CN114545864A - Friction compensation control method of electro-hydraulic servo system - Google Patents

Abstract

The invention discloses a friction compensation control method of an electro-hydraulic servo system, which comprises the steps of firstly collecting signals of the system flow, oil supply pressure, acceleration and the like of the electro-hydraulic servo system, modeling the system friction by using an improved LuGre friction model, identifying parameters of the system friction by using a genetic algorithm in an off-line manner, and performing feedforward compensation by using an estimated value generated by an identification model; then introducing a nonlinear state error feedback and extended state observer part of a hyperbolic-like sine function with better smoothness for designing a variable coefficient active disturbance rejection controller; on the basis, a fuzzy self-adaptive control method is combined, and the nonlinear state feedback coefficient is adjusted through errors and error differentiation; the contradiction between rapidity and overshoot is solved, and the stability and the limited time convergence of the system are ensured. The method effectively improves the compensation capability of the system to the friction nonlinearity, improves the motion performance of the system, and improves the tracking accuracy and the disturbance resistance capability of the system.

Description

A friction compensation control method for electro-hydraulic servo system

technical field

The invention relates to a friction compensation control method of an electro-hydraulic servo system, belonging to the technical field of high-precision servo control systems.

Background technique

With the improvement of the control precision requirements of electro-hydraulic servo system, friction has become an important problem that cannot be ignored. Non-linear friction has a great influence on the dynamic and static performance of the system, mainly manifested as creeping phenomenon at low speed, waveform distortion when the speed crosses zero, large static error at steady state, and even unexpected limit cycles. oscillation. Therefore, in order to improve the position control accuracy of the electro-hydraulic servo system and change the low-speed performance of the system, its controller needs to realize the compensation control of friction.

In order to eliminate the influence of friction, improving the control performance of the system depends to a large extent on whether the established mathematical model can accurately reflect the friction characteristics. The friction model of the existing electro-hydraulic servo system controller generally adopts a simplified nonlinear friction model, such as the Coulomb model, the Coulomb sliding friction model or the Stribeck model, etc., but the actual friction has more complex nonlinear characteristics. The friction model is difficult to describe the real friction characteristics.

As a multivariable, nonlinear and strongly coupled controlled phenomenon, electro-hydraulic servo system has the characteristics of nonlinearity and uncertainty. To achieve high-precision servo control, the impact of nonlinear friction on system performance must be overcome. Traditional feedback control strategies, such as high-gain PID control methods, have the advantages of simple structure and easy implementation. Usually, better performance can be obtained under the condition of parameter matching, but in practical engineering, excessive gain will lead to system oscillation. , unstable. The extended state observer in Active Disturbance Rejection Control (ADRC) is used to estimate and compensate for friction. The compensation control method does not depend on the object model nor the friction model, and the algorithm is simple and robust. , easy for engineering application.

SUMMARY OF THE INVENTION

In view of the above defects or improvement requirements of the prior art, the present invention provides a friction compensation control method for an electro-hydraulic servo system and its application, thereby solving the problems of low positioning accuracy and high-speed motion in the existing electro-hydraulic servo system. Technical problems with large following errors.

In order to realize the above technical purpose, the present invention will sample the following technical solutions:

A friction compensation control method for an electro-hydraulic servo system. Firstly, the system flow, oil supply pressure, acceleration and other signals of the electro-hydraulic servo system are collected, and the system friction is modeled by the improved LuGre friction model. The estimated value generated by the identification model is used for feedforward compensation, and then the nonlinear state error feedback and the extended state observer part of the variable coefficient ADRC controller designed by the hyperbolic sine function with better smoothness are introduced. Combined with the fuzzy adaptive control method, the nonlinear state feedback coefficient is adjusted through the error and error differential to realize the control of the electro-hydraulic servo system under the influence of friction.

The improved LuGre friction model is expressed as:

where v is the relative velocity of the two objects (m/s), σ ₀ is the stiffness coefficient (N/m), σ ₁ is the damping coefficient (N s/m), z is the average deformation of the bristles, and σ ₂ is the viscosity _The friction slope factor (N), σ3 is the viscous friction variation factor (s/m), v _s is the Stribeck effect velocity (m/s), h(v) is the lubricating oil film, and its mathematical expression is as follows:

In the formula: f _C is the Coulomb friction force (N), F _S is the static friction force (N), γ _h is the time constant of the lubrication thickness, h _ss is the steady-state oil film thickness, only when the negative damping and external force remain unchanged Variable down, v ₁ and v ₂ are critical speeds, and 0<v ₁ <v ₂ .

In the improved LuGre friction model, the genetic algorithm is used for offline identification of each friction parameter, and the estimated value generated by the identification model is used for feedforward compensation.

The ADRC includes a tracking differentiator, an extended state observer and a nonlinear control rate, the tracking differentiator and the nonlinear control rate arrange a transition process for a given position signal; the extended state observer observes and Over-compensation and under-compensation of the friction feedforward compensation amount, the uncertainty generated by the friction modeling error of the electro-hydraulic servo system, and the external disturbance are compensated, so as to maintain the stability and finite-time convergence of the electro-hydraulic servo system.

Further, the tracking differentiator is established based on the following formula:

Among them, fh=fhan(x ₁ , x ₂ , r, h) is the optimal control synthesis function, and its form is as follows:

In the formula, x ₁ and x ₂ are the system signal states, r is the gain of the control quantity, u is the input signal, h is the sampling step size, and h ₁ is the fast factor. For different systems, by adjusting the parameter r and selecting an appropriate h ₁ , the original signal can be approximated with high precision, and the corresponding differential signal can be obtained.

Further, the nonlinear state error feedback is established based on the following formula:

1. Nonlinear combination

u ₀ = _k pa atanh(x ₁ ,e ₁ ,δ ₁ )+k _d1 atanh(x ₂ ,e ₂ ,δ ₂ )+k _d2 atanh(x ₃ ,Z ₃ ,δ ₃ )

Among them, δ is the interval length of the linear segment, e ₁ is the difference between the command signal and the signal output by the controlled object, e ₂ is the difference between the command signal differential and the output differential, k _p , k _d1 , and k _d2 are the nonlinear gain. Adjust parameters.

2. Non-linear gain adjustable parameters

Considering the existence of frictional interference, the position transfer function is simplified to the third order, and the ideal model of the electro-hydraulic servo system is:

Considering the existence of interference f, the above formula can be written as:

Among them, the function:

原来的系统变成串联积分形式

反馈控制量配置极点部分应该是：F _f is incorporated into the extended state observer as the friction torque deterministic part of the modeling, which can reduce the burden of the observer and play the role of model assistance. The state representing the real-time action is fed back to the control terminal. There are many nonlinear feedback parameters. In order to make the parameter selection easier, all the poles can be placed in the same place, so that the system control input becomes

The original system becomes a series integral form

The pole part of the feedback control quantity configuration should be:

Substituting it into the above formula, we get:

k_d2＝3ω_c-2ξ_svω_sv。The available extremes are:

k _d2 =3ω _c -2ξ _sv ω _sv .

Limiting the controller due to the presence of a threshold on the actual actuator output:

In the formula, u _max is the maximum value of the control signal set to adapt to the output saturation characteristics of the actuator.

Further, the expanded state observer is established based on the following formula:

Suppression of signal chattering by using quasi-hyperbolic sine function

In the formula, β ₁ , β ₂ , β ₃ , and β ₄ are adjustable parameters, which are the feedback gain of the state error, and b ₀ is the amplification factor. The nonlinear state feedback coefficient is adjusted through the error and error differentiation, and the nonlinear gain adjustable parameters k _p , k _d1 , and k _d2 are equivalent to proportional and differential gains. For any channel, the fuzzy adaptive ADRC controller uses the error The parameters k _p , k _d1 , and k _d2 are modified online by using the fuzzy control rules with e ₁ and the error differential e ₂ as input, so as to meet the requirements of e ₁ and e ₂ for ADRC parameter tuning at different times.

In general, compared with the prior art, the following beneficial results can be achieved by the above technical solutions conceived by the present invention:

1) The present invention uses genetic algorithm to identify friction model parameters offline, and optimizes the parameters of the friction model for the purpose of minimizing the difference between the simulated friction force and the collected friction force, and the identification speed is fast. accuracy of the results. There is no need to know the specific initial value of the parameter, and the optimization search can be carried out as long as a range of parameters is required, and at the same time, the local minima can be avoided, the adaptability is wide, and the robustness is strong.

2) The present invention is improved based on the LuGre friction model, which can reflect the nonlinear characteristics of friction more comprehensively, has higher fitting accuracy to the friction state of the electro-hydraulic servo system, improves the accuracy of dynamic analysis and simulation, and effectively saves time and calculation costs. .

3) By modeling and predicting the friction force of the electro-hydraulic servo system and further based on the feedforward compensation of the friction force, the present invention can improve the stability of the speed and the positional accuracy of the action, compensate for the drift change of the friction characteristics, and make up for its excessive speed. Zero-time compensation for the defects of limited ability, improve the robustness of the system, and easy to implement.

4) The present invention observes the uncertainty, over-compensation or under-compensation of friction and external disturbances caused by modeling errors in the system through ESO, and uses this observation to compensate, reducing the friction model-based friction compensation method. It depends on the identification accuracy, and at the same time ensures the anti-disturbance capability of the system.

Description of drawings

Fig. 1 is the system block diagram of the friction compensation control method of electro-hydraulic servo system designed in the method of the present invention;

Fig. 2 is the torque diagram of experiment and identification friction model in the embodiment of the present invention;

3 is a schematic diagram of a hyperbolic sine function of the present invention;

Fig. 4 is gain optimization parameter fuzzy rule diagram in the present invention;

Fig. 5 is the error curve of the sinusoidal signal position tracking by different controllers in the embodiment of the present invention;

FIG. 6 is an error curve of the position tracking of the triangular wave signal by different controllers in the embodiment of the present invention.

Detailed ways

The accompanying drawings disclose, without limitation, a schematic structural diagram of a preferred embodiment of the present invention, and the technical solutions of the present invention will be described in detail below with reference to the accompanying drawings.

As shown in Figure 1, it discloses a system block diagram of a friction compensation control method for an electro-hydraulic servo system according to the present invention. The system friction is modeled, the genetic algorithm is used to identify its parameters off-line, and the estimated value generated by the identification model is used for feedforward compensation, and then a smoother quasi-hyperbolic sine function is introduced to design the nonlinearity of the active disturbance rejection controller. The state error feedback and the expanded state observer are combined with the fuzzy adaptive control method, and the nonlinear state feedback coefficient is adjusted through the error and error differential to realize the control of the electro-hydraulic servo system under the influence of friction.

Specifically, the friction compensation control method for an electro-hydraulic servo system includes the following four steps:

Step 1: Select the system friction model

where v is the relative velocity of the two objects (m/s), σ ₀ is the stiffness coefficient (N/m), σ ₁ is the damping coefficient (N s/m), z is the average deformation of the bristles, and σ ₂ is the viscosity _The friction slope factor (N), σ3 is the viscous friction variation factor (s/m), v _s is the Stribeck effect velocity (m/s), h(v) is the lubricating oil film, and its mathematical expression is as follows:

In the formula: F _C is the Coulomb friction force (N), F _S is the static friction force (N), γ _h is the time constant of the lubrication thickness, h _ss is the steady-state oil film thickness, only when the negative damping and external force remain unchanged Variable down, v ₁ and v ₂ are critical speeds, and 0<v ₁ <v ₂ .

Step 2: Identification of friction model parameters

The invention adopts the genetic algorithm to identify the friction parameters of the system. Genetic algorithm is an adaptive global optimization probabilistic search algorithm formed by simulating the genetic and evolutionary process of organisms in the natural environment. Compared with the optimization methods based on gradient descent and least squares, the genetic algorithm does not require the model information of the object when solving nonlinear problems. Wide range and strong robustness. The method is as follows:

1. Static identification (σ ₂ , σ ₃ , E _C , F _S , and v _s are the static parameters to be identified)

时，鬃毛的稳态平均位移z_ss为：When the system is in steady state, i.e.

When , the steady-state average displacement z _ss of the bristles is:

The relationship between the steady state friction force F _ss and the velocity v is expressed as:

It is established that the identification value of the static friction parameters obtained by the genetic algorithm identification is:

Among them, M represents the population size of the genetic algorithm.

The identification value of friction force can be obtained by the following formula:

Then the identification error is:

The objective function of the selected genetic algorithm is:

2. Dynamic identification (σ ₀ , σ ₁ , α, δ are dynamic parameters to be identified)

The dynamic friction parameter identification is almost the same as the genetic algorithm procedure of the static friction parameter identification, and it is carried out under the condition that the static parameters are known.

The steps of the genetic algorithm are as follows:

Step 1 Initialization: the population size is set to M=200, thereby forming the initial population P(0), and the maximum number of iterations is taken as i=20000;

Step 2: Individual evaluation: Calculate the fitness value of each group of parameters in the population P(t);

Step 3 Selection operation: apply the selection operator to the group;

Step 4: Crossover operation: apply the crossover operator to the population;

Step 5 Mutation operation: apply mutation operator to the population. After the population P(t) is selected, crossed and mutated, the next generation population P(t+1) is obtained;

Step 6: Judgment of termination conditions: Judging whether the termination conditions are met, if so, the individual with the largest fitness obtained in the process is used as the optimal solution output, and the calculation is terminated; otherwise, go to step 2.

Step 3: Feedforward compensation based on friction model

The identification result is shown in Figure 2. From the system block diagram of Figure 1, it can be seen that the friction compensation value is determined according to the friction model obtained by the identification to perform feedforward compensation.

Step 4: Active Disturbance Rejection Controller Design and Implementation

Active disturbance rejection controller consists of three parts: tracking differentiator (TD), extended state observer (ESO), nonlinear control law (NLSEF).

1. Tracking Differentiator

Among them, fh=fhan(x ₁ , x ₂ , r, h) is the optimal control synthesis function, and its form is as follows:

In the formula, x ₁ and x ₂ are the system signal states, r is the gain of the control quantity, y is the input signal, h is the sampling step size, and h ₁ is the fast factor. For different systems, by adjusting the parameter r and selecting an appropriate h ₁ , the original signal can be approximated with high precision, and the corresponding differential signal can be obtained.

2. Nonlinear control law

1) Nonlinear combination

u ₀ = _k pa atanh(x ₁ ,e ₁ ,δ ₁ )+k _d1 atanh(x ₂ ,e ₂ ,δ ₂ )+k _d2 atanh(x ₃ ,Z ₃ ,δ ₃ )

Among them, δ is the interval length of the linear segment, e ₁ is the difference between the command signal and the signal output by the controlled object, e ₂ is the difference between the command signal differential and the output differential, k _p , k _d1 , and k _d2 are the nonlinear gain. Tuning parameters, atanh(x, e, δ) is a hyperbolic sine-like function, and its function image is shown in Figure 3.

2) Nonlinear gain adjustable parameters

Considering the existence of frictional interference, the position transfer function is simplified to the third order, and the ideal model of the electro-hydraulic servo system is:

Considering the existence of interference f, the above formula can be written as:

Among them, the function:

原来的系统变成串联积分形式

反馈控制量配置极点部分应该是：F _f is incorporated into the extended state observer as the friction torque deterministic part of the modeling, which can reduce the burden of the observer and play the role of model assistance. Place all poles in the same place so that the system control input becomes

The original system becomes a series integral form

The pole part of the feedback control quantity configuration should be:

Substituting it into the above formula, we get:

k_d2＝3ω_c-2ξ_svω_sv。The available extremes are:

k _d2 =3ω _c -2ξ _sv ω _sv .

Limiting the controller due to the presence of a threshold on the actual actuator output:

In the formula, u _max is the maximum value of the control signal set to adapt to the output saturation characteristics of the actuator.

3. Extended State Observer

Suppression of signal chattering by using quasi-hyperbolic sine function

In the formula, β ₁ , β ₂ , β ₃ , and β ₄ are adjustable parameters, which are the feedback gain of the state error, and b ₀ is the amplification factor.

4. Fuzzy adaptive control method

Assuming that the nonlinear gain adjustable parameters k _p , k _d1 , and k _d2 satisfy k _p ∈(k _pmin ,k _pmax ), k _d1 ∈(k _d1min ,k _d1max ), k _d2 ∈(k _d2min ,k _d2max ), as For convenience, it is normalized to a value between 0 and 1.

The establishment of fuzzy rules is shown in Figure 4, where the universe of discourse for e ₁ is [-0.6, 0.6], the universe of discourse for e ₂ is [-0.06, 0.06], and each element in the {NBNS ZO PS PB} subset represents "negative large, Negative small, zero, positive small, positive big", k ₁ , k ₂ , k ₃ universes are [0,1], and each element in the {SB} subset represents "small, large" respectively. The defuzzifier adopts the centroid defuzzifier, and the three-channel nonlinear gain optimization parameters k _p , k _d1 , and k _d2 can be obtained in real time.

Preferably, the given desired trajectory is a sine curve x _id =20sin(0.4πt)mm, with friction, the typical active disturbance rejection control and the control method of this embodiment (Fuzzy Variable Gain Active Disturbance Rejection ControlBased on Feedforward Friction Compensation, referred to as BFFAC ) control effect is shown in Figure 5, the comparison between the two is obvious: the tracking error of the typical ADRC control is large, and high-precision control cannot be achieved; while the tracking error of the method in this embodiment is smaller than that of the typical ADRC control, which satisfies high-precision control. Control requirements. Given the expected trajectory is a triangular wave curve, with friction, the control effect of the typical ADRC and the control method of this embodiment is shown in Figure 6. The comparison between the two is obvious: the use of the typical ADRC has the defect that the overshoot becomes larger. However, in the method of this embodiment, since ADRC arranges the transition process in advance, it can also ensure a small overshoot while improving the rapidity of the system response.

Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, those of ordinary skill in the art can also Make more deformations and improvements. Therefore, all equivalent technical solutions should belong to the scope of the present invention and be defined by the various claims of the present invention.

Claims (7)

1. an electro-hydraulic servo system friction compensation control method is characterized in that: at first collect signals such as system flow, oil supply pressure, acceleration of electro-hydraulic servo system, utilize improved LuGre friction model to model system friction, apply genetic algorithm Its parameters are identified off-line, and the estimated values generated by the identification model are used for feedforward compensation; then, nonlinear state error feedback and expanded state observation of the variable coefficient ADRC controller with better smoothness quasi-hyperbolic sine function are introduced On this basis, combined with the fuzzy adaptive control method, the nonlinear state feedback coefficient is adjusted through the error and error differential to realize the control of the electro-hydraulic servo system under the influence of friction. 2. electro-hydraulic servo system friction compensation control method according to claim 1, is characterized in that: described improved LuGre friction model is established based on following formula:

where v is the relative velocity of the two objects (m/s), σ ₀ is the stiffness coefficient (N/m), σ ₁ is the damping coefficient (N s/m), z is the average deformation of the bristles, and σ ₂ is the viscosity The friction slope factor (N), σ ₃ is the viscous friction variation factor (s/m), v _s is the Stribeck effect velocity (m/s), and h(v) is the lubricating oil film. 3. friction model modeling method according to claim 2, is characterized in that: lubricating oil film mathematical expression is as follows:

In the formula: F _C is the Coulomb friction force (N), F _S is the static friction force (N), γ _h is the time constant of the lubrication thickness, h _ss is the steady-state oil film thickness, only when the negative damping and external force remain unchanged Variable down, v ₁ and v ₂ are critical speeds, and 0<v ₁ <v ₂ . 4. The friction compensation control method of an electro-hydraulic servo system according to claim 1, wherein the expansion state observer is established based on the following formula: The fourth-order extended state observer of the system is:

Using a hyperbolic sine-like function to suppress signal chattering:

In the formula, β ₁ , β ₂ , β ₃ , and β ₄ are adjustable parameters, which are the feedback gain of the state error, and b ₀ is the amplification factor. 5. The friction compensation control method of an electro-hydraulic servo system according to claim 1, wherein the nonlinear state error feedback is established based on the following formula: 1) Nonlinear combination u ₀ = _k pa atanh(x ₁ ,e ₁ ,δ ₁ )+k _d1 atanh(x ₂ ,e ₂ ,δ ₂ )+k _d2 atanh(x ₃ ,Z ₃ ,δ ₃ )

Among them, δ is the interval length of the linear segment, e ₁ is the difference between the command signal and the signal output by the controlled object, e ₂ is the difference between the command signal differential and the output differential, k _p , k _d1 , and k _d2 are the nonlinear gain. adjust parameters; 2) Nonlinear gain adjustable parameters Considering the existence of frictional interference, the position transfer function is simplified to the third order, and the ideal model of the electro-hydraulic servo system is:

Considering the existence of interference f, the above formula can be written as:

Among them, the function:

F _f is incorporated into the expanded state observer as the friction torque deterministic part of the modeling, which can reduce the burden of the observer and play the role of model assistance; the system control input becomes

The original system becomes a series integral form

The pole part of the feedback control quantity configuration should be:

Substituting it into the above formula, we get:

The available extremes are:

k _d2 =3ω _c -2ξ _sv ω _sv . 6. The friction compensation control method of electro-hydraulic servo system according to claim 5, is characterized in that: Limiting the controller due to the presence of a threshold on the actual actuator output:

In the formula, u _max is the maximum value of the control signal set to adapt to the output saturation characteristics of the actuator. 7. The friction compensation control method of electro-hydraulic servo system according to claim 5, is characterized in that: The non-linear gain adjustable parameters k _p , k _d1 , and k _d2 are equivalent to proportional and differential gains. For any channel, the fuzzy adaptive ADRC controller takes the error e ₁ and the error differential e ₂ as inputs, and uses the fuzzy control rules to online The parameters k _p , k _d1 , and k _d2 are modified to meet the requirements for ADRC parameter tuning by e ₁ and e ₂ at different times.

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