A design method, device and storage device for active disturbance rejection controller

Abstract

The present application provides a design method, device, and storage device for an auto-disturbance rejection controller. The method includes: obtaining a second-order intelligent agent system, converting the second-order intelligent agent system into two first-order systems in series, transforming the second-order extended state observer into a reduced-order cascade extended state observer, determining the total disturbance of the intelligent agents in the second-order intelligent agent system, determining the workload of each intelligent agent based on sensors, designing a reduced-order cascade automatic disturbance rejection controller based on the total disturbance and the workload, and determining the convergence of the reduced-order cascade extended state observer based on the reduced-order cascade automatic disturbance rejection controller. By transforming the second-order extended state observer into a reduced-order cascade extended state observer and testing the reduced-order cascade extended state observer using a reduced-order cascade automatic disturbance rejection controller, the observed quantity and total disturbance of the system are determined. The robustness of the multi-agent system is improved, the impact of disturbances on the system is reduced, and the communication cost is reduced.

Description

Technical Field

[0001] The present application relates to the field of complex systems, and in particular to a design method, device, and storage device for an active disturbance rejection controller. Background Art

[0002] With the development of complex systems theory, multi-agent systems have become a cutting-edge discipline in the field of complex systems. Multi-agent coverage has been widely applied in fields such as search and rescue, cleaning, and disaster monitoring. The problem of workload partitioning among agents is one of the fundamental issues in multi-agent coverage. It can shorten the multi-agent coverage time and reduce the workload of each agent. Therefore, it is very meaningful to study a control method for online workload partitioning among multi-agent agents.

[0003] During actual multi-agent operation, multi-agent systems face various disturbances and uncertainties, both from the external environment and from internal system changes. These disturbances may include sensor noise, communication delays, dynamic environmental changes, faults, and attacks, which can adversely affect the agents' perception, decision-making, and execution capabilities. Research on disturbance rejection is crucial for the normal operation, stability, performance coordination, safety, and reliability of multi-agent systems. By developing algorithms and control strategies with robust disturbance rejection capabilities, the robustness and adaptability of multi-agent systems can be enhanced to cope with various disturbances and uncertainties.

[0004] Most existing multi-agent distributed algorithms are based on idealized scenarios where the model is known and the effects of disturbances are not considered. This makes them difficult to implement in practice or even fails to achieve the desired results. Furthermore, multi-agent systems require vast amounts of data to process, making existing algorithms computationally intensive and failing to consider the actual process execution time. This requires advanced hardware support, increasing manufacturing costs. Summary of the Invention

[0005] The purpose of this application is to solve the technical problems that the current multi-agent online workload partitioning algorithm is severely affected by disturbances, has a large amount of calculation and is high in cost, and to provide a design method, device and storage device for an anti-disturbance controller.

[0006] The above-mentioned purpose of this application is achieved through the following technical solutions:

[0007] S1: Obtain a second-order agent system;

[0008] S2: transform the second-order agent system into two first-order systems in series;

[0009] S3: transforming the second-order extended state observer into a reduced-order cascade extended state observer to determine the total disturbance of the agents in the second-order agent system;

[0010] S4: Determine the workload of each of the intelligent agents according to the sensor;

[0011] S5: Designing a reduced-order cascade active disturbance rejection controller according to the total disturbance and the workload;

[0012] S6: determining a convergence result of the reduced-order cascade extended state observer according to the reduced-order cascade active disturbance rejection controller;

[0013] S7: Determine the validity of the second-order intelligent system according to the convergence result.

[0014] Optionally, step S1 includes:

[0015] S11: The dynamic model of the second-order agent system is as follows:

[0016]

[0017] Where q is the state matrix, u is the input matrix, M and C are parameter matrices, d is the disturbance and noise, ΔM and ΔC are the parameter uncertainties of the dynamic equations;

[0018] S12: According to the series integral form of the active disturbance rejection control, the dynamic model is rewritten as follows:

[0019]

[0020] Where f1 and f2 are two first-order systems equivalent to the second-order system, d′ is the unknown disturbance in f1, d″ is the unknown disturbance in f2, i = 1…n, q i is the system state variable, v i is the equivalent velocity component, u i is the system input, d′ i and d″ i are the external disturbances in the equivalent system.

[0021] Optionally, step S3 includes:

[0022] S31: Design the reduced-order cascade extended state observer as follows:

[0023]

[0024]

[0025] Among them, e′ i 、e″ i is the observer error, is the observation state, is the observed disturbance, β1 and β2 are the observer coefficients, β1, β2>0, γ is the adjustment coefficient, γ>0;

[0026] S32: Determine the total disturbance of the agent according to the reduced-order cascade extended state observer as follows:

[0027]

[0028]

[0029] Among them, ξ and ψ are adjustment coefficients, is the total observed disturbance, is the disturbance compensation term, including the external disturbances suffered by the agent and the internal disturbances generated by itself, is the actual disturbance of the system, Estimate the disturbance for the observer.

[0030] Optionally, step S5 includes:

[0031] S51: Determine the workload difference between two adjacent agents as follows:

[0032] Δm i (t) = m i (t)-m i+1 (t)

[0033] Among them, m i To ensure that the workload of each agent is equal, we only need to ensure that Δm i =0;

[0034] S52: Design the reduced-order cascade active disturbance rejection controller according to the total disturbance and the segmentation algorithm as follows:

[0035]

[0036] Wherein, k, k1, k2 are the parameters of the reduced-order cascade active disturbance rejection controller, k, k1, k2>0; is the optimization term of the segmentation algorithm, Δm i (t) is a consistent term, is the observer coefficient.

[0037] Optionally, step S6 includes:

[0038] S61: Derive the transfer function of the reduced-order series extended state observer as follows:

[0039]

[0040]

[0041]

[0042]

[0043] S62: Order The following formula is obtained:

[0044]

[0045]

[0046] S63: According to the form of the second-order intelligent agent system, the expression of the total disturbance of the system is obtained:

[0047]

[0048] Therefore, let The following formula is obtained:

[0049]

[0050] S64: According to the final value theorem, the steady-state error estimate of the extended state observer designed above can be obtained as follows:

[0051]

[0052] S65: Based on the reduced-order cascade extended state observer, conclusion 1 is obtained as follows:

[0053] If the solution of the system is globally bounded, then:

[0054]

[0055] A storage device stores instructions and data for implementing a design method of an active disturbance rejection controller.

[0056] A device for designing an active disturbance rejection controller comprises a processor and a storage device. The processor loads and executes instructions and data in the storage device to implement a method for designing an active disturbance rejection controller.

[0057] The beneficial effects of the technical solution provided by this application are:

[0058] By converting a high-order intelligent agent system into two first-order systems connected in series, transforming a second-order extended state observer into two first-order extended state observers connected in series, and taking the disturbance estimated by the two first-order extended state observers as the total disturbance of the system after algebraic operations, a new reduced-order cascade active disturbance rejection controller is designed. Compared with conventional control algorithms, a low-order reduced-order cascade active disturbance rejection controller is used instead of a high-order reduced-order cascade active disturbance rejection controller to suppress the total disturbance during the multi-agent operation, reduce data processing time, alleviate the burden of system operation, and save manufacturing costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The present application will be further described below with reference to the accompanying drawings and embodiments, in which:

[0060] Figure 1 is a step diagram of a design method of an active disturbance rejection controller in an embodiment of the present application;

[0061] Figure 2 : is a trajectory tracking diagram of the design method of the active disturbance rejection controller in the embodiment of the present application under the condition of no disturbance;

[0062] Figure 3 is an error curve diagram of the design method of the active disturbance rejection controller in the embodiment of the present application under the condition of no disturbance;

[0063] Figure 4 : is a trajectory tracking diagram of the design method of the active disturbance rejection controller in the embodiment of the present application under disturbance conditions;

[0064] Figure 5 is an error curve diagram of the design method of the active disturbance rejection controller in the embodiment of the present application under disturbance conditions;

[0065] Figure 6 RMSE diagram of the distributed control algorithm of the design method of the active disturbance rejection controller in the embodiment of the present application;

[0066] Figure 7 is a reduced-order cascade active disturbance rejection control flow chart of the design method of the active disturbance rejection controller in an embodiment of the present application;

[0067] Figure 8 It is a schematic diagram of the operation of the hardware device in the embodiment of the present application. DETAILED DESCRIPTION

[0068] In order to have a clearer understanding of the technical features, purposes and effects of this application, the specific implementation methods of this application are now described in detail with reference to the accompanying drawings.

[0069] Embodiments of the present application provide a design method, device, and storage device for an active disturbance rejection controller.

[0070] Please refer to Figure 1 , Figure 1 This is a step diagram of a design method for an active disturbance rejection controller in an embodiment of the present application, which specifically includes the following steps:

[0071] S1: Obtain a second-order agent system;

[0072] S2: transform the second-order agent system into two first-order systems in series;

[0073] S3: transforming the second-order extended state observer into a reduced-order cascade extended state observer to determine the total disturbance of the agents in the second-order agent system;

[0074] S4: Determine the workload of each of the intelligent agents according to the sensor;

[0075] S5: Designing a reduced-order cascade active disturbance rejection controller according to the total disturbance and the workload;

[0076] S6: determining a convergence result of the reduced-order cascade extended state observer according to the reduced-order cascade active disturbance rejection controller;

[0077] S7: Determine the validity of the second-order intelligent system according to the convergence result.

[0078] Specifically, the second-order agent system is transformed into two first-order systems connected in series. The second-order extended state observer is converted into a reduced-order cascade extended state observer. The disturbances of the first-order reduced-order cascade extended state observer are processed to improve the robustness of the multi-agent system and reduce the impact of disturbances on the system. By designing a reduced-order cascade active disturbance rejection controller, the total disturbance during the operation of each robot is suppressed, reducing the computational complexity and observation requirements of the high-order active disturbance rejection controller, thereby reducing costs.

[0079] Step S1 includes:

[0080] S11: The dynamic model of the second-order agent system is as follows:

[0081]

[0082] Where q is the state matrix, u is the input matrix, M and C are parameter matrices, d is the disturbance and noise, ΔM and ΔC are the parameter uncertainties of the dynamic equations;

[0083] S12: According to the series integral form of the active disturbance rejection control, the dynamic model is rewritten as follows:

[0084]

[0085] Where f1 and f2 are two first-order systems equivalent to the second-order system, d′ is the unknown disturbance in f1, d″ is the unknown disturbance in f2, i = 1…n, q i is the system state variable, v i is the equivalent velocity component, u i is the system input, d′ i and d″ i are the external disturbances in the equivalent system.

[0086] Step S3 includes:

[0087] S31: Design the reduced-order cascade extended state observer as follows:

[0088]

[0089]

[0090] Among them, e′ i 、e″ i is the observer error, is the observation state, is the observed disturbance, β1 and β2 are the observer coefficients, β1, β2>0, γ is the adjustment coefficient, γ>0;

[0091] S32: Determine the total disturbance of the agent according to the reduced-order cascade extended state observer as follows:

[0092]

[0093]

[0094] Among them, ξ and ψ are adjustment coefficients, is the total observed disturbance, is the disturbance compensation term, including the external disturbances suffered by the agent and the internal disturbances generated by itself, is the actual disturbance of the system, Estimate the disturbance for the observer.

[0095] Step S5 includes:

[0096] S51: Determine the workload difference between two adjacent agents as follows:

[0097] Δm i (t) = m i (t)-m i+1 (t)

[0098] Among them, m i To ensure that the workload of each agent is equal, we only need to ensure that Δm i =0;

[0099] S52: Design the reduced-order cascade active disturbance rejection controller according to the total disturbance and the segmentation algorithm as follows:

[0100]

[0101] Wherein, k, k1, k2 are the parameters of the reduced-order cascade active disturbance rejection controller, k, k1, k2>0; is the optimization term of the segmentation algorithm, Δm i (t) is a consistent term, is the observer coefficient.

[0102] For details, see Figure 7 , Figure 7 This is a reduced-order cascade active disturbance rejection control flow chart of the design method of the active disturbance rejection controller in the embodiment of the present application. The design process is as follows: the general second-order system is converted into the form of two first-order systems f1 and f2 connected in series, and then the two first-order systems are respectively designed with corresponding first-order extended state observers to observe their states and total disturbances. The output results of the system are fed back to the reduced-order cascade active disturbance rejection controller through workload sensor detection. The reduced-order cascade active disturbance rejection controller gives system input according to the workload of its adjacent intelligent agents, thereby realizing collaborative segmentation.

[0103] Step S6 includes:

[0104] S61: Derive the transfer function of the reduced-order series extended state observer as follows:

[0105]

[0106]

[0107]

[0108]

[0109] S62: Order The following formula is obtained:

[0110]

[0111]

[0112] S63: According to the form of the second-order intelligent agent system, the expression of the total disturbance of the system is obtained:

[0113]

[0114] Therefore, let The following formula is obtained:

[0115]

[0116] S64: According to the final value theorem, the steady-state error estimate of the extended state observer designed above can be obtained as follows:

[0117]

[0118] S65: Based on the reduced-order cascade extended state observer, conclusion 1 is obtained as follows:

[0119] If the solution of the system is globally bounded, then:

[0120]

[0121] Specifically, the reduced-order cascade extended state observer measures or estimates the inputs and outputs of the agent's system to obtain an approximate value for the system state and the total disturbance it experiences, thus filtering the state measurements affected by disturbances. The approximate value of the system state and the total disturbance experienced are used to design a reduced-order cascade active disturbance rejection controller and optimize the control strategy. The observer estimation results are required for controller design, and compensation for the total disturbance can also improve controller performance.

[0122] Specifically, a simulation experiment is designed to verify the effectiveness and superiority. Taking a four-wheeled robot as an example, its dynamic model can be described as:

[0123]

[0124]

[0125]

[0126] Among them, in planar motion, the motion of a rigid body can be decomposed into three independent components: translation in the x-axis direction, translation in the y-axis direction, and spin in the z-axis direction, so q = (x, y, θ); m is the mass of the robot, m = 5 kg; R is the radius of the wheel, R = 0.038 m; l is the distance from the wheel axis to the center of mass of the robot, l = 0.167 m; μ is the friction coefficient between the wheel and the ground, μ = 0.4; J ω ,J z are the moments of inertia of the wheels and the robot, J ω =1.25×10 -3 kg·m 2 ,J z =0.33kg·m 2 , A, B, φ are matrix coefficients.

[0127] Rewrite the dynamic model into a rotational form. Considering the actual operation of the robot, add external disturbances as follows:

[0128] d′=[-cos(t),cos(t),sin(t)] T ,d″=[sin(3t),-sin(3t),cos(3t)] T

[0129] Add random white noise with an amplitude of 0.05; considering the uncertainty of model parameters, add Δm i The uncertainty of ∈(-1,1).

[0130] The parameters of the reduced-order cascade active disturbance rejection controller are adjusted, and the simulation results are as follows.

[0131] In the absence of external disturbances, noise and parameter uncertainty, the trajectory tracking of the online distributed segmentation algorithm is compared with the classic PID algorithm and the second-order active disturbance rejection control method, such as Figure 2 As shown; the error curve of the online distributed segmentation algorithm is as follows Figure 3 shown.

[0132] In the presence of external disturbances, noise and parameter uncertainty, compared with the classic PID algorithm and the second-order active disturbance rejection control method, the trajectory tracking of the online distributed segmentation algorithm is as follows: Figure 4 As shown in the figure, the error curve of the online distributed segmentation algorithm is as follows: Figure 5 shown.

[0133] The performance indicator RMSE is used to measure the quality of trajectory tracking, as follows:

[0134]

[0135] Among them, x i (t) is the state of the i-th agent at time t; r i (t) is the expected state of the i-th agent at time t; n is the total number of samples in the entire experimental process; RMSE is used to measure the difference between the control effect of the designed control method and the expected effect. The lower the RMSE value, the better the control effect of the algorithm. The RMSE of the invented distributed control algorithm in the case of no disturbance, noise and parameter uncertainty and in the case of disturbance, noise and parameter uncertainty is as follows: Figure 6 shown.

[0136] Through theoretical analysis and simulation verification, combined with the motion trajectory comparison with the PID algorithm and the active disturbance rejection control method, the effectiveness and superiority of the design method of the active disturbance rejection controller of the present application are verified.

[0137] See Figure 8 , Figure 8 4 is a schematic diagram of the working of the hardware device of the embodiment of the present application. The hardware device specifically includes: a design device 401 of an active disturbance rejection controller, a processor 402 and a storage device 403.

[0138] A design device 401 for an active disturbance rejection controller: A design device 401 for an active disturbance rejection controller implements a design method for an active disturbance rejection controller.

[0139] Processor 402: The processor 402 loads and executes instructions and data in the storage device 403 to implement a design method for an active disturbance rejection controller.

[0140] Storage device 403: The storage device 403 stores instructions and data; the storage device 403 is used to implement a design method for an active disturbance rejection controller.

[0141] The above are only preferred embodiments of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A design method for an active disturbance rejection controller, characterized in that: The method comprises the following steps: S1: Get the second-order agent system; Step S1 includes: S11: The dynamic model of the second-order agent system is as follows: Where q is the state matrix, u is the input matrix, M and C are parameter matrices, d is the disturbance and noise, ΔM and ΔC are the parameter uncertainties of the dynamic equations; S12: According to the series integral form of the active disturbance rejection control, the dynamic model is rewritten as follows: Where f1 and f2 are two first-order systems equivalent to the second-order system, d′ is the unknown disturbance in f1, d″ is the unknown disturbance in f2, i = 1…n; q i is the system state variable, v i is the equivalent velocity component, u i is the system input, d′ i and d″ i are the external disturbances in the equivalent system respectively; S2: transform the second-order agent system into two first-order systems in series; S3: transforming the second-order extended state observer into a reduced-order cascade extended state observer to determine the total disturbance of the agents in the second-order agent system; Step S3 includes: S31: Design the reduced-order cascade extended state observer as follows: Among them, e′ i 、e″ i is the observer error, is the observation state, is the observed disturbance, β1 and β2 are the observer coefficients, β1, β2>0, γ is the adjustment coefficient, γ>0; S32: Determine the total disturbance of the agent according to the reduced-order serial extended state observer as follows: Among them, ξ and ψ are adjustment coefficients, is the total observed disturbance, is the disturbance compensation term, including the external disturbances suffered by the agent and the internal disturbances generated by itself, is the actual disturbance of the system, Estimate the disturbance for the observer; S4: Determine the workload of each of the intelligent agents according to the sensor; S5: Designing a reduced-order cascade active disturbance rejection controller according to the total disturbance and the workload; S6: determining a convergence result of the reduced-order cascade extended state observer according to the reduced-order cascade active disturbance rejection controller; S7: Determine the effectiveness of the second-order agent system based on the convergence result.

2. A design method for an active disturbance rejection controller according to claim 1, characterized in that: Step S5 includes: S51: Determine the workload difference between two adjacent agents as follows: Δm i (t)=m i (t)-m i+1 (t) Among them, m i To ensure that the workload of each agent is equal, we only need to ensure that Δm i =0; S52: Design the reduced-order cascade active disturbance rejection controller according to the total disturbance and the segmentation algorithm as follows: Wherein, k, k1, k2 are the parameters of the reduced-order cascade active disturbance rejection controller, k, k1, k2>0; is the optimization term of the segmentation algorithm, Δm i (t) is a consistent term, is the observer coefficient.

3. A design method for an active disturbance rejection controller as claimed in claim 2, characterized in that: Step S6 includes: S61: Derive the transfer function of the reduced-order series extended state observer as follows: S62: Order The following formula is obtained: S63: According to the form of the second-order intelligent agent system, the expression of the total disturbance of the system is obtained: Therefore, let The following formula is obtained: S64: According to the final value theorem, the steady-state error estimate of the extended state observer designed above can be obtained as follows: S65: Based on the reduced-order cascade extended state observer, conclusion 1 is obtained as follows: If the solution of the system is globally bounded, then:

4. A storage device, characterized in that: The storage device stores instructions and data for implementing any one of the active disturbance rejection controller design methods of claims 1 to 3.

5. A design device for an active disturbance rejection controller, characterized in that: include: A processor and a storage device; the processor loads and executes instructions and data in the storage device to implement any one of the active disturbance rejection controller design methods of claims 1 to 3.

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