A preset performance control method for micro steering engine based on load estimation

Abstract

The application discloses a preset performance control method for a micro steering engine based on load estimation, and comprises the following steps: firstly, a state space mathematical model of an electric steering engine is established; secondly, an extended state observer is designed to estimate an external load torque in real time; then, a control law is designed based on a preset performance control theory, a performance function is used to constrain transient and steady state performances of a tracking error, and an error transformation, a backstepping method and Lyapunov stability theory are combined to complete controller design; finally, a radial basis function neural network is constructed, the load characteristics estimated in real time are used as inputs, an optimal performance boundary convergence rate matched with a current working condition is predicted and outputted on line, and the preset performance boundary is dynamically adjusted. The application realizes self-adaption of control performance to a load, effectively suppresses overshoot, avoids input saturation, and significantly improves control precision, stability and robustness of the micro steering engine system under a variable load condition.

Description

Technical Field

[0001] This invention belongs to the field of high-precision servo control technology, specifically relating to a method for preset performance control of a micro servo motor based on load estimation. Background Technology

[0002] Miniature servo motors, as key actuators in high-precision servo control systems, are widely used in aerospace, robotics, precision instruments, and other applications requiring rapid response and high dynamic performance. In actual operation, servo motors are often under load, and their dynamic performance is significantly affected by various uncertainties such as load fluctuations, frictional nonlinearity, and time-varying parameters. Traditional servo motor control methods typically design performance indicators based on no-load conditions, such as controlling no-load overshoot to within 10%. However, they lack clear specifications and adaptive adjustment mechanisms for transient performance under load, leading to problems such as increased overshoot, hysteresis, and even instability in real-world high-load, high-precision applications.

[0003] To improve the control performance of servo motors under complex operating conditions, researchers have proposed various improvement schemes. For example, the paper "Inversion Sliding Mode Control for an Electric Load Simulator Based on an Extended State Observer" uses active disturbance rejection control combined with an inversion sliding mode strategy. It estimates the total system disturbance in real time using an extended state observer and designs a sliding mode controller for compensation. This method improves torque tracking accuracy under certain conditions, but its controller structure is complex and sensitive to parameter perturbations. Other research designs robust controllers based on quantitative feedback theory, such as the paper "Robust fault-tolerant controller design for aerodynamic load simulator." This method exhibits strong robustness under model uncertainty, but often at the cost of transient response speed, making it difficult to meet high dynamic performance requirements. Still other researchers combine cerebellar model neural networks with fuzzy control and PD control for load simulation and parameter tuning, such as the paper "Semi-fuzzy CMAC and PDhybrid controller with compressed memory and semi-regularisation for electric load simulator." This method improves steady-state accuracy but cannot effectively suppress overshoot during dynamic processes.

[0004] In recent years, preset performance control methods have attracted attention because they can directly constrain the transient response indicators of a system (such as overshoot and convergence time). This method, through the design of performance functions and error transformation mechanisms, ensures that the tracking error is always confined within preset time-varying boundaries, thereby achieving precise shaping of the system's dynamic behavior. However, the effectiveness of preset performance control is highly dependent on the selection of performance boundary parameters, especially the boundary convergence rate, which must match the actual load characteristics. If the parameter settings do not match the current load state, it can easily lead to control input saturation, resulting in system performance degradation or even instability. Most existing anti-saturation compensation strategies fail to fundamentally resolve the contradiction between strict transient performance requirements and actuator saturation limitations, thus restricting the application of preset performance control in complex environments with frequent or large load changes. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a preset performance control method for micro servos based on load estimation. This method estimates the load in real time and dynamically adjusts the preset performance boundaries, enabling the control system to automatically adapt to load changes. While ensuring strict transient performance indicators (such as overshoot and convergence speed), it effectively avoids input saturation, thereby significantly improving the control accuracy, stability, and robustness of micro servos under complex, time-varying load conditions.

[0006] The technical solution of this invention is as follows:

[0007] A method for pre-setting performance control of a micro servo motor based on load estimation includes the following steps:

[0008] Step 1: Establish a mathematical model for the electric servo motor;

[0009] Step 2: Based on the mathematical model, design an extended state observer to estimate the control surface load acting on the servo motor in real time;

[0010] Step 3: Design a control law based on a preset performance control theory. The control law constrains the transient and steady-state performance of the system tracking error through a performance function and is implemented through error transformation and backstepping method.

[0011] Step 4: Construct a radial basis function neural network, using the real-time estimated control surface load and electric servo system state as input, to predict and output the optimal performance boundary convergence rate that matches the current load state; use the optimal convergence rate to dynamically update the performance function in Step 3, so as to realize the adaptive adjustment of the preset performance boundary to load changes.

[0012] In a further preferred embodiment, in step 1, the mathematical model of the electric servo motor is a state-space model established based on the armature circuit equation, the electromagnetic torque equation, and the mechanical motion equation, and its state variables include angular displacement, angular velocity, and armature current.

[0013] In a further optimized approach, the state-space model established in step 1 is as follows:

[0014]

[0015] in For servo angular displacement, For the servo motor angular velocity, For armature current, The viscous damping coefficient is... This refers to the total moment of inertia of the electric servo motor shaft and the load, calculated on the same side. Let be the torque constant of the electric servo motor. For rudder surface load, The back electromotive force coefficient, The inductance of the armature winding, The resistance of the armature winding, This is the terminal voltage applied to the armature.

[0016] A further preferred option, step 2, is as follows: based on the servo motor speed loop motion equation, the servo surface load is regarded as the total disturbance, and an extended state observer is designed to perform real-time observation and estimation to obtain the estimated value of the servo surface load.

[0017] In a further preferred embodiment, in step 2, the extended state observer is:

[0018]

[0019] in The observation error of the state observer, and Angular velocity and rudder load The estimated value, and This is the observer gain.

[0020] In a further preferred embodiment, in step 3, the performance function is a time-varying function used to define the time-varying boundary of the tracking error; the error transformation is a nonlinear transformation that maps the original tracking error constrained by the performance function into an unconstrained transformation error.

[0021] A further optimized approach, in step 3, is the performance function. for:

[0022]

[0023] in, These are the initial boundary values. For steady-state boundary values, The boundary convergence rate; in step 3, according to the formula

[0024]

[0025] diagonal displacement Tracking error Perform nonlinear transformation, This represents the conversion error after the mapping transformation.

[0026] In a further preferred embodiment, in step 3, based on the conversion error, a virtual control law and the final actual control law are designed using the backstepping method to ensure that the closed-loop system is stable and the tracking error always meets the preset performance boundary constraints.

[0027] In a further optimized approach, step 3 involves designing the virtual control law and the final actual control law using the backstepping method, as follows:

[0028] Conversion error Regarding time Differentiating, we have:

[0029]

[0030] in , ;

[0031] Combining the state-space equations of the electric servo motor, the system equations after error transformation are obtained as follows:

[0032]

[0033] Systematic error is defined as:

[0034]

[0035] in and This is a virtual control variable;

[0036] The system equations after error transformation

[0037]

[0038] Transform into

[0039]

[0040] Then design virtual control laws for:

[0041]

[0042] in express The reciprocal, Indicates control gain;

[0043] The system equations after error transformation

[0044]

[0045] Transform into

[0046]

[0047] Then design virtual control laws for:

[0048]

[0049] The system equations after error transformation

[0050]

[0051] Transform into

[0052]

[0053] Then design the actual control law for:

[0054] .

[0055] In a further preferred embodiment, step 4, the training process of the radial basis function neural network includes: offline collection of system data and corresponding optimal convergence rate labels under different load conditions; using a clustering algorithm to determine the center and width parameters of the hidden layers of the network; and solving the output weights and biases of the network using the least squares method.

[0056] Beneficial effects

[0057] The beneficial effects of this invention are as follows:

[0058] 1. This invention utilizes sensors to collect motion state data such as displacement and velocity of a micro servo motor in real time, and designs a specialized load estimation algorithm to accurately derive the current load state, laying the foundation for the design of a preset controller;

[0059] 2. Based on the load estimate, the present invention dynamically adjusts the preset performance indicators so that the set transient performance requirements such as overshoot can match the actual load conditions, thereby reducing the overshoot in a targeted manner under high bandwidth control conditions and avoiding input saturation problems and system instability caused by load mismatch.

[0060] 3. Based on ensuring accurate feedback of dynamic load information, this invention optimizes the servo control signal through a preset performance control strategy to achieve real-time adjustment of the system's transient response and overshoot performance.

[0061] 4. The present invention verifies the superiority of the pre-set performance control method based on load estimation through MATLAB numerical simulation, proving that the control method designed in this invention can adjust the transient performance of micro servo motors in real time under strict saturation constraints, taking into account the uncertainty caused by load changes and the strict requirements of high-precision control, effectively solving the shortcomings of traditional control methods in high-load and high-precision application scenarios, and significantly improving the stability and robustness of micro servo motor control systems.

[0062] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0063] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0064] Figure 1 This is the control block diagram of the mathematical model of the electric servo motor of the present invention.

[0065] Figure 2 These are the angular displacement curves of the servo motor under no-load and loaded states under conventional control laws.

[0066] Figure 3 This is the tracking error change curve under the preset control law of this invention (convergence rate is 1).

[0067] Figure 4 This is the tracking error change curve under the preset control law of this invention (convergence rate is 0.8). Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and do not constitute a limitation thereof.

[0069] The technical problem to be solved in this embodiment is that the no-load overshoot standard of the traditional servo control method does not match the actual load requirements, and the preset performance control method is unable to meet the strict transient response index due to load changes.

[0070] This embodiment provides a micro servo motor preset performance control method based on load estimation. The core process is as follows: First, establish an accurate mathematical model of the electric servo motor; then, estimate the control surface load in real time; next, design a controller that can guarantee preset transient performance (such as overshoot and convergence speed); finally, establish the relationship between the preset performance boundary convergence rate and the estimated load through a neural network, and dynamically adjust the performance boundary parameters to match the real-time load, thereby achieving optimal control in the entire operating range.

[0071] The following is in conjunction with the appendix Figures 1 to 4 The specific implementation steps of the present invention will be described below.

[0072] Step 1: Establish a mathematical model for the electric servo motor;

[0073] This invention uses a miniature DC electric servo motor as the controlled object. First, based on the physical characteristics of the DC servo motor, a precise mathematical model is established. This mathematical model is a state-space model based on the armature circuit equation, electromagnetic torque equation, and mechanical motion equation, and its state variables include angular displacement, angular velocity, and armature current.

[0074] Considering the inductance of the armature winding and resistance According to Kirchhoff's voltage law, the armature circuit voltage balance equation is:

[0075]

[0076] in For armature current, The angular velocity of the motor shaft of the electric servo motor. The back electromotive force coefficient, The terminal voltage applied to the armature, Indicates time.

[0077] Electromagnetic torque generated by armature current in magnetic field With armature current Proportional:

[0078]

[0079] in is the torque constant of the electric servo motor.

[0080] According to Newton's second law for rotating systems, electromagnetic torque is characterized... With motor shaft angular velocity The motor shaft dynamics equation is:

[0081]

[0082] in, This refers to the total moment of inertia of the electric servo motor shaft and the load, calculated on the same side. The viscous damping coefficient is... The load on the control surface is positive (with the direction of resistance to rotation being positive).

[0083] Combining the three formulas above, such as Figure 1 As shown, the three state variables of the electric servo system are defined as angular displacement. angular velocity and armature current Establish the state-space equations for the electric servo motor:

[0084]

[0085] The block diagram of the model is as follows: Figure 1 As shown, this provides a foundation for subsequent controller design.

[0086] Step 2: Based on the mathematical model, design an extended state observer to estimate the control surface load acting on the servo motor in real time:

[0087] To cope with unknown time-varying control surface loads To mitigate the impact of [the influence of the state], this invention employs an Extended State Observer (ESO) to estimate it in real time.

[0088] According to the velocity loop motion equation in the state-space equation of the electric servo motor

[0089]

[0090] Control surface load Consider it as an extended state that needs to be observed, that is, let And assume that its rate of change is bounded. Design the following linear ESO:

[0091]

[0092] in, The observation error of the state observer, and Angular velocity and rudder load The estimated value. and By using appropriate placement methods such as pole placement to optimize the observer gain, observation errors can be quickly converged, thereby obtaining a high-precision load estimate. .

[0093] Step 3: Design a control law based on a preset performance control theory. The control law constrains the transient and steady-state performance of the system tracking error through a performance function, and is implemented through error transformation and backstepping.

[0094] This step aims to design a controller that enables angular displacement. Able to track expected instructions Meanwhile, its tracking error The transient performance is strictly constrained within preset ranges, such as maximum overshoot and convergence speed.

[0095] Step 3.1: Preset performance boundaries and error transformation:

[0096] First, design the performance function of the controlled system. To characterize the error boundary, the performance function is a time-varying function used to define the time-varying boundary of the tracking error, and the boundary convergence rate parameter in the performance function determines the system response speed and the strictness of the overshoot constraint. In this embodiment, the performance function... for:

[0097]

[0098] in, These are the initial boundary values. For steady-state boundary values, The boundary convergence rate is related to the system bandwidth and directly determines the rate at which the error boundary shrinks, thus affecting the system's response speed.

[0099] Angular displacement Tracking error Constrained within the following time-varying boundaries, i.e., its preset performance boundary design is as follows:

[0100]

[0101] in The design parameters are given. To transform the constrained control problem into an unconstrained problem, a smooth, strictly monotonically increasing nonlinear transformation function is introduced to address the tracking error. Perform nonlinear transformation:

[0102]

[0103] in This represents the transformation error after the mapping transformation, which ensures that only the transformation error is considered. Bounded, original tracking error It will inevitably be constrained within the preset performance boundaries.

[0104] Step 3.2: Controller Design Based on Backstepping Method

[0105] Conversion error Regarding time Differentiating, we have:

[0106]

[0107] in , .

[0108] Combining the state-space equations of the electric servo motor, the system equations after error transformation are obtained as follows:

[0109]

[0110] Systematic error is defined as:

[0111]

[0112] in and This is a virtual control variable.

[0113] For the system equations after error transformation

[0114]

[0115] Transform into

[0116]

[0117] Then design virtual control laws for:

[0118]

[0119] in express The reciprocal, This represents the control gain. Define the Lyapunov function. Differentiate it and apply the virtual control law Substitute and get By designing virtual control laws ,ensure Stability.

[0120] For the system equations after error transformation

[0121]

[0122] Transform into

[0123]

[0124] Then design virtual control laws for:

[0125]

[0126] in For control surface load The estimated value, let To estimate the error, define the Lyapunov function. Differentiate it and apply the virtual control law Substitute and get

[0127]

[0128] By designing virtual control laws This can effectively offset the estimated load impact.

[0129] For the system equations after error transformation

[0130]

[0131] Transform into

[0132]

[0133] Then design the actual control law for:

[0134]

[0135] Define Lyapunov functions Differentiate it and apply it to the actual control law Substitute and get

[0136]

[0137] Based on Lyapunov's stability theory, it is proved that all signals in the closed-loop system are bounded, and the conversion error... It converges asymptotically and always satisfies the preset performance boundary constraints.

[0138] Step 4: Construct a radial basis function neural network, taking the real-time estimated control surface load and electric servo system state as input, predict and output the optimal performance boundary convergence rate that matches the current load state; use the optimal convergence rate to dynamically update the performance function in Step 3, so as to realize the adaptive adjustment of the preset performance boundary to load changes.

[0139] The controller established in step 3 is highly dependent on the performance function. Convergence rate in A fixed convergence rate cannot consistently achieve optimal transient performance under varying loads. Therefore, this invention introduces a radial basis function neural network (RBFNN), using online estimated load characteristics (such as load torque, current angular displacement, angular velocity, and error magnitude) as input. The RBFNN then optimizes the convergence rate for the current environment. Make predictions.

[0140] Network structure:

[0141] RBFNN employs a three-layer structure: an input layer, a hidden layer, and an output layer. The hidden layer consists of several radial basis function units (usually Gaussian functions), each unit corresponding to a central vector. and width parameters The network input is mapped to hidden layer features via a set of Gaussian functions, then multiplied by the linear weights of the output layer to obtain the final output.

[0142]

[0143] in The optimal convergence rate of the radial basis function neural network under the current environment. The predicted value, This is the normalized input vector, which contains the estimated load torque, current angular displacement, angular velocity, and error magnitude. This represents the number of hidden layer nodes. , , , All of these are parameters to be trained.

[0144] Offline training:

[0145] On a simulation or experimental platform, the servo motor is operated under a series of load conditions covering the expected operating range. For each condition, through trial and error or optimization algorithms, a convergence rate value that optimizes the system's transient performance (such as the combined indicators of overshoot and settling time) is found. Record the input vector and corresponding optimal label for each working condition. This constitutes the training dataset.

[0146] Clustering algorithms (such as K-means) are used to cluster the input samples to obtain... individual centers Then, based on the variance information of each cluster after clustering, a corresponding width is assigned. After fixing the center and width parameters, the output matrix of the hidden layer for all training samples is compared with the optimal convergence rate value. The labels construct a system of linear equations, which are then solved using the least squares method or regularized least squares method to output the weights. and bias .

[0147] When running online, the system will collect the status and estimate the load in real time. The input vector is constructed, normalized, and then fed into the pre-trained RBFNN. The network outputs in real time the predicted optimal convergence rate applicable to the current operating conditions. . This The value is used to dynamically update the performance function in the control law. This enables adaptive adjustment of performance boundaries to the load.

[0148] To evaluate the effectiveness of the load estimation-based preset performance control algorithm designed in this invention, MATLAB was used for simulation, and the results were compared with conventional PID control methods.

[0149] Testing the performance of conventional control methods:

[0150] Based on Simulink Figure 1 Servo system block diagram: Build a PID controller and determine the proportional gain. Integral coefficient Differential coefficients The parameters of the servo motor mathematical model are:

[0151]

[0152] Set the command angular displacement to Under no-load and under load (take the load) respectively The system is simulated under the following conditions, and the angular displacement output is as follows: Figure 2 As shown, the load has a significant impact on conventional control methods, greatly increasing the system's overshoot and reducing the system's transient response rate.

[0153] Test the performance of the preset performance control method based on load estimation:

[0154] Build a pre-defined performance controller in Simulink, where the servo motor mathematical model parameters are:

[0155]

[0156] Set the command angular displacement to Under no-load and under load (take the load) respectively Simulate the system under these conditions to track errors. The relationship with the preset performance envelope is as follows: Figure 3 and Figure 4 As shown. When the convergence rate is set to 1, the system exhibits good dynamic performance under no-load conditions, while the response curve touches the boundary under load conditions; when the convergence rate is set to 0.8, the tracking error under load conditions... It can be controlled within a preset performance envelope. It can be seen that the preset performance control algorithm based on load estimation proposed in this invention can perform real-time adjustment of the transient performance of micro servos under strict saturation constraints, significantly improving the stability and robustness of the micro servo control system.

[0157] This invention takes a micro electric servo motor as its application object and innovatively combines load estimation, error transformation, neural network prediction and robust control strategy. By optimizing the servo motor control signal through a preset performance control strategy, it realizes real-time adjustment of the system's transient response and overshoot performance, providing a more efficient control solution for dynamic control systems.

[0158] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for preset performance control of a micro servo motor based on load estimation, characterized in that: Includes the following steps: Step 1: Establish the mathematical model of the electric servo motor; the mathematical model of the electric servo motor is a state-space model based on the armature circuit equation, electromagnetic torque equation, and mechanical motion equation, and its state variables include angular displacement, angular velocity, and armature current; the established state-space model is as follows: in For servo angular displacement, For the servo motor angular velocity, For armature current, The viscous damping coefficient is... This refers to the total moment of inertia of the electric servo motor shaft and the load, calculated on the same side. Let be the torque constant of the electric servo motor. For rudder surface load, The back electromotive force coefficient, The inductance of the armature winding, The resistance of the armature winding, This is the terminal voltage applied to the armature; Step 2: Based on the mathematical model, design an extended state observer to estimate the control surface load acting on the servo motor in real time; Step 3: Design a control law based on a preset performance control theory. The control law constrains the transient and steady-state performance of the system tracking error through a performance function and is implemented through error transformation and backstepping method. The performance function for: in, These are the initial boundary values. For steady-state boundary values, The boundary convergence rate; in step 3, according to the formula diagonal displacement Tracking error Perform nonlinear transformation, This represents the conversion error after the mapping transformation; Step 4: Construct a radial basis function neural network, using the real-time estimated control surface load and electric servo system state as input, to predict and output the optimal performance boundary convergence rate that matches the current load state; dynamically update the performance function in Step 3 using the optimal performance boundary convergence rate to achieve adaptive adjustment of the preset performance boundary to load changes; the training process of the radial basis function neural network includes: offline collection of system data and corresponding optimal convergence rate labels under different load conditions; using a clustering algorithm to determine the center and width parameters of the network hidden layers; and solving the network output weights and biases using the least squares method.

2. The method for preset performance control of a micro servo motor based on load estimation according to claim 1, characterized in that: Step 2 specifically involves: based on the servo motor speed loop motion equation, treating the servo surface load as the total disturbance, designing an extended state observer for real-time observation and estimation, and obtaining an estimated value of the servo surface load.

3. The method for preset performance control of a micro servo motor based on load estimation according to claim 1, characterized in that: In step 2, the extended state observer is: in The observation error of the state observer, and Angular velocity and control surface load The estimated value, and This is the observer gain.

4. The method for preset performance control of a micro servo motor based on load estimation according to claim 1, characterized in that: In step 3, the performance function is a time-varying function used to define the time-varying boundary of the tracking error; the error transformation is a nonlinear transformation that maps the original tracking error constrained by the performance function into an unconstrained transformation error.

5. The method for preset performance control of a micro servo motor based on load estimation according to claim 1, characterized in that: In step 3, based on the conversion error, the virtual control law and the final actual control law are designed using the backstepping method to ensure that the closed-loop system is stable and the tracking error always meets the preset performance boundary constraints.

6. The method for preset performance control of a micro servo motor based on load estimation according to claim 1, characterized in that: In step 3, the process of designing the virtual control law and the final actual control law using the backstepping method is as follows: Conversion error Regarding time Differentiating, we have: in , ; Combining the state-space equations of the electric servo motor, the system equations after error transformation are obtained as follows: Systematic error is defined as: in and This is a virtual control variable; The system equations after error transformation Transform into Then design virtual control laws for: in express The reciprocal, Indicates control gain; The system equations after error transformation Transform into Then design virtual control laws for: The system equations after error transformation Transform into Then design the actual control law for: 。

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