Method for motion control of a nonlinear electromechanical servo system

Abstract

The application discloses a motion control method of a nonlinear electromechanical servo system and relates to the technical field of electromechanical system management; a dynamic model of the nonlinear electromechanical servo system is established, the electrical dynamics of a motor current loop corresponding to the nonlinear electromechanical servo system is simplified into a proportional link; the uncertainty of the dynamic model of the nonlinear electromechanical servo system is approximately fitted by using a radial basis neural network; the strong external time-varying disturbance of the nonlinear electromechanical servo system is estimated by using an extended state observer in combination with the dynamic model; and the desired motion trajectory of the nonlinear electromechanical servo system is fed back by using an error sign robust integral control method according to the estimation result, so that the actual motion trajectory of the nonlinear electromechanical servo system is controlled.

Description

Technical Field

[0001] This invention discloses a method relating to the field of electromechanical system management technology, specifically a motion control method for a nonlinear electromechanical servo system. Background Technology

[0002] Currently, existing control methods for nonlinear electromechanical servo systems mainly include computational torque control, adaptive robust control, sliding mode control, and active disturbance rejection control. However, computational torque control requires an accurate dynamic model of the nonlinear system to achieve control, but in practical applications, it is difficult to control accurately using a dynamic model. Adaptive robust control adaptively designs parameters to address uncertainties in the system model, but the control effect deteriorates or even leads to system instability when other disturbances, especially strong external disturbances, are present in the estimation of model parameters. Sliding mode control is widely used due to its strong ability to suppress bounded disturbances, but the chattering problem caused by discontinuous control input is a defect that cannot be solved by existing technologies. Active disturbance rejection control estimates external disturbances to the system through a state observer, but it has many overall design parameters, is cumbersome to debug, and is not conducive to widespread application. Summary of the Invention

[0003] This invention addresses the problem in existing technologies where nonlinear uncertainties such as system dynamics model parameter uncertainty and external time-varying disturbances affect the control accuracy of nonlinear electromechanical servo systems. It provides a motion control method for nonlinear electromechanical servo systems, ensuring that the nonlinear electromechanical servo system can accurately track the desired motion trajectory and avoid system instability.

[0004] The specific solution proposed in this invention is as follows: This invention provides a motion control method for a nonlinear electromechanical servo system: Step S1: Establish the dynamic model of the nonlinear electromechanical servo system, and simplify the electrical dynamics of the motor current loop corresponding to the nonlinear electromechanical servo system as a proportional element; Step S2: Use a radial basis function neural network to approximate the uncertainty of the dynamic model of the nonlinear electromechanical servo system; Step S3: Combine the dynamic model with the extended state observer to estimate the strong external time-varying disturbances of the nonlinear electromechanical servo system; Step S4: Based on the estimation results, the error sign robust integral control method is used to feed back the desired motion trajectory of the nonlinear electromechanical servo system and control the actual motion trajectory of the nonlinear electromechanical servo system.

[0005] Furthermore, in the motion control method for a nonlinear electromechanical servo system, the nonlinear electromechanical servo system in step S1 is a nonlinear dual-axis electromechanical servo system. The dynamic model of the nonlinear dual-axis electromechanical servo system is established using the second type of Lagrange equations. The nominal parameters of the nonlinear dual-axis electromechanical servo system are obtained based on the dynamic model. The set of uncertainties, including those caused by nonlinear factors, the set function of uncertainties, and external unknown disturbances, are determined based on the nominal parameters.

[0006] Furthermore, in step S2 of the motion control method for a nonlinear electromechanical servo system, the following formula is used: , A radial basis function neural network is used to approximate the uncertainty of the dynamic model of the nonlinear electromechanical servo system, where... ε For neural network fitting error, f It is the output of a multi-layer neural network. W These are the weights between the hidden layers and the output layer of a multi-layer neural network. σ For the activation function of a multilayer neural network, the radial basis function is selected.

[0007] Furthermore, in step S3 of the motion control method for a nonlinear electromechanical servo system, the expansion state and the rate of change of disturbance are defined based on the estimation error of the uncertainty of the dynamic model, and the state equation of the expanded nonlinear electromechanical servo system is obtained based on the estimation error and the rate of change of disturbance. The observation error dynamic equation is obtained based on the state equation and the bandwidth of the expanded state observer, which is used for error estimation.

[0008] Furthermore, in step S4 of the motion control method for a nonlinear electromechanical servo system, the error symbol robust integral control method is used to control the actual motion trajectory of the nonlinear electromechanical servo system by feeding back the desired motion trajectory of the nonlinear electromechanical servo system based on the adjustable control gain, the feedforward compensation control term of the dynamic model, the radial basis neural network estimation term, the observation term of the extended state observer, and the robust control term.

[0009] The present invention also provides a motion control device for a nonlinear electromechanical servo system, comprising a control module, wherein the control module includes a model control module, a radial basis function neural network module, and an extended state observation module. The model control module establishes a dynamic model of the nonlinear electromechanical servo system, and simplifies the electrical dynamics of the motor current loop corresponding to the nonlinear electromechanical servo system into a proportional element. The radial basis function neural network module uses a radial basis function neural network to approximate the uncertainty of the dynamic model of a nonlinear electromechanical servo system; The extended state observation module, combined with the dynamic model, uses the extended state observer to estimate the strong external time-varying disturbances of the nonlinear electromechanical servo system. The control module uses the error sign robust integral control method to feed back the expected motion trajectory of the nonlinear electromechanical servo system based on the estimation results, and controls the actual motion trajectory of the nonlinear electromechanical servo system.

[0010] Furthermore, in the motion control device of the nonlinear electromechanical servo system, the nonlinear electromechanical servo system in the model control module is a nonlinear dual-axis electromechanical servo system. The dynamic model of the nonlinear dual-axis electromechanical servo system is established using the second type of Lagrange equations. The nominal parameters of the nonlinear dual-axis electromechanical servo system are obtained based on the dynamic model. The set of uncertainties, including uncertainties caused by nonlinear factors, the set function of uncertainties, and external unknown disturbances, are determined based on the nominal parameters.

[0011] Furthermore, the radial basis function neural network module in the motion control device of the nonlinear electromechanical servo system utilizes the following formula: , A radial basis function neural network is used to approximate the uncertainty of the dynamic model of the nonlinear electromechanical servo system, where... ε For neural network fitting error, f It is the output of a multi-layer neural network. W These are the weights between the hidden layers and the output layer of a multi-layer neural network. σ For the activation function of a multilayer neural network, the radial basis function is selected.

[0012] Furthermore, in the motion control device of the nonlinear electromechanical servo system, the expansion state observation module defines the rate of change of expansion state and disturbance based on the estimation error of the uncertainty of the dynamic model, and obtains the state equation of the expanded nonlinear electromechanical servo system based on the estimation error and the rate of change of disturbance. The observation error dynamic equation is obtained based on the state equation and the bandwidth of the expansion state observer, which is used for error estimation.

[0013] Furthermore, in the motion control device of the nonlinear electromechanical servo system, the control module utilizes an error-symmetric robust integral control method to control the actual motion trajectory of the nonlinear electromechanical servo system by feeding back the desired motion trajectory of the nonlinear electromechanical servo system based on the adjustable control gain, the feedforward compensation control term of the dynamic model, the radial basis function neural network estimation term, the observation term of the extended state observer, and the robust control term.

[0014] The advantages of this invention are: This invention provides a motion control method for a nonlinear electromechanical servo system. It utilizes a radial basis function (RBF) neural network to approximate the uncertainties of the servo system model, employs an extended state observer to estimate the approximation error of the RDF and external disturbances, and uses a robust feedback method to further reduce feedforward compensation errors and improve system robustness. This method can accurately track the desired motion trajectory and control the actual motion trajectory of the nonlinear electromechanical servo system under the simultaneous presence of model uncertainties and strong external time-varying disturbances. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the position closed-loop control framework of the nonlinear electromechanical servo system involved in this invention.

[0016] Figure 2 This is a schematic diagram of the motion control process of the method of the present invention.

[0017] Figure 3 This is a schematic diagram illustrating the trajectory tracking performance of the nonlinear electromechanical servo system controlled by the method of this invention.

[0018] Figure 4 This is a schematic diagram comparing the tracking error of the method of the present invention with other methods.

[0019] Figure 5 This is a schematic diagram comparing the tracking error of the method of the present invention with that of other methods in the range of 50s to 60s.

[0020] Figure 6 This is a schematic diagram illustrating the estimation performance of the uncertainty of the system dynamics model involved in the method of this invention.

[0021] Figure 7 This is a schematic diagram illustrating the estimated performance of a system under strong external time-varying disturbances, as described in the method of this invention.

[0022] Figure 8 This is a schematic diagram of the waveform of the input voltage in the method of the present invention. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0024] This invention provides a motion control method for a nonlinear electromechanical servo system: Step S1: Establish the dynamic model of the nonlinear electromechanical servo system, and simplify the electrical dynamics of the motor current loop corresponding to the nonlinear electromechanical servo system as a proportional element; Step S2: Use a radial basis function neural network to approximate the uncertainty of the dynamic model of the nonlinear electromechanical servo system; Step S3: Combine the dynamic model with the extended state observer to estimate the strong external time-varying disturbances of the nonlinear electromechanical servo system; Step S4: Based on the estimation results, the error sign robust integral control method is used to feed back the desired motion trajectory of the nonlinear electromechanical servo system and control the actual motion trajectory of the nonlinear electromechanical servo system.

[0025] In specific applications, based on the technical solution of the method of the present invention, in some embodiments of the method of the present invention, the nonlinear electromechanical servo system in step S1 is a nonlinear dual-axis electromechanical servo system, and the dynamic model of the nonlinear dual-axis electromechanical servo system is established using the second kind of Lagrange equations:

[0026] In the formula: Let be the state vector of the system. It is an inertial symmetric positive definite matrix. The Coriolis force centrifugal matrix, The gravity term matrix is ​​expressed in the following form:

[0027]

[0028] The nominal parameters of the dynamic model are expressed as Therefore, the actual dynamic model terms are expressed as follows:

[0029] in, It is an uncertainty caused by nonlinear factors.

[0030] Define the system's state variables The nonlinear state-space equation of the system can be written as:

[0031] in, Let be the set function of the uncertainties in the system model. d(t) It is a set of uncertainties that include unknown external disturbances.

[0032] Furthermore, the motor current loop is approximated as a proportional element, assuming that the motor output is proportional to the input. T u It can be represented as: T u = n i k ui u i ,i =1,2; In the formula, These are the transmission ratios of the directional axis and the pitch axis, respectively. These are the torque amplification factors for the servo motors of the azimuth and pitch axes, respectively. These are the control voltage inputs for the servo motors of the azimuth and pitch axes, respectively. The nominal parameters of the dynamic model... Calculations show that other unmodeled components related to the system state are also classified as uncertainties in the system model. Given the desired trajectory and its first derivative. Second derivative All are continuous and bounded, and All can be measured; and x 1 ,x 2 All can be measured; and d(t) It is sufficiently smooth and bounded, and:

[0033] θ 1 θ 2 ，v 1 ,v 2 All are unknown positive numbers.

[0034] In step 2, the radial basis function neural network (RBN) approximates the model uncertainty of the nonlinear electromechanical servo system. RBNs possess excellent nonlinear function approximation capabilities, capable of approximating arbitrary nonlinear functions, and exhibit strong self-learning and fault-tolerant abilities. They can perceive the dynamic characteristics of uncertain systems. Therefore, considering the specific characteristics of RISE control design, let:

[0035] in, ε For neural network fitting error, f It is the output of a multi-layer neural network. W These are the weights between the hidden layers and the output layer of a multi-layer neural network. σ For the activation function of a multilayer neural network, the radial basis function is selected as the activation function, and its specific expression is as follows:

[0036] Setting the neural network fitting error ε It is bounded, and:

[0037] All are sufficiently small positive numbers.

[0038] In step 3, an extended state observer is designed using a radial basis neural network to estimate strong external time-varying disturbances in the nonlinear electromechanical servo system. Uncertainty in dynamic model Estimation can be performed using a multi-layer neural network, which can be set as follows: , Define the extended state of the system to represent the estimation error of the model uncertainty in the system. ,and , The rate of change of the disturbance, i.e. And assume Let be an unknown but bounded function. Based on the formula, the expanded system state equations can be obtained:

[0039] The following extended state observation model can be obtained:

[0040] In the formula, System status The estimate, The bandwidth of the extended state observer is the only parameter in the observer that needs to be adjusted.

[0041] Combining the formulas, we can obtain the dynamic equation for the observation error:

[0042] in, This is for estimating the error.

[0043] definition The formula can be written as:

[0044] in:

[0045] From the matrix A 0 As defined, it satisfies the Herwitz criterion, and therefore there exists a positive definite and symmetric matrix. Make Established.

[0046] In step 4, the desired motion trajectory of the nonlinear electromechanical servo system is fed back based on the estimation results using an error-signed robust integral control method. Specifically: Define the system output angle error: z 1=x 1 -x 1d make for Virtual control input, definition and The error between them is: z 2 =x 2 -α 1 And because , Virtual control input for , In the formula, For adjustable control gain, k 11 , k 12 All are positive numbers.

[0047] because In the formula It is a stable transfer function, when When it approaches 0, It will inevitably tend to 0; Define an auxiliary error signal r:

[0048] Expanding on r further:

[0049] As shown below:

[0050] In the formula, For adjustable control gain, k r1 , k r2 All are positive numbers. Feedforward compensation control terms based on system model, where For multi-layer neural network estimation terms, For the observations of the extended state observer. u s For robust control terms, among which u s1 To suppress the linear robust term in the nominal model of the system, u s2 Let be the nonlinear robust term used to suppress unmodeled perturbations. , The adaptive law for weights in a multilayer neural network is: , Further analysis reveals:

[0051] To handle residual disturbances in the system, the nonlinear integral robustness term is handled using the following formula:

[0052] Differentiating the expression, we get:

[0053] in,

[0054] Define error parameters ,Depend on As can be seen from the structure, there must exist a globally invertible non-decreasing positive function ρ such that , Based on the initial settings, we can obtain:

[0055] in, All are normal numbers.

[0056] Define auxiliary functions L(t), , like β satisfy Then the function defined as follows P(t) Always positive.

[0057] prove:

[0058] Integrating the above equation by parts, we get:

[0059] Furthermore, we can obtain:

[0060] like β If the above formula is satisfied, then the function P(t) Always be right.

[0061] To verify system stability, define the Lyapunov function:

[0062] Differentiating the above equation, we get:

[0063] From Young's inequality, we get:

[0064] Furthermore, we can obtain:

[0065] in: if For a value less than 0, C must be a positive number, that is:

[0066] According to the formula, for any time interval t≥0, , therefore, z 1 、z 2 、r Both are bounded.

[0067] It can be proven that the method of the present invention can stably control the motion trajectory of a nonlinear dual-axis electromechanical servo system.

[0068] The verification process can refer to the parameter selection of the electromechanical servo system in the simulation as follows: The parameters of the inertia tensor matrix are:

[0069] Given the desired trajectory of the system:

[0070] The time-varying perturbation in this simulation is Model uncertainty , RBFESORISE: This indicates the high-performance control method designed in this invention, and the control parameters are selected as follows:

[0071] RBFRISE: This indicates that the method of the present invention does not have a state observer. This comparison is set up mainly to verify the disturbance compensation performance of the method of the present invention against strong external time-varying disturbances. For a fair comparison, the selected control parameters are exactly the same as those of RBFESORISE.

[0072] RISE: This indicates that the method of the present invention does not have RBF neural network and ESO. This comparison is set up mainly to verify the compensation performance of the high-performance controller designed in this invention for strong external time-varying disturbances and uncertain models. For a fair comparison, the selected control parameters are exactly the same as those of RBFESORISE.

[0073] Effects of the method of this invention: Figure 3 This is a graph showing the actual trajectory tracking performance under the method of this invention. Figure 4 This is a comparison chart of the tracking error under the method of this invention with other controllers. Figure 5 This is a comparison chart of the tracking error under the method of this invention with other controllers at 50s to 60s, combined with... Figure 3 , Figure 4 and Figure 5 It can be seen that under the action of the method of the present invention, the steady-state tracking error is smaller and the error curve is smoother, thus verifying the effectiveness of the RBFESO control performance. Figure 5 This is a performance graph showing the estimation of system model uncertainty under the method of this invention. Figure 6 This is an estimation performance diagram of the system under strong external time-varying disturbances under the method of the present invention. It can be seen from the diagram that they eventually approach the true value, thus enabling effective estimation of disturbances in the system. Figure 7 The figure shows the magnitude of the controller input voltage under the action of the method of the present invention. As can be seen from the figure, the magnitude of the control input voltage obtained by the present invention is continuously differentiable and bounded, which is beneficial for practical engineering applications.

[0074] The present invention also provides a motion control device for a nonlinear electromechanical servo system, comprising a control module, wherein the control module includes a model control module, a radial basis function neural network module, and an extended state observation module. The model control module establishes a dynamic model of the nonlinear electromechanical servo system, and simplifies the electrical dynamics of the motor current loop corresponding to the nonlinear electromechanical servo system into a proportional element. The radial basis function neural network module uses a radial basis function neural network to approximate the uncertainty of the dynamic model of a nonlinear electromechanical servo system; The extended state observation module, combined with the dynamic model, uses the extended state observer to estimate the strong external time-varying disturbances of the nonlinear electromechanical servo system. The control module uses the error sign robust integral control method to feed back the expected motion trajectory of the nonlinear electromechanical servo system based on the estimation results, and controls the actual motion trajectory of the nonlinear electromechanical servo system.

[0075] The information interaction and execution process between the modules in the above-mentioned device are based on the same concept as the method embodiment of the present invention, and the specific details can be found in the description of the method embodiment of the present invention, and will not be repeated here.

[0076] Similarly, the device of this invention utilizes a radial basis function neural network to approximate the uncertainty of the servo system model. An extended state observer is used to estimate the approximation error of the radial basis function neural network and external disturbances. A robust feedback method is employed to further reduce the error of feedforward compensation and improve the robustness of the system. The device of this invention can accurately track the desired motion trajectory and control the actual motion trajectory of the nonlinear electromechanical servo system under the simultaneous presence of model uncertainty and strong external time-varying disturbances and other nonlinear dynamic influences.

[0077] It should be noted that not all steps and modules in the above processes and device structures are mandatory; some steps or modules can be omitted as needed. The execution order of each step is not fixed and can be adjusted as required. The system structure described in the above embodiments can be a physical structure or a logical structure. That is, some modules may be implemented by the same physical entity, or some modules may be implemented by multiple physical entities, or they may be jointly implemented by certain components in multiple independent devices.

[0078] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A motion control method for a nonlinear electromechanical servo system, Its characteristic is step S1: establish the dynamic model of the nonlinear electromechanical servo system, and simplify the electrical dynamics of the motor current loop corresponding to the nonlinear electromechanical servo system as a proportional element; Step S2: Use a radial basis function neural network to approximate the uncertainty of the dynamic model of the nonlinear electromechanical servo system; Step S3: Combine the dynamic model with the extended state observer to estimate the strong external time-varying disturbance of the nonlinear electromechanical servo system; wherein the rate of change of the extended state and the disturbance is defined according to the estimation error of the uncertainty of the dynamic model, and the state equation of the extended nonlinear electromechanical servo system is obtained according to the estimation error and the rate of change of the disturbance, and the dynamic equation of the observation error is obtained according to the state equation and the bandwidth of the extended state observer, which is used for error estimation. Step S4: Based on the estimation results, the error sign robust integral control method is used to feed back the desired motion trajectory of the nonlinear electromechanical servo system and control the actual motion trajectory of the nonlinear electromechanical servo system.

2. The motion control method for a nonlinear electromechanical servo system according to claim 1, characterized in that: In step S1, the nonlinear electromechanical servo system is a nonlinear dual-axis electromechanical servo system. The dynamic model of the nonlinear dual-axis electromechanical servo system is established using the second type of Lagrange equations. The nominal parameters of the nonlinear dual-axis electromechanical servo system are obtained based on the dynamic model. The set of uncertainties, including uncertainties caused by nonlinear factors, the set function of uncertainties, and external unknown disturbances, are determined based on the nominal parameters.

3. A motion control method for a nonlinear electromechanical servo system according to claim 1 or 2, characterized in that: The following formula is used in step S2: , A radial basis function neural network is used to approximate the uncertainty of the dynamic model of the nonlinear electromechanical servo system, where... ε For neural network fitting error, f It is the output of a multi-layer neural network. W These are the weights between the hidden layers and the output layer of a multi-layer neural network. σ For the activation function of a multilayer neural network, the radial basis function is selected.

4. The motion control method for a nonlinear electromechanical servo system according to claim 1, characterized in that: In step S4, the error symbol robust integral control method is used to control the actual motion trajectory of the nonlinear electromechanical servo system by feeding back the desired motion trajectory of the nonlinear electromechanical servo system based on the adjustable control gain, the feedforward compensation control term of the dynamic model, the radial basis neural network estimation term, the observation term of the extended state observer, and the robust control term.

5. A motion control device for a nonlinear electromechanical servo system, characterized in that: The system includes a control module, which comprises a model control module, a radial basis function neural network module, and an extended state observation module. The model control module establishes a dynamic model of the nonlinear electromechanical servo system, and simplifies the electrical dynamics of the motor current loop corresponding to the nonlinear electromechanical servo system into a proportional element. The radial basis function neural network module uses a radial basis function neural network to approximate the uncertainty of the dynamic model of a nonlinear electromechanical servo system; The extended state observation module combines the dynamic model with the extended state observer to estimate the strong external time-varying disturbance of the nonlinear electromechanical servo system. The extended state observation module defines the rate of change of the extended state and the disturbance based on the estimation error of the uncertainty of the dynamic model, and obtains the state equation of the extended nonlinear electromechanical servo system based on the estimation error and the rate of change of the disturbance. The dynamic equation of the observation error is obtained based on the state equation and the bandwidth of the extended state observer, which is used for error estimation. The control module uses the error sign robust integral control method to feed back the expected motion trajectory of the nonlinear electromechanical servo system based on the estimation results, and controls the actual motion trajectory of the nonlinear electromechanical servo system.

6. The motion control device for a nonlinear electromechanical servo system according to claim 5, characterized in that: The nonlinear electromechanical servo system in the model control module is a nonlinear dual-axis electromechanical servo system. The dynamic model of the nonlinear dual-axis electromechanical servo system is established using the second type of Lagrange equations. The nominal parameters of the nonlinear dual-axis electromechanical servo system are obtained based on the dynamic model. The set of uncertainties, including those caused by nonlinear factors, the set function of uncertainties, and external unknown disturbances, are determined based on the nominal parameters.

7. The motion control device for a nonlinear electromechanical servo system according to claim 5, characterized in that: The radial basis function neural network module utilizes the following formula: , A radial basis function neural network is used to approximate the uncertainty of the dynamic model of the nonlinear electromechanical servo system, where... ε For neural network fitting error, f It is the output of a multi-layer neural network. W These are the weights between the hidden layers and the output layer of a multi-layer neural network. σ For the activation function of a multilayer neural network, the radial basis function is selected.

8. The motion control device for a nonlinear electromechanical servo system according to claim 5, characterized in that: The control module utilizes the error-symmetric robust integral control method to control the actual motion trajectory of the nonlinear electromechanical servo system by feeding back the desired motion trajectory of the nonlinear electromechanical servo system based on the adjustable control gain, the feedforward compensation control term of the dynamic model, the radial basis function neural network estimation term, the observation term of the extended state observer, and the robust control term.

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