Compound Control Method of ADRC and FNTSM for Airborne Object Tracking System

doi:10.12382/bgxb.2022.0890

Abstract

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

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.

Figures/Tables 26

Fig.1 Airborne optoelectronic tracking system

Fig.2 Two-axis four-gimbal platform structure

Fig.3 Transformation from coordinate system v to A

Fig.4 Transformation from coordinate system A to E

Fig.5 Transformation from coordinate system E to a

Fig.6 Transformation from coordinate system a to e

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

Fig.8 Diagram of inner gimbal control system

Fig.9 Equivalent model of DC torque motor

Fig.10 Mathematical model of inner gimbal control system

Fig.11 Time-delay system model with miss distance

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

Fig.13 Simulation model of FCADRNTSM

Fig.14 Tracking simulation of step response

Fig.15 Tracking error curve of step response

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

Fig.16 Tracking simulation with sinusoidal input

Fig.17 Tracking error curve with sinusoidal input

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

Fig.18 Controller input u of compound control method

Fig.19 Controller input u of sliding mode control

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

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

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

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

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

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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