A friction compensation control method for electro-hydraulic servo system

Abstract

The present invention discloses a friction compensation control method for an electro-hydraulic servo system. The method first collects signals such as system flow, oil supply pressure, acceleration, etc. of the electro-hydraulic servo system, models the system friction using an improved LuGre friction model, identifies its parameters offline using a genetic algorithm, and uses the estimated value generated by the identification model for feedforward compensation; then, a hyperbolic sine function with better smoothness is introduced to design the nonlinear state error feedback and extended state observer part of the variable coefficient self-disturbance rejection controller; and on this basis, a fuzzy adaptive control method is combined to adjust the nonlinear state feedback coefficient through error and error differential; the "contradiction between rapidity and overshoot" is solved, and the stability and finite time convergence of the system are guaranteed. This method effectively improves the system's compensation capability for friction nonlinearity, improves the system's motion performance, and improves the system's tracking accuracy and anti-disturbance capability.

Description

Technical Field

[0001] The invention relates to a friction compensation control method for an electro-hydraulic servo system, belonging to the technical field of high-precision servo control systems. Background Art

[0002] With the increasing requirements for control accuracy of electro-hydraulic servo systems, friction has become an important issue that cannot be ignored. Nonlinear friction has a great impact on the dynamic and static performance of the system, which is mainly manifested in creeping at low speed, waveform distortion when the speed passes through zero, large static error in steady state, and even unexpected limit cycle 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 compensation control of friction.

[0003] In order to eliminate the influence of friction and improve the control performance of the system, it 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 plus sliding friction model or the Stribeck model, etc. However, the actual friction has more complex nonlinear characteristics, and it is difficult to describe the real friction characteristics using a simplified friction model.

[0004] As a multivariable, nonlinear and strongly coupled controlled phenomenon, the electro-hydraulic servo system has the characteristics of nonlinearity and uncertainty. To achieve high-precision servo control, the influence 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, good performance can be obtained under the condition of parameter matching, but in actual engineering, too high gain will cause system oscillation and instability. The extended state observer in the Active Disturbance Rejection Control (ADRC) is used to estimate and compensate for friction. This compensation control method does not rely on either the object model or the friction model, has a simple algorithm, strong robustness, and is easy to apply in engineering. Summary of the invention

[0005] In view of the above defects or improvement needs 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 technical problems of low positioning accuracy during low-speed movement and large following error during high-speed movement in the existing electro-hydraulic servo system.

[0006] In order to achieve the above technical objectives, the present invention will sample the following technical solutions:

[0007] A friction compensation control method for an electro-hydraulic servo system, firstly, collects signals such as system flow, oil supply pressure, acceleration, etc. of the electro-hydraulic servo system, uses an improved LuGre friction model to model the system friction, applies a genetic algorithm to identify its parameters offline, and uses the estimated value generated by the identification model to perform feedforward compensation, then introduces a hyperbolic sine function with better smoothness to design the nonlinear state error feedback and extended state observer parts of a variable coefficient anti-disturbance controller, and on this basis, combines a fuzzy adaptive control method, adjusts the nonlinear state feedback coefficient through the error and error differential, and realizes the control of the electro-hydraulic servo system under the influence of friction.

[0008] The improved LuGre friction model is expressed as follows:

[0009]

[0010] Where v is the relative velocity of the two objects (m / s), σ0 is the rigidity coefficient (N / m), σ1 is the damping coefficient (N·s / m), z is the average deformation of the bristle, σ2 is the viscous friction slope factor (N), σ3 is the viscous friction variation factor (s / m), and v s is the Stribeck effect velocity (m / s), h(v) is the lubricating oil film, and its mathematical expression is as follows:

[0011]

[0012]

[0013]

[0014] Where: f C is the Coulomb friction force (N), F S is the static friction (N), γ h is the time constant of lubrication thickness, h ss is the steady-state oil film thickness, which can only be changed when the negative damping and external force remain unchanged, v1 and v2 are the critical speeds, and 0 <v1<v2。

[0015] In the improved LuGre friction model, each friction parameter is identified offline using a genetic algorithm, and feedforward compensation is performed using an estimated value generated by the identification model.

[0016] The anti-disturbance controller includes a tracking differentiator, an extended state observer and a nonlinear control rate, wherein the tracking differentiator and the nonlinear control rate arrange a transition process for a given position signal; the extended state observer observes and compensates for over-compensation and under-compensation of the friction feedforward compensation, the uncertainty caused by the friction modeling error of the electro-hydraulic servo system, and external disturbances, so as to maintain the stability and finite-time convergence of the electro-hydraulic servo system.

[0017] Furthermore, the tracking differentiator is established based on the following formula:

[0018]

[0019] Among them, fh = fhan (x1, x2, r, h) is the optimal control comprehensive function, which is in the following form:

[0020]

[0021] In the formula, x1 and x2 are the system signal states, r is the control gain, u is the input signal, h is the sampling step, and h1 is the fast factor. For different systems, by adjusting the parameter r and selecting the appropriate h1, the original signal can be approximated with high accuracy and the corresponding differential signal can be obtained.

[0022] Furthermore, the nonlinear state error feedback is established based on the following formula:

[0023] 1. Nonlinear combination

[0024] u0=k p atanh(x1,e1,δ1)+k d1 atanh(x2,e2,δ2)+k d2 atanh(x3,Z3,δ3)

[0025]

[0026] Among them, δ is the interval length of the linear segment, e1 is the difference between the command signal and the signal output by the controlled object, e2 is the difference between the differential of the command signal and the differential of the output, k p , k d1 , k d2 is the nonlinear gain adjustable parameter.

[0027] 2. Nonlinear gain adjustable parameters

[0028] Taking into account the existence of friction interference, the position transfer function is simplified to third order, and the ideal model of the electro-hydraulic servo system is:

[0029]

[0030] Considering the existence of interference f, the above formula can be written as:

[0031]

[0032] Among them, the function:

[0033]

[0034] F fThe friction torque known part of the model is incorporated into the extended state observer, which can reduce the burden of the observer and play a role in model assistance. The state representing the real-time action is fed back to the control end. There are many nonlinear feedback parameters. In order to make the parameters easy to select, all the poles can be configured in the same place, so that the system control input becomes The original system becomes a series integral form The feedback control quantity configuration pole part should be:

[0035]

[0036] Substituting it into the above formula, we can get:

[0037]

[0038] The obtained extreme points are: k d2 =3ω c -2ξ sv ω sv .

[0039] Since the actual actuator output has a threshold, the controller is limited:

[0040]

[0041] In the formula, u max The maximum value of the control signal is set to adapt to the actuator output saturation characteristics.

[0042] Furthermore, the extended state observer is established based on the following formula:

[0043]

[0044] Using a quasi-hyperbolic sine function to suppress signal jitter

[0045]

[0046] In the formula, β1, β2, β3, and β4 are adjustable parameters, which are used as feedback gains of state errors, and b0 is the amplification factor. The nonlinear state feedback coefficient is adjusted by error and error differential, and the nonlinear gain adjustable parameter k p , k d1 , k d2 Equivalent to proportional and differential gain, for any channel, the fuzzy adaptive ADRC controller takes the error e1 and the error differential e2 as input, and uses the fuzzy control rule to adjust the parameter k online. p , k d1 , k d2 Correction is made to meet the requirements of ADRC parameter setting for e1 and e2 at different times.

[0047] In general, the above technical solutions conceived by the present invention can achieve the following beneficial results compared with the prior art:

[0048] 1) The present invention uses a genetic algorithm to identify friction model parameters offline, optimizes the friction model parameters with the purpose of minimizing the difference between the simulated friction force and the collected friction force, has a fast identification speed, and further determines whether the parameters meet the requirements after identification, further improving the accuracy of the identification results. It is not necessary to know the specific initial value of the parameter, as long as the range of a parameter can be optimized and searched, while avoiding local minima, with a wide range of adaptability and strong robustness.

[0049] 2) The present invention is based on the improvement of the LuGre friction model, which can more comprehensively reflect the nonlinear characteristics of friction, has a higher fitting accuracy for the friction state of the electro-hydraulic servo system, improves the accuracy of dynamic analysis and simulation, and effectively saves time and computing costs.

[0050] 3) The present invention can improve the speed stability and position accuracy of the action, compensate for the drift change of the friction characteristics, make up for the defect of limited compensation ability when the speed passes through zero, improve the robustness of the system, and be easy to implement by modeling and predicting the friction force of the electro-hydraulic servo system and further based on the feedforward compensation of the friction force.

[0051] 4) The present invention observes the uncertainty caused by the modeling error in the system, the over-compensation or under-compensation of friction and the external disturbance through ESO, and uses this observation value for compensation, thereby reducing the dependence of the friction compensation method based on the friction model on the friction model and its identification accuracy, while ensuring the system's anti-disturbance ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A system block diagram of the friction compensation control method for the electro-hydraulic servo system designed in the method of the present invention;

[0053] Figure 2 It is a torque diagram of the experimental and identified friction model in the embodiment of the present invention;

[0054] Figure 3 It is a schematic diagram of a quasi-hyperbolic sine function in the present invention;

[0055] Figure 4 is a fuzzy rule diagram of gain optimization parameters in the present invention;

[0056] Figure 5 : is a sinusoidal signal position tracking error curve of different controllers in the embodiment of the present invention;

[0057] Figure 6 1 is a curve of position tracking error of a triangular wave signal by different controllers in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The accompanying drawings disclose a schematic structural diagram of a preferred embodiment of the present invention without limitation. The technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0059] like Figure 1 As shown, it discloses a system block diagram of a friction compensation control method for an electro-hydraulic servo system described in the present invention. According to the collected signals such as system flow, oil supply pressure, acceleration, etc. of the electro-hydraulic servo system, the system friction is modeled using an improved LuGre friction model, and its parameters are identified offline using a genetic algorithm. The estimated value generated by the identification model is used for feedforward compensation, and then a hyperbolic sine function with better smoothness is introduced to design the nonlinear state error feedback and extended state observer parts of the self-disturbance rejection controller. On this basis, the fuzzy adaptive control method is combined to adjust the nonlinear state feedback coefficient through the error and error differential to realize the control of the electro-hydraulic servo system under the influence of friction.

[0060] Specifically, the friction compensation control method of an electro-hydraulic servo system includes the following four steps:

[0061] Step 1: Select the system friction model

[0062]

[0063] Where v is the relative velocity of the two objects (m / s), σ0 is the rigidity coefficient (N / m), σ1 is the damping coefficient (N·s / m), z is the average deformation of the bristle, σ2 is the viscous friction slope factor (N), σ3 is the viscous friction variation factor (s / m), and v s is the Stribeck effect velocity (m / s), h(v) is the lubricating oil film, and its mathematical expression is as follows:

[0064]

[0065]

[0066]

[0067] Where: F C is the Coulomb friction force (N), F S is the static friction (N), γ h is the time constant of lubrication thickness, h ss is the steady-state oil film thickness, which can only be changed when the negative damping and external force remain unchanged, v1 and v2 are the critical speeds, and 0 <v1<v2。

[0068] Step 2: Friction model parameter identification

[0069] The present invention uses a genetic algorithm to identify the friction parameters of the system. The genetic algorithm is a probabilistic search algorithm for adaptive global optimization formed by simulating the genetic and evolutionary processes of organisms in the natural environment. Compared with the optimization methods based on gradient descent and least squares, the genetic algorithm does not require model information of the object when solving nonlinear problems. It only needs a range of parameters to perform optimization search, while avoiding local minima. Therefore, it has a wide range of adaptability and strong robustness. The method is as follows:

[0070] 1. Static identification (σ2, σ3, E C 、F S 、v s is the static parameter to be identified)

[0071] When the system is in steady state, When the steady-state average displacement z of the bristle is ss for:

[0072]

[0073] Steady-state friction force F ss The relationship with speed v is expressed as:

[0074]

[0075] The identification value of the static friction parameter obtained by genetic algorithm is established as:

[0076]

[0077] Among them, M represents the population size of the genetic algorithm.

[0078] The identification value of friction can be obtained by the following formula:

[0079]

[0080] The identification error is:

[0081]

[0082] The objective function of the genetic algorithm is selected as:

[0083]

[0084] 2. Dynamic identification (σ0, σ1, α, δ are dynamic parameters to be identified)

[0085] The genetic algorithm procedure for dynamic friction force parameter identification is almost the same as that for static friction force parameter identification, and is performed when the static parameters are known.

[0086] The steps of genetic algorithm are as follows:

[0087] Step 1: Initialization: The population size is set to M = 200 to form the initial population P(0), and the maximum number of iterations is i = 20000;

[0088] Step 2 Individual evaluation: Calculate the fitness value of each set of parameters in the population P(t);

[0089] Step 3: Select operation: Apply the selection operator to the group;

[0090] Step 4: Crossover operation: Apply the crossover operator to the group;

[0091] Step 5: Mutation operation: Apply the mutation operator to the population. After selection, crossover, and mutation operations, the population P(t) is converted into the next generation population P(t+1);

[0092] Step 6: Determine whether the termination condition is met. If so, the individual with the maximum fitness obtained during the process is output as the optimal solution and the calculation is terminated. Otherwise, go to step 2.

[0093] Step 3: Feedforward compensation based on friction model

[0094] The identification results are as follows Figure 2 As shown by Figure 1 As can be seen from the system block diagram, the friction compensation value is determined based on the friction model obtained by identification to perform feedforward compensation.

[0095] Step 4: Design and implementation of ADRC

[0096] The ADRC consists of three parts: tracking differentiator (TD), extended state observer (ESO), and nonlinear control law (NLSEF).

[0097] 1. Tracking Differentiator

[0098]

[0099] Among them, fh = fhan (x1, x2, r, h) is the optimal control comprehensive function, which is in the following form:

[0100]

[0101] In the formula, x1 and x2 are the system signal states, r is the control gain, y is the input signal, h is the sampling step, and h1 is the fast factor. For different systems, by adjusting the parameter r and selecting the appropriate h1, the original signal can be approximated with high accuracy and the corresponding differential signal can be obtained.

[0102] 2. Nonlinear control law

[0103] 1) Nonlinear combination

[0104] u0=k p atanh(x1,e1,δ1)+k d1 atanh(x2,e2,δ2)+k d2 atanh(x3,Z3,δ3)

[0105]

[0106] Among them, δ is the interval length of the linear segment, e1 is the difference between the command signal and the signal output by the controlled object, e2 is the difference between the differential of the command signal and the differential of the output, k p , k d1 , k d2 is a nonlinear gain adjustable parameter, atanh(x,e,δ) is a quasi-hyperbolic sine function, and its function graph is as follows Figure 3 shown.

[0107] 2) Nonlinear gain adjustable parameters

[0108] Taking into account the existence of friction interference, the position transfer function is simplified to third order, and the ideal model of the electro-hydraulic servo system is:

[0109]

[0110] Considering the existence of interference f, the above formula can be written as:

[0111]

[0112] Among them, the function:

[0113]

[0114] F f Incorporating the known friction torque into the extended state observer can reduce the burden on the observer and play a role in model assistance. All poles are configured in the same place, so that the system control input becomes The original system becomes a series integral form The feedback control quantity configuration pole part should be:

[0115]

[0116] Substituting it into the above formula, we can get:

[0117]

[0118] The obtained extreme points are: k d2 =3ω c -2ξ sv ω sv .

[0119] Since the actual actuator output has a threshold, the controller is limited:

[0120]

[0121] In the formula, u max The maximum value of the control signal is set to adapt to the actuator output saturation characteristics.

[0122] 3. Extended State Observer

[0123]

[0124] Using a quasi-hyperbolic sine function to suppress signal jitter

[0125]

[0126] Where β1, β2, β3, and β4 are adjustable parameters, serving as feedback gains of state errors, and b0 is the amplification factor.

[0127] 4. Fuzzy adaptive control method

[0128] Assume that the nonlinear gain adjustable parameter k p , k d1 , k d2 Satisfy k p ∈(k pmin ,k pmax ), k d1 ∈(k d1min ,k d1max ), k d2 ∈(k d2min ,k d2max ), and for convenience, it is normalized to a value between 0 and 1.

[0129]

[0130]

[0131]

[0132] Establish fuzzy rules such as Figure 4 As shown, the domain of e1 is [-0.6, 0.6], the domain of e2 is [-0.06, 0.06], the elements in the {NBNS ZO PS PB} subset represent "negative large, negative small, zero, positive small, positive large", the domains of k1, k2, and k3 are [0, 1], and the elements in the {SB} subset represent "small, large". The defuzzifier uses the centroid defuzzifier to obtain the nonlinear gain optimization parameter k of the three channels in real time. p , k d1 , k d2 .

[0133] Preferably, the desired trajectory is given as a sinusoidal curve x id =20sin(0.4πt)mm, with friction, the control effects of the typical active disturbance rejection control and the control method of this embodiment (Fuzzy Variable Gain Active Disturbance Rejection Control Based on Feedforward Friction Compensation, referred to as BFFAC) are as follows Figure 5 As shown in the figure, the comparison between the two shows that the typical ADRC has a large tracking error and cannot achieve high-precision control; while the tracking error of the method in this embodiment is smaller than that of the typical ADRC, meeting the requirements of high-precision control. Given that the desired trajectory is a triangular wave curve with friction, the control effects of the typical ADRC and the control method in this embodiment are shown in the figure. Figure 6 As shown, the comparison between the two clearly shows that the typical ADRC has the defect of increasing overshoot; while the method of this embodiment, since ADRC arranges the transition process in advance, it can improve the system response speed while ensuring a smaller overshoot.

[0134] It is easy for those skilled in the art to understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Without departing from the spirit and scope of the present invention, those skilled in the art may make more modifications and improvements. Therefore, all equivalent technical solutions shall belong to the scope of the present invention and be defined by the claims of the present invention.

Claims

1. A friction compensation control method for an electro-hydraulic servo system, characterized in that: The following steps are involved: Step 1: collect the system flow, oil supply pressure and acceleration signals of the electro-hydraulic servo system, use the improved LuGre friction model to model the system friction, apply the genetic algorithm to identify its parameters offline, and use the estimated values ​​generated by the identification model to perform feedforward compensation; Step 2, a hyperbolic sine function with better smoothness is introduced to design the nonlinear state error feedback and extended state observer part of the variable coefficient ADRC; Step 3, 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; The LuGre friction model described in step 1 is established based on the following formula: Where v is the relative velocity of the two objects (m / s), σ0 is the rigidity coefficient (N / m), σ1 is the damping coefficient (N·s / m), z is the average deformation of the bristle, σ2 is the viscous friction slope factor (N), σ3 is the viscous friction variation factor (s / m), and v s is the Stribeck effect velocity (m / s), h(v) is the lubricating oil film; The mathematical expression of lubricating oil film is as follows: Where: F c is the Coulomb friction force (N), F s is the static friction (N), y h is the time constant of lubrication thickness, h ss is the steady-state oil film thickness, which can only be changed when the negative damping and external force remain unchanged, v a and v b is the critical speed (m / s), and 0 <v a <v b .

2. The friction compensation control method of the electro-hydraulic servo system according to claim 1, characterized in that: The extended state observer in step 2 is established based on the following formula: The fourth-order extended state observer of the system is: Use a quasi-hyperbolic sine function to suppress signal jitter: In the formula, β1, β2, β3, β4 are adjustable parameters, which are used as feedback gains of state errors, b0 is the amplification factor, x is the state variable, y is the control output of the controlled object, u is the control input of the controlled object, e is the observation error, and δ4-δ6 are different linear interval lengths; The nonlinear state error feedback is established based on the following formula: 1) Nonlinear combination <h2 style=";text-align:left;direction:ltr">u0=k<h2 style=";text-align:left;direction:ltr"> p <h2 style=";text-align:left;direction:ltr"> atanh(x1,e1,δ1)+k<h2 style=";text-align:left;direction:ltr"> d1 <h2 style=";text-align:left;direction:ltr"> atanh(x2,e2,δ2)+k<h2 style=";text-align:left;direction:ltr"> d2 <h2 style=";text-align:left;direction:ltr"> atanh(x3,Z3,δ3) Among them, δ is the interval length of the linear segment, e1 is the difference between the command signal and the signal output by the controlled object, e2 is the difference between the differential of the command signal and the differential of the output, k p , k d1 , k d2 is the nonlinear gain adjustable parameter, δ1-δ3 are different linear interval lengths; 2) Nonlinear gain adjustable parameters Taking into account the existence of friction interference, the position transfer function is simplified to 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 Incorporating the known part of the friction torque model into the extended state observer can reduce the burden of the observer and play a role in model assistance; the system control input is transformed into The original system becomes a series integral form The feedback control quantity configuration pole part should be: Substituting it into the above formula, we can get: The obtained extreme points are: Among them, A P is the effective area of ​​the hydraulic cylinder piston, k l is the spring stiffness of the load, k sv is the flow gain of the servo valve, ω c is the cut-off frequency of the servo valve, ξ sv is the servo valve damping ratio, ω sv is the natural frequency of the servo valve (rad / s), r is the control gain, and u0 is the feedback control law; among them, the nonlinear gain adjustable parameter k p , k d1 , k d2 Equivalent to proportional and differential gain, for any channel, the fuzzy adaptive ADRC controller takes the error e1 and the error differential e2 as input, and uses the fuzzy control rule to adjust the parameter k online. p , k d1 , k d2 Correction to meet the requirements of e1 and e2 for ADRC parameter setting at different times; Since the actual actuator output has a threshold, the controller is limited: In the formula, u max The maximum value of the control signal is set to adapt to the actuator output saturation characteristics.

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