Composite self-adaptive anti-disturbance flow pulsation compensation control method for electro-hydrostatic actuator

Abstract

The invention discloses a composite self-adaptive anti-disturbance flow pulsation compensation control method for an electro-hydrostatic actuator. The control method is constructed based on a theoretical flow pulsation representation normal form, a composite self-adaptive rate is fused for processing parameter uncertainty, and two expansion state observers designed based on a position signal and a pressure signal are combined for online estimation. Aiming at the flow pulsation compensation problem of the electro-hydrostatic actuator, the adaptive estimation of unknown parameters of the system can be realized, the uncertain nonlinearity of matching and mismatching can be compensated in real time, and the control performance of the system is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electromechanical servo control, and in particular to a composite adaptive anti-disturbance flow pulsation compensation control method (CAADRC) for an electrostatic hydraulic actuator. Background Art

[0002] Electro-hydraulic servo systems have the advantages of strong load capacity, high power-to-weight ratio, and flexible layout. They are widely used in industrial machinery, weapons, aviation, aerospace and other fields, realizing high-performance drive and motion control of intelligent industry and high-end equipment. Electro-hydraulic servo systems include valve control systems and pump control systems. At present, valve control systems dominate the application of defense and industry. However, valve control systems achieve load-carrying motion of actuators by controlling the opening size of servo valves, so there is throttling loss, resulting in low system efficiency. For some occasions with high power ratio requirements, valve control systems are often unsatisfactory, and a more efficient driving method is urgently needed. For high power ratio requirements, a typical solution to replace valve control systems is electrostatic hydraulic actuators. Electrostatic hydraulic actuators adopt closed-loop design, without main control valve group, pressure, flow and system requirements are strictly matched, and system efficiency can reach 70%; no distributed oil source, few pipelines, small leakage, high reliability; it has the advantages of both hydraulic drive and electric drive actuators, and only includes electrical interfaces and mechanical installation structures to the outside, which has the advantages of faster and lighter. However, due to the inherent low bandwidth, large inertia and strong nonlinear characteristics of the electrostatic-hydraulic actuator system, the electrostatic-hydraulic actuator system has a slow response and low precision. How to achieve high-performance control of the electrostatic-hydraulic actuator has always been a core issue in the field of hydraulic control at home and abroad.

[0003] In order to pursue higher control accuracy of electrostatic hydraulic actuator system, compensation for nonlinear characteristics of the system is essential. At present, the model compensation of various nonlinearities of pump control system (including friction coefficient and leakage coefficient of actuator, flow gain and leakage coefficient of plunger pump, elastic modulus of hydraulic oil, etc.) is becoming more and more perfect, but how to compensate flow pulsation is still less considered. Flow pulsation is an inherent property of plunger pump. Theoretically, it is mainly caused by the reciprocating motion of multiple plungers. In actual engineering, the manifestation of flow pulsation is often accompanied by the influence of residual pressure accumulated by the plunger in the cylinder bore sealing cavity when the plunger squeezes and discharges the oil again and again. There is a deviation between theoretical flow pulsation and actual flow pulsation, which is the typical "reality gap" problem in the characterization of plunger pump flow pulsation. In the existing research on electrostatic hydraulic actuator, the consideration of flow pulsation often stays in the design simulation. For the control strategy research, most of them ignore the flow pulsation of plunger pump and approximate it as a proportional link, that is, the output flow of plunger pump is simply considered as the product of displacement and speed. Such modeling allows all pump control systems to be expressed in a paradigm, and the controller design can be realized without studying the mechanism of flow generation of various pumps. However, since flow pulsation is not considered in the modeling, the matching uncertainty bound is enlarged, which makes the controller design often need to increase the gain parameter to "counter" the expansion of the uncertainty upper bound caused by not considering flow pulsation compensation. At the same time, too large control gain is likely to amplify unfavorable factors such as noise, limiting the further improvement of the control accuracy of the electrostatic hydraulic actuator. Summary of the invention

[0004] The purpose of the present invention is to provide a flow pulsation compensation control method for an electrostatic hydraulic actuator with high parameter adaptation, interference estimation and tracking performance, which can not only realize the adaptive estimation of unknown system parameters, but also compensate for the uncertainty nonlinearity of matching and mismatching in real time, effectively improving the system control performance.

[0005] The technical solution to achieve the purpose of the present invention is: a composite adaptive anti-disturbance flow pulsation compensation control method for an electrostatic hydraulic actuator, comprising the following steps:

[0006] Step 1: Establish a mathematical model of the electrostatic hydraulic actuator system and proceed to step 2.

[0007] Step 2: Based on the mathematical model of the electrostatic hydraulic actuator system, design a composite adaptive anti-disturbance controller that takes flow pulsation compensation into consideration, and then proceed to step 3.

[0008] Step 3: Use Lyapunov stability theory to prove the stability of the composite adaptive anti-disturbance controller and obtain the result that the system tracking error is bounded and stable.

[0009] Compared with the prior art, the present invention has the following significant advantages: (1) it realizes adaptive estimation of unknown system parameters; (2) it compensates for the uncertainty nonlinearity of matching and mismatching in real time, thereby improving the system control performance. The simulation results verify its effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a schematic diagram of the principle of the composite adaptive self-anti-disturbance flow pulsation compensation control method of the electrostatic hydraulic actuator of the present invention.

[0011] Figure 2 It is a schematic diagram of the principle of the electrostatic hydraulic actuator system of the present invention.

[0012] Figure 3 It is a curve diagram of the tracking process of the system output to the expected instruction under the action of the CAADRC controller designed by the present invention.

[0013] Figure 4 It is a comparison curve of the tracking errors of the system under the action of the CAADRC controller designed by the present invention and the other two controllers.

[0014] Figure 5 It is a parameter estimation curve diagram of the system under the action of the CAADRC controller designed by the present invention.

[0015] Figure 6 It is a parameter estimation curve diagram of the system under the action of the CAADRC controller designed by the present invention.

[0016] Figure 7 It is a control input curve diagram of the system under the action of the CAADRC controller designed by the present invention. DETAILED DESCRIPTION

[0017] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] Combination Figure 1 and Figure 2 The composite adaptive anti-disturbance flow pulsation compensation control method of the electrostatic hydraulic actuator of the present invention comprises the following steps:

[0019] Step 1: Establish a mathematical model of the electrostatic hydraulic actuator system.

[0020] Step 1-1, the electrostatic hydraulic actuator system is applied to the linear motion of large industrial heavy-duty hydraulic equipment, wherein the load is fixedly connected to the piston rod on the hydraulic cylinder, and the plunger pump controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move. According to the dynamic characteristics of the load, the hydraulic cylinder and the plunger pump, the mathematical model of the electrostatic hydraulic actuator system is derived;

[0021] According to Newton's second law, the dynamic equation of the electrostatic hydraulic actuator system is:

[0022]

[0023] In formula (1), m represents the mass of the load, y represents the displacement of the hydraulic cylinder piston rod, Indicates the speed of the hydraulic cylinder piston rod. represents the acceleration of the hydraulic cylinder piston rod, A represents the effective action area of ​​the hydraulic cylinder piston, p1 represents the oil pressure of the hydraulic cylinder inlet chamber, p2 represents the oil pressure of the hydraulic cylinder outlet chamber, B represents the viscous damping coefficient of the hydraulic cylinder ...2 represents the effective action area of ​​the hydraulic cylinder piston, p2 represents the effective action area of ​​the hydraulic cylinder piston, p2 represents the effective action area of ​​the hydraulic cylinder f S f is the Coulomb friction force, A f represents the amplitude of Coulomb friction, S f represents the continuous approximate Coulomb friction shape function, d2(t) represents the unmodeled mechanical disturbance of the system, and t represents time.

[0024] In the electrostatic hydraulic actuator system, considering the flow changes in the two chambers of the double-rod hydraulic cylinder, the pressure dynamic equation is:

[0025]

[0026] In formula (2), β e Indicates the effective elastic modulus of the oil, C t1 Indicates the leakage coefficient of the hydraulic cylinder, the oil pressure difference p between the inlet and outlet chambers on both sides of the cylinder L =p1-p2, the control volume of the oil inlet chamber V1 = V 01 +Ay, the control volume of the oil outlet chamber V2 = V 02 -Ay, V 01 Represents the initial volume of the oil inlet chamber, V 02 Indicates the initial volume of the oil chamber, Q p represents the output flow of the pump, q1 represents the unmodeled disturbance of p1, q2 represents the unmodeled disturbance of p2, represents the first-order derivative of p1, represents the first derivative of p2.

[0027] For a single plunger of a plunger pump, the instantaneous theoretical flow equation is:

[0028]

[0029] Where Q i represents the instantaneous theoretical flow rate of the ith plunger, d p represents the plunger diameter, R represents the radius of the distribution circle of the plunger axis in the cylinder body, ω represents the mechanical rotation angular velocity of the motor, β represents the inclination angle of the swash plate; N represents the number of plungers.

[0030] The leakage flow equation of a single plunger based on the Poiseuille effect is:

[0031]

[0032] In formula (4), μ represents the dynamic viscosity of the fluid under average pressure, l c Indicates the contact length between the plunger rod and the cylinder, d c Indicates the gap diameter between the plunger rod and the cylinder.

[0033] According to equations (3) and (4), the axial piston pump model with flow pulsation and leakage can be obtained as follows:

[0034] Q p =k p ωg sum -C t2 (p1-p2)+z Q (5)

[0035] The flow gain coefficient Piston pump leakage coefficient z Q It indicates the residual between the actual flow pulsation and the theoretical flow. Usually, this part of the value accounts for a small proportion of the entire plunger pump output flow. sum The fluctuation function representing the theoretical flow pulsation is defined as:

[0036]

[0037] Among them, g i Represents an intermediate variable.

[0038] Step 1-2: To facilitate controller design, define state variables and convert the derived electrostatic hydraulic actuator system mathematical model into state space equations, as follows:

[0039] Define the state variables: Among them, the intermediate variable x1 = y, the intermediate variable Intermediate variable x3 = p L , the motor mechanical rotation angular velocity ω = k m u, u represents the system control input, k m represents the voltage input coefficient, then equations (1) and (2) are converted into state space equations:

[0040]

[0041] Formula (7), represents the first-order derivative of x1, represents the first-order derivative of x2, represents the first derivative of x3, the total leakage coefficient C t =C t1 +C t2 , intermediate variable Intermediate variables Intermediate variables System unknown dynamics

[0042] definition Intermediate variables Intermediate variables Intermediate variables Intermediate variables Intermediate variables Formula (7) can be rewritten as follows:

[0043]

[0044] To facilitate the design of the controller, the following assumptions are made:

[0045] Assumption 1: The position command xd that the system expects to track is continuously differentiable to the third order, and the position command, velocity command, acceleration command, and jerk command that the system expects are all bounded;

[0046] Assumption 2: System unknown parameters The size range of is known, that is,

[0047]

[0048] In the formula, the vector The known upper and lower bounds of

[0049] Assumption 3: The unmodeled disturbances d2 and d3 satisfy:

[0050]

[0051] In formula (10), δ1, δ2, δ3 and δ4 are all unknown positive numbers; is the first-order derivative of d2(t), is the first-order derivative of d3(t).

[0052] Assumption 4: M1(t) and M2(t) are the redundant states x of the matching and mismatching uncertainty expansions, respectively. e1 and x e2 The derivatives of are all unknown but bounded in function form, and their upper bounds are |M1(t)| max ,|M2(t)| max .

[0053] Go to step 2.

[0054] Step 2: Based on the mathematical model of the electrostatic hydraulic actuator system, a composite adaptive anti-disturbance controller considering flow pulsation compensation is designed. The specific steps are as follows:

[0055] Step 2-1, design a composite adaptive law to estimate unknown parameters. Rewrite equation (8) into the following form. The present invention proposes the following composite adaptive law for estimating unknown parameters using parameter errors:

[0056]

[0057] Among them, the intermediate variable Intermediate variables Intermediate variable φ1=[-x2,-s f (x2)] T , intermediate variable φ2=[g sum f1u,-f2,-f3] T .

[0058] Performing first-order filtering on both sides of equation (11) yields the following relationship:

[0059]

[0060] Here (·) f represents the first-order filter output of (·), where:

[0061]

[0062] In formula (13), k represents the first-order filter coefficient, and k is always greater than 0; represents the first-order derivative of φ1, represents the first-order derivative of φ2.

[0063] Define the intermediate variables H1, H2, I1 and I2, then:

[0064]

[0065] Among them, j represents the variable attenuation factor coefficient, and j is always greater than 0;

[0066] Then the solution of formula (14) is:

[0067]

[0068] Where s represents the integral variable.

[0069] Obviously, from formula (15), we can know:

[0070]

[0071] After a series of filtering changes and variable calculations, the unknown parameters can be finally represented by the known information of the system. for The estimate, is the error in parameter estimation, then:

[0072]

[0073] Among them, N1 and N2 both represent intermediate variables.

[0074] Therefore, the composite adaptive law Can be constructed as:

[0075]

[0076] Where Γ1 and Γ2 are positive definite diagonal matrices.

[0077] Step 2-2: Design a disturbance observer to observe the matching and mismatching uncertainties as follows:

[0078] Based on formula (8), the following two extended state observers are constructed:

[0079]

[0080]

[0081] In the formula For the system state x = [x1, x2, x3] T Estimates, definitions is the estimation error, and They are expansion states x e1 and x e2 Estimates, definitions is the corresponding estimation error, ω o1 and ω o2 are the bandwidths of the two extended state observers in equation (19).

[0082] Since the model uncertainty of the system includes parameter uncertainty and uncertainty nonlinearity, the expansion state x is defined as e1 and x e2 as follows:

[0083]

[0084] Then formula (8) can be written as follows:

[0085]

[0086] Defining state and disturbance observation errors State and disturbance observation errors Combining equations (19), (20) and (22), we can obtain the state and disturbance observation error dynamics: for:

[0087]

[0088] In the formula

[0089] Among them, B1 and B2 are intermediate variables.

[0090] Obviously, A1 and A2 are Hurwitz matrices, so there exist two symmetric positive definite matrices P1 and P2 such that holds, where I is the identity matrix. Where P1 and P2 are:

[0091]

[0092] Step 2-3: Design a composite adaptive anti-disturbance controller that takes into account flow pulsation compensation to ensure that the system tracking error tends to 0, as follows:

[0093] Define the error variable:

[0094]

[0095] In the formula, the position tracking error z1 = x1-x 1d , α1 is the virtual control law of state x2, x 1d is the position tracking expectation, z2 is the deviation between x2 and α1, and k1 is the positive feedback gain;

[0096] Combining equation (8) and equation (25), we get the first-order derivative of z2 for:

[0097]

[0098] Define α2 as the virtual control law of state x3, and the deviation between the two is z3 = x3-α2; is the first-order derivative of α1.

[0099] Based on formula (26), the virtual control law α2 can be designed as follows:

[0100]

[0101] Where k2 is the positive feedback gain; α 2a is a feedforward compensation control item based on composite adaptation and disturbance estimation; α 2s is a robust control term.

[0102] Substituting formula (27) into formula (26), we can obtain:

[0103]

[0104] Combined with equation (8), find the first-order derivative of z3

[0105]

[0106] Since in formula (29) contains unknown parts, so it is split into the following two parts:

[0107]

[0108] In the formula express The known computable part of express The unknown and uncomputable part of

[0109] Based on equations (29) and (30), the input of the final composite adaptive active disturbance rejection controller can be designed as:

[0110]

[0111] Where k3 is the positive feedback gain; (g sum ) min g sum The minimum value of u a is a feedforward compensation control item based on composite adaptation and disturbance observation; u s is the robust control law;

[0112] Substituting the designed control input u into equation (26) yields:

[0113]

[0114] Go to step 3.

[0115] Step 3, using Lyapunov stability theory to prove the stability of the composite adaptive disturbance rejection controller, we get the result that the system tracking error is bounded and stable, as follows:

[0116] Define the intermediate variables w2, w3, u2 and u3, and select the Lyapunov function as follows:

[0117]

[0118] Define the following intermediate variables:

[0119]

[0120] Select sufficiently large control gains k1, k2, k3 and observer bandwidth ω o1 and ω o2 , the appropriate coordination parameters w2, w3, u2 and u3 make the matrix Λ1 defined as follows positive definite:

[0121]

[0122] The elements of the matrix Λ1 are as follows:

[0123]

[0124] Combining equations (33), (34), (35) and (36), define the intermediate variable Intermediate variable z = [|z1|,|z2|,|z3|] T , the intermediate variable η a =[|η1|,η2|,|η3|] T , the intermediate variable χ a =[|χ1|,|χ2|] T , the derivative of V1 is:

[0125]

[0126] Wherein, ε2 represents a positive real number.

[0127] Define the intermediate variable μ1:

[0128]

[0129] where λ max (·) and λ min (·) represent the maximum eigenvalue and minimum eigenvalue of the matrix respectively. From the matrix Λ1 positive definite, we can get:

[0130]

[0131] From formula (39), we can see that the error is bounded, and further, we can conclude that the closed-loop system signals are bounded.

[0132] Therefore, it is concluded that by adjusting the control parameters k1, k2, k3 and the observer bandwidth ω o1 ,ω o2 , accelerate the exponential convergence rate of tracking error, make the final error upper bound as small as possible, the schematic diagram of the control principle of composite adaptive anti-disturbance flow pulsation compensation of electrostatic hydraulic actuator is shown in Figure 1 shown.

[0133] Example

[0134] In order to evaluate the performance of the designed controller, the physical parameters of the electrostatic hydraulic actuator system in the simulation are shown in Table 1:

[0135] Table 1 System physical parameters

[0136]

[0137] Given a system with the expected instruction x d=0.01sin(πt)×(1-e -t )m.

[0138] The following controllers are used for comparison in the simulation:

[0139] Composite adaptive self-disturbance rejection flow pulsation compensation controller: take control gain k1 = 1200, k2 = 600, k3 = 50, k = 0.01, j = 1, observer bandwidth ω o1 =8,ω o2 =20, the initial value of the unknown parameter estimation of the system is set to The adaptive gain is Γ1=diag{1×10 3 , 50}, Γ2=diag{1×10 -8 , 100, 1×10 -19}.

[0140] Composite adaptive active disturbance rejection controller without flow pulsation compensation (CAADRC-FPC): The difference between this method and CAADRC is that in the design of the control input u, g is used sum The average value of g sum To ensure fairness in comparison, the remaining parameters are consistent with CAADRC.

[0141] Composite Adaptive Robust Controller (CARC): The difference between CARC and the CAADRC proposed in this section is that it does not use an extended state observer to estimate the disturbances of the second and third channels. The control gain, initial value of parameter estimation and composite adaptive gain used by CARC are consistent with those of CAADRC, that is, ω o1 =0,ω o2 = 0. Comparison with this controller can verify the effectiveness of disturbance estimation compensation based on extended state observer in CAADRC controller in improving control performance.

[0142] The expected command of the system and the tracking error comparison of the three controllers are shown as follows: Figure 3 ,and Figure 4 As shown. Figure 4 It can be seen that under the action of the CAADRC controller, the position output of the electrostatic hydraulic actuator system has a high tracking accuracy for the command, and the amplitude of the steady-state tracking error is about 1.77×10 -4 m, it can be seen that the tracking performance of the CAADRC controller proposed in the present invention is more superior.

[0143] Figure 5 and Figure 6 It is the estimation of the unknown parameters of the system. It can be seen from the figure that the estimation of the unknown parameters of the system still has good convergence performance under the condition of uncertainty, which verifies the effectiveness of the designed composite parameter adaptive law. Figure 7It is a curve diagram of the system control input changing with time under the action of CAADRC controller, and its amplitude is within ±0.5V, which has good feasibility.

Claims

1. A composite adaptive anti-disturbance flow pulsation compensation control method for an electrostatic hydraulic actuator, characterized in that: The following steps are involved: Step 1, establish a mathematical model of the electrostatic hydraulic actuator system, and proceed to step 2; Step 2: Based on the mathematical model of the electrostatic hydraulic actuator system, a composite adaptive anti-disturbance controller considering flow pulsation compensation is designed, and then the process goes to step 3; Step 3: Use Lyapunov stability theory to prove the stability of the composite adaptive anti-disturbance controller and obtain the result that the system tracking error is bounded and stable.

2. The electrostatic hydraulic actuator composite adaptive anti-disturbance flow pulsation compensation control method according to claim 1 is characterized in that: In step 1, a mathematical model of the electrostatic hydraulic actuator system is established as follows: Step 1-1, the electrostatic hydraulic actuator system is applied to the linear motion of large industrial heavy-duty hydraulic equipment, wherein the load is fixedly connected to the piston rod on the hydraulic cylinder, and the plunger pump controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move. According to the dynamic characteristics of the load, the hydraulic cylinder and the plunger pump, the mathematical model of the electrostatic hydraulic actuator system is derived; Step 1-2: To facilitate controller design, define state variables and convert the derived electrostatic hydraulic actuator system mathematical model into state space equations.

3. The electrostatic hydraulic actuator composite adaptive anti-disturbance flow pulsation compensation control method according to claim 2 is characterized in that: In step 1-1, the electrostatic hydraulic actuator system is applied to the linear motion of large industrial heavy-duty hydraulic equipment, in which the load is fixedly connected to the piston rod on the hydraulic cylinder, and the plunger pump controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move. According to the dynamic characteristics of the load, hydraulic cylinder and plunger pump, the mathematical model of the electrostatic hydraulic actuator system is derived, as follows: According to Newton's second law, the dynamic equation of the electrostatic hydraulic actuator system is: In formula (1), m represents the mass of the load, y represents the displacement of the hydraulic cylinder piston rod, Indicates the speed of the hydraulic cylinder piston rod. represents the acceleration of the hydraulic cylinder piston rod, A represents the effective action area of ​​the hydraulic cylinder piston, p1 represents the oil pressure of the hydraulic cylinder inlet chamber, p2 represents the oil pressure of the hydraulic cylinder outlet chamber, B represents the viscous damping coefficient of the hydraulic cylinder ...2 represents the effective action area of ​​the hydraulic cylinder piston, p2 represents the effective action area of ​​the hydraulic cylinder piston, p2 represents the effective action area of ​​the hydraulic cylinder f S f is the Coulomb friction force, A f represents the amplitude of Coulomb friction, S f represents the continuous approximate Coulomb friction shape function, d2(t) represents the unmodeled mechanical disturbance of the system, and t represents time; In the electrostatic hydraulic actuator system, considering the flow changes in the two chambers of the double-rod hydraulic cylinder, the pressure dynamic equation is: In formula (2), β e Indicates the effective elastic modulus of the oil, C t1 Indicates the leakage coefficient of the hydraulic cylinder, the oil pressure difference p between the inlet and outlet chambers on both sides of the cylinder L =p1-p2, the control volume of the oil inlet chamber V1 = V 01 +Ay, the control volume of the oil outlet chamber V2 = V 02 -Ay, V 01 Represents the initial volume of the oil inlet chamber, V 02 Indicates the initial volume of the oil chamber, Q p represents the output flow of the pump, q1 represents the unmodeled disturbance of p1, q2 represents the unmodeled disturbance of p2, represents the first-order derivative of p1, represents the first-order derivative of p2; For a single plunger of a plunger pump, the instantaneous theoretical flow equation is: Where Q i represents the instantaneous theoretical flow rate of the ith plunger, d p represents the plunger diameter, R represents the radius of the distribution circle of the plunger axis in the cylinder, ω represents the mechanical rotation angular velocity of the motor, β represents the inclination angle of the swash plate; N represents the number of plungers; Based on the Poiseuille effect, the leakage flow rate Q of a single plunger is obtained t The equation is: In formula (4), μ represents the dynamic viscosity of the fluid under average pressure, l c Indicates the contact length between the plunger rod and the cylinder, d c Indicates the gap diameter between the plunger rod and the cylinder; According to equations (3) and (4), the axial piston pump model Q with flow pulsation and leakage is obtained: p for: Q p =k p ωg sum -C t2 (p1-p2)+z Q (5) Among them, the flow gain coefficient Piston pump leakage coefficient z Q It represents the residual between the actual flow pulsation and the theoretical flow, g sum The fluctuation function representing the theoretical flow pulsation is defined as: Among them, g i Represents an intermediate variable.

4. The electrostatic hydraulic actuator composite adaptive anti-disturbance flow pulsation compensation control method according to claim 3 is characterized in that: In step 1-2, in order to facilitate the design of the controller, the state variables are defined and the derived mathematical model of the electrostatic hydraulic actuator system is converted into a state space equation, as follows: Define the state variables: Among them, the intermediate variable x1 = y, the intermediate variable Intermediate variable x3 = p L , the motor mechanical rotation angular velocity ω = k m u, u represents the system control input, k m represents the voltage input coefficient, then equations (1) and (2) are converted into state space equations: Formula (7), represents the first-order derivative of x1, represents the first-order derivative of x2, represents the first derivative of x3, the total leakage coefficient C t =C t1 +C t2 , intermediate variable Intermediate variables Intermediate variables System unknown dynamics Define the unknown parameters of the system θ=[θ1,θ2,θ3,θ4,θ5] T , intermediate variable θ1 = B, intermediate variable θ2 = A f , intermediate variable θ3 = β e k m k p , intermediate variable θ4 = β e , intermediate variable θ5 = β e C t , formula (7) is rewritten as follows: Where T stands for transpose.

5. The electrostatic hydraulic actuator composite adaptive anti-disturbance flow pulsation compensation control method according to claim 4, characterized in that: In step 1, the following assumptions are made to facilitate controller design: Assumption 1: The system is expected to track the position command x d The system is continuously differentiable to the third order, and the position command, velocity command, acceleration command and jerk command expected by the system are all bounded; Assumption 2: The range of the unknown parameter θ of the system is known, that is: θ∈{θ:θ min ≤θ≤θ max } (9) The known upper bound of the vector θ is θ max =[θ 1max ,θ 2max ,θ 3max ,θ 4max ,θ 5max ] T , the lower bound is θ min =[θ 1min ,θ 2min ,θ 3min ,θ 4min ,θ 5min ] T ; Assumption 3: The unmodeled disturbances d2 and d3 satisfy: In formula (10), δ1, δ2, δ3 and δ4 are all unknown positive numbers; is the first-order derivative of d2(t), is the first-order derivative of d3(t); Assumption 4: M1(t) is a redundant state x that matches the uncertainty expansion e1 The derivative of M2(t) is the redundant state x that does not match the uncertainty expansion. e2 The derivatives of are all unknown but bounded in function form, and their upper bounds are |M1(t)| max ,|M2(t)| max ; Go to step 2.

6. The electrostatic hydraulic actuator composite adaptive anti-disturbance flow pulsation compensation control method according to claim 5, characterized in that: In step 2, based on the mathematical model of the electrostatic hydraulic actuator system, a composite adaptive anti-disturbance controller considering flow pulsation compensation is designed as follows: Step 2-1, design a composite adaptive law to estimate unknown parameters; Step 2-2, design a disturbance observer to observe the matching and mismatching uncertainties; Step 2-3: Design a composite adaptive anti-disturbance controller that takes into account flow pulsation compensation to ensure that the system tracking error tends to 0.

7. The electrostatic hydraulic actuator composite adaptive anti-disturbance flow pulsation compensation control method according to claim 6, characterized in that: Step 2-1: Design a composite adaptive law to estimate unknown parameters, as follows: In order to complete the design of the composite adaptive law, formula (8) is rewritten as follows: Among them, the intermediate variable θ1=[θ1,θ2] T , intermediate variable θ2 = [θ3, θ4, θ5] T , intermediate variable φ1=[-x2,-s f (x2)] T , intermediate variable φ2=[g sum f1u,-f2,-f3] T ; Performing first-order filtering on both sides of equation (11) yields the following relationship: Among them, R 2f and R 3f All represent intermediate variables, where (·) f represents the first-order filter output of (·), where: In formula (13), k represents the first-order filter coefficient, and k is always greater than 0; represents the first-order derivative of φ1, represents the first-order derivative of φ2; Define the intermediate variables H1, H2, I1 and I2, then: Among them, j represents the variable attenuation factor coefficient, and j is always greater than 0; represents the first-order derivative of H1, represents the first-order derivative of H2, represents the first-order derivative of I1, represents the first derivative of I2; Then the solution of formula (14) is: In the formula, s represents the integral variable; From formula (15), we can know that: After a series of filtering changes and variable calculations, the unknown parameters are finally represented by the known information of the system. definition is the estimate of θ, the error of parameter estimation but: Among them, N1 and N2 both represent intermediate variables; Therefore, the composite adaptive law is constructed as: Where Γ1 and Γ2 are positive definite diagonal matrices.

8. The electrostatic hydraulic actuator composite adaptive anti-disturbance flow pulsation compensation control method according to claim 7, characterized in that: Step 2-2: Design a disturbance observer to observe the matching and mismatching uncertainties as follows: Based on formula (8), the following two extended state observers are constructed: In the formula, For the system state x = [x1, x2, x3] T Estimates, definitions is the estimation error, and They are expansion states x e1 and x e2 The estimate, for The first derivative of for The first derivative of for The first derivative of is defined as for and The corresponding estimation error, ω o1 and ω o2 are the bandwidths of the two extended state observers in equation (19); Since the model uncertainty of the system includes parameter uncertainty and uncertainty nonlinearity, the expansion state x is defined as e1 and x e2 as follows: Then formula (8) can be written as follows: Defining state and disturbance observation errors State and disturbance observation errors Combining equations (19), (20) and (22), we can obtain the state and disturbance observation error dynamics: for: In the formula, Among them, B1 and B2 are intermediate variables; Obviously, A1 and A2 are Hurwitz matrices, so there exist two symmetric positive definite matrices P1 and P2 such that holds, where I is the identity matrix; Where P1 and P2 are:

9. The method for controlling the hydrostatic actuator composite adaptive anti-disturbance flow pulsation compensation according to claim 8, characterized in that: Step 2-3: Design a composite adaptive anti-disturbance controller that takes into account flow pulsation compensation to ensure that the system tracking error tends to 0, as follows: Define the error variable: In the formula, the position tracking error z1 = x1-x 1d , α1 is the virtual control law of state x2, x 1d is the position tracking expectation, z2 is the deviation between x2 and α1, and k1 is the positive feedback gain; Combining equation (8) and equation (25), we get the first-order derivative of z2 for: Define α2 as the virtual control law of state x3, and the deviation between the two is z3 = x3-α2; is the first-order derivative of α1; Based on formula (26), the virtual control law α2 is designed as follows: Where k2 is the positive feedback gain; α 2a is a feedforward compensation control item based on composite adaptation and disturbance estimation; α 2s is the robust control term; Substituting formula (27) into formula (26), we can obtain: Combined with equation (8), find the first-order derivative of z3 In the formula, is the first-order derivative of α2; Since in formula (29) contains unknown parts, so it is split into the following two parts: In the formula express The known computable part of express The unknown and uncomputable part of ; Based on equations (29) and (30), the input u of the final composite adaptive active disturbance rejection controller is designed as: Where k3 is the positive feedback gain; (g sum ) min g sum The minimum value of u a is a feedforward compensation control item based on composite adaptation and disturbance observation; u s is the robust control law; Substituting u into equation (26), we get the first-order derivative of z3 Go to step 3.

10. The electrostatic hydraulic actuator composite adaptive anti-disturbance flow pulsation compensation control method according to claim 9, characterized in that: In step 3, the stability of the composite adaptive disturbance rejection controller is proved by using Lyapunov stability theory, and the result that the system tracking error is bounded and stable is obtained, as follows: Define the intermediate variables w2, w3, u2 and u3, and select the Lyapunov function V1 as follows: The stability is proved by using Lyapunov stability theory, and the result is that the system tracking error is bounded and stable.

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