Non-cooperative game cooperative control method for air floating type microgravity test platform

Abstract

The invention relates to a non-cooperative game cooperative control method for an air floating type microgravity test platform. A planar motor and a servo platform are defined as two participants of a non-cooperative game when the air floating type microgravity test platform works; the core target of the game strategy is that the resultant force borne by the air floating type microgravity test platform is close to zero, that is, the resultant force is minimum; determining an optimization problem of the game strategy; after the game forms a situation, revenue functions are introduced to serve as evaluation criteria for strategy selection of participants, and two revenue functions, namely air floating type microgravity test platform resultant force revenue and speed revenue, are constructed; a final result generated by the game is a Nash equilibrium solution.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace microgravity simulation platform control, and in particular relates to a cooperative control method of an air-floating microgravity test platform based on non-cooperative game. Background Art

[0002] With the rapid development of aerospace technology, large deployable structures such as solar panels and satellite antennas, as important components of spacecraft, have a performance stability and accuracy that is directly related to the success or failure of the entire space mission. Since it is difficult for these structures to fully simulate their microgravity working state in space under the ground environment, it is particularly important to build an efficient and reliable microgravity simulation system.

[0003] The traditional air-floating microgravity test platform simulates the microgravity environment through the collaborative work of the planar motor and the servo platform. Among them, the cooperative game theory is applied to the collaborative control of the servo platform and the planar motor, aiming to achieve the optimal control effect through close cooperation and information sharing between the two parties. However, this method faces a series of challenges in practical applications: first, the cooperative game requires a large amount of information exchange between the servo platform and the planar motor, which not only increases the communication burden of the system, but also may cause delays and errors in information transmission; second, the complex information processing mechanism increases the complexity and cost of the system, and reduces the overall efficiency and reliability of the system; finally, under extreme working conditions or sudden failures, the cooperative control of the cooperative game may fail due to information interruption or processing delay, affecting the accuracy and stability of the microgravity simulation. In view of the above problems, a new type of non-cooperative game collaborative control strategy is urgently needed to replace or optimize the existing cooperative game control method. Summary of the invention

[0004] In order to solve the existing problems, the purpose of the present invention is to propose a non-cooperative game collaborative control model for an air-floating microgravity test platform. On a limited air-floating microgravity test platform, the non-cooperative goal of minimizing the combined force is achieved by selecting strategies for each leveling output. The core idea of ​​the non-cooperative game collaborative control strategy is that, through an intelligent control algorithm, the servo platform and the planar motor can achieve autonomous and efficient collaborative work without relying on a large amount of information exchange. This control strategy not only reduces the complexity and cost of the system, but also improves the robustness and adaptability of the system, and can maintain stable control performance under various working conditions. The technical solution is as follows:

[0005] A non-cooperative game collaborative control method for an air-floating microgravity test platform, the air-floating microgravity test platform includes an upper support structure, a measuring substrate and an air-floating bearing, a planar motor and a servo platform are defined as two participants in a non-cooperative game when the air-floating microgravity test platform is working, in a non-cooperative task, the goal of the participants is to achieve the leveling goal as soon as possible, the motion mode of the planar motor is simplified to uniformly accelerated linear motion; each participant is aware of each other's current state information; the non-cooperative game collaborative control method is:

[0006] In the game process, the set of the participants’ current optional movement strategies is called the participants’ strategy set, Indicates that the subscript i represents the i-th step strategy to be executed. represents the strategy of the servo-following system at step i, is the angle (°) that the servo platform will move in the i-th step, represents the strategy of the planar motor at step i, is the electromagnetic force required to be output by the planar motor in step i (N);

[0007] The core goal of the game strategy is to make the combined force on the air-floating microgravity test platform close to zero, that is, the combined force is minimal, while ensuring that the following two constraints are met:

[0008] Planar motor displacement distance constraint: ensure that after each strategy step is executed, the position of the planar motor on the servo platform is always within the maximum allowable displacement range to prevent the motor from leaving the servo platform;

[0009] Planar motor static state constraint: the moving speed of the planar motor is required to be strictly 0;

[0010] Determine the optimization problem of the i-th (i=1,2,...,n) step game strategy;

[0011] When the game forms a situation, the profit function is introduced as a participant The evaluation criteria for strategy selection are used to construct two benefit functions: one is the combined benefit of the air-floating microgravity test platform. The combined force threshold is preset. At each step of control, according to the current control effect and combined force state, in order to gradually approach the optimal combined force control state, when the difference between the combined force generated by each participant and the target is within the combined force threshold, the smaller the value, the greater the benefit the participant obtains. Otherwise, the combined force sub-item benefit value is set to zero. The other is the speed benefit of the air-floating microgravity test platform. A speed threshold is preset. When the planar motor speed value is less than the speed threshold, the smaller the planar motor speed value, the greater the benefit the participant obtains. Otherwise, the speed sub-item benefit value is set to zero.

[0012] The final result of the game is the Nash equilibrium solution. It is necessary to determine the strategy of the initial control period servo platform and the planar motor; perform iterative solution to obtain the strategy set T consisting of the Nash equilibrium solution i , T i It represents the strategy that the servo platform and planar motor can achieve the optimal performance at the i-th step.

[0013] Furthermore,

[0014] The optimization problem of the i-th (i=1,2,...,n) step game strategy is defined as follows:

[0015]

[0016] Among them, the angle θ between the servo platform and the horizontal plane under the i-th step game strategy is i As the decision vector, F i (θ i ,F em,i ) represents the actual value of the horizontal force of the planar motor under the game strategy in the i-th step, expressed as F i (θ i ,F em,i )=F em,i -G i sinθ i , is the mapping of the decision vector on the target set; F em,i represents the actual output electromagnetic force of the planar motor under the strategy in step i, obtained from the electromagnetic characteristics of the planar motor, G i Represents the gravity acting on the planar motor; x i represents the displacement of the planar motor under the game strategy in the i-th step, and its absolute value |x i |, h is the maximum allowable displacement of the planar motor; for the movement speed of the planar motor, assuming that its movement direction is in the same direction as the force, its movement speed is expressed as where v i-1 That is, the speed of the i-1th step (mm / s). In the initial state, v0=0, m is the weight of the planar motor, and t is the movement time.

[0017] Furthermore, the combined benefits of the air-floating microgravity test platform The definition is as follows:

[0018] Assume that the difference between the current combined force of each participant and the expected target is F i,goal (θ i ,F em,i ),

[0019] F i,goal (θ i ,F em,i )=F i (θ i,F em,i )-R (1)

[0020] In the formula, F i (θ i ,F em,i ) is the current combined force generated by each participant, and the expected target is the minimum value R that the combined force approaches;

[0021] Preset resultant force threshold F safe,i , the combined benefits of the air-floating microgravity test platform It is expressed as:

[0022]

[0023] When the difference between the combined force generated by each participant and the target F i,goal (θ i ,F em,i ) is within the combined force threshold, the smaller its value is, the greater the benefit the participants will get. i,goal (θ i ,F em,i ) is greater than F safe,i When , let the value of the combined partial benefit be zero.

[0024] In each further control step, according to the current control effect and resultant force state, in order to gradually approach the optimal resultant force control state, the resultant force threshold F is adjusted by dichotomy safe,i .

[0025] Furthermore, the speed gain of the air-floating microgravity test platform The definition is as follows:

[0026] Let v i (θ i ) is the current speed value of the planar motor, which is calculated by the planar motor moving speed solution model; the preset speed threshold v safe,i ;

[0027] Speed ​​Gains of Air-floating Microgravity Experiment Platform It is expressed as:

[0028]

[0029] When the planar motor speed is less than the speed threshold v safe,i When i (θ i ) is smaller, the greater the benefit the participant gets. i (θ i ) is greater than v safe,i When , let the speed sub-item benefit value be zero.

[0030] Furthermore, at each control step, according to the current control effect and speed state, in order to gradually approach the state of speed being 0, the speed threshold v is adjusted by dichotomy safe,i .

[0031] Furthermore, the strategy of the initial control cycle servo platform and the planar motor is: θ0 takes the angle of the servo platform in the initial state, and F0 takes the electromagnetic force that needs to be output when the planar motor is started.

[0032] Furthermore, the strategy set is solved by the Nash equilibrium solution of the game model constitute, is the angle that the servo platform will move at step i, is the displacement of the planar motor in the i-th step, is the speed at which the planar motor will move in the i-th step, satisfy

[0033]

[0034] In the formula, the subscript i represents the i-th step, j = 1, 2 represents two types of profit functions, namely formula (2) and formula (3), θ i ,x i ,v i They are respectively the platform inclination angle value, plane motor displacement distance value and speed value measured in the i-th step, collectively referred to as the measured state value.

[0035] Furthermore, the method of iteratively solving and obtaining a strategy set consisting of Nash equilibrium solutions is as follows:

[0036] Preset the number of iterations. At each step of control, first, the measured state value and the resultant force threshold F safe,i , speed threshold v safe,i , calculate the combined force gain and speed gain of both participants; when the first iteration is performed, substitute the currently measured platform inclination angle value θ i , Planar motor displacement distance value x i With speed value v i , solve equation (4), if the expected value of the platform inclination angle can be obtained Expected displacement distance of planar motor Planar motor speed expectation The minimum value of is used as the next strategy, and the iteration ends. If the minimum value of a certain expected value is found, the minimum value is used as the new expected value for re-iteration until the minimum value of all expected values ​​is found. The minimum value is used as the next strategy, and the iteration ends; if the minimum value of all expected values ​​cannot be solved after reaching the number of iterations, the expected value used in the last iteration is taken, and the current strategy combination is considered to be a Nash equilibrium solution, which is used as the next strategy; the executable strategy for each participant in the i-th step is obtained Then, the first two steps of strategy are and Re-substitute the combined force benefit and speed benefit, take the strategy with the largest benefit, and form the strategy set T i .

[0037] The technical effects of the present invention are as follows:

[0038] 1. By constructing a non-cooperative game collaborative control model, the servo platform and the planar motor can intelligently select the leveling output strategy based on the principle of maximizing their respective interests. This strategy selection mechanism ensures that the two can effectively reduce the combined force when working together to achieve the goal of minimizing the combined force. Through simulation verification, the model can maintain stable leveling capabilities in the face of frequent sinusoidal combined force changes, and effectively respond to complex and changing working conditions.

[0039] 2. During the design process, constraint functions were introduced specifically for the speed and displacement control of the planar motor. These constraint functions effectively limit the motion range of the planar motor and prevent it from sliding out of the limited cast iron platform due to excessive motion, thereby ensuring the safe and stable operation of the system. This design not only improves the reliability of the system, but also reduces the maintenance costs caused by unexpected failures.

[0040] 3. Strict maximum constraints are imposed on the number of iterations and the number of steps for strategy replacement. This measure significantly reduces the amount of calculation, allowing the system to complete the strategy selection and optimization process in a shorter time. Therefore, the system response speed has been greatly improved, and it can adapt to changes in the external environment more quickly, improving the overall control efficiency. At the same time, due to the reduction in the amount of calculation, the application scenarios of the present invention have also been widely expanded, and are suitable for more industrial control fields with higher real-time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 :Force conditions when the servo platform is working

[0042] Figure 2 : Air-floating workbench, in the figure: 1—servo drive; 2—upper support structure; 3—measurement substrate; 4—air-floating bearing.

[0043] Figure 3 : Planar motor force output response curve when the system initial force is given as a 100Hz sine change

[0044] Figure 4: Servo platform force output response curve when the system initial force is given as a 100Hz sine change

[0045] Figure 5 : Resultant force output response curve of the air-floating microgravity test platform when the system initial resultant force is given as a 100Hz sine change

[0046] Figure 6 : Planar motor force output response curve when the system initial force is given as a 10Hz sine change

[0047] Figure 7 : Servo platform force output response curve when the system initial force is given as a 10Hz sine change

[0048] Figure 8 : The force output response curve of the air-floating microgravity test platform when the initial force of the system is given as a 10Hz sine change;

[0049] Fig. 9 The process of solving the collaborative control game strategy of the air-floating microgravity experimental platform. DETAILED DESCRIPTION

[0050] The present invention proposes a non-cooperative game model for cooperative control of an air-floating microgravity test platform, which is described in detail below in conjunction with the accompanying drawings and embodiments.

[0051] Based on the idea of ​​non-cooperative game, this paper studies how each participant makes decisions to maximize their own interests. The basic research idea is to take the planar motor and servo platform as game participants, use their respective leveling output as the strategy set, take the resultant force in the horizontal direction as the benefit function, and establish a non-cooperative game collaborative control model for the air-floating microgravity test platform.

[0052] The non-cooperative game is more concerned with the strategy selection of maximizing the individual interests of the participants. The set of all motion strategies that the servo platform and the planar motor can choose in the current environment is set as the strategy set of the participant. The profit functions are defined for the air-floating microgravity test platform. These functions evaluate their respective performance or interests according to the current strategy combination, and solve the Nash equilibrium to ensure that the coordinated control of the air-floating microgravity test platform achieves the minimum resultant force.

[0053] In order to describe the motion status of the participants, the leveling time is discretized and a scenario model is constructed. The working status of each participant is analyzed separately below.

[0054] Figure 2The figure shows the overall structure of the air-floating workbench. It consists of an upper support structure 2, a measuring substrate 3 and an air-floating bearing 4. The air-floating bearing is arranged as a whole at the center of the upper part of the air-floating workbench and is coaxial with the measuring substrate. The air-floating bearing is a sliding bearing that uses gas as a lubricant. It supports the load with the help of a pressure air film formed between the sliding surfaces of the bearing. When working, the sliding surfaces are completely separated by the air film, so it can be used to simulate the weightless state when supporting the exhibition board.

[0055] The planar motor structure consists of porous air static pressure bearings, rotor cores and windings, fixed backplane housing and other components. The porous air static pressure bearing is composed of a bearing housing and porous graphite. The bearing housing acts as an air supply and support structure, and an air supply hole is opened on its outer side and communicates with the annular groove on the bearing end face; the porous graphite material is used as a throttling element, and the interior is filled with uniform micro-pores and embedded in the annular groove of the bearing housing. The bearing is introduced with high-pressure gas from the air supply channel, and enters the bearing gap through countless capillaries in the porous graphite to form a pressure gas film. Due to the characteristics of the porous material, the pressure distribution on the bearing surface is uniform, which makes the bearing have good load-bearing capacity and rigidity, and can provide a stable air floating repulsion to balance the gravity of a large deployment mechanism.

[0056] The force conditions of the air-floating microgravity test platform during operation are as follows: Figure 1 As shown in the figure, the forces acting on the two participants in the horizontal and vertical directions can be defined to represent the equilibrium of the participants in the narrow space. For the two participants, the forces acting on them in equilibrium can be expressed as

[0057]

[0058] In the non-cooperative task, the goal of the participants is to achieve the leveling goal as quickly as possible. In order to fully study the problem of achieving leveling with zero combined force, the following assumptions are made:

[0059] (1) The participants are non-cooperative opponents, and both parties know each other’s current state information;

[0060] (2) Participants have the ability to independently balance, and should try their best to achieve the goal of zero combined force;

[0061] (3) During the continuous movement of the planar motor above the servo platform, assuming that the resultant force acting on the system changes slightly in adjacent time periods and can be approximately regarded as remaining constant, the motion mode of the motor can be simplified to uniformly accelerated linear motion.

[0062] (4) Take the minimum value R and define the successful force F of the leveling task i The judgment condition of (t) is

[0063] F i (t)<R (2)

[0064] In the game process, the set of the participants’ current optional movement strategies is called the participants’ strategy set, Indicates that the subscript i represents the i-th step strategy to be executed. represents the strategy of the servo-following system at step i, is the angle (°) that the servo platform will move in the i-th step, represents the strategy of the planar motor at step i, is the electromagnetic force (N) that needs to be output by the planar motor in the i-th step.

[0065] The core goal of the single-step game strategy is to make the combined force on the air-floating microgravity test platform close to zero, that is, the combined force is minimal, while ensuring that the following two key constraints are met:

[0066] Planar motor displacement distance constraint: ensure that after each step of the strategy is executed, the position of the planar motor on the servo platform is always within the maximum allowable displacement range to prevent the motor from leaving the servo platform.

[0067] Planar motor static state constraint: Furthermore, the moving speed of the planar motor is required to be strictly 0. This condition not only simplifies the system dynamic model and prevents the planar motor from leaving the platform, but also may reduce energy consumption in specific application scenarios, which is of great significance for maintaining the long-term stable operation of the system.

[0068] Based on the above, the optimization problem of the i-th (i=1,2,...,n) step game strategy is defined as follows:

[0069]

[0070] Among them, the angle θ between the servo platform and the horizontal plane i As the decision vector in this problem, F i (θ i ,F em,i ) represents the actual value of the horizontal force of the planar motor under the game strategy in the i-th step, expressed as F i (θ i ,F em,i )=F em,i -G i sinθ i , is the mapping of the decision vector on the target set. em,i represents the actual electromagnetic force output by the planar motor under the strategy of step i, which can be obtained from the electromagnetic characteristics of the planar motor, and h is the maximum allowable displacement of the planar motor. The movement speed of the planar motor can be obtained from the principle of classical dynamics. To simplify the analysis, it is assumed that its movement direction is the same as the force, and its movement speed can be expressed as where v i-1That is, the speed of the i-1th step (mm / s), in the initial state, v0 = 0, m is the weight of the plane motor, and t is the movement time. Therefore, in the leveling process, the optimization constraint of the next strategy of the system depends on the execution result of the previous strategy.

[0071] In the construction of a collaborative control system for a simulated microgravity platform, the planar motor and the servo platform are two key participants. The non-cooperative game theory method is used to achieve effective collaboration between them to ensure the stability of the platform, that is, the resultant force approaches zero. When the game forms a situation, in order to evaluate the pros and cons of the situation, the profit function I is introduced. i , as a participant Evaluation criteria for strategy selection. In order to effectively achieve non-cooperative goals while maintaining the competitive relationship between participants, the following profit function is constructed:

[0072] 1. The combined benefits of the air-floating microgravity test platform

[0073] The difference between the current resultant force generated by the participant (air-floating microgravity test platform) and the desired target (i.e., the minimum value R that the resultant force approaches) is set as

[0074] F i,goal (θ i ,F em,i )=F i (θ i ,F em,i )-R (4)

[0075] In order to assess whether the current resultant force (i.e., the force generated by the participants or their contribution to the resultant force) is within a safe range, a resultant force threshold F is preset. safe,i , its initial value (i=1) is taken as 10N, and its final value (i=∞) is taken as 0. At each control step, according to the current control effect and resultant force state, in order to gradually approach the optimal resultant force control state, the safety value is adjusted by dichotomy, that is:

[0076]

[0077] Air-floating microgravity test platform joint benefits It is expressed as:

[0078]

[0079] When the difference between the combined force generated by each participant and the target F i,goal (θ i ,F em,i ) is within the safety threshold, the smaller its value is, the greater the benefit the participants will get. i,goal (θ i ,F em,i ) is greater than Fsafe,i At this time, the system resultant force may not meet the requirements. In order to avoid this situation, the resultant force sub-item benefit value is set to zero.

[0080] 2. Speed ​​gain of air-floating microgravity test platform

[0081] Current planar motor speed value v i (θ i ) can be calculated by solving the planar motor moving speed model. In order to evaluate whether the current planar motor moving speed is within the safe range, the preset speed threshold v safe,i , the initial value (i=1) is taken as 200mm / s, and the final value (i=∞) is taken as 0. At each control step, according to the current control effect and speed state, in order to gradually approach the state of speed being 0, the safety value v is adjusted by dichotomy. safe,i Right now:

[0082]

[0083] Speed ​​gain of servo / air floating system It is expressed as:

[0084]

[0085] When the planar motor speed is less than the safety value v safe,i When i (θ i ) is smaller, the greater the benefit the participant gets. i (θ i ) is greater than v safe,i In order to avoid entering this state, the payoff value is set to zero.

[0086] In game theory, when participants cannot increase their own benefits no matter what strategy they adopt, the strategy combination chosen by each participant is called a Nash equilibrium solution. In game theory, a Nash equilibrium solution can be understood as finding a strategy that gives no participants the motivation to change their strategy when all benefits are given. Obviously, the Nash equilibrium solution is the optimal strategy for each participant.

[0087] In the coordinated control of the air-floating microgravity test platform, represents the Nash equilibrium solution of the participant in step i, which satisfies

[0088]

[0089] in, represents two types of profit functions, namely, equation (6) and equation (8), θ i ,x i ,vi They are respectively the currently measured platform tilt angle value, plane motor displacement distance value and speed value.

[0090] To find the Nash equilibrium solution in the non-cooperative game of air-floating microgravity experimental platform First, we need to give the strategy for step 0, that is, the initial control cycle servo platform and planar motor. To simplify the analysis process, θ0 takes the angle of the servo platform in the initial state, and F0 takes the electromagnetic force that needs to be output when the planar motor starts.

[0091] In each subsequent control step, first, the measured state value and the resultant force threshold F safe,i , speed threshold v safe,i , calculate the benefit of each participant according to formula (6) and formula (8). When the first iteration is performed, substitute the currently measured platform tilt angle value θ i , Planar motor displacement distance value x i With speed value v i , solve equation (9), if the expected value of the platform inclination angle can be obtained Expected displacement distance of planar motor Planar motor speed expectation The minimum value of is used as the next strategy, and the iteration ends. If the minimum value of a certain expected value is found, the minimum value is used as the new expected value for re-iteration until the minimum value of all expected values ​​is found. The minimum value is used as the next strategy, and the iteration ends. In order to simplify the calculation, each strategy is set to iterate up to 5 times. If the minimum value of all expected values ​​cannot be solved after 5 iterations, the expected value used in the 5th iteration is taken, and the current strategy combination is considered to be a Nash equilibrium solution, which is used as the next strategy.

[0092] Find the executable strategy for each participant in step i Then, the first two steps of strategy are and Substitute the profit function again, take the strategy with the largest profit, and form the strategy set T i , T i It represents the strategy that the servo platform and the planar motor can achieve the optimal performance at the i-th step, which is defined as:

[0093]

[0094] The solution process of the servo / air floating platform collaborative control game strategy is as follows Fig. 9 As shown. Fig. 9 The process is modeled and simulated using the MATLAB / Simulink platform to verify the effectiveness of the control strategy.

[0095] Assuming that the initial force of the system is a sinusoidal change with an amplitude of 1.55 and a frequency of 100 Hz, the game model is used to solve the planar motor force output response curve and the servo follower system force output response curve. Figure 3 and Figure 4 .according to Figure 5 As shown in the figure, the initial force is 1.55 N, and after 0.8 seconds, the platform force drops to 0 N. This shows that the platform can be leveled after the non-cooperative game, which reduces the output of each air-floating microgravity test platform and reduces energy consumption, proving the feasibility of the scheme.

[0096] Assuming that the initial resultant force of the system is a sinusoidal change with an amplitude of 1.55 and a frequency of 10 Hz, the game model is used to solve the resultant force output response curve of the planar motor and the resultant force output response curve of the servo follower system. Figure 6 and Figure 7 .according to Figure 8 As shown in the figure, the initial force is 1.55 N, and after 0.6 seconds, the platform force drops to 0 N. This shows that the platform can be leveled after the non-cooperative game, which reduces the output of each air-floating microgravity test platform and reduces energy consumption. In addition, as the frequency of the system's force changes decreases, the system's adjustment speed becomes faster, proving the feasibility of the solution.

Claims

1. A non-cooperative game collaborative control method for an air-floating microgravity test platform, the air-floating microgravity test platform includes an upper support structure, a measuring substrate and an air-floating bearing, a planar motor and a servo platform are defined as two participants in a non-cooperative game when the air-floating microgravity test platform is working, in a non-cooperative task, the goal of the participants is to achieve the leveling goal as soon as possible, the motion mode of the planar motor is simplified to uniformly accelerated linear motion; each participant is aware of each other's current state information; the non-cooperative game collaborative control method is: In the game process, the set of the participants’ current optional movement strategies is called the participants’ strategy set, Indicates that the subscript i represents the i-th step strategy to be executed. represents the strategy of the servo-following system at step i, θ i * is the angle (°) that the servo platform will move in the i-th step, represents the strategy of the planar motor at step i, is the electromagnetic force required to be output by the planar motor in step i (N); The core goal of the game strategy is to make the combined force on the air-floating microgravity test platform close to zero, that is, the combined force is minimal, while ensuring that the following two constraints are met: Planar motor displacement distance constraint: ensure that after each step of the strategy is executed, the position of the planar motor on the servo platform is always within the maximum allowable displacement range to prevent the motor from leaving the servo platform; Planar motor static state constraint: the moving speed of the planar motor is required to be strictly 0; Determine the optimization problem of the step game strategy; When the game forms a situation, the profit function is introduced as the participant s i j The evaluation criteria for strategy selection are used to construct two benefit functions: one is the combined force benefit of the air-floating microgravity test platform: a combined force threshold is preset, and at each step of control, in order to gradually approach the optimal combined force control state, when the difference between the combined force generated by each participant and the target is within the combined force threshold, the smaller the value, the greater the benefit the participant obtains, otherwise, the combined force sub-item benefit value is set to zero; the other is the speed benefit of the air-floating microgravity test platform: a speed threshold is preset, and when the planar motor speed value is less than the speed threshold, the smaller the planar motor speed value, the greater the benefit the participant obtains, otherwise, the speed sub-item benefit value is set to zero; The final result of the game is the Nash equilibrium solution, which requires determining the initial control cycle servo platform and planar motor strategy; performing iterative solutions to obtain a strategy set consisting of Nash equilibrium solutions.

2. The non-cooperative game collaborative control method of the air-floating microgravity test platform according to claim 1 is characterized in that: The optimization problem of the i-th (i=1,2,...,n) step game strategy is defined as follows: Among them, the angle θ between the servo platform and the horizontal plane under the i-th step game strategy is i As the decision vector, F i (θ i ,F em,i ) represents the actual value of the horizontal force of the planar motor under the game strategy in the i-th step, expressed as F i (θ i ,F em,i )=F em,i -G i sinθ i , is the mapping of the decision vector on the target set; F em,i represents the actual output electromagnetic force of the planar motor under the strategy in step i, obtained from the electromagnetic characteristics of the planar motor, G i Represents the gravity acting on the planar motor; x i represents the displacement of the planar motor under the game strategy in the i-th step, and its absolute value |x i |, h is the maximum allowable displacement of the planar motor; for the movement speed of the planar motor, assuming that its movement direction is in the same direction as the force, its movement speed is expressed as where v i-1 That is, the speed of the i-1th step (mm / s). In the initial state, v0=0, m is the weight of the planar motor, and t is the movement time.

3. The non-cooperative game collaborative control method of the air-floating microgravity test platform according to claim 1 is characterized in that: Air-floating microgravity test platform joint benefits The definition is as follows: Assume that the difference between the current combined force of each participant and the expected target is F i,goal (θ i ,F em,i ), F i,goal (i i ,F em,i )=F i (i i ,F em,i )-R (1) In the formula, F i (θ i ,F em,i ) is the current combined force generated by each participant, and the expected target is the minimum value R that the combined force approaches; Preset resultant force threshold F safe,i , combined benefit of air-floating microgravity test platform I i 1 It is expressed as: When the difference between the combined force generated by each participant and the target F i,goal (θ i ,F em,i ) is within the combined force threshold, the smaller its value is, the greater the benefit the participants will get. i,goal (θ i ,F em,i ) is greater than F safe,i When , let the value of the combined partial benefit be zero.

4. The non-cooperative game collaborative control method of the air-floating microgravity test platform according to claim 3 is characterized in that: At each control step, according to the current control effect and resultant force state, in order to gradually approach the optimal resultant force control state, the resultant force threshold F is adjusted by dichotomy. safe,i .

5. The non-cooperative game collaborative control method of the air-floating microgravity test platform according to claim 1 is characterized in that: Speed ​​Gains of Air-floating Microgravity Experiment Platform The definition is as follows: Let v i (θ i ) is the current speed value of the planar motor, which is calculated by the planar motor moving speed solution model; the preset speed threshold v safe,i ; Speed ​​Gains of Air-floating Microgravity Experiment Platform It is expressed as: When the planar motor speed is less than the speed threshold v safe,i When i (θ i ) is smaller, the greater the benefit the participant gets. i (θ i ) is greater than v safe,i When , let the speed sub-item benefit value be zero.

6. The non-cooperative game collaborative control method of the air-floating microgravity test platform according to claim 5 is characterized in that: At each control step, according to the current control effect and speed state, in order to gradually approach the state of speed being 0, the speed threshold v is adjusted by dichotomy. safe,i .

7. The non-cooperative game collaborative control method of the air-floating microgravity test platform according to claim 1 is characterized in that: The strategy of the initial control cycle servo platform and planar motor is: θ0 takes the angle of the servo platform in the initial state, and F0 takes the electromagnetic force that needs to be output when the planar motor starts.

8. The non-cooperative game collaborative control method of the air-floating microgravity test platform according to claim 1 is characterized in that: The strategy set is solved by the Nash equilibrium of the game model Composition, θ i * is the angle that the servo platform will move at step i, is the displacement of the planar motor in the i-th step, is the speed at which the planar motor will move in the i-th step, satisfy In the formula, the subscript i represents the i-th step, j = 1, 2 represents two types of profit functions, namely formula (2) and formula (3), θ i ,x i ,v i They are respectively the platform inclination angle value, plane motor displacement distance value and speed value measured in the i-th step, collectively referred to as the measured state value.

9. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 8, characterized in that: The method of iteratively solving and obtaining a strategy set consisting of Nash equilibrium solutions is: Preset the number of iterations. At each step of control, first, the measured state value and the resultant force threshold F safe,i , speed threshold v safe,i , calculate the combined force gain and speed gain of both participants; when the first iteration is performed, substitute the currently measured platform inclination angle value θ i , Planar motor displacement distance value x i With speed value v i , solve equation (4), if the expected value of the platform inclination angle can be obtained Expected displacement distance of planar motor Planar motor speed expectation The minimum value of is used as the next strategy, and the iteration ends. If the minimum value of a certain expected value is found, the minimum value is used as the new expected value for re-iteration until the minimum value of all expected values ​​is found. The minimum value is used as the next strategy, and the iteration ends; if the minimum value of all expected values ​​cannot be solved after reaching the number of iterations, the expected value used in the last iteration is taken, and the current strategy combination is considered to be a Nash equilibrium solution, which is used as the next strategy; the executable strategy for each participant in the i-th step is obtained Then, the first two steps of strategy are and Re-substitute the combined force benefit and speed benefit, take the strategy with the largest benefit, and form the strategy set T i .

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