Adaptive control method and system for two-axis stabilized platform of aviation remote sensing based on Kane method

Abstract

The present invention proposes an adaptive control method and system for an aerial remote sensing two-axis stabilized platform based on the Kane method, and the method comprises the following steps: establishing a generalized coordinate system to derive the generalized speed, deflection speed and deflection angular speed corresponding to the aerial remote sensing two-axis stabilized platform; analyzing the generalized active force and generalized inertial force acting on the aerial remote sensing two-axis stabilized platform; bringing the obtained speed and generalized force into the equation of the Kane method to obtain the dynamic model of the aerial remote sensing two-axis stabilized platform; constructing a heading controller and a pitch controller respectively; the heading controller and the pitch controller are both adaptive controllers based on a PID controller; inputting the desired heading deflection angle and the desired pitch deflection angle, and realizing the control of the aerial remote sensing two-axis stabilized platform based on the dynamic model through the constructed heading controller and pitch controller. The present invention simplifies the modeling process of the aerial remote sensing two-axis stabilized platform and improves the control performance of the aerial remote sensing two-axis stabilized platform.

Description

Technical Field

[0001] The present invention relates to the field of adaptive control technology, and in particular to an adaptive control method and system for an aviation remote sensing two-axis stabilized platform based on the Kane method. Background Art

[0002] The aerial remote sensing two-axis platform is a device that ensures the stable operation of the sensor on a mobile platform. When the aerial remote sensing two-axis stabilized platform is adaptively controlled, it is necessary to first establish a mathematical model of the aerial remote sensing two-axis stabilized platform and design an adaptive controller based on the mathematical model. When the traditional classical mechanics (Newton-Euler method and Lagrange method) is used to model the aerial two-axis stabilized platform, its limitations will complicate the modeling process. Specifically, when constructing the Newton-Euler equations of the aerial two-axis stabilized platform, the constraint force of the hinge between them needs to be considered. This not only increases the number of unknown variables, but also complicates the equations. Although the Lagrange method can effectively avoid the analysis of the hinge constraint when modeling the aerial two-axis stabilized platform. However, due to the need to solve the second-order differential equation, it causes the problem of low computational efficiency.

[0003] In view of this, the present invention proposes an adaptive control method and system for an aviation remote sensing two-axis stabilized platform based on the Kane method. Summary of the invention

[0004] The purpose of the present invention is to propose an adaptive control method and system for an aerial remote sensing two-axis stabilized platform based on the Kane method, to simplify the modeling process of the aerial remote sensing two-axis stabilized platform, and to improve the control performance of the aerial remote sensing two-axis stabilized platform.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] In a first aspect, the present invention provides an adaptive control method for an aerial remote sensing two-axis stabilized platform based on the Kane method, which specifically comprises the following steps:

[0007] Step S1: establishing a generalized coordinate system to derive the generalized velocity, deflection velocity and angular velocity corresponding to the aerial remote sensing two-axis stabilized platform, wherein the two-axis stabilized platform includes a heading platform and a pitching platform; analyzing the generalized active force and generalized inertial force acting on the aerial remote sensing two-axis stabilized platform; bringing the obtained velocity and generalized force into the equation of the Kane method to obtain the dynamic model of the aerial remote sensing two-axis stabilized platform;

[0008] Step S2: constructing a heading controller and a pitch controller respectively; both the heading controller and the pitch controller are adaptive controllers based on a PID controller, and adaptively adjusting and optimizing the control parameters of the PID controller by adding a particle swarm algorithm with an iterative subset initialization strategy;

[0009] Step S3: input the desired heading deflection angle and the desired pitch deflection angle, and control the aerial remote sensing two-axis stabilized platform through the constructed heading controller and pitch controller based on the dynamic model of the aerial remote sensing two-axis stabilized platform.

[0010] Preferably, the dynamic model of the aerial remote sensing two-axis stabilized platform is specifically:

[0011]

[0012]

[0013] In the formula, M 1 、M 2 They represent the control forces required for the heading platform and the pitching platform, respectively. J 11 、J 21 、J 22 、J 23 They represent the moment of inertia of the heading platform in direction 1 and the moment of inertia of the pitch platform in directions 1, 2, and 3. 1, 2, and 3 correspond to the x, y, and z directions, respectively. is the relative pitch angle between the pitch platform and heading platform coordinate systems, is the pitch angular velocity, is the derivative of the pitch angular velocity, is the heading angular velocity, is the derivative of the angular velocity.

[0014] Preferably, the control equation of the PID controller is:

[0015]

[0016] In the formula, Output signal for controller; is the system error; is the system error integral; K p 、 K i and K d They are the weighted values ​​of the system error signal and its integral and derivative components respectively.

[0017] Preferably, the adaptive adjustment and optimization of the control parameters of the PID controller by adding the particle swarm algorithm with iterative subset initialization strategy is specifically as follows:

[0018] Step S21: Initialize the particle swarm, including the three control parameters of the PID controllerK p 、K i and K d Set the search space dimension to 3, set the number of particles and the total number of iterations k sum , maximum inertia weight w max and minimum inertia weight w min , and set K p 、K i and K d range, initialize particle position and velocity;

[0019] Step S22: Set the current iteration number k=1, calculate the fitness of each particle, and determine the global optimal value by calculating and comparing the fitness. p gd and the historical optimal value of the individual particle p id ;

[0020] Step S23: When k<k sum Execute the following loop until k=k sum End the loop when

[0021] Through the iterative subset initialization strategy, the historical optimal value of the particle individual is initialized before updating the speed and position in each iteration. p id At the previous global optimum p gd After initializing the position, a random speed is assigned for update, based on the historical optimal value of the updated particle individual p id and the previous global optimum p gd Update the speed and position of all particles, calculate the fitness of the new position of the particles and update the global optimal value p gd and the historical optimal value of the individual particle p id After that, k←k+1 ;

[0022] Step S24: Based on the global optimal value p gd The decomposition of the position in three spatial dimensions obtains the corresponding optimal control parameters K p 、Ki and K d .

[0023] Preferably, the speed and position of all updated particles are specifically:

[0024]

[0025]

[0026] In the formula, represents random velocity, represents the velocity information of the ith particle in the dth dimension in the k+1th iteration, represents the position information of the ith particle in the dth dimension in the k+1th iteration, , They represent the velocity information and position information of the ith particle in the dth dimension in the kth iteration, c1 and c2 are learning factors, w is the inertia weight, r 1 、r 2 are two random numbers.

[0027] Preferably, the fitness is calculated by taking the decomposition of each particle position in three spatial dimensions as the control parameter of the PID controller K p 、K i and K d , simulate the dynamic response of the control system and record the system error As time t changes, ITAE is approximately calculated by presetting the time T:

[0028]

[0029] In the formula, Represents the fitness value.

[0030] In the second aspect, the present invention provides an adaptive control system for an aerial remote sensing two-axis stabilized platform based on the Kane method. The system is implemented using the above-mentioned adaptive control method for an aerial remote sensing two-axis stabilized platform based on the Kane method, and includes a heading platform control module and a pitch platform control module; the heading platform control module includes a heading controller, a heading motor, and a heading platform; the pitch platform control module includes a pitch controller, a pitch motor, and a pitch platform.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] Compared with the existing modeling method of the aerial remote sensing two-axis stabilized platform, the modeling method of the aerial remote sensing two-axis stabilized platform proposed by the present invention avoids the hinge constraint force and the consideration and calculation of the second-order differential equation in the traditional method, and is more concise and efficient. In addition, after the traditional aerial remote sensing two-axis stabilized platform model, if a new rigid body is added, the overall model needs to be rebuilt, while the modeling method of the present invention can be further superimposed in the original force direction, and has good scalability. Therefore, the modeling process can be simplified when modeling a multi-rigid body system. For example, when modeling an aerial remote sensing three-axis stabilized platform, it can be directly expanded on the basis of two axes.

[0033] The adaptive control method proposed in the present invention can automatically adjust the control parameters of the controller according to the specific working environment, thereby enhancing the adaptability of the controller and the stability of the two-axis stabilized platform of the aerial remote sensing. The iterative subset initialization strategy improves the optimization efficiency of the algorithm and obtains a better adaptive control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A flow chart for designing a control system for an aviation remote sensing two-axis stabilized platform based on the Kane method of the present invention;

[0035] Figure 2 This is a schematic diagram of a two-axis stable platform in one embodiment of the present invention;

[0036] Figure 3 A diagram showing the conversion relationship of a vector basis coordinate system in one embodiment of the present invention;

[0037] Figure 4 This is a control system diagram of the aviation remote sensing two-axis stabilized platform of the present invention;

[0038] Figure 5 This is a flow chart of adaptive adjustment of control parameters of the present invention;

[0039] FIG6 (a) is a graph showing a step angle deflection error curve of an adaptive controller in a simulation result of an embodiment of the present invention;

[0040] FIG6( b ) is a curve diagram of sinusoidal angle deflection error of an adaptive controller in simulation results of an embodiment of the present invention;

[0041] FIG6 (c) is a graph showing a step angle deflection error curve of a conventional controller in a simulation result of an embodiment of the present invention;

[0042] FIG6( d ) is a curve diagram of sinusoidal angle deflection error of a conventional controller in simulation results of an embodiment of the present invention;

[0043] FIG. 7 (a) is a performance diagram of an adaptive controller without an iterative subset initialization strategy in simulation results according to an embodiment of the present invention;

[0044] FIG. 7( b ) is a performance diagram of an adaptive controller with an iterative subset initialization strategy in simulation results according to an embodiment of the present invention;

[0045] Figure 8 This is a semi-physical simulation verification platform of an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0047] The invention proposes an adaptive control method and system for an aviation remote sensing two-axis stabilized platform based on the Kane method.

[0048] The adaptive control method of the aviation remote sensing two-axis stabilized platform based on the Kane method of the present invention specifically comprises the following steps:

[0049] Step S1: establishing a generalized coordinate system to derive the generalized velocity, deflection velocity and angular velocity corresponding to the aerial remote sensing two-axis stabilized platform, wherein the two-axis stabilized platform includes a heading platform and a pitching platform; analyzing the generalized active force and generalized inertial force acting on the aerial remote sensing two-axis stabilized platform; bringing the obtained velocity and generalized force into the equation of the Kane method to obtain the dynamic model of the aerial remote sensing two-axis stabilized platform;

[0050] Step S2: constructing a heading controller and a pitch controller respectively; both the heading controller and the pitch controller are adaptive controllers based on a PID controller, and adaptively adjusting and optimizing the control parameters of the PID controller by adding a particle swarm algorithm with an iterative subset initialization strategy;

[0051] Step S3: input the desired heading deflection angle and the desired pitch deflection angle, and control the aerial remote sensing two-axis stabilized platform through the constructed heading controller and pitch controller based on the dynamic model of the aerial remote sensing two-axis stabilized platform.

[0052] 1. The implementation process of step S1 is as follows:

[0053] The three orthogonal unit vectors that intersect at point O are , and are called basis vectors. They form an orthogonal coordinate system called a basis, expressed as , where the symbol of the basis is The base coordinate system used in this paper is defined as follows: (1) is a fixed reference base coordinate system; (2) is the heading basis vector coordinate system; (3) It is the pitch basis vector coordinate system. For the convenience of the following description, the upper left corner 0, 1, and 2 of e represent the reference basis, heading basis, and pitch basis respectively; the lower right corner 1, 2, and 3 of e represent the x, y, and z directions.

[0054] (1) Generalized coordinate system and partial velocity:

[0055] Consider an aerial remote sensing two-axis stabilized platform system, such as Figure 2 As shown in the figure, the heading and pitch platforms are shown. The sensor is placed on the pitch platform. The stable platform is considered to be a rigid body. The heading platform is referred to as rigid body No. 1, and the pitch platform is referred to as rigid body No. 2. 1, 2, and 3 correspond to the x, y, and z directions respectively.

[0056] In the working state, the three vector bases will have the following Figure 3 The relationship shown in Figure 2 is: is the relative heading angle between the heading platform and the reference coordinate system. It is the relative pitch angle between the pitch platform and heading platform coordinate systems.

[0057] The angular velocity of the heading platform coordinate system is:

[0058]

[0059] in , , They respectively represent the angular velocities of rigid body No. 1 in directions 1, 2, and 3.

[0060] The coordinate transformation between the heading and pitch platform coordinate systems is given by express:

[0061]

[0062] The relationship between the angular velocity of the heading platform coordinate system and the velocity vector of the pitch platform coordinate system is:

[0063]

[0064] in , , They respectively represent the angular velocities of rigid body 2 in directions 1, 2, and 3.

[0065] Indicates the inertial velocity of the heading platform; Indicates the inertial velocity of the pitch platform. Figure 3 We can deduce the relative generalized velocity of the two-axis stabilized platform and its corresponding partial velocity and angular velocity ,in, denote the relative generalized velocities in the x, y, and z directions, respectively. They represent the eccentric velocity of rigid body 1 and rigid body 2 respectively. They represent the angular velocity of rigid body No. 1 and the angular velocity of rigid body No. 2 respectively, as shown in Table 1.

[0066] Table 1 Generalized speed , deflection velocity and angular velocity

[0067] r 1 2 3 #timg# #timg# #timg# #timg# #timg# #timg# 0 #timg# #timg# #timg# #timg# #timg# #timg# 0 0 0 #timg# 0 0 0

[0068] The corresponding velocities and accelerations of rigid body 1 and rigid body 2 are:

[0069]

[0070] in are the first-order derivatives of the corresponding parameters.

[0071] (2) Kane's law kinetic equation:

[0072] The basic idea of ​​the Kane method is to use generalized velocity instead of generalized coordinates as the independent variable of the system, and to establish the dynamic equation using the D'Alembert principle and the virtual displacement principle. By analyzing the forces on the two-axis stable platform, it can be seen that the generalized main force is the driving force of the motor, and the main vector of the torque is and , and They represent the driving torque of the heading platform and the pitching platform respectively.

[0073] Generalized speed The generalized driving force

[0074]

[0075] In the formula It represents the main force of rigid body No. 1 in direction 1, It represents the main force of rigid body 2 in direction 1, Represents the resultant force of rigid bodies 1 and 2 in direction 1.

[0076] Generalized speed The generalized driving force

[0077]

[0078] In the formula It represents the main force of rigid body 1 in direction 2. It represents the main force of rigid body 2 in direction 2, It represents the resultant force of rigid bodies 1 and 2 in two directions.

[0079] Generalized speed The generalized driving force

[0080]

[0081] In the formula It represents the main force of rigid body 1 in 3 directions. It represents the main force of rigid body 2 in 3 directions. It represents the resultant force of rigid bodies 1 and 2 in three directions.

[0082] Generalized speed The generalized inertial force

[0083]

[0084] In the formula It represents the inertial force of rigid body 1 in direction 1. Indicates the inertia force of rigid body 2 in direction 1, It represents the resultant force of the inertia force of rigid bodies 1 and 2 in direction 1. represents the moment of inertia of rigid body 1 in direction 1, Represents the moment of inertia of rigid body 2 in direction 1.

[0085] Generalized speed The generalized inertial force

[0086]

[0087] In the formula It represents the inertial force of rigid body 1 in the 2 directions. Represents the inertial force of rigid body 2 in two directions, It represents the resultant force of inertia of rigid bodies 1 and 2 in two directions. represents the moment of inertia of rigid body 2 in 2 directions, Represents the moment of inertia of rigid body 2 in three directions.

[0088] Generalized speed The generalized inertial force

[0089]

[0090] In the formula Represents the inertial force of rigid body 1 in three directions, Represents the inertial force of rigid body 2 in three directions, It represents the resultant force of inertia of rigid bodies 1 and 2 in three directions.

[0091] After rearranging the above formula, we get the dynamic equation of the two-axis stabilized platform for aerial remote sensing:

[0092]

[0093] In the above formula, is the pitch angular velocity, is the derivative of the pitch angular velocity, is the heading angular velocity, is the derivative of the angular velocity.

[0094] 2. The design of the adaptive controller in step S2 is as follows:

[0095] The present invention designs an adaptive controller for adjusting the parameters of the PID controller based on an intelligent optimization algorithm. The general form of the PID controller is:

[0096]

[0097] in: Output signal for controller; is the system error; is the system error integral; K p 、 K i and K d are the weighted values ​​of the system error signal and its integral and derivative components respectively. The optimization problem of the PID controller is to determine a set of appropriate K p 、K i and K d Parameters are used to make the output of the controlled object reach a more reasonable ideal effect. In the optimization process, the parameters of the PID controller are adjusted in a search manner, so a control performance index is needed as a basis for judging the quality of the parameters.

[0098] The particle swarm algorithm is a classic intelligent optimization algorithm. Its entire optimization process is: first initialize the position and speed of the initial particles in the particle swarm, and then perform the iterative process of the particle swarm algorithm. In the iterative process, the fitness value of the particles in each iteration is calculated. According to the fitness value, the particles update the speed and position information until the iterative process ends. After the iteration, the global optimal particle is obtained, and the controller parameter combination also reaches the optimal under the preset conditions, thereby improving the control ability of the controller. The particle swarm algorithm mainly includes particles, extreme values, and fitness functions.

[0099] Particles: Each iteration of the algorithm updates the particle position and velocity at the same time. The particle position represents the required solution, and the velocity is the adjustment step size of the position at each iteration. In order to avoid blind search of particles in the algorithm, the upper and lower limits of the position and step size are usually set according to the specific range of the actual control quantity. The particle position and step size are updated as follows:

[0100]

[0101]

[0102] In the formula represents random velocity, represents the velocity information of the ith particle in the dth dimension in the k+1th iteration, represents the position information of the ith particle in the dth dimension in the k+1th iteration, c1 and c2 are learning factors, w is the inertia weight, k sum is the total number of iterations, r 1 、r 2 are two random numbers, and their value range is between 0 and 1. The main function of these two random numbers is to increase the randomness of particle flight, so that the algorithm can explore the solution space more widely, help the algorithm to jump out of the local optimal solution, and improve the global search capability.

[0103] Extreme values: Each iteration of the algorithm needs to refer to two extreme values, i.e., the global optimal value p gd and the historical optimal value of the individual particle p id The two extreme values ​​are obtained by continuously comparing and calculating the fitness value of each particle in the population.

[0104] Fitness function: In the particle swarm algorithm, in order to test the quality of the value, the fitness function is introduced. So far, the most comprehensive and reasonable evaluation index among all fitness value functions is the ITEA method, that is,

[0105]

[0106] In the formula, represents the fitness value, represents the system error, and t is the sampling time. Since it is impossible to calculate to infinity, a sufficiently large time T is preset for approximate calculation. The fitness calculation is specifically as follows:

[0107] The decomposition of each particle position in three spatial dimensions is used as the control parameter of the PID controller K p 、K i and K d , simulate the dynamic response of the control system and record the system error As time t changes, ITAE is approximately calculated by presetting the time T:

[0108] .

[0109] Among them, the optimization characteristics of the particle swarm algorithm are used to adjust the three parameters of the PID controller, so the dimension of the PSO algorithm is set to 3, and the decomposition of the position information of each particle in these three dimensions corresponds to a set of PID parameter values.

[0110] The traditional particle swarm algorithm does not make full use of all particles in the process of finding the optimal position. Specifically, the particle initialization follows a random distribution. Therefore, when a particle is determined to be optimal, other particles need to keep moving closer to the optimal particle during the iteration process. However, calculating the fitness value after each iterative update may cause unnecessary computational burden. Because there may be a situation where no solution can be found, the computational burden in this regard is very large. To solve this problem, we propose an iterative subset initialization strategy. Before updating the speed and position of each iteration, the historical optimal value of the individual particle is initialized. p id At the previous global optimum p gd After initializing the position, a random speed is assigned for update, based on the historical optimal value of the updated particle individual p id and the previous global optimum p gd Update the speed and position of all particles. Repeat this process until the iteration ends.

[0111] The process of adjusting control parameters by the adaptive controller with iterative subset initialization strategy is as follows: Figure 5 The controller algorithm with iterative subset initialization strategy is shown in Table 2:

[0112] Table 2 Controller algorithm for iterative subset initialization strategy

[0113] Intelligent optimization algorithm process <![CDATA[Input: number of particles, k sum , w max ,w min value, and K p 、K i and K d range]]> <![CDATA[Output: Optimal K p 、K i and K d control parameters]]> 1. Initialize particle position and velocity <![CDATA[2. Calculate the fitness of each particle and determine p gd 、p id > <![CDATA[3. Loop ( k<k sum )]]> <![CDATA[4. Previous Optimal p gd Initialize the historical optimal value of this iteration near p id > <![CDATA[5. Give the historical optimal value p id Add a random speed to update it]]> 6. Update the particle's velocity and position <![CDATA[7. Calculate the fitness of the new position of the particle and update p gd 、 p id > 8. k+1 9. End the loop

[0114] 3. Simulation analysis:

[0115] In order to verify the effectiveness of the proposed adaptive controller, an angle deflection task of an aerial remote sensing two-axis stabilized platform is designed. When the desired deflection angle is input, the initial angle is deflected to the desired angle. Based on the established model of the aerial remote sensing two-axis stabilized platform, the simulation results of the angle deflection task are shown in Figure 6 (a), Figure 6 (b), Figure 6 (c), and Figure 6 (d). The performance of the adaptive controller with and without the iterative subset initialization strategy is shown in Figure 7 (a) and Figure 7 (b).

[0116] According to the above analysis, the adaptive control of the two-axis stabilized platform for aerial remote sensing based on the Kane method has the advantages of fast response speed and small tracking error, which verifies the effectiveness of the proposed modeling and adaptive control based on the Kane method. The comparison also proves the effectiveness of the iterative subset initialization strategy after adding the intelligent optimization algorithm.

[0117] The adaptive control system of the aviation remote sensing two-axis stabilized platform based on the Kane method of the present invention has a system flow chart as shown in FIG. Figure 1 As shown in the figure, the control objectives are: a. To achieve accurate position deflection control of the aerial remote sensing two-axis stabilized platform; b. The time to deflect to the desired position should be as short as possible. Based on the above objectives, the control system of the aerial remote sensing two-axis stabilized platform is designed as shown in Figure 4 As shown, it includes a heading platform control module and a pitch platform control module; the heading platform control module includes a heading controller, a heading motor, and a heading platform; the pitch platform control module includes a pitch controller, a pitch motor, and a pitch platform. The system is implemented using the above-mentioned adaptive control method for an aerial remote sensing two-axis stabilized platform based on the Kane method.

[0118] The present invention can verify the performance of the proposed control algorithm based on the quad-rotor UAV test bench provided by Lingsi Chuangqi Company, such as Figure 8 As shown. First, the controller is built and simulated in MATLAB / Simulink. Then, with the help of the host computer software provided by Lingsi Chuangqi, the controller module in Simulink is converted into C language using the code generation technology in MATLAB, and downloaded to the control chip of the drone using WIFI to burn the code. Finally, the performance of the adaptive control algorithm of the two-axis stabilized platform of aerial remote sensing is verified experimentally.

[0119] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions do not exceed the scope of the technical solution of the present invention, belong to the protection scope of the present invention.

Claims

1. An adaptive control method for an aviation remote sensing two-axis stabilized platform based on the Kane method, characterized in that: The specific steps include: Step S1: establishing a generalized coordinate system to derive the generalized velocity, deflection velocity and angular velocity corresponding to the aerial remote sensing two-axis stabilized platform, wherein the two-axis stabilized platform includes a heading platform and a pitching platform; analyzing the generalized active force and generalized inertial force acting on the aerial remote sensing two-axis stabilized platform; bringing the obtained velocity and generalized force into the equation of the Kane method to obtain the dynamic model of the aerial remote sensing two-axis stabilized platform; Step S2: constructing a heading controller and a pitch controller respectively; both the heading controller and the pitch controller are adaptive controllers based on a PID controller, and adaptively adjusting and optimizing the control parameters of the PID controller by adding a particle swarm algorithm with an iterative subset initialization strategy; Step S3: input the desired heading deflection angle and the desired pitch deflection angle, and control the aerial remote sensing two-axis stabilized platform through the constructed heading controller and pitch controller based on the dynamic model of the aerial remote sensing two-axis stabilized platform.

2. The adaptive control method for an aviation remote sensing two-axis stabilized platform based on the Kane method according to claim 1 is characterized in that: The dynamic model of the aerial remote sensing two-axis stabilized platform is specifically: In the formula, M 1 、M 2 They represent the control forces required for the heading platform and the pitching platform respectively. J 11 、J 21 、J 22 、J 23 They represent the moment of inertia of the heading platform in direction 1, and the moment of inertia of the pitch platform in directions 1, 2, and 3. 1, 2, and 3 represent the x, y, and z directions, respectively. is the relative pitch angle between the pitch platform and heading platform coordinate systems, is the pitch angular velocity, is the derivative of the pitch angular velocity, is the heading angular velocity, is the derivative of the angular velocity.

3. The adaptive control method for an aviation remote sensing two-axis stabilized platform based on the Kane method according to claim 1 is characterized in that: The control equation of the PID controller is: In the formula, Output signal for controller; is the system error; is the system error integral; K p 、K i and K d They are the weighted values ​​of the system error signal and its integral and derivative components respectively.

4. The adaptive control method for an aviation remote sensing two-axis stabilized platform based on the Kane method according to claim 3 is characterized in that: The particle swarm algorithm with iterative subset initialization strategy is used to adaptively adjust and optimize the control parameters of the PID controller as follows: Step S21: Initialize the particle swarm, including the three control parameters of the PID controller K p 、K i and K d Set the search space dimension to 3, set the number of particles and the total number of iterations k sum , maximum inertia weight w max and minimum inertia weight w min , and set K p 、K i and K d range, initialize particle position and velocity; Step S22: Set the current iteration number k=1, calculate the fitness of each particle, and determine the global optimal value by calculating and comparing the fitness. p gd and the historical optimal value of the individual particle p id ; Step S23: When k<k sum Execute the following loop until k=k sum End the loop when Through the iterative subset initialization strategy, the historical optimal value of the particle individual is initialized before updating the speed and position in each iteration. p id At the previous global optimum p gd After initializing the position, a random speed is assigned for update, based on the historical optimal value of the updated particle individual p id and the previous global optimum p gd Update the speed and position of all particles, calculate the fitness of the new position of the particles and update the global optimal value p gd and the historical optimal value of the individual particle p id After that, k←k+1 ; Step S24: Based on the global optimal value p gd The decomposition of the position in three spatial dimensions obtains the corresponding optimal control parameters K p 、K i and K d .

5. The adaptive control method for an aviation remote sensing two-axis stabilized platform based on the Kane method according to claim 4 is characterized in that: The updating of the speed and position of all particles is specifically as follows: In the formula, represents random velocity, represents the velocity information of the ith particle in the dth dimension in the k+1th iteration, represents the position information of the ith particle in the dth dimension in the k+1th iteration, , They represent the velocity information and position information of the ith particle in the dth dimension in the kth iteration, c1 and c2 are learning factors, w is the inertia weight, r 1 、r 2 are two random numbers.

6. The adaptive control method for an aviation remote sensing two-axis stabilized platform based on the Kane method according to claim 4 is characterized by: The fitness is calculated as follows: the decomposition of each particle position in three spatial dimensions is used as the control parameter of the PID controller K p 、K i and K d , simulate the dynamic response of the control system and record the system error As time t changes, ITAE is approximately calculated by presetting the time T: In the formula, Represents the fitness value.

7. The adaptive control system of the two-axis stabilized platform for aviation remote sensing based on the Kane method is characterized by: The system is implemented by the adaptive control method of the aerial remote sensing two-axis stabilized platform based on the Kane method as described in any one of claims 1-6, including a heading platform control module and a pitch platform control module; the heading platform control module includes a heading controller, a heading motor, and a heading platform; the pitch platform control module includes a pitch controller, a pitch motor, and a pitch platform.

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