fig.20 Comparison of tracking error curves with input signal 5sin 2 π 20 tt

图21 输入信号为5sin 2 π 10 t的跟踪误差比较

Fig.21 Comparison of tracking error curves with input signal 5sin 2 π 10 t

图22 输入信号为5sin 2 π 2 t的跟踪误差比较

Fig.22 Comparison of tracking error curves with input signal 5sin 2 π 2 t

图23 输入信号为5sin 2 π 1 t的跟踪误差比较

Fig.23 Comparison of tracking error curves with input signal 5sin 2 π 1 t

表3 不同输入信号下的跟踪误差比较

Table 3 Comparison of tracking errors with different input signals

输入信号	到达时间/s		最大误差/rad		RMSE/rad
输入信号	FCADRNTSM 方法	DOB+AETVSMC 方法	FCADRNTSM 方法	DOB+AETVSMC 方法	FCADRNTSM 方法	DOB+AETVSMC 方法
5sin $2 π 20 t$	0.088	0.927	0.026	0.028	0.0047	0.0042
5sin $2 π 10 t$	0.087	0.942	0.026	0.029	0.0049	0.0043
5sin $2 π 2 t$	0.342	0.978	0.027	0.028	0.0053	0.0048
5sin $2 π 1 t$	0.339	1.017	0.026	0.027	0.0054	0.0053

表3 不同输入信号下的跟踪误差比较

Table 3 Comparison of tracking errors with different input signals

输入信号	到达时间/s		最大误差/rad		RMSE/rad
输入信号	FCADRNTSM 方法	DOB+AETVSMC 方法	FCADRNTSM 方法	DOB+AETVSMC 方法	FCADRNTSM 方法	DOB+AETVSMC 方法
5sin $2 π 20 t$	0.088	0.927	0.026	0.028	0.0047	0.0042
5sin $2 π 10 t$	0.087	0.942	0.026	0.029	0.0049	0.0043
5sin $2 π 2 t$	0.342	0.978	0.027	0.028	0.0053	0.0048
5sin $2 π 1 t$	0.339	1.017	0.026	0.027	0.0054	0.0053

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