Conversion Control for Remote Sensing Stable Platforms for Transient and Continuous Disturbances

An airborne electro-optical stabilized platform is a device situated between the aircraft and the imaging components, which serves to isolate external disturbances and maintain imaging axis stability for the imaging components. In light of the impact of transient and continuous attitude changes of the aircraft on the axis-stabilized imaging in visible light unmanned aerial vehicle (UAV) remote sensing missions, a control method combining a proportional-integral (PI) controller and a backpropagation neural network (BPNN) PID conversion control was devised. The specific procedure involved the following steps: firstly, the transfer mechanism of external disturbances between platforms was derived using the state transition matrix through mechanistic modelling. Secondly, the multi-rigid body dynamics equations of the airborne electro-optical platform were established based on Newton’s laws of motion and Euler’s laws. Subsequently, the relationship between the stable platform rotation angle and external disturbances was obtained using Laplace transformation, and an analysis was conducted on the effects of different disturbances on the stable platform. Lastly, conversion control was incorporated into the system model for simulation analysis. The simulation results demonstrated that transient disturbances could be effectively and rapidly isolated by the PI controller, while continuous disturbances exhibited improved performance when handled by the neural network PID controller, thus validating the efficacy of the designed conversion control method.


Introduction
UAV remote sensing is widely used for acquiring ground information using UAV platforms equipped with remote sensing sensors.It is employed in various fields such as geological exploration, agricultural monitoring, and disaster response [1] .High-quality images are crucial for visible light UAV remote sensing, requiring a stable platform with visible light sensors to isolate external disturbances and maintain optical axis stability.However, transient [2] and continuous attitude disturbances [3] during UAV missions can degrade image quality.To address this, research focuses on rapidly isolating disturbances and ensuring optical axis stability.
Researchers discuss control approaches for stabilizing the platform and improving image quality [4]- [9]   .However, limitations exist in analyzing disturbance coupling, designing precise controllers, and separating disturbances accurately.In this paper, we propose a composite control approach that combines proportional-integral (PI) control and backpropagation neural network (BPNN) PID conversion control.The PI control rapidly counteracts transient disturbances, while the BPNN PID control ensures stability against continuous disturbances by approximating nonlinear models.
Our contributions include analysing disturbance coupling, establishing dynamic equations, and designing the PI controller and BPNN PID conversion controller.The paper is organized into chapters focusing on the platform model, controller design, performance verification, and conclusions.

Coordinate System Definition
Tang [10]  OX Y Z )) for the two-axis two-frame stable platform.These systems represent the geometric constraints and transformations among the components.Figure 1 depicts the spatial coordinate system diagram, with origins and rotation centre labelled as 0, and torque motors of the azimuth frame and pitch frame denoted as 0 G and 1 G .

Kinematic Analysis of Inner and Outer Frames
Using matrix notation, the transformation matrix from the body coordinate system to the outer frame coordinate system is denoted as the matrix o b C , and the rotation transformation matrix from the outer frame coordinate system to the inner frame coordinate system is denoted as the matrix I o C .The angular velocities of the body along its three axes are represented by the matrix > @ T b t p q r Z , and the angular velocities of the outer frame coordinate system are represented by the matrix . Based on the relationship between attitudes, the expression is as follows.
Defining the angular velocity of the inner frame as the matrix > @ , the angular velocity of the inner frame can be obtained using the following expression: The angular velocity of the inner frame corresponds to the electro-optical device's angular velocity, which is mounted on the inner frame.Any angular velocity generated by the electro-optical device can result in deviations or jitter in the imaging axis, ultimately affecting the quality of the captured images.

Dynamic Models of Inner and Outer Frames
Based on the Newton-Euler equations in multi-body dynamics, the dynamic model of the inner frame can be expressed as follows: where I M is the resultant moment vector, I J is the inertia matrix, and I Z is the angular velocity vector of the inner frame.
In the X-axis direction, the pitch frame has rotational freedom.The external torque acting on the inner frame comprises the motor driving torque, wire interference torque, and friction torque.The motor driving torque is denoted as dI M , while the interference and friction torque are considered disturbances within the mechanical structure, denoted as rI M .Thus, the dynamic equation for the inner frame can be expressed as follows.
Since the inner frame is mounted on the outer frame and moves together with it, the effect of the inner frame on the outer frame can be treated as a reaction moment exerted by the inner frame on the outer frame.The equation of the outer frame is expressed as follows: The external forces acting on the outer frame are also similar to those on the inner frame, which dO M represents the motor torque and rO M represents the disturbance torque.The dynamic equation of the outer frame is as follows: The motor current loop model is defined as follows: In the equation, a u represents the motor's input voltage adjustment; a L denotes the motor's armature inductance; a R represents the motor's armature resistance; T k is the motor's torque coefficient; e k is the motor's back electromotive force coefficient, and Z denotes the motor's rotational angular velocity, which can be either the angular velocity of the inner frame or the outer frame.
Neglecting the motor's current time constant, the framework model is transformed using the Laplace transform.This establishes the relationship between the framework's rotational angles and external disturbances for the two-axis stabilization platform: cos sin The equal sign in the equation represents the relationship between the control input, unknown disturbances, and the coupling between the carrier and the framework.

Composite Transformation Controller Design
During UAV remote sensing tasks, flight attitude can be affected by continuous or transient gusts, resulting in deviations in the LOS and degradation of image quality.To address these disturbances, a composite transformation control approach is implemented.The stable platform initially utilizes PI control but switches to BPNN PID control when disturbances persist.

PI Controller
Proportional-Integral (PI) controller is designed with control gains for both the inner and outer frames: where p k and i k represent the proportional and integral coefficients of the outer frame controller, respectively.The Outer Frame Angular Error is the difference between the desired angle and the realtime angle of the outer frame.
In both cases 0 Q and 0 Z represent the desired angle and desired angular velocity, respectively, while p Q and p Z represent the real-time angle and angular velocity of the respective frame.

Simulation Validation
A simulation module was built in the MATLAB/Simulink environment using the equation.The model employed identical DC torque motors for both the inner and outer frames, with actual parameters incorporated into the simulation. .

Open-Loop Characteristics Analysis
The electro-optical platform mounted on a UAV was subjected to a step disturbance of 0.01 radians at different positions.Various scenarios were designed to examine the effects of open-loop disturbance on line-of-sight azimuth and elevation.The scenario settings are presented in Table 1. Figure 3(a) shows that when a disturbance is added, the pitch angular velocity disturbance opposes the added torque.The optical axis's angular velocity increases under continuous perturbation moments until reaching a steady state, depending on the moment of inertia.
Figure 3(b) demonstrates that the outer frame's angular velocity can increase to a steady state, while the inner frame cannot.Comparing both figures, unknown disturbances significantly impact system stability but can be mitigated through mechanical processing.However, if the frame's deflection angular velocity is non-zero, it will continue to affect the optical axis's stability.

Closed loop response analysis
Assuming an unknown disturbance of 0, the carrier's three-axis angular velocity is subjected to a pulse signal with an amplitude of 1N m and a width of 0.01 s at 1 second (simulating instantaneous attitude disturbance) and a step signal with an amplitude of 0.1 rad/s at 1 second (simulating sustained attitude disturbance).The deflection angle of the framework is then compared and analyzed.2 presents a comparison of control performance between the two controllers under instantaneous and continuous interference.

Conversion Control
Figure 6 shows the simulation results when a step signal with an amplitude of 0.1 rad/s is applied to the carrier's three-axis angular velocity for 1 second, followed by a controller conversion at 5 seconds.

Figure 6 Conversion Control
Figure 6 demonstrates that the optical axis stability is achieved through controller conversion at 5 seconds, validating the efficacy of the proposed PI controller and BPNN PID conversion control method.However, it is observed that significant oscillation deflection occurs during the conversion moment.To ensure excessive stability, future research should focus on introducing a smooth transition parameter during the conversion process, which is a crucial direction to explore.

Conclusion
This study addressed image quality degradation caused by transient and continuous attitude disturbances in carrier aircraft.A composite transformation control approach combining PI control and BPNN PID control was designed to stabilize the platform.Simulation results showed that unknown disturbance torques had a significant impact, but could be eliminated through mechanical assembly.
The PI controller effectively mitigated transient disturbances, while the BPNN PID controller was superior for continuous disturbances.However, severe oscillations were observed during controller transitions.Future work will focus on designing transition functions to reduce these oscillations.
establishes the coordinate systems (body( b b b OX Y Z ), azimuth frame( o o o OX Y Z ), and pitch frame( I I I

Table 1 : 1 :
Scenario Settings (" " for disturbance, "×" for no disturbance) Step disturbance with 0.01 radians in unknown disturbance component.Scenario 2: Step disturbance with 0.01 radians in external three-axis disturbance component.(a) Example 1 perturbation (b) Example 2 perturbation Figure 3 Disturbed Image palstance/rad.s palstance/rad.s2023 3rd International Conference on Computer, Remote Sensing and Aerospace Journal of Physics: Conference Series 2640 (2023) 012015 Figure 4 indicates that the PI control outperforms the BPNN PID controller in handling instantaneous disturbances.This is attributed to the introduction of differential variables in the BPNN PID, which reduces control time but increases oscillation amplitude.
(a) Inner frame pitch angular velocity (b) Outer frame azimuth angular velocity Figure 5 illustrates the disturbance angular velocity under sustained gusts

Figure 5
Figure5shows BPNN PID controller outperforms the PI controller in handling continuous disturbances.Unlike the PI controller, the BPNN PID controller achieves stabilization of the outer frame angular velocity, preventing continuous deflection of the optical axis.Table2presents a comparison of control performance between the two controllers under instantaneous and continuous interference.

Table 2
compares the performance of the controllers under instantaneous and continuous interference