A region tracking control method for servo systems based on extended state observer

Abstract

The present invention discloses a servo system regional tracking control method based on an extended state observer, the purpose of which is to improve the transient and steady-state performance of the servo system tracking error while improving the system's active anti-disturbance capability. The method comprises the following steps: setting the desired signal and error region of the servo system. Calculating the position estimation error based on the output position of the servo system, and calculating and updating the variable gain term based on the position estimation error. Constructing an extended state with the total unknown nonlinearity in the servo system, and constructing a variable gain extended state observer in combination with the variable gain term. Obtaining the estimated values ​​of the unknown speed and unknown nonlinearity in the servo system by the variable gain extended state observer, and calculating the comprehensive tracking error in combination with the desired signal of the servo system; constructing a non-smooth regional tracking controller using the comprehensive tracking error, the error region and the constrained intermediate control quantity for calculating the input torque control value, sending the input torque control value to the servo system, and realizing control of the servo system.

Description

Technical Field

[0001] The present invention relates to the field of electromechanical control, and specifically designs a servo system area tracking control method based on an extended state observer. Background Art

[0002] In the actual tracking control of servo systems, uncertainties such as unmodeled dynamics, external disturbances, and measurement noise reduce tracking effectiveness. Measurement noise can also make it difficult to accurately acquire velocity signals. Therefore, it is necessary to design an active disturbance rejection mechanism to estimate and compensate for these uncertainties in real time. Furthermore, in the face of increasingly complex operating environments, it is necessary to ensure that the servo system's tracking error remains within a desired range while improving its disturbance rejection capabilities.

[0003] In the research of active disturbance rejection methods, online estimation and compensation methods based on neural networks require online learning of a large number of parameters, which is not conducive to engineering applications. Existing online estimation and compensation methods based on observers generally do not consider the transient performance of the observer during the startup phase. In research on ensuring the tracking performance of servo systems, model predictive control is too computationally intensive. Preset performance control based on backstepping or dynamic surfaces generally requires a known servo system velocity signal, which is difficult to obtain directly from position signals contaminated by uncertainties such as noise. Furthermore, while constraining the servo system tracking error to a desired range, it is necessary to further improve tracking performance. Summary of the Invention

[0004] In view of this, the present invention provides a servo system area tracking control method based on an extended state observer, the purpose of which is to improve the system's active anti-disturbance capability while improving the transient and steady-state performance of the servo system's tracking error.

[0005] To achieve the above object, the technical solution of the present invention includes the following steps:

[0006] S1. Set the expected signal and error range of the servo system. The expected signal includes the expected position, expected speed, and expected acceleration.

[0007] S2. Obtain the current input torque and the current output position of the servo system, calculate the position estimation error according to the output position of the servo system, and calculate and update the variable gain term according to the position estimation error.

[0008] S3. The expanded state is constructed based on the total unknown nonlinearity in the servo system, and a variable gain expanded state observer is constructed by combining the variable gain term.

[0009] S4, obtaining estimated values ​​of unknown speed and unknown nonlinearity in the servo system by a variable gain extended state observer, and calculating a comprehensive tracking error in combination with a desired signal of the servo system;

[0010] S5. Using the comprehensive tracking error, error region and constrained intermediate control quantity, a non-smooth region tracking controller is constructed to calculate the input torque control value, so that the servo system tracking error is always within the error region.

[0011] S6. Send the input torque control value to the servo system to achieve control of the servo system.

[0012] Furthermore, the expected signal and error range of the servo system are set as follows:

[0013] Including setting the desired position of the servo system to y d The expected speed is The expected acceleration is Comprehensive tracking error e s The default area for (t) is -F s (t) <e s <F s (t), F s (t) is the comprehensive tracking error e s (t) is the amplitude of the preset region boundary.

[0014] Furthermore, the current input torque and the current output position of the servo system are obtained, specifically:

[0015] The current input torque τ and output position y of the servo system are obtained through sensors.

[0016] Furthermore, in S2, the position estimation error is calculated based on the output position of the servo system, and the variable gain term is calculated and updated based on the position estimation error, specifically:

[0017] According to the above servo system output position y, the position estimation error z1 is calculated and the variable gain term is calculated. Among them, r0>0,ε>0,κ>0 are set constants.

[0018] Furthermore, the total unknown nonlinearity in the servo system is used to construct the extended state, and combined with the variable gain term, a variable gain extended state observer is constructed, specifically:

[0019] According to the physical structure and electrical principles of the motor-driven servo system, the dynamic model of the servo system with unknown nonlinearity can be described as:

[0020] Among them, q, They represent the position and velocity of the servo system output, J is the equivalent moment of inertia of the servo system, b is the viscosity coefficient of the servo system, f represents the total unknown nonlinearity in the servo system, and τ represents the input torque of the servo system;

[0021] According to the dynamic model (1) of the servo system, the new system states x1 and x2 are defined as x1 = q, Then the dynamic model (1) of the servo system is transformed into:

[0022]

[0023] Where y is the position of the servo system output;

[0024] For the transformed system formula (2), the expanded state is constructed based on the total unknown nonlinearity in the servo system. The expanded state is defined as x3 = -f / J, and the following variable gain expanded state observer is constructed:

[0025]

[0026] in, is the estimated value of the variable gain extended state observer, is the estimated error of the output position of the servo system by the variable gain extended state observer, is the variable gain term in the variable gain extended state observer.

[0027] Furthermore, the estimated values ​​of the unknown speed and unknown nonlinearity in the servo system are obtained by the variable gain extended state observer, and the comprehensive tracking error is calculated in combination with the expected signal of the servo system, specifically:

[0028] is the constructed comprehensive tracking error, is the estimated value of velocity tracking error, 0<η≤1 is the constant parameter of the design.

[0029] Furthermore, a non-smooth region tracking controller is constructed using the comprehensive tracking error, error region, and constrained intermediate control variables to calculate the input torque control value, specifically:

[0030] Based on speed estimates Unknown nonlinear estimates Expected position y d , expected speed Expected acceleration Preset Tracking Error Area-F s (t) <z1<F s (t) and the constructed comprehensive tracking error e s (t), construct Equation (4) as a non-smooth region tracking controller to calculate the input torque τ(t):

[0031]

[0032] λ(e s(t)) is the intermediate control variable based on the Funnel constraint function; J is the equivalent moment of inertia of the servo system, b is the viscosity coefficient of the servo system, and 0<η≤1 is a constant parameter of the design;

[0033] Among them, p and q are two positive odd numbers, and they satisfy 0 <p<q<2p;F s (t) = ae -μt +c is the comprehensive tracking error e s (t), where a+c>c>0 is the initial value of the boundary, c is the steady-state value of the boundary, μ>0 is the boundary convergence rate, t is the time, and e s (0) <F s (0).

[0034] Beneficial effects:

[0035] The advantages of this invention include: combining the variable gain concept with the extended state observer (ESO), avoiding deterioration in estimation performance caused by excessive position observation errors during the startup phase; utilizing the integrated tracking error and constrained intermediate control variables to design a non-smooth region tracking controller, ensuring that the servo system tracking error remains within a set range. This invention combines the variable gain extended state observer (ESO) with the non-smooth region tracking controller, improving the observer's transient estimation performance for unknown speeds and unknown fast-varying nonlinearities by adding a variable gain term to the ESO. Based on the estimated values ​​of speed and nonlinearity, a non-smooth region tracking controller is designed, enhancing active interference rejection, tracking performance, and practicality while ensuring the safety of the servo system. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flowchart of a method for controlling a servo system region tracking based on an extended state observer is provided;

[0037] Figure 2 This is a control block diagram of a servo system area tracking control method based on an extended state observer;

[0038] Figure 3 Estimation curve diagram of variable gain extended state observer;

[0039] Figure 4 This is the position tracking error curve of the servo system. DETAILED DESCRIPTION

[0040] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0041] Figure 1 The flowchart of a servo system area tracking control method based on an extended state observer specifically includes:

[0042] S1, setting the expected signal and error range of the servo system, wherein the expected signal includes the expected position, expected speed, and expected acceleration; in the embodiment of the present invention, S1 specifically includes: setting the expected position y of the servo system d , expected speed The expected acceleration is Error Zone-F s (t) <e s (t) <F s (t).

[0043] S2. Obtain the current input torque and the current output position of the servo system, calculate the position estimation error according to the output position of the servo system, and calculate and update the variable gain term according to the position estimation error;

[0044] In the embodiment of the present invention, S2 specifically includes: obtaining the current input torque τ and output end position y of the servo system through sensors.

[0045] Calculate the position estimation error based on the output position y of the servo system above Calculate variable gain terms Among them, r0>0,ε>0,κ>0 are set constants.

[0046] S3. The expanded state is constructed based on the total unknown nonlinearity in the servo system, and a variable gain expanded state observer is constructed by combining the variable gain term.

[0047] In the embodiment of the present invention, based on the physical structure and electrical principles of the motor-driven servo system, the dynamic model of the servo system with unknown nonlinearity can be described as:

[0048] Among them, q, They represent the position and velocity of the servo system output end respectively, J is the equivalent moment of inertia of the servo system, b is the viscosity coefficient of the servo system, f represents the total unknown nonlinearity in the servo system, and τ represents the input torque of the servo system.

[0049] Define the new state as x1=q, Then system (1) can be transformed into:

[0050]

[0051] For the transformed system (2), define the expanded state x3 = -f / J. The input torque τ of the servo system and the position estimation error and variable gain terms Substitute the following variable gain extended state observer:

[0052]

[0053] in, is the estimated value of the variable gain extended state observer, is the estimated error of the output position of the servo system by the variable gain extended state observer.

[0054] S4. Obtain estimated values ​​of unknown speed and unknown nonlinearity in the servo system by using a variable gain expanded state observer, and calculate a comprehensive tracking error in combination with a desired signal of the servo system.

[0055] is the constructed comprehensive tracking error, is the estimated value of velocity tracking error, 0<η≤1 is the constant parameter of the design.

[0056] S5. Using the comprehensive tracking error, error region and constrained intermediate control quantity, a non-smooth region tracking controller is constructed to calculate the input torque control value, so that the servo system tracking error is always within the error region.

[0057] In the embodiment of the present invention, S5 is implemented in the following manner:

[0058] According to the speed estimation value obtained in S5 above Nonlinear estimates Expected position y d , expected speed Expected acceleration and the preset tracking error area -F s (t) <z1<F s (t), the input torque is calculated by the following formula:

[0059]

[0060] Among them, the intermediate control quantity based on the Funnel constraint function is

[0061]

[0062] Among them F s (t) = ae -μt +c is the comprehensive tracking error e s (t), where a+c>c>0 is the initial value of the boundary, c is the steady-state value of the boundary, μ>0 is the boundary convergence rate, t is the time, and e s (0) <F s (0); p and q are two positive odd numbers, and satisfy 0 <p<q<2p。

[0063] S6. Send the input torque control value to the servo system to achieve control of the servo system.

[0064] Figure 2This is a control block diagram for a servo system region tracking control method based on an extended state observer. The method consists of a servo system, a variable-gain extended state observer, and a nonsmooth region tracking controller. Incorporating an improved variable-gain extended state observer, the designed nonsmooth region tracking controller eliminates the need for accurate output velocity information, ensuring that the position tracking error remains within a specified region and improving both transient and steady-state performance.

[0065] The technical solution disclosed in the present invention is simulated and verified as follows:

[0066] Step 1: Establish the servo system state equation

[0067] According to the general model of the servo system (1), the moment of inertia is set to J = 0.11 kg·m 2 , the viscous friction coefficient is b = 0.25 Nm·s / rad, and the system nonlinearity is The initial state of the system is According to formula (2), the state equation of the servo system after the expanded state is obtained as follows:

[0068]

[0069] in, is the total disturbance of the servo system.

[0070] Step 2: Set the parameters of the variable gain extended state observer to r0 = 28, ε = 0.01, κ = 0.2, and the initial estimate is The parameter of the non-smooth region tracking controller is η = 0.1, and the bounding amplitude of the position tracking error constraint region is F s (t)=1·e -4t +0.1, p=7,q=11; the preset reference position is y d =0.4sin(πt), the reference speed is The reference acceleration is y d =-0.4π 2 sin(πt).

[0071] Step 3: Simulate the entire system and obtain the estimated values ​​of the servo system position and extended state by the variable gain non-smooth extended state observer ( Figure 3 ) and the actual position tracking error curve ( Figure 4 ).

[0072] Figure 3 is the estimation curve of the variable gain extended state observer. Although the initial estimation error of the observer is relatively large, but there is no large peak in the estimated value of speed and the estimated value of total disturbance. Therefore, the designed variable gain term improves the transient estimation performance of the extended state observer.

[0073] Figure 4 Figure 1 is the position tracking error curve for the servo system. It can be seen that the position tracking error, e1, is always constrained within the pre-set region, with minimal overshoot and a steady-state value far below the boundary of the set region. This indicates that the designed non-smooth region tracking controller does improve the tracking performance of the servo system.

[0074] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A servo system area tracking control method based on an extended state observer, characterized by: The specific steps include: S1. Setting the expected signal and error range of the servo system, wherein the expected signal includes the expected position, the expected speed, and the expected acceleration; S2. Obtain the current input torque and the current output position of the servo system, calculate the position estimation error according to the output position of the servo system, and calculate and update the variable gain term according to the position estimation error; specifically: The position estimation error z1 is calculated based on the output position y of the servo system described above, and the variable gain term is calculated. Among them, r0>0,ε>0,κ>0 are set constants; S3, constructing an extended state based on the total unknown nonlinearity in the servo system, and combining the variable gain term to construct a variable gain extended state observer; S4, obtaining estimated values ​​of unknown speed and unknown nonlinearity in the servo system by the variable gain extended state observer, and calculating a comprehensive tracking error in combination with a desired signal of the servo system; S5. Using the comprehensive tracking error, the error region, and the constrained intermediate control variable, a non-smooth region tracking controller is constructed to calculate the input torque control value, so that the servo system tracking error is always within the error region; specifically: Based on speed estimates Unknown nonlinear estimates Expected position y d , expected speed Expected acceleration Preset Tracking Error Area-F s (t) <z1<F s (t) and the constructed comprehensive tracking error e s (t), construct Equation (4) as a non-smooth region tracking controller to calculate the input torque τ(t): λ(e s (t)) is the intermediate control variable based on the Funnel constraint function; J is the equivalent moment of inertia of the servo system, b is the viscosity coefficient of the servo system, and 0<η≤1 is a constant parameter of the design; S6. Send the input torque control value to the servo system to control the servo system.

2. The servo system area tracking control method based on the extended state observer according to claim 1, characterized in that: The setting of the expected signal and error range of the servo system is specifically as follows: Including setting the desired position of the servo system to y d The expected speed is The expected acceleration is Comprehensive tracking error e s The default area for (t) is -F s (t) <e s (t) <F s (t), F s (t) is the comprehensive tracking error e s (t) is the amplitude of the preset region boundary.

3. The servo system area tracking control method based on extended state observer according to claim 1, characterized in that: The acquisition of the current input torque and the current output position of the servo system is specifically as follows: The current input torque τ and output position y of the servo system are obtained through sensors.

4. The servo system area tracking control method based on the extended state observer according to claim 1, characterized in that: In S3, the expanded state is constructed based on the total unknown nonlinearity in the servo system, and the variable gain extended state observer is constructed in combination with the variable gain term, specifically: According to the physical structure and electrical principles of the motor-driven servo system, the dynamic model of the servo system with unknown nonlinearity can be described as: Among them, q, They represent the position and velocity of the servo system output, f represents the total unknown nonlinearity in the servo system, and τ represents the input torque of the servo system; According to the dynamic model (1) of the servo system, the new system states x1 and x2 are defined as x1 = q, Then the dynamic model (1) of the servo system is transformed into: Where y is the position of the servo system output; For the transformed system formula (2), the expanded state is constructed based on the total unknown nonlinearity in the servo system. The expanded state is defined as x3 = -f / J, and the following variable gain expanded state observer is constructed: in, is the estimated value of the variable gain extended state observer, is the estimated error of the output position of the servo system by the variable gain extended state observer, is the variable gain term in the variable gain extended state observer.

5. The servo system area tracking control method based on extended state observer according to claim 4, characterized in that: In S4, the variable gain extended state observer obtains estimated values ​​of unknown speed and unknown nonlinearity in the servo system, and calculates the comprehensive tracking error in combination with the desired signal of the servo system, specifically: is the constructed comprehensive tracking error, is the estimated value of velocity tracking error, 0<η≤1 is the constant parameter of the design.

6. The method for area tracking control of a servo system based on an extended state observer according to claim 5, characterized in that: In the above S5, λ[e s (t)] is the intermediate control quantity based on the Funnel constraint function: Among them, p and q are two positive odd numbers, and they satisfy 0 <p<q<2p;F s (t) = ae -μt +c is the comprehensive tracking error e s (t), where a+c>c>0 is the initial value of the boundary, c is the steady-state value of the boundary, μ>0 is the boundary convergence rate, t is the time, and e s (0) <F s (0).

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