An electro-hydraulic actuator composite adaptive anti-interference flow pulsation compensation control method

Abstract

The application discloses a kind of electro-hydraulic actuator compound adaptive anti-interference flow pulsation compensation control methods, this control method is based on theoretical flow pulsation representation paradigm construction, compound adaptive rate is used for processing parameter uncertainty, and two extended state observers designed based on position signal and pressure signal are combined to estimate online.For the flow pulsation compensation problem of electro-hydraulic actuator, the application can realize adaptive estimation of unknown parameters of system, and can compensate the uncertainty of matching and mismatching nonlinearity in real time, improve the control performance of system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electromechanical servo control, and particularly relates to a composite adaptive anti-disturbance flow pulsation compensation control method (CAADRC) for an electro-hydraulic actuator. BACKGROUND

[0002] An electro-hydraulic servo system has the advantages of strong load capacity, high power-to-weight ratio, flexible arrangement, etc., and is widely used in industrial machinery, weapons, aviation, aerospace and other fields, and realizes high-performance driving and motion control of intelligent industry and high-end equipment. The electro-hydraulic servo system includes a valve control system and a pump control system. At present, the valve control system occupies a dominant position in the application of the national defense and the industry, but the valve control system realizes the load movement of the actuator by controlling the opening size of the servo valve, so there is a throttling loss, resulting in low system efficiency. For some occasions with high power ratio requirements, the valve control system is often unsatisfactory, and there is an urgent need for a more efficient driving mode. For occasions with high power ratio requirements, a typical scheme to replace the valve control system is an electro-hydraulic actuator. The electro-hydraulic actuator adopts a closed loop design, has no master control valve group, and the pressure and flow are strictly matched with the system requirements, so the system efficiency can reach 70%. The electro-hydraulic actuator has no distributed oil source, less pipeline, small leakage and high reliability, and has the advantages of hydraulic drive and electric drive actuator. It only includes an electrical interface and a mechanical installation structure, and has the advantages of rapidity and lightness. However, due to the inherent characteristics of the electro-hydraulic actuator system, such as low frequency width, large inertia and strong nonlinearity, the electro-hydraulic actuator system has slow response and low precision. How to realize high-performance control of the electro-hydraulic actuator has been a core problem in the field of hydraulic control at home and abroad.

[0003] In order to pursue higher control accuracy of the electro-hydraulic actuator system, compensation of the nonlinear characteristics of the system is essential. At present, the model compensation of various nonlinearities (including the friction coefficient of the actuator, the leakage coefficient, the flow gain, the leakage coefficient of the piston pump, the elastic modulus of the hydraulic oil, etc.) of the pump control system is increasingly perfect, but the compensation of the flow pulsation is still less considered. The flow pulsation is an inherent property of the piston pump, and in theory, it is mainly caused by the reciprocating motion of multiple pistons, and in actual engineering, the performance form of the flow pulsation is also added by the influence of the residual pressure accumulated by the extrusion and discharge of the oil in the cylinder hole sealing cavity. There is a deviation between the theoretical flow pulsation and the actual flow pulsation, which is the typical "reality gap" problem existing in the characterization of the flow pulsation of the piston pump. In the existing research of the electro-hydraulic actuator, the consideration of the flow pulsation often only stays in the design simulation, and for the control strategy research, the flow pulsation of the piston pump is often approximated as a proportional link, that is, the output flow of the piston pump is simply considered as the product of the displacement and the speed. Such modeling can make all pump control systems adopt a paradigm expression, and the controller design can be realized without studying the mechanism of the flow generation of various pumps. However, since the flow pulsation is not considered in the modeling, the uncertainty boundary matching is enlarged, which makes the controller design often need to increase the gain parameter to "oppose" the uncertainty upper bound expansion problem caused by not considering the flow pulsation compensation, and at the same time, the excessive control gain may amplify the noise and other adverse factors, which limits the further improvement of the control accuracy of the electro-hydraulic actuator. SUMMARY

[0004] The purpose of the present application is to provide an electro-hydraulic actuator flow pulsation compensation control method with high tracking performance, which can realize adaptive estimation of unknown parameters of the system and real-time compensation of matching and non-matching uncertainty nonlinearities, and effectively improve the control performance of the system.

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

[0006] Step 1, establish a mathematical model of the electro-hydraulic actuator system, and go to step 2.

[0007] Step 2, based on the mathematical model of the electro-hydraulic actuator system, design a composite adaptive anti-disturbance controller considering flow pulsation compensation, and go 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 tracking error of the system is bounded and stable.

[0009] Compared with the prior art, the present application has the following advantages: (1) adaptive estimation of unknown parameters of the system is realized; (2) real-time compensation of matching and non-matching uncertainty nonlinearity is realized, and the control performance of the system is improved, and the simulation results verify the effectiveness. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 is a principle diagram of the compound adaptive active disturbance rejection flow pulsation compensation control method of the electro-hydraulic actuator of the present application.

[0011] Figure 2 is a principle diagram of the electro-hydraulic actuator system of the present application.

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

[0013] Figure 4 is a tracking error comparison curve diagram of the system under the action of the CAADRC controller designed in the present application and the action of two other controllers.

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

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

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

[0017] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0018] In combination with Figure 1 and Figure 2 , the compound adaptive active disturbance flow pulsation compensation control method of the electro-hydraulic actuator of the present application comprises the following steps:

[0019] Step 1, a mathematical model of the electro-hydraulic actuator system is established.

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

[0021] According to Newton's second law, the dynamic equation of the electro-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, represents the velocity 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, A f S f represents the Coulomb friction, A f represents the amplitude of the Coulomb friction, S f represents a continuous approximation Coulomb friction shape function, d2(t) represents a system mechanical unmodeled disturbance, and t represents time.

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

[0025]

[0026] In formula (2), β e represents the effective elastic modulus of the oil, C t1 represents the leakage coefficient of the hydraulic cylinder, the pressure difference p L =p1-p2 between the inlet and outlet chambers of the hydraulic cylinder, the control volume V1 of the inlet chamber =V 01 +Ay, and the control volume V2 of the outlet chamber =V 02 -Ay, V 01 represents the initial volume of the inlet chamber, V 02 represents the initial volume of the outlet 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 derivative of p1, represents the first derivative of p2.

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

[0028]

[0029] where Q i represents the instantaneous theoretical flow of the i-th plunger, d p represents the plunger diameter, R represents the distribution circle radius of the plunger axis in the cylinder body, ω represents the mechanical rotation speed of the motor, β represents the inclination angle of the swash plate; and N represents the number of plungers.

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

[0031]

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

[0033] According to formulas (3) and (4), the model of the axial plunger pump containing flow pulsation and leakage is obtained as follows:

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

[0035] where the flow gain coefficient is the leakage coefficient of the plunger pump z Q represents the residual error of the actual flow pulsation and the theoretical flow, and generally, the value of this part accounts for a small proportion in the entire output flow of the plunger pump.g sum represents the fluctuation function of the theoretical flow pulsation, and is defined as follows:

[0036]

[0037] where g i represents an intermediate variable.

[0038] Step 1-2, for the convenience of designing the controller, the state variables are defined, the derived mathematical model of the electro-hydraulic actuator system is converted into a state space equation, and the details are as follows:

[0039] The state variables are defined as follows: where the intermediate variable x1=y, the intermediate variable The intermediate variable x3=p L , and the mechanical rotation speed of the motor ω=k m u, u represents the control input of the system, and k m represents the voltage input coefficient, then formulas (1) and (2) are converted into a state space equation as follows:

[0040]

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

[0042] Definition Intermediate variable Intermediate variable Intermediate variable Intermediate variable Intermediate variable Equation (7) is rewritten as follows:

[0043]

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

[0045] Assumption 1: The system is expected to track the position command xd, which is three times continuously differentiable, and the system expected position command, velocity command, acceleration command, and jerk command are all bounded.

[0046] Assumption 2: The unknown parameters of the system are known within a certain range, i.e.

[0047]

[0048] In the equation, the known upper and lower bounds of the vector are

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

[0050]

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

[0052] Assumption 4: M1(t) and M2(t) are the derivatives of the redundant states x e1 and x e2 of the matched and unmatched uncertainty expansion, respectively, whose functional forms are unknown but bounded, with upper bounds |M1(t)| max and |M2(t)| max , respectively.

[0053] Go to Step 2.

[0054] Step 2, based on the mathematical model of the electro-hydraulic actuator system, design a compound adaptive disturbance rejection controller considering flow pulsation compensation, the specific steps are as follows:

[0055] Step 2-1, design a compound adaptive law to estimate unknown parameters, and rewrite equation (8) into the following form, the present application proposes a compound adaptive law for estimating unknown parameters by using parameter error as follows:

[0056]

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

[0058] First-order filter both sides of equation (11) to obtain the following relationship:

[0059]

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

[0061]

[0062] In equation (13), k represents a 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 intermediate variables H1, H2, I1 and I2, then:

[0064]

[0065] wherein, j represents a variable attenuation factor coefficient, and j is always greater than 0;

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

[0067]

[0068] In the equation, s represents an integral variable.

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

[0070]

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

[0072]

[0073] where N1 and N2 are both intermediate variables.

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

[0075]

[0076] where Γ1, Γ2 are positive definite diagonal matrices.

[0077] Step 2-2, design disturbance observer, observe the matching and mismatching uncertainties, as follows:

[0078] Based on equation (8), construct the following two extended state observers:

[0079]

[0080]

[0081] where is the estimate of the system state x = [x1, x2, x3] T , define as the estimation error, and are the estimates of the extended states x e1 and x e2 , define as the corresponding estimation errors, 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 uncertain nonlinearities, define the extended states x e1 and x e2 as follows:

[0083]

[0084] Then equation (8) can be written in the following form:

[0085]

[0086] Define the state and disturbance observation errors State and disturbance observation errors Combining equation (19), equation (20) and equation (22), the state and disturbance observation error dynamics are:

[0087]

[0088] wherein

[0089] wherein B1 and B2 are intermediate variables.

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

[0091]

[0092] Step 2-3, design the compound adaptive active disturbance rejection controller with flow fluctuation compensation to ensure that the system tracking error tends to 0, as follows:

[0093] Define error variable:

[0094]

[0095] wherein position tracking error z1 = x1 - x 1d , a1 is the virtual control law of state x2, x 1d is the position tracking expectation, z2 is the deviation between x2 and a1, and k1 is a positive feedback gain;

[0096] Combining equation (8) and equation (25), the first derivative of z2 is :

[0097]

[0098] Define a2 as the virtual control law of state x3, and the deviation between the two is z3 = x3 - a2; is the first derivative of a1.

[0099] Based on equation (26), the virtual control law a2 can be designed as follows:

[0100]

[0101] wherein k2 is a positive feedback gain; a 2a is a feedforward compensation control item based on compound adaptive and disturbance estimation; a 2s is a robust control item.

[0102] Substitute equation (27) into equation (26) to obtain:

[0103]

[0104] Combining equation (8), the first derivative of z3 is

[0105]

[0106] Since the unknown part in , it is split into two parts as follows:

[0107]

[0108] where represents the known computable part in , and represents the unknown non-computable part in

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

[0110]

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

[0112] Substitute the designed control input u into equation (26) to obtain:

[0113]

[0114] Go to step 3.

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

[0116] Define 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 bandwidths ω o1 and ω o2 , and appropriate coordination parameters w2, w3, u2 and u3 to make the matrix Λ1 defined as follows positive definite:

[0121]

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

[0123]

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

[0125]

[0126] where 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 the minimum eigenvalue of the matrix respectively, and it can be obtained from the positive definiteness of matrix Λ1 that:

[0130]

[0131] From equation (39), it can be seen that the error is bounded, and further it can be obtained that the signals of the closed-loop system are all bounded.

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

[0133] Embodiment

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

[0135] Table 1 System physical parameters

[0136]

[0137] The desired command of the given system is x d= 0.01 sin (πt) x (1 - e -t ) m.

[0138] The following controllers are taken as comparison in simulation:

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

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

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

[0142] The desired instruction of the system, the tracking error comparison of the three controllers are shown in Figure 3 , and Figure 4 . It can be seen from Figure 4 that under the action of the CAADRC controller, the position output of the electro-hydraulic actuator system has high tracking accuracy to the instruction, and the amplitude of the steady-state tracking error is about 1.77 x 10 -4 m. It can be seen that the tracking performance of the CAADRC controller proposed in the application is more superior.

[0143] Figure 5 and Figure 6 are the estimations of the unknown parameters of the system. It can be seen from the figures that the estimation of the unknown parameters of the system still has good convergence performance under the condition of uncertainty, thereby verifying the effectiveness of the designed composite parameter adaptive law. Figure 7The CAADRC controller is a system control input curve over time, the amplitude within ± 0.5V, good realization.

Claims

1. A compound adaptive anti-disturbance flow ripple compensation control method for an electro-hydraulic actuator, characterized in that, The method comprises the following steps: Step 1, a mathematical model of the electro-hydrostatic actuator system is established, and the mathematical model is as follows: Step 1-1, the electro-hydrostatic actuator system is applied to linear motion of large industrial heavy load hydraulic equipment, wherein the load is fixedly connected with a piston rod on a hydraulic cylinder, a plunger pump controls movement of the piston rod on the hydraulic cylinder, thereby driving the load to move, and the mathematical model of the electro-hydrostatic actuator system is derived according to dynamic characteristics of the load, the hydraulic cylinder and the plunger pump, and the mathematical model is as follows: According to Newton's second law, the dynamic equation of the electro-hydrostatic actuator system is as follows: In formula (1), m represents the mass of the load, y represents the displacement of the hydraulic cylinder piston rod, represents the velocity 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, A f S f represents the Coulomb friction, A f represents the amplitude of the Coulomb friction, S f represents the continuous approximate Coulomb friction shape function, d2(t) represents the system mechanical unmodeled disturbance, and t represents time. In the electro-hydrostatic actuator system, considering the flow variation of two cavities of the double-rod hydraulic cylinder, the pressure dynamic equation is as follows: In formula (2), β e represents the effective elastic modulus of the oil, C t1 represents the leakage coefficient of the hydraulic cylinder, the pressure difference p L =p1-p2 between the oil chambers on both sides of the oil cylinder, the control volume V1 of the inlet oil chamber =V 01 +Ay, and the control volume V2 of the outlet oil chamber =V 02 -Ay, V 01 represents the initial volume of the inlet oil chamber, V 02 represents the initial volume of the outlet 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 derivative of p1, represents the first derivative of p2; For a single plunger of the plunger pump, the instantaneous theoretical flow equation is as follows: where Q i represents the instantaneous theoretical flow rate of the i-th piston, d p represents the piston diameter, R represents the distribution circle radius of the piston axis in the cylinder, ω represents the mechanical rotation angular velocity of the motor, β represents the swash plate inclination angle; N represents the number of pistons; Leakage flow rate Q of a single plunger based on Poiseuille effect t The equation is: In formula (4), μ represents the fluid dynamic viscosity under average pressure, l c represents the contact length of the plunger rod with the cylinder, d c represents the gap diameter between the plunger rod and the cylinder; According to the formula (3), formula (4), the flow pulsation and leakage axial piston pump model Q is obtained p is: Q p = k p ωg sum -C t2 (p1-p2)+z Q (5) wherein the flow gain coefficient Plunger pump leakage coefficient z Q denotes the residual of the actual flow pulsation from the theoretical flow, g sum denotes a fluctuation function of the theoretical flow pulsation, defined as wherein g i denotes an intermediate variable; Step 1-2, for the convenience of designing the controller, state variables are defined, and the derived mathematical model of the electro-hydrostatic actuator system is converted into a state space equation; Step 2 is entered. Step 2, based on the mathematical model of the electro-hydrostatic actuator system, a compound adaptive active disturbance rejection controller considering flow pulsation compensation is designed, and step 3 is entered. Step 3, Lyapunov stability theory is used to prove the stability of the compound adaptive active disturbance rejection controller, and a result that the system tracking error is bounded stable is obtained.

2. The electro-hydrostatic actuator compound adaptive disturbance rejection flow ripple compensation control method of claim 1, wherein, In step 1-2, for the convenience of designing the controller, state variables are defined, and the derived mathematical model of the electro-hydrostatic actuator system is converted into a state space equation, and the state space equation is as follows: Define state variables: where, the intermediate variable x1 = y, the intermediate variable The intermediate variable x3 = p L , the mechanical rotation speed of the motor ω = k m u, u represents the system control input, k m represents the voltage input coefficient, then the equation (1), equation (2) is converted into state space equation: Equation (7), denotes the first derivative of x1, denotes the first derivative of x2, denotes the first derivative of x3, the total leakage coefficient C t = C t1 + C t2 , intermediate variable intermediate variable intermediate variable system unknown dynamics Defining system unknown parameters Intermediate variable Intermediate variable Intermediate variable Intermediate variable Intermediate variable Equation (7) is rewritten in the following form: Wherein, T represents transposition.

3. The electro-hydrostatic actuator compound adaptive disturbance rejection flow ripple compensation control method of claim 2, wherein, In step 1, for the convenience of designing the controller, the following assumptions are made: Assumption 1: The system is expected to track position command x d Third order continuous differentiable, and the system expected position command, velocity command, acceleration command, and jerk command are all bounded. Assumption 2: Unknown parameters of the system the size range is known, i.e.: where the vector has a known upper bound of and a lower bound of Assumption 3: the unmodeled disturbances d2 and d3 satisfy: In formula (10), δ1, δ2, δ3, and δ4 are all unknown positive numbers; is a first derivative of d2(t), is a first derivative of d3(t); Assumption 4: M1(t) is the derivative of the redundant state x of the matching uncertainty expansion e1 M2(t) is the derivative of the redundant state x of the non-matching uncertainty expansion e2 Both of which are unknown in function form but bounded, with upper bounds |M1(t)| max , |M2(t)| max ; Step 2 is entered.

4. The electro-hydrostatic actuator compound adaptive disturbance rejection flow ripple compensation control method of claim 3, wherein, In step 2, based on the mathematical model of the electro-hydrostatic actuator system, a compound adaptive active disturbance rejection controller considering flow pulsation compensation is designed, and the compound adaptive active disturbance rejection controller is as follows: Step 2-1, a compound adaptive law is designed to estimate unknown parameters; Step 2-2, a disturbance observer is designed to observe matched and unmatched uncertainties; Step 2-3, a compound adaptive active disturbance rejection controller considering flow pulsation compensation is designed to ensure that the system tracking error tends to 0.

5. The electro-hydrostatic actuator compound adaptive disturbance rejection flow ripple compensation control method of claim 4, wherein, In step 2-1, a compound adaptive law is designed to estimate unknown parameters, and the compound adaptive law is as follows: In order to complete the design of the compound adaptive law, equation (8) is rewritten in the following form: where the intermediate variable intermediate variable intermediate variable φ1= [-x2, -s f (x2)] T , intermediate variable φ2= [g sum f1u, -f2, -f3] T ; First-order filtering is performed on both sides of equation (11) to obtain the following relationship: where R 2f and R 3f both represent intermediate variables, here (·) f represents the first order filtered output of (·), where: In formula (13), k represents a first-order filter coefficient, and k is always greater than 0; denotes a first derivative of φ1, denotes a first derivative of φ2; Define intermediate variables H1, H2, I1 and I2, then: where j represents a variable attenuation factor coefficient, j is always greater than 0; denotes the first derivative of H1, denotes the first derivative of H2, denotes the first derivative of I1, denotes the first derivative of I2; The solution of equation (14) is as follows: In the formula, s represents an integral variable; From equation (15), it can be seen that: Through the above series of filtering changes and variable calculations, the unknown parameters of the system are finally represented by the known information of the system; Definition To The error of the parameter estimate Then: Wherein, N1 and N2 represent intermediate variables; Thus, the composite adaptation law is configured to: Wherein, Γ1 and Γ2 are positive definite diagonal matrices.

6. The electro-hydrostatic actuator compound adaptive disturbance rejection flow ripple compensation control method of claim 5, wherein, In step 2-2, a disturbance observer is designed to observe matched and unmatched uncertainties, and the disturbance observer is as follows: Based on equation (8), the following two extended state observers are constructed: where is the estimate of the system state x = [x1, x2, x3] T , define as the estimation error, and are the estimates of the extended states x e1 and x e2 , respectively, is the first derivative of , is the first derivative of , is the first derivative of , define as and are the corresponding estimation errors, ω o1 and ω o2 are the bandwidths of the two extended state observers in (19), respectively; Due to the model uncertainty of the system including parametric uncertainty and uncertain nonlinearity, the extended state x e1 and x e2 is defined as follows: Equation (8) is written in the following form: State and disturbance observation error State and disturbance observation error Combining equations (19), (20) and (22), the state and disturbance observation error dynamics is: In the formulae, Wherein, B1 and B2 are intermediate variables; It is clear that A1and A2are Hurwitz matrices, so there exist two symmetric positive definite matrices P1and P2such that where I is the identity matrix; Wherein, P1 and P2 are respectively:

7. The hydrostatic actuator compound adaptive disturbance rejection flow ripple compensation control method of claim 6, wherein, In step 2-3, a compound adaptive active disturbance rejection controller considering flow pulsation compensation is designed to ensure that the system tracking error tends to 0, and the compound adaptive active disturbance rejection controller is as follows: Define the error variable: where the position tracking error z1 = x1 - x 1d , a1 is a virtual control law for the state x2, x 1d is the position tracking reference, z2 is the deviation of x2 from a1, and k1 is a positive feedback gain; Combining equations (8) and (25), the first derivative of z2is is: define a2 as a virtual control law for state x3, with a deviation z3 = x3 - a2 between them; is the first derivative of a1; Based on equation (26), the virtual control law α2 is designed in the following form: where k2 is a positive feedback gain; a 2a is a feedforward compensation control term based on composite adaptive and disturbance estimation; a 2s is a robust control term; Substitute formula (27) into formula (26) to obtain: Combining equation (8), the first derivative of z3is found wherein is the first derivative of a2; Since the unknown part is contained in the expression (29) is split into the following two parts: wherein represents the known computable part of represents the unknown non-computable part of Based on formula (29) and formula (30), the input u of the final composite adaptive active disturbance rejection controller is designed as: where k3 is a positive feedback gain; (g sum ) min is a minimum value of g sum ; u a is a feedforward compensation control term based on composite adaptation and disturbance observation; u s is a robust control law; Substitute u into equation (26) to get the first derivative of z3 Go to step 3.

8. The electro-hydrostatic actuator compound adaptive disturbance rejection flow ripple compensation control method according to claim 7, characterized by, In step 3, Lyapunov stability theory is used to prove the stability of the composite adaptive active disturbance rejection controller, and the bounded stability of the system tracking error is obtained, as follows: Define intermediate variables w2, w3, u2 and u3, and select Lyapunov function V1 as follows: Use Lyapunov stability theory to prove stability and obtain the bounded stability of the system tracking error.

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