Proportional servo valve spool displacement control method taking unknown hysteresis compensation into consideration

Abstract

A proportional servo valve spool displacement control method taking unknown hysteresis compensation into consideration. The control method is based on the idea of using a parameter adaptive law to learn an inverse model of an unknown hysteresis phenomenon and making a desired output signal undergo an estimated inverse hysteresis model in advance, thereby designing a non-linear robust position controller for online inverse compensation of the unknown hysteresis phenomenon. To address the problem of there being hysteresis nonlinearity in the output electromagnetic force of a proportional solenoid that drives a spool to move, the method can not only ensure the active elimination of unknown hysteresis nonlinearity, but can also eliminate other disturbances that are difficult to model in a spool motion system, thereby improving the operability and performance consistency of a hydraulic valve and realizing high-precision tracking of the spool position.

Description

A proportional servo valve spool displacement control method considering unknown hysteresis compensation Technical Field

[0001] The present invention relates to the technical field of electromechanical servo control, and in particular to an electro-hydraulic proportional servo valve spool displacement control method (UHIRAC) considering unknown hysteresis inverse compensation. Background Art

[0002] Proportional servo valves are a product of combining the strengths of servo and proportional valves. They offer low manufacturing and maintenance costs, strong resistance to oil contamination, and the ability to integrate multiple sensing elements based on input electrical signals to achieve proportional control of operating oil pressure, flow, and direction. They are widely used in high-end hydraulic systems such as intelligent engineering machinery and defense equipment. With increasing research, the degree of intelligence has become a key metric for measuring electro-hydraulic proportional servo valves. This intelligence is primarily reflected in two aspects: improved performance and consistent performance. However, the electro-hydraulic proportional servo valve spool motion system is a typical nonlinear system, which contains many nonlinear characteristics and modeling uncertainties. The nonlinear characteristics include hysteresis, friction nonlinearity, etc. The modeling uncertainty includes parameter uncertainty and uncertainty nonlinearity. Among them, parameter uncertainty mainly includes the mass of the moving components in the valve, the viscous friction coefficient of the valve spool, the leakage coefficient, etc. The uncertainty nonlinearity mainly includes unmodeled friction dynamics, system high-order dynamics, external interference and unmodeled leakage, etc. Among them, the most prominent influence on the working performance of the valve spool is the hysteresis nonlinearity between the output electromagnetic force of the proportional solenoid and the input voltage signal. As the key component for driving the valve spool movement, the working characteristics of the proportional solenoid directly affect the valve spool movement accuracy. Therefore, it is necessary to study more advanced nonlinear control strategies for the hysteresis nonlinear characteristics in the electro-hydraulic proportional servo valve spool motion system.

[0003] Over the past few decades, numerous methods have been proposed to compensate for the hysteresis nonlinearity in the spool motion system of electro-hydraulic proportional servo valves. Hysteresis compensation methods can be divided into two categories. Direct compensation involves dividing the established hysteresis model into a linearizable and a non-linearizable portion, using adaptive control to perform online learning to compensate for the unknown parameters of the linear component. The nonlinear component is handled similarly to the treatment of various disturbances, employing robust control, feedforward compensation after disturbance estimation, or other intelligent learning methods such as neural networks and fuzzy logic systems. However, direct compensation for hysteresis nonlinearity ignores the essential characteristics of hysteresis. Another approach involves inverse compensation control, which pre-processes the motion system through an inverse hysteresis model before undergoing the hysteresis model to achieve the desired effect. However, in actual use, the hysteresis characteristics of proportional solenoids are not fully known. Designing an appropriate inverse hysteresis model to account for this unknown hysteresis phenomenon is a crucial consideration in inverse compensation control methods. Inspired by the adaptive online learning method to estimate and compensate for the unknown parameters in the system, an adaptive learning method is designed to learn the unknown hysteresis parameters by utilizing the deviation between the estimated hysteresis model and the actual hysteresis model, and then substitute them into the inverse hysteresis model to achieve effective compensation for hysteresis nonlinearity.

[0004] Summary of the Invention

[0005] The present invention proposes a proportional servo valve spool displacement control method considering unknown hysteresis compensation, which can not only ensure the active elimination of unknown hysteresis nonlinearity, but also eliminate other interferences in the spool motion system that are difficult to model, improve the hydraulic valve maneuverability and performance consistency, and achieve high-precision tracking of the spool position.

[0006] The technical solution for achieving the purpose of the present invention is a method for controlling the displacement of a proportional servo valve spool taking into account unknown hysteresis compensation, comprising the following steps:

[0007] Step 1: Establish a mathematical model of the electro-hydraulic proportional servo valve core motion system, and then go to step 2.

[0008] Step 2: Establish an estimated hysteresis model and an estimated inverse hysteresis model based on Prandtl-Ishlinskii, and then proceed to step 3.

[0009] Step 3: Based on the mathematical model of the electro-hydraulic proportional servo valve spool motion system, the Prandtl-Ishlinskii estimated hysteresis model and the estimated inverse hysteresis model, design an electro-hydraulic proportional servo valve spool displacement controller that takes into account unknown hysteresis nonlinear compensation, and then go to step 4.

[0010] Step 4: Use Lyapunov stability theory to prove the stability of the electro-hydraulic proportional servo valve spool displacement controller considering unknown hysteresis nonlinear compensation, and obtain the result that the system tracking error is asymptotically stable.

[0011] Compared with the prior art, the present invention has the following significant advantages:

[0012] (1) The estimated inverse hysteresis model is used to actively compensate for the unknown hysteresis nonlinearity of the system, and has strong anti-interference ability.

[0013] (2) The influence of other unmodeled disturbances in the system on the control accuracy is avoided, and high-precision tracking performance is achieved. The simulation results verify its effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] FIG1 is a schematic diagram showing the principle of a proportional servo valve core displacement control method considering unknown hysteresis compensation according to the present invention.

[0015] FIG2 is a schematic diagram of the structure and principle of the electro-hydraulic proportional servo valve of the present invention.

[0016] FIG3 is a curve diagram showing the tracking process of the system output to the desired instruction under the action of the UHIRAC controller designed in the present invention.

[0017] FIG4 is a graph showing the tracking error of the system changing with time under the action of the UHIRAC controller designed by the present invention.

[0018] FIG5 is a comparative graph of tracking errors of the system under the action of the UHIRAC controller, the RAC controller and the unified PID controller designed by the present invention.

[0019] FIG6 is a curve diagram of unknown hysteresis parameter estimation under the action of the UHIRAC controller designed by the present invention.

[0020] FIG7 is a curve diagram of unknown system parameter estimation under the action of the UHIRAC controller designed by the present invention.

[0021] FIG8 is a curve diagram showing an upper bound estimation of the total uncertainty of an unknown system under the action of the UHIRAC controller designed by the present invention. DETAILED DESCRIPTION

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] 1 and 2 , the present invention provides a proportional servo valve spool displacement control method considering unknown hysteresis compensation, comprising the following steps:

[0024] Step 1: Establish a mathematical model of the electro-hydraulic proportional servo valve spool motion system, as follows:

[0025] Step 1-1: The electro-hydraulic proportional servo valve is used in aerospace, precision casting, intelligent robotics and other fields, wherein the hydraulic valve core is driven by a proportional solenoid to overcome spring force, hydraulic force, etc., and reciprocate in the valve sleeve according to the command electrical signal;

[0026] According to Newton's second law, the force balance equation of the electro-hydraulic proportional servo valve spool motion system is:

[0027] Formula (1), m represents the total mass of the valve core, electromagnetic armature and other moving components, x v Indicates the displacement of the hydraulic valve core, Indicates the hydraulic valve spool speed, Indicates the acceleration of the hydraulic valve spool, F t represents electromagnetic force, B represents the viscous damping coefficient of the hydraulic valve, A f represents the Coulomb friction amplitude of the hydraulic valve, represents the approximate shape function of the Coulomb friction of the hydraulic valve, F s represents the spring force, d(t) represents the unmodeled disturbance of the system, and t represents time.

[0028] Due to the magnetic loss of the proportional electromagnet, the output electromagnetic force and the input voltage signal are not linear. Therefore, the relationship between the electromagnetic force and voltage can be described as: F t =H(u(t))[t] (2)

[0029] In formula (2), H(u(t))[t] describes the hysteresis phenomenon, and u(t) represents the voltage input signal.

[0030] When the proportional servo valve is not powered, the valve core is pushed to the area outside the non-working stroke under the action of the spring force. Before the hydraulic valve is actually used, the input electrical signal is adjusted to push the valve core to move. When the load flow through the valve is 0, it is calibrated as the working center of the valve. During the entire movement of the valve core, the spring force is always in a compressed state, thereby applying a force in the opposite direction of the electromagnetic force to the valve core. The spring force is described as F s =c1x v +F0 (3)

[0031] In formula (3), c1 represents the elastic coefficient and F0 represents the spring compression coefficient.

[0032] Step 1-2, define state variables: Among them, the intermediate variable x1=x v , intermediate variables Unknown system parameters θ = [θ1, θ2] T , intermediate variable θ1=B, intermediate variable θ2=A f , then transform Equation (2) into the state equation:

[0033] Formula (4), represents the first-order derivative of x1, Represents the first derivative of x2, an intermediate variable

[0034] Go to step 2.

[0035] Step 2: Establish a hysteresis model based on Prandtl-Ishlinskii and an estimated inverse hysteresis model, as follows:

[0036] Step 2-1: First introduce the play operator F r Definition of [v(t)](t):

[0037] In formula (5), v(t) represents the input signal, f r (a,b)=max{ac,min{a+c,b}} is the play operator change function, a is the first input value, b is the second input value, c is the threshold operator, t i is the previous moment of t, t i+1 is the next moment after t, i is the time sequence number, N is the total number of time periods, and the play operator F r [v(t)](t) in [0,t N ] Any subinterval within the time range (t i ,t i+1 ] are monotonous, t N For the total time.

[0038] The hysteresis nonlinearity based on the play operator is defined as

[0039] In formula (6), is the hysteresis constant, p(r) represents the hysteresis density function, satisfying p(r)>0, r represents the integral variable, Λ represents the upper bound of the integral. Since p(r)→0 when r→∞, a fixed value Λ is chosen as the upper bound of the definite integral instead of ∞.

[0040] In order to simplify the control design and execution, the definite integral in Equation (6) is approximated as a discrete cumulative sum

[0041] In formula (7), M represents the number of approximate discrete intervals, r j represents the threshold value in the jth discrete interval, Δr j represents the length of the jth discrete interval, H L (u(t))[t] represents the discrete hysteresis nonlinearity, and ε(t) represents the hysteresis discrete approximation error.

[0042] Step 2-2, since the density function is only related to the threshold r j The threshold r is usuallyj and the discrete interval length Δr j Select as a fixed value and define the unknown hysteresis density constant π j =p(r j )Δr j , the discrete hysteresis nonlinear expression is

[0043] In formula (8), p0 and π j Essentially, they are constants related to the density function. However, the hysteresis phenomenon is often unknown, and it is difficult to obtain an accurate expression for the hysteresis density function. Therefore, p0 and π can be used. j An estimate of is used to describe the unknown hysteresis phenomenon:

[0044] In formula (9), F td To estimate the expected output electromagnetic force under hysteresis parameters, is the estimated value of p0, is π j estimated value.

[0045] Based on the estimated hysteresis model of formula (9), the estimated inverse hysteresis model is derived as follows:

[0046] In formula (10), the inverse hysteresis parameter is expressed as The inverse hysteresis parameter is expressed as The inverse threshold is k is an intermediate variable.

[0047] According to equations (7) and (9), the expected output electromagnetic force value F under the estimated hysteresis parameters is derived t (t) and the output electromagnetic force F under actual hysteresis parameters td The deviation between (t) is

[0048] In formula (11), the hysteresis constant deviation Hysteresis density constant deviation Write Equation (11) in vector form, and we get

[0049] In formula (12), the hysteresis constant deviation vector is The hysteresis constant vector is The hysteresis constant estimation vector is The play operator vector is

[0050] To facilitate the design of the controller and the unknown dynamic observer, the following assumptions are made:

[0051] Assumption 1: The system is expected to track the position command x d It is second-order continuous, and the system expects position command, velocity command and acceleration command to be bounded;

[0052] Assumption 2: The system unmodeled disturbance d(t) and the hysteresis discrete approximation error ε(t) satisfy: ||d(t)||≤δ1,||ε(t)||≤δ2 (13)

[0053] In formula (13), δ1 and δ2 are both unknown positive constants.

[0054] Go to step 3.

[0055] Step 3: Based on the mathematical model of the electro-hydraulic proportional servo valve spool motion system, the Prandtl-Ishlinskii hysteresis model and its estimated inverse hysteresis model, design an electro-hydraulic proportional servo valve spool displacement controller that takes into account the unknown hysteresis nonlinear compensation. The specific steps are as follows:

[0056] Step 3-1: To facilitate controller design, define the tracking error of the system as z1 = x1 - x d , x d is the position instruction that the system expects to track, and the intermediate variable z2=x2-α1 is defined. Taking the derivative of z1, we get

[0057] In formula (14), represents the first-order derivative of z1, Represents x d The first derivative of , gain k1>0;

[0058] Design the virtual control α1 as:

[0059] Substituting formula (15) into formula (14) yields:

[0060] Step 3-2, take the derivative of z2 and get:

[0061] Multiply both sides of equation (17) by m

[0062] Substituting formula (4) into formula (18), we get:

[0063] Substituting formula (12) into formula (19) yields:

[0064] In formula (20), D(t) = d(t) + ε(t) is the total uncertainty of the system, including the unmodeled disturbance of the system and the hysteresis discrete approximation error. According to assumption 2, it can be seen that the total uncertainty of the system has an unknown upper bound, satisfying D(t) < δ, where δ is an unknown positive constant.

[0065] According to formula (20), the expected output electromagnetic force under the hysteresis parameter is estimated to be

[0066] Formula (21), linear robust term gain constant k2>0, represents the estimated value of θ, χ(t) represents the nonlinear robust term, and σ2(t) represents a function that is always positive and satisfies Where ν represents the integration variable, Represents a constant that is always positive, and the nonlinear robust term gain constant k3>0, Represents an estimate of the upper bound of the total uncertainty of the system.

[0067] The expected output electromagnetic force F under the estimated hysteresis parameters is derived td (t) is substituted into the estimated inverse hysteresis model (11) to obtain the final input electrical signal.

[0068] The update law for

[0069] In formula (22), Estimate the gain matrix for the unknown hysteresis constant.

[0070] The update law for

[0071] In formula (23), Γ θ Estimate the gain matrix for unknown system parameters.

[0072] Update law of δ for

[0073] In formula (24), γ is the estimated gain coefficient of the unknown upper bound of the total uncertainty of the system.

[0074] Substituting formula (21) into formula (20), we get:

[0075] Go to step 4.

[0076] Step 4: Use Lyapunov stability theory to prove the stability of the electro-hydraulic proportional servo valve spool displacement controller considering unknown hysteresis nonlinear compensation, and obtain the result that the system tracking error is asymptotically stable. The specific steps are as follows:

[0077] The Lyapunov function is defined as follows:

[0078] Derivative (26) and substitute (16), (21), and (25) into it to obtain:

[0079] Note that 0≤z2tanh[z2 / σ2(t)]≤|z2| (28)

[0080] Available

[0081] Substituting formula (28) into (27), we can get

[0082] Substituting equations (22)-(24) into equation (30), we can obtain

[0083] Notice

[0084] Then formula (31) can be rewritten as

[0085] Define the intermediate variables z and Λ as: z=[z1,z2] (34)

[0086] By adjusting the gains k1 and k2, the symmetric matrix Λ can be made a positive definite matrix, and then we can get:

[0087] In formula (36), the intermediate variable W = λmin(Λ)(z1 2 +z2 2 ),λmin(Λ) represents the minimum eigenvalue of Λ;

[0088] Integrating both sides of equation (36), we can get

[0089] From Equation (37), we can see that V is bounded, the integral of W is bounded, and thus all signals in the system are bounded. Therefore, W is uniformly continuous. According to Barbalat's lemma, as time tends to positive infinity, the tracking error z1 tends to 0.

[0090] Therefore, it is concluded that by adjusting the controller gains k1, k2, k3 and adaptive gain Γ θ and γ. For the electro-hydraulic proportional servo valve spool motion system, the electro-hydraulic proportional servo valve spool displacement controller considering unknown hysteresis nonlinear compensation is designed, which can make the system obtain the result that the tracking error converges to 0 asymptotically. The principle diagram of the electro-hydraulic proportional servo valve spool displacement controller considering unknown hysteresis nonlinear compensation is shown in Figure 2.

[0091] Example

[0092] In order to evaluate the performance of the designed controller, the physical parameters of the electro-hydraulic proportional servo valve spool motion system in the simulation are shown in Table 1:

[0093] Table 1 System physical parameters

[0094] In order to verify the effectiveness of the inverse hysteresis compensation in the simulation, it is necessary to set the hysteresis link in the simulation, hysteresis p0 = 2, and hysteresis density function The upper bound of the integral M = 20, the expected instruction of the given system is x d =sin(πt)×(1-e -0.5t ) mm, the Coulomb friction shape function is S f (x2) = 2arctan(1000x2) / π.

[0095] The following controllers are used for comparison in the simulation:

[0096] Considering unknown hysteresis inverse compensation for electro-hydraulic proportional servo valve spool displacement controller (UHIRAC): During debugging, it was found that the number of discrete intervals in the inverse estimated hysteresis model does not have to be equal to the number of discrete intervals in the hysteresis model. When the number of discrete intervals in the inverse estimated hysteresis model is m=2, the control effect obtained is significantly better than the PID controller and the electro-hydraulic proportional servo valve spool displacement controller (RAC) without considering hysteresis compensation. It is necessary to estimate three hysteresis constants, that is, the hysteresis constant estimation vector is The play operator vector is Take gains k1=400, k2=10, k3=1, Γ θ =diag{1,1},γ=10 -4 ,σ2(t)=5000 / (1+t 2 ).

[0097] Electro-hydraulic proportional servo valve spool displacement controller (RAC) without considering hysteresis compensation: Compared with the electro-hydraulic proportional servo valve spool displacement controller considering unknown hysteresis inverse compensation, this controller has no inverse compensation model, and the output value is the expected output electromagnetic force F td, and the rest of the parameters are consistent with UHIRAC.

[0098] PID controller: The steps for selecting PID controller parameters are: first, ignoring the nonlinear dynamics of the electro-hydraulic proportional servo valve spool motion system, obtain a set of controller parameters through the PID parameter self-tuning function in Matlab, and then fine-tune the obtained self-tuning parameters after adding the nonlinear dynamics of the system to achieve the best tracking performance. The selected controller parameters are k P =10000, k I =1000,k D =50.

[0099] The system's desired command, UHIRAC controller tracking error, and the comparisons of the tracking errors of the UHIRAC controller, RAC controller, and PID controller are shown in Figure 3, Figure 4, and Figure 5, respectively.

[0100] As shown in Figure 4, under the action of the UHIRAC controller, the position output of the proportional servo valve spool motion system has a high tracking accuracy for the command, and the amplitude of the steady-state tracking error is about 4×10 -4 From the comparison of the tracking errors of the three controllers in FIG5 , it can be seen that the tracking error of the UHIRAC controller proposed in the present invention is much smaller than that of the PID controller, and the tracking performance is more superior.

[0101] Figures 6, 7, and 8 are the estimation trends of the upper bounds of unknown hysteresis parameters, unknown system parameters, and unknown total uncertainty interference under the action of the UHIRAC controller. It can be seen from the figures that the three different unknown parameter estimates all show a convergence trend, and the controller works stably.

Claims

1. A proportional servo valve spool displacement control method considering unknown hysteresis compensation, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the electro-hydraulic proportional servo valve core motion system, and then proceed to step 2; Step 2: Establish an estimated hysteresis model and an estimated inverse hysteresis model based on Prandtl-Ishlinskii, and proceed to step 3; Step 3: Based on the mathematical model of the electro-hydraulic proportional servo valve spool motion system, the Prandtl-Ishlinskii estimated hysteresis model and the estimated inverse hysteresis model, design an electro-hydraulic proportional servo valve spool displacement controller that takes into account unknown hysteresis nonlinear compensation, and then proceed to step 4. Step 4: Use Lyapunov stability theory to prove the stability of the electro-hydraulic proportional servo valve spool displacement controller considering unknown hysteresis nonlinear compensation, and obtain the result that the system tracking error is asymptotically stable.

2. The method for controlling the displacement of a proportional servo valve core considering unknown hysteresis compensation according to claim 1, characterized in that: In step 1, a mathematical model of the electro-hydraulic proportional servo valve spool motion system is established as follows: Step 1-1: Based on Newton's second law, derive the mathematical model of the hydraulic proportional servo valve spool motion system; Step 1-2: To facilitate controller design, define state variables and convert the derived mathematical model of the electro-hydraulic proportional servo valve spool motion system into a state space equation.

3. The proportional servo valve spool displacement control method considering unknown hysteresis compensation according to claim 2 is characterized in that: Step 1-1: Based on Newton's second law, derive the mathematical model of the hydraulic proportional servo valve spool motion system, as follows: According to Newton's second law, the force balance equation of the electro-hydraulic proportional servo valve spool motion system is: Formula (1), m represents the total mass of the valve core, electromagnetic armature and other moving components, x v Indicates the displacement of the hydraulic valve core, Indicates the hydraulic valve spool speed, Indicates the acceleration of the hydraulic valve spool, F t represents electromagnetic force, B represents the viscous damping coefficient of the hydraulic valve, A f represents the Coulomb friction amplitude of the hydraulic valve, represents the approximate shape function of the Coulomb friction of the hydraulic valve, F s represents the spring force, d(t) represents the unmodeled disturbance of the system, and t represents time; Due to the magnetic loss of the proportional electromagnet, the output electromagnetic force and the input voltage signal are not linear. Therefore, the relationship between the electromagnetic force and voltage can be described as: F t =H(u(t))[t] (2) In formula (2), H(u(t))[t] describes the hysteresis phenomenon, and u(t) represents the voltage input signal; When the proportional servo valve is not powered, the valve core is pushed to the area outside the non-working stroke under the action of the spring force; before the actual use of the hydraulic valve, adjust the input electrical signal to push the valve core to move. When the load flow through the valve is 0, it is calibrated as the working middle position of the valve. During the entire movement of the valve core, the spring force is always in a compressed state, thereby giving the valve core a force in the opposite direction of the electromagnetic force. The spring force F s Described as F s =c1x v +F0 (3) In formula (3), c1 represents the elastic coefficient and F0 represents the spring compression coefficient.

4. The method for controlling the displacement of a proportional servo valve core considering unknown hysteresis compensation according to claim 3, characterized in that: Step 1-2: To facilitate controller design, define state variables and convert the derived mathematical model of the electro-hydraulic proportional servo valve spool motion system into a state space equation, as follows: Define state variables: Among them, the intermediate variable x1=x v , intermediate variables Unknown system parameters θ = [θ1, θ2] T , intermediate variable θ1=B, intermediate variable θ2=A f , then transform Equation (2) into the state equation: Formula (4), represents the first-order derivative of x1, Represents the first derivative of x2, an intermediate variable T stands for transpose; Go to step 2.

5. The proportional servo valve spool displacement control method considering unknown hysteresis compensation according to claim 4 is characterized in that: In step 2, an estimated hysteresis model and an estimated inverse hysteresis model based on Prandtl-Ishlinskii are established as follows: Step 2-1, use the play operator to define the hysteresis model, estimate the hysteresis model and estimate the inverse hysteresis model; Step 2-2: Establish a hysteresis model and estimate the deviation relationship of the hysteresis model.

6. The method for controlling the displacement of a proportional servo valve core considering unknown hysteresis compensation according to claim 5, characterized in that: In step 2-1, the play operator is used to define the hysteresis model, the estimated hysteresis model, and the estimated inverse hysteresis model, as follows: Step 2-1: First introduce the play operator F r Definition of [v(t)](t) For t i <t≤t i+1 And 0≤i≤N-1 In formula (5), v(t) represents the input signal, f r (a,b)=max{ac,min{a+c,b}} is the play operator change function, a is the first input value, b is the second input value, c is the threshold operator, t i is the previous moment of t, t i+1 is the next moment after t, i is the time sequence number, N is the total number of time periods, and the play operator F r [v(t)](t) in [0,t N ] Any subinterval within the time range (t i ,t i+1 ] are monotonous, t N is the total time; The hysteresis nonlinearity based on the play operator is defined as In formula (6), is the hysteresis constant, p(r) represents the hysteresis density function, satisfying r represents the integral variable, Λ represents the upper bound of the integral. Since p(r)→0 when r→∞, a fixed value Λ is chosen as the upper bound of the definite integral instead of ∞. In order to simplify the control design and execution, the definite integral in Equation (6) is approximated as a discrete cumulative sum In formula (7), M represents the number of approximate discrete intervals, r j represents the threshold value in the jth discrete interval, Δr j represents the length of the jth discrete interval, H L (u(t))[t] represents the discrete hysteresis nonlinearity, ε(t) represents the magnetic Hysteresis discrete approximation error; Since the density function is only related to the threshold r j The threshold r is usually j and the discrete interval length Δr j Select as a fixed value and define the unknown hysteresis density constant π j =p(r j )Δr j , the discrete hysteresis nonlinear expression is: In formula (8), p0 and π j Essentially, they are constants related to the density function. However, the hysteresis phenomenon is often unknown, and it is difficult to obtain an accurate expression for the hysteresis density function. Therefore, p0 and π are used. j An estimate of is used to describe the unknown hysteresis phenomenon: In formula (9), F td To estimate the expected output electromagnetic force under hysteresis parameters, is the estimated value of p0, is π j estimated value of; Based on the estimated hysteresis model of formula (9), the estimated inverse hysteresis model u(t) is derived as follows: In formula (10), the inverse hysteresis parameter is expressed as The inverse hysteresis parameter is expressed as The inverse threshold is k is an intermediate variable.

7. The method for controlling the displacement of a proportional servo valve core considering unknown hysteresis compensation according to claim 6, characterized in that: Step 2-2: Establish the hysteresis model and estimate the deviation relationship of the hysteresis model, as follows: According to equations (7) and (9), the expected output electromagnetic force value F under the estimated hysteresis parameters is derived: t (t) and the output electromagnetic force F under actual hysteresis parameters td The deviation between (t) is In formula (11), the hysteresis constant deviation Hysteresis density constant deviation Write equation (11) in vector form, and we get In formula (12), the hysteresis constant deviation vector is The hysteresis constant vector is The hysteresis constant estimation vector is The play operator vector is To facilitate the design of the controller and the unknown dynamic observer, the following assumptions are made: Assumption 1: The system is expected to track the position command x d It is second-order continuous, and the system expects position command, velocity command and acceleration command to be bounded; Assumption 2: The system unmodeled disturbance d(t) and the hysteresis discrete approximation error ε(t) satisfy: ||d(t)||≤δ1,||ε(t)||≤δ2 (13) In formula (13), δ1 and δ2 are both unknown positive constants; Go to step 3.

8. The method for controlling the displacement of a proportional servo valve core considering unknown hysteresis compensation according to claim 7, characterized in that: In step 3, based on the mathematical model of the electro-hydraulic proportional servo valve spool motion system, the Prandtl-Ishlinskii estimated hysteresis model, and the estimated inverse hysteresis model, an electro-hydraulic proportional servo valve spool displacement controller is designed with unknown hysteresis nonlinear compensation in mind. The specific steps are as follows: Step 3-1: Define the tracking error of the system z1 = x1 - x d , where x d The system expects to track the position command. In order to facilitate the system state x1 to track the expected position command x as accurately as possible under the designed controller drive. d , it is necessary to ensure that the tracking error z1 tends to 0; Step 3-2, define the error z2 = x2-α1, where α1 represents the virtual control of x2, to ensure The error z1 tends to 0, and the error z2 must also tend to 0.

9. The method for controlling the displacement of a proportional servo valve core considering unknown hysteresis compensation according to claim 8, characterized in that: Step 3-1: Define the tracking error of the system z1 = x1 - x d , where x d The system expects to track the position command. In order to facilitate the system state x1 to track the expected position command x as accurately as possible under the designed controller drive. d , it is necessary to ensure that the tracking error z1 tends to 0, as follows: In order to facilitate the design of the controller, the tracking error of the system is defined as z1 = x1-x d , x d is the position instruction that the system expects to track, and the intermediate variable z2=x2-α1 is defined. Taking the derivative of z1, we get In formula (13), represents the first-order derivative of z1, Represents x d The first derivative of , gain k1>0; Design the virtual control α1 as: Substituting formula (15) into formula (14) yields:

10. The proportional servo valve spool displacement control method considering unknown hysteresis compensation according to claim 9, characterized in that: Step 3-2: Define error z2 = x2 - α1, where α1 represents the virtual control of x2. To ensure that error z1 tends to 0, error z2 must also tend to 0, as follows: Taking the derivative of z2 we get: Multiply both sides of equation (17) by m: Substituting formula (4) into formula (18), we get: Substituting formula (11) into formula (18) yields: In formula (20), D(t) = d(t) + ε(t) is the total uncertainty of the system, including the system unmodeled disturbance and the hysteresis discrete approximation error. According to assumption 2, it can be seen that the total uncertainty of the system has an unknown upper bound, satisfying D(t) < δ, where δ is an unknown positive constant; According to formula (19), the expected output electromagnetic force under the hysteresis parameter is estimated to be Formula (21), linear robust term gain constant k2>0, represents the estimated value of θ, χ(t) represents the nonlinear robust term, and σ2(t) represents a function that is always positive and satisfies Where ν represents the integration variable, Represents a constant that is always positive, and the nonlinear robust term gain constant k3>0, represents an estimate of the upper bound of the total uncertainty of the system; The expected output electromagnetic force F under the estimated hysteresis parameters is derived td (t) is substituted into the estimated inverse hysteresis model (11) to obtain the final input electrical signal; The update law for In formula (22), Estimate the gain matrix for the unknown hysteresis constant; The update law for In formula (23), Γ θ Estimate the gain matrix for unknown system parameters; Update law of δ for In formula (24), γ is the unknown upper bound estimation gain coefficient of the total uncertainty of the system; Substituting formula (21) into formula (20), we get: Go to step 4.

11. The method for controlling the displacement of a proportional servo valve core considering unknown hysteresis compensation according to claim 10, characterized in that: The stability of the electro-hydraulic proportional servo valve spool displacement controller considering unknown hysteresis nonlinear compensation is proved by using Lyapunov stability theory as described in step 4, and the result that the system tracking error is asymptotically stable is obtained. The specific steps are as follows: The Lyapunov function is defined as follows: The stability is proved by using Lyapunov stability theory, and the result that the system tracking error is asymptotically stable is obtained.

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