An adaptive control method for electro-hydrostatic actuator with guaranteed parameter estimation

Abstract

The present invention discloses an adaptive control method for an electric hydrostatic actuator that ensures parameter estimation. The method includes: establishing an adaptive backstepping controller; establishing an unknown parameter matrix of the electric hydrostatic actuator, inputting the tracking desired displacement into a first adaptive controller, outputting a first adaptive control law, controlling the displacement tracking of the actuator rod of the electric hydrostatic actuator to track the desired displacement; inputting the first adaptive control law into a second adaptive controller, outputting a second adaptive control law, controlling the output force tracking of the electric hydrostatic actuator to track the first adaptive control law; performing real-time online parameter estimation through adaptive iteration, realizing continuous tracking of the position and force of the actuator rod of the electric hydrostatic actuator, and finally realizing adaptive control of the electric hydrostatic actuator. The present invention solves the problem of poor parameter convergence performance of the existing adaptive control method, can better overcome the influence of model uncertainty in the control process, and improve the control accuracy of the electric hydrostatic actuator.

Description

Technical Field

[0001] The present invention relates to an adaptive control method, in particular to an adaptive control method for an electric hydrostatic actuator for ensuring parameter estimation in view of parameter uncertainty (especially hydraulic parameter uncertainty) existing in the electric hydrostatic actuator. Background Art

[0002] The electric hydrostatic actuator (EHA) is a new type of direct-drive volumetrically controlled electro-hydraulic servo system. Compared with the traditional valve-controlled hydraulic system, it has the advantages of high reliability, high integration, high energy utilization efficiency, and easy installation and maintenance. It can replace the traditional centralized oil source valve-controlled actuation system and is used in heavy-load occasions such as aircraft, robots and submarines.

[0003] In some practical application scenarios, certain requirements are put forward for the position control of EHA. However, due to the strong nonlinear characteristics of the EHA system itself, parameter uncertainties such as the internal parameter perturbations of the hydraulic system and the inevitable modeling errors will seriously affect the position tracking accuracy of the EHA system. In response to the above problems, adaptive control is proposed to obtain effective model compensation, which solves the parameter uncertainty problem in the EHA system by parameter adaptation. At present, in most studies on adaptive control of EHA systems, their control laws and parameter adaptation laws are established based on the stability criterion with the only goal of reducing tracking errors, and many practical studies have shown that such parameter adaptive estimates are usually not convergent or cannot quickly approach their true values. Therefore, some existing adaptive controllers are difficult to guarantee the online estimation performance of parameters, which affects the control accuracy of the system to a certain extent. Summary of the invention

[0004] In order to solve the problems existing in the background technology, the present invention provides an adaptive control method for an electric hydrostatic actuator that ensures parameter estimation, which is used to solve the problem that the parameters do not converge or cannot converge to the true value during the online parameter estimation process. This method adopts a backstepping control strategy for the high-order nonlinear model of the EHA system, and uses the established adaptive law to perform online unknown parameter estimation in each step. While ensuring the stability of the control system, it reduces the position tracking error of the EHA system and improves the online parameter estimation performance, improves the convergence performance of the online parameter estimation, and thus improves the control performance of the entire electric hydrostatic actuator.

[0005] The technical solution adopted by the present invention is:

[0006] like Figure 1 As shown, the adaptive control method of the electric hydrostatic actuator of the present invention comprises the following steps:

[0007] 1) Establish a system dynamics model of the electric hydrostatic actuator; based on the system dynamics model, use the modeling method of the Newton-Euler equation and the flow continuity equation to establish a hydraulic nonlinear dynamics model of the electric hydrostatic actuator.

[0008] 2) Based on the hydraulic nonlinear dynamic model of the electric hydrostatic actuator, an adaptive backstepping control method is used to establish an adaptive backstepping controller, which includes a first adaptive controller and a second adaptive controller.

[0009] 3) The desired tracking displacement of the actuating rod of the electric hydrostatic actuator is input into the first adaptive controller, and the first adaptive controller outputs a first adaptive control law. The displacement tracking of the actuating rod of the electric hydrostatic actuator is controlled by the first adaptive control law to track the desired displacement, thereby realizing the position tracking of the actuating rod of the electric hydrostatic actuator.

[0010] 4) Establish a second coefficient regression matrix of each unknown parameter in the parameter estimation matrix in the second adaptive controller, and input the first adaptive control law into the second adaptive controller. The second adaptive controller outputs the second adaptive control law. The output force of the electric hydrostatic actuator is controlled by the second adaptive control law to track the first adaptive control law, thereby realizing the force tracking of the electric hydrostatic actuator.

[0011] 5) Use the parameter online adaptive estimation method to adaptively iterate the first adaptive controller and the second adaptive controller. In each adaptive iteration, the unknown parameter matrices in the first adaptive controller and the second adaptive controller are updated, and steps 3)-5) are repeated to achieve continuous tracking of the position of the actuator rod of the electric hydrostatic actuator and continuous tracking of the force of the electric hydrostatic actuator, and finally achieve adaptive control of the electric hydrostatic actuator.

[0012] In the step 1), the system dynamics model of the electro-hydrostatic actuator established using the Newton-Euler equation is as follows:

[0013]

[0014] F L =P1A1-P2A2

[0015]

[0016]

[0017] ||Δ d ||≤ε d ,ε d >0

[0018] Among them, m Lrepresents the total mass of the hydraulic cylinder piston and the unknown inertial load of the electrohydrostatic actuator; x L , and They represent the displacement, velocity and acceleration of the actuator rod of the electro-hydrostatic actuator respectively; F L Indicates the output force of the electric hydrostatic actuator; B m Indicates the piston viscous friction coefficient; A f Represents the piston Coulomb friction coefficient; S f () represents the switching function sgn() of smooth transition, which can meet the requirements of equation differentiability and continuity for the subsequent controller establishment; d() represents the lumped uncertain nonlinear term of the electro-hydrostatic actuator caused by external interference, unmodeled friction and other disturbances that are difficult to model; P1 and P2 represent the pressure of the rodless cavity and the rod cavity of the electro-hydrostatic actuator respectively; A1 and A2 represent the piston area of ​​the rodless cavity and the piston area of ​​the rod cavity of the electro-hydrostatic actuator respectively; d n The nominal value of the lumped uncertain nonlinear term d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model, d n is a constant value or a slowly changing value; Δ d The uncertain nonlinear terms in the lumped uncertain nonlinear terms d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model; d M Represents a preset constant; ε d Represents the maximum value of the uncertain nonlinear term.

[0019] The electrostatic actuator mainly consists of a hydraulic cylinder, a hydraulic pump, a motor and a flow compensator. The motor of the electrostatic actuator is connected to the hydraulic pump, and the hydraulic pump is connected to the hydraulic cylinder through a valve block. At the same time, the flow compensator is used to compensate for the flow mismatch characteristics caused by the mismatched cylinder.

[0020] The electric hydrostatic actuator is equipped with displacement sensors, speed sensors and pressure sensors. The displacement sensor and speed sensor are used to obtain the displacement and speed measurement values ​​of the actuator rod of the electric hydrostatic actuator; the pressure sensor is used to obtain the measurement values ​​of the pressure on both sides of the hydraulic cylinder, and then obtain the output force of the electric hydrostatic actuator. The state of the electric hydrostatic actuator measured by these sensors will be transmitted to the adaptive controller. The measurement values ​​obtained by the sensor measurement are fed back to the adaptive controller in real time, and the parameter adaptive law realizes the adaptive iterative update of its own parameters. The adaptive control law controls the electric hydrostatic actuator in real time, forming a complete electric hydrostatic actuator closed-loop control system, and finally realizing the effective control of the electric hydrostatic actuator by the adaptive controller.

[0021] In the step 1), based on the system dynamics model, the hydraulic nonlinear dynamics model of the electric hydrostatic actuator is established using the modeling method of the flow continuity equation, which is as follows:

[0022]

[0023]

[0024] V1=V 01 +A1x L

[0025] V2=V 02 -A2x L

[0026] Where V1 and V2 represent the volumes of the two connected chambers of the hydraulic cylinder of the electro-hydrostatic actuator, V 01 and V 02 They represent the initial values ​​of the volumes V1 and V2 of the two chambers of the hydraulic cylinder of the electro-hydrostatic actuator respectively; β e represents the effective elastic modulus; represents the derivative of the pressure P1 of the rodless chamber of the electrostatic hydrostatic actuator; Q1 and Q2 represent the flow rates of the two chambers of the electrostatic hydrostatic actuator respectively; C i Indicates the internal leakage coefficient of the hydraulic cylinder of the electro-hydrostatic actuator; Represents the derivative of the pressure P2 in the rod chamber of the electrohydrostatic actuator.

[0027] Acceleration of the actuator rod of an electro-hydrostatic actuator The details are as follows:

[0028]

[0029] F2=F L / m L

[0030] Δ=Δ d / m L

[0031] Wherein, F2 represents the equivalent force of the ratio of the actuator output force to the total mass of the system; Δ represents the equivalent interference of the ratio of the uncertain nonlinear term to the total mass of the system.

[0032] Output force F of electro-hydrostatic actuator L The differentials are as follows:

[0033]

[0034] F3=θ4D p A v w r

[0035] Among them, F3 represents the equivalent force related to the control speed; θ4 represents the elastic modulus of the fourth parameter variable representing the unknown parameter matrix.

[0036] The flow rates Q1 and Q2 of the two chambers of the electrostatic hydrostatic actuator under the extension condition of the electrostatic hydrostatic actuator are as follows:

[0037] Q1=Q p ,Q2=Q p -Q c

[0038] Q p =D p wxya p (P p -P t )

[0039]

[0040] Among them, Q p Indicates the pump flow rate of the electro-hydrostatic actuator; Q c Indicates the flow compensation amount of the electric hydrostatic actuator; D p represents the preset pump displacement of the electrostatic hydraulic actuator; w represents the rotation speed of the pump of the electrostatic hydraulic actuator; C p Indicates the pump leakage flow coefficient of the electrostatic actuator; P p and P t They represent the pump outlet pressure and pump inlet pressure of the electric hydrostatic actuator respectively; in the extended condition, the pump flows to the rodless chamber; the flow rate of the variable speed pump is related to the speed and its leakage.

[0041] The flow rates Q1 and Q2 of the two chambers of the electrostatic hydraulic actuator under the retracted condition of the electrostatic hydraulic actuator are as follows:

[0042] Q1=Q p +Q c ,Q2=Q p

[0043] In the retracted condition, the pump pumps flow to the rod chamber.

[0044] The hydraulic cylinder of the electric hydrostatic actuator is an asymmetric cylinder. When the piston of the electric hydrostatic actuator moves left and right, the effective areas on both sides are not equal. When the volume changes on both sides of the hydraulic cylinder are different during the piston movement process, a flow balance can be achieved through flow compensation. Separate modeling of the extension and retraction conditions can distinguish the flow compensation Q under the extension and retraction conditions. c The direction is different.

[0045] In the step 2), the first adaptive controller is specifically as follows:

[0046]

[0047]

[0048]

[0049] θ=[B m / m L ,A f / m L ,d n / m L ,β e ,β e C] T

[0050]

[0051] F Ld =F Lda +F Ldr

[0052]

[0053] F Ldr =-m L k2z2

[0054] Where τ2 represents the first adaptive function; Φ2() represents the parameter estimation matrix The first coefficient regression matrix of each unknown parameter in the first adaptive controller; z2 represents the position conversion error of the electrostatic actuator; W2 represents the auxiliary term of the first adaptive parameter estimation error law; κ2 represents the positive definite gain for constructing the auxiliary term W2 of the first adaptive parameter estimation error law; W2(t) represents the auxiliary term of the first adaptive parameter estimation error law at time t; M2(t) and They represent the value of the auxiliary variable M2 introduced at time t and its derivative value; N2(t) and Respectively represent the value of the auxiliary variable N2 and its derivative at time t; M2(t), N2(t), W2(t) are the auxiliary variables introduced to construct the parameter estimation error term; N2(0) represents the value of the auxiliary variable M2 at the initial time 0; the unknown parameter matrix includes several unknown parameters of the electrostatic actuator, θ and denote the unknown parameter matrix and parameter estimation matrix of the electro-hydrostatic actuator, respectively. represents the parameter estimation error between the unknown parameter matrix of the electro-hydrostatic actuator and its parameter estimation matrix; ψ2 represents a bounded matrix, ||ψ2||≤ε ψ , ε ψ >0,εψ represents the maximum value of the bounded matrix ψ2; C = C i +C p It represents the equivalent total leakage coefficient of the sum of the internal leakage coefficient of the hydraulic cylinder of the electric hydrostatic actuator and the pump leakage flow coefficient; l represents an adjustable parameter, l>0; Φ 2f The first coefficient regression matrix Φ2() representing each unknown parameter in the filtered parameter estimation matrix in the first adaptive controller; Indicates the velocity of the actuator rod of the electro-hydrostatic actuator after filtering F 2f Represents the first equivalent force F2 after filtering, F2 = F L / m L ; k represents the constant filter parameter, k>0; N2(0) represents the value of the auxiliary variable N2 at the initial time 0; F Ld represents the first adaptive control law, F Lda represents the compensation parameter term of the first adaptive control law, F Ldr represents a first robust feedback term of the first adaptive control law; represents the parameter estimate of the piston's viscous friction coefficient; represents the parameter estimate of the piston Coulomb friction coefficient; The nominal quantity d represents the lumped uncertain nonlinear term d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model. n Parameter estimates of ; represents the preset acceleration of the actuator rod of the electric hydrostatic actuator; k2 represents the positive feedback gain coefficient of the position conversion error z2 of the electric hydrostatic actuator.

[0055] B m / m L ,A f / m L ,d n / m L ,β e ,β e C is the unknown parameters in the unknown parameter matrix θ of the electro-hydrostatic actuator, and the parameter estimation matrix The unknown parameters in are the estimated values ​​of the unknown parameters in the unknown parameter matrix θ.

[0056] The bounded matrix ψ2 is as follows:

[0057]

[0058] Among them, Φ 2f (r) represents the first coefficient regression matrix Φ2() of each unknown parameter in the parameter estimation matrix after filtering at time r in the first adaptive controller; Δf (r) represents the equivalent interference Δ after filtering at time r.

[0059] Three auxiliary variables are introduced to achieve parameter estimation, namely Where N is the number of unknown parameters. The first adaptive controller establishes a virtual control quantity (force) F Ld To achieve position tracking of the actuator rod.

[0060] The position conversion error z2 of the electro-hydrostatic actuator is as follows:

[0061]

[0062]

[0063] z1=x L -x 1d

[0064] where z1 and They represent the actual displacement x of the actuator rod of the electro-hydrostatic actuator. L and the error between tracking the expected displacement and its derivative; k1 represents the actual displacement x of the actuator rod of the electro-hydrostatic actuator L The positive feedback gain coefficient of the error z1 between the tracking desired displacement; x 2eq Indicates the preset speed of the actuator rod of the electro-hydrostatic actuator; x 1d and They are the tracking expected displacement and its derivative of the actuator rod of the electro-hydrostatic actuator, respectively.

[0065] Due to G 12 (s) = z1(s) / z2(s) = 1 / (s+k1) is a stable transfer function. Therefore, when z2 is very small or approaches 0, z1 will also be very small or approach zero. The first adaptive control law is established to make z2 approach 0 as much as possible while ensuring the transient characteristics and accuracy of the system.

[0066] In the step 2), the second adaptive controller is specifically as follows:

[0067]

[0068]

[0069]

[0070] w=w a +w r

[0071]

[0072]

[0073]

[0074] Where τ3 represents the second adaptive function; Φ3() represents the parameter estimation matrix The second coefficient regression matrix of each unknown parameter in the second adaptive controller; z3 represents the pressure parameter error of the electric hydrostatic actuator; W3 represents the auxiliary term of the second adaptive parameter estimation error law; κ3 represents the positive definite gain for constructing the auxiliary term W3 of the second adaptive parameter estimation error law; W3(t) represents the auxiliary term of the second adaptive parameter estimation error law at time t; M3(t) and Respectively represent the value of auxiliary variable M3 and its derivative at time t; N3(t) and Respectively represent the auxiliary flow variables and their derivatives at time t; M3(t), N3(t), W3(t) are auxiliary variables introduced to construct parameter estimation error terms; Φ 3f represents the second coefficient regression matrix Φ3 after filtering; M3(0) represents the value of the auxiliary variable M3 at the initial time 0; F 3f Represents the second equivalent force F3 after filtering, F3 = β e D p A v w r ; N3(0) represents the value of the auxiliary variable N3 at the initial time 0; w represents the second adaptive control law, w a represents the compensation parameter term of the adaptive control law, w r represents a second robust feedback term of the second adaptive control law; represents the effective elastic modulus β e The parameter estimates of A v Represents the equivalent variable related to the area and volume of the two chambers of the hydraulic cylinder; D p Indicates the pump displacement of the hydraulic pump; β e C represents the effective elastic modulus β e The estimated value of the parameter w of the product of the equivalent total leakage coefficient C; Denotes the first adaptive control law F Ld Differential The calculable part; k3 represents the positive feedback gain coefficient of the pressure parameter error z3 of the electric hydrostatic actuator;

[0075] Three auxiliary variables are introduced to realize parameter estimation, namely The second adaptive controller achieves force tracking by establishing the actual control variable w (rotation speed).

[0076] The pressure parameter error z3 of the electric hydrostatic actuator is as follows:

[0077] z3=F L -F Ld

[0078] The second adaptive control law is established to make the pressure parameter error z3 approach 0 while ensuring the transient performance and accuracy of the system.

[0079] In the step 5), the unknown parameter matrix is ​​adaptively iterated using the parameter online adaptive estimation method, and an updated unknown parameter matrix is ​​obtained in each adaptive iteration, as follows:

[0080]

[0081]

[0082] τ=τ2+τ3

[0083] in, represents the parameter estimation matrix The initial value of Represents the parameter estimation matrix The differential of is the parameter estimation matrix The law of change of t s represents the sampling time of the adaptive backstepping controller; Γ represents the preset parameter adaptive gain matrix; τ represents the adaptive function of the entire system, including the first adaptive function τ2 and the second adaptive function τ3.

[0084] is the updated parameter estimation matrix and serves as the initial matrix for parameter adaptation in the next iteration. Continuously perform adaptive iterations to continuously update the parameter estimation matrix and the second adaptive model compensation parameter term w a , while the model uncertainty parameter matrix θ approaches the true value, the second adaptive model compensation parameter term w a It continuously approaches the ideal control value, thus overcoming the influence of model uncertainty on the system control effect and improving the control accuracy.

[0085] The parameter estimation matrix in the system model is adjusted by using the method of online adaptive estimation and adjustment of parameters. Adaptive iteration can reduce the uncertainty of model parameters in the established nonlinear dynamics. The parameter estimation matrix used is is not completely accurate, and the hydraulic parameter β e It is difficult to obtain accurate results, and the parameter estimation matrix can be reduced. The adverse effects caused.

[0086] The beneficial effects of the present invention are:

[0087] The present invention takes into account the model uncertainty problem existing in the electric hydrostatic actuator and the poor parameter convergence performance of the existing adaptive control method, and proposes an adaptive control method that ensures parameter estimation. The parameter convergence performance is improved by introducing a parameter estimation error term in the adaptive law, and the parameter estimation matrix is ​​continuously updated by using an online adaptive iteration method to obtain a more ideal control input. While overcoming the influence of model uncertainty in the control process, the control accuracy of the electric hydrostatic actuator is further improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 It is a schematic diagram of the framework of the adaptive control system of the present invention;

[0089] Figure 2 It is a schematic diagram of the target trajectory of the actuating rod of the electric hydrostatic actuator of the present invention;

[0090] Figure 3 is a schematic diagram for comparing the position tracking results of the present invention;

[0091] Figure 4 is a schematic diagram for comparing position tracking error results of the present invention;

[0092] Figure 5 2 is a schematic diagram for comparing parameter estimation results of the present invention. DETAILED DESCRIPTION

[0093] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0094] 1. An adaptive control method for an electro-hydrostatic actuator with guaranteed parameter estimation, characterized in that:

[0095] The method comprises the following steps:

[0096] 1) Establish a system dynamics model of the electric hydrostatic actuator; based on the system dynamics model, use the modeling method of the Newton-Euler equation and the flow continuity equation to establish a hydraulic nonlinear dynamics model of the electric hydrostatic actuator.

[0097] In step 1), the system dynamics model of the electro-hydrostatic actuator established using the Newton-Euler equation is as follows:

[0098]

[0099] F L =P1A1-P2A2

[0100]

[0101]

[0102] ||Δ d ||≤ε d ,ε d >0

[0103] Among them, m L represents the total mass of the hydraulic cylinder piston and the unknown inertial load of the electrohydrostatic actuator; x L , and They represent the displacement, velocity and acceleration of the actuator rod of the electro-hydrostatic actuator respectively; F L Indicates the output force of the electric hydrostatic actuator; B m Indicates the piston viscous friction coefficient; A f Represents the piston Coulomb friction coefficient; S f () represents the switching function sgn() of smooth transition, which can meet the requirements of equation differentiability and continuity for the subsequent controller establishment; d() represents the lumped uncertain nonlinear term of the electro-hydrostatic actuator caused by external interference, unmodeled friction and other disturbances that are difficult to model; P1 and P2 represent the pressure of the rodless cavity and the rod cavity of the electro-hydrostatic actuator respectively; A1 and A2 represent the piston area of ​​the rodless cavity and the piston area of ​​the rod cavity of the electro-hydrostatic actuator respectively; d n The nominal value of the lumped uncertain nonlinear term d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model, d n is a constant value or a slowly changing value; Δ d The uncertain nonlinear terms in the lumped uncertain nonlinear terms d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model; d M Represents a preset constant; ε d Represents the maximum value of the uncertain nonlinear term.

[0104] The electrostatic actuator mainly consists of a hydraulic cylinder, a hydraulic pump, a motor and a flow compensator. The motor of the electrostatic actuator is connected to the hydraulic pump, and the hydraulic pump is connected to the hydraulic cylinder through a valve block. At the same time, the flow compensator is used to compensate for the flow mismatch characteristics caused by the mismatched cylinder.

[0105] The electric hydrostatic actuator is equipped with displacement sensors, speed sensors and pressure sensors. The displacement sensor and speed sensor are used to obtain the displacement and speed measurement values ​​of the actuator rod of the electric hydrostatic actuator; the pressure sensor is used to obtain the measurement values ​​of the pressure on both sides of the hydraulic cylinder, and then obtain the output force of the electric hydrostatic actuator. The state of the electric hydrostatic actuator measured by these sensors will be transmitted to the adaptive controller. The measurement values ​​obtained by the sensor measurement are fed back to the adaptive controller in real time, and the parameter adaptive law realizes the adaptive iterative update of its own parameters. The adaptive control law controls the electric hydrostatic actuator in real time, forming a complete electric hydrostatic actuator closed-loop control system, and finally realizing the effective control of the electric hydrostatic actuator by the adaptive controller.

[0106] In step 1), based on the system dynamics model, the hydraulic nonlinear dynamics model of the electric hydrostatic actuator is established using the modeling method of the flow continuity equation, as follows:

[0107]

[0108]

[0109] V1=V 01 +A1x L

[0110] V2=V 02 -A2x L

[0111] Where V1 and V2 represent the volumes of the two connected chambers of the hydraulic cylinder of the electro-hydrostatic actuator, V 01 and V 02 They represent the initial values ​​of the volumes V1 and V2 of the two chambers of the hydraulic cylinder of the electro-hydrostatic actuator respectively; β e represents the effective elastic modulus; represents the derivative of the pressure P1 of the rodless chamber of the electrostatic hydrostatic actuator; Q1 and Q2 represent the flow rates of the two chambers of the electrostatic hydrostatic actuator respectively; C i Indicates the internal leakage coefficient of the hydraulic cylinder of the electro-hydrostatic actuator; Represents the derivative of the pressure P2 in the rod chamber of the electrohydrostatic actuator.

[0112] Acceleration of the actuator rod of an electro-hydrostatic actuator The details are as follows:

[0113]

[0114] F2=F L / m L

[0115] Δ=Δ d / mL

[0116] Wherein, F2 represents the equivalent force of the ratio of the actuator output force to the total mass of the system; Δ represents the equivalent interference of the ratio of the uncertain nonlinear term to the total mass of the system.

[0117] Output force F of electro-hydrostatic actuator L The differentials are as follows:

[0118]

[0119] F3=θ4D p A v w r

[0120] Among them, F3 represents the equivalent force related to the control speed; θ4 represents the elastic modulus of the fourth parameter variable representing the unknown parameter matrix.

[0121] The flow rates Q1 and Q2 of the two chambers of the electrostatic hydraulic actuator under the extension condition of the electrostatic hydraulic actuator are as follows:

[0122] Q1=Q p ,Q2=Q p -Q c

[0123] Q p =D p wxya p (P p -P t )

[0124]

[0125] Among them, Q p Indicates the pump flow rate of the electro-hydrostatic actuator; Q c Indicates the flow compensation amount of the electric hydrostatic actuator; D p represents the preset pump displacement of the electrostatic hydraulic actuator; w represents the rotation speed of the pump of the electrostatic hydraulic actuator; C p Indicates the pump leakage flow coefficient of the electrostatic actuator; P p and P t Respectively represent the pump outlet pressure and pump inlet pressure of the electric hydrostatic actuator; in the extended condition, the pump flows to the rodless chamber; the flow rate of the variable speed pump is related to the speed and its leakage;

[0126] The flow rates Q1 and Q2 of the two chambers of the electrostatic hydraulic actuator under the retracted condition of the electrostatic hydraulic actuator are as follows:

[0127] Q1=Q p +Q c,Q2=Q p

[0128] In the retracted condition, the pump pumps flow to the rod chamber.

[0129] The hydraulic cylinder of the electric hydrostatic actuator is an asymmetric cylinder. When the piston of the electric hydrostatic actuator moves left and right, the effective areas on both sides are not equal. When the volume changes on both sides of the hydraulic cylinder are different during the piston movement process, a flow balance can be achieved through flow compensation. Separate modeling of the extension and retraction conditions can distinguish the flow compensation Q under the extension and retraction conditions. c The direction is different.

[0130] 2) Based on the hydraulic nonlinear dynamic model of the electric hydrostatic actuator, an adaptive backstepping control method is used to establish an adaptive backstepping controller, which includes a first adaptive controller and a second adaptive controller.

[0131] In step 2), the first adaptive controller is specifically as follows:

[0132]

[0133]

[0134]

[0135] θ=[B m / m L ,A f / m L ,d n / m L ,β e ,β e C] T

[0136]

[0137] F Ld =F Lda +F Ldr

[0138]

[0139] F Ldr =-m L k2z2

[0140] Where τ2 represents the first adaptive function; Φ2() represents the parameter estimation matrix The first coefficient regression matrix of each unknown parameter in the first adaptive controller; z2 represents the position conversion error of the electrostatic actuator; W2 represents the auxiliary term of the first adaptive parameter estimation error law; κ2 represents the positive definite gain for constructing the auxiliary term W2 of the first adaptive parameter estimation error law; W2(t) represents the auxiliary term of the first adaptive parameter estimation error law at time t; M2(t) and They represent the value of the auxiliary variable M2 introduced at time t and its derivative value; N2(t) and Respectively represent the value of the auxiliary variable N2 and its derivative at time t; M2(t), N2(t), W2(t) are the auxiliary variables introduced to construct the parameter estimation error term; N2(0) represents the value of the auxiliary variable M2 at the initial time 0; the unknown parameter matrix includes several unknown parameters of the electrostatic actuator, θ and denote the unknown parameter matrix and parameter estimation matrix of the electro-hydrostatic actuator, respectively. represents the parameter estimation error between the unknown parameter matrix of the electro-hydrostatic actuator and its parameter estimation matrix; ψ2 represents a bounded matrix, ||ψ2||≤ε ψ , ε ψ >0,ε ψ represents the maximum value of the bounded matrix ψ2; C = C i +C p It represents the equivalent total leakage coefficient of the sum of the internal leakage coefficient of the hydraulic cylinder of the electric hydrostatic actuator and the pump leakage flow coefficient; l represents an adjustable parameter, l>0; Φ 2f The first coefficient regression matrix Φ2() representing each unknown parameter in the filtered parameter estimation matrix in the first adaptive controller; Indicates the velocity of the actuator rod of the electro-hydrostatic actuator after filtering F 2f Represents the first equivalent force F2 after filtering, F2 = F L / m L ; k represents the constant filter parameter, k>0; N2(0) represents the value of the auxiliary variable N2 at the initial time 0; F Ld represents the first adaptive control law, F Lda represents the compensation parameter term of the first adaptive control law, F Ldr represents a first robust feedback term of the first adaptive control law; represents the parameter estimate of the piston's viscous friction coefficient; represents the parameter estimate of the piston Coulomb friction coefficient; The nominal quantity d represents the lumped uncertain nonlinear term d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model. n Parameter estimates of ; represents the preset acceleration of the actuator rod of the electric hydrostatic actuator; k2 represents the positive feedback gain coefficient of the position conversion error z2 of the electric hydrostatic actuator.

[0141] B m / m L ,A f / m L ,d n / m L ,β e ,β e C is the unknown parameters in the unknown parameter matrix θ of the electro-hydrostatic actuator, and the parameter estimation matrix The unknown parameters in are the estimated values ​​of the unknown parameters in the unknown parameter matrix θ.

[0142] The bounded matrix ψ2 is as follows:

[0143]

[0144] Among them, Φ 2f (r) represents the first coefficient regression matrix Φ2() of each unknown parameter in the parameter estimation matrix after filtering at time r in the first adaptive controller; Δ f (r) represents the equivalent interference Δ after filtering at time r.

[0145] Three auxiliary variables are introduced to achieve parameter estimation, namely Where N is the number of unknown parameters. The first adaptive controller establishes a virtual control quantity (force) F Ld To achieve position tracking of the actuator rod.

[0146] The position conversion error z2 of the electro-hydrostatic actuator is as follows:

[0147]

[0148]

[0149] z1=x L -x 1d

[0150] where z1 and They represent the actual displacement x of the actuator rod of the electro-hydrostatic actuator. L and the error between tracking the expected displacement and its derivative; k1 represents the actual displacement x of the actuator rod of the electro-hydrostatic actuator L The positive feedback gain coefficient of the error z1 between the tracking desired displacement; x 2eq Indicates the preset speed of the actuator rod of the electro-hydrostatic actuator; x 1d and They are the tracking expected displacement and its derivative of the actuator rod of the electro-hydrostatic actuator, respectively.

[0151] Due to G 12 (s) = z1(s) / z2(s) = 1 / (s+k1) is a stable transfer function. Therefore, when z2 is very small or approaches 0, z1 will also be very small or approach zero. The first adaptive control law is established to make z2 approach 0 as much as possible while ensuring the transient characteristics and accuracy of the system.

[0152] In step 2), the second adaptive controller is specifically as follows:

[0153]

[0154]

[0155]

[0156] w=w a +w r

[0157]

[0158]

[0159]

[0160] Where τ3 represents the second adaptive function; Φ3() represents the parameter estimation matrix The second coefficient regression matrix of each unknown parameter in the second adaptive controller; z3 represents the pressure parameter error of the electric hydrostatic actuator; W3 represents the auxiliary term of the second adaptive parameter estimation error law; κ3 represents the positive definite gain for constructing the auxiliary term W3 of the second adaptive parameter estimation error law; W3(t) represents the auxiliary term of the second adaptive parameter estimation error law at time t; M3(t) and Respectively represent the value of auxiliary variable M3 and its derivative at time t; N3(t) and Respectively represent the auxiliary flow variables and their derivatives at time t; M3(t), N3(t), W3(t) are auxiliary variables introduced to construct parameter estimation error terms; Φ 3f represents the second coefficient regression matrix Φ3 after filtering; M3(0) represents the value of the auxiliary variable M3 at the initial time 0; F 3f Represents the second equivalent force F3 after filtering, F3 = β e D p A v w r ; N3(0) represents the value of the auxiliary variable N3 at the initial time 0; w represents the second adaptive control law, w arepresents the compensation parameter term of the adaptive control law, w r represents a second robust feedback term of the second adaptive control law; represents the effective elastic modulus β e The parameter estimates of A v Represents the equivalent variable related to the area and volume of the two chambers of the hydraulic cylinder; D p Indicates the pump displacement of the hydraulic pump; β e C represents the effective elastic modulus β e The estimated value of the parameter w of the product of the equivalent total leakage coefficient C; Denotes the first adaptive control law F Ld Differential The calculable part; k3 represents the positive feedback gain coefficient of the pressure parameter error z3 of the electric hydrostatic actuator;

[0161] Three auxiliary variables are introduced to realize parameter estimation, namely The second adaptive controller achieves force tracking by establishing the actual control variable w (rotation speed).

[0162] The pressure parameter error z3 of the electric hydrostatic actuator is as follows:

[0163] z3=F L -F Ld

[0164] The second adaptive control law is established to make the pressure parameter error z3 approach 0 while ensuring the transient performance and accuracy of the system.

[0165] 3) The desired tracking displacement of the actuating rod of the electric hydrostatic actuator is input into the first adaptive controller, and the first adaptive controller outputs a first adaptive control law. The displacement tracking of the actuating rod of the electric hydrostatic actuator is controlled by the first adaptive control law to track the desired displacement, thereby realizing the position tracking of the actuating rod of the electric hydrostatic actuator.

[0166] 4) Establish a second coefficient regression matrix of each unknown parameter in the parameter estimation matrix in the second adaptive controller, and input the first adaptive control law into the second adaptive controller. The second adaptive controller outputs the second adaptive control law. The output force of the electric hydrostatic actuator is controlled by the second adaptive control law to track the first adaptive control law, thereby realizing the force tracking of the electric hydrostatic actuator.

[0167] 5) Use the parameter online adaptive estimation method to adaptively iterate the first adaptive controller and the second adaptive controller. In each adaptive iteration, the unknown parameter matrices in the first adaptive controller and the second adaptive controller are updated, and steps 3)-5) are repeated to achieve continuous tracking of the position of the actuator rod of the electric hydrostatic actuator and continuous tracking of the force of the electric hydrostatic actuator, and finally achieve adaptive control of the electric hydrostatic actuator.

[0168] In step 5), the unknown parameter matrix is ​​adaptively iterated using the parameter online adaptive estimation method, and an updated unknown parameter matrix is ​​obtained in each adaptive iteration, as follows:

[0169]

[0170]

[0171] τ=τ2+τ3

[0172] in, Represents the parameter estimation matrix The initial value of Represents the parameter estimation matrix The differential of is the parameter estimation matrix The law of change of t s represents the sampling time of the adaptive backstepping controller; Γ represents the preset parameter adaptive gain matrix; τ represents the adaptive function of the entire system, including the first adaptive function τ2 and the second adaptive function τ3.

[0173] is the updated parameter estimation matrix and serves as the initial matrix for parameter adaptation in the next iteration. Continuously perform adaptive iterations to continuously update the parameter estimation matrix and the second adaptive model compensation parameter term w a , while the model uncertainty parameter matrix θ approaches the true value, the second adaptive model compensation parameter term w a It continuously approaches the ideal control value, thus overcoming the influence of model uncertainty on the system control effect and improving the control accuracy.

[0174] The parameter estimation matrix in the system model is adjusted by using the method of online adaptive estimation and adjustment of parameters. Adaptive iteration can reduce the uncertainty of model parameters in the established nonlinear dynamics. The parameter estimation matrix used is is not completely accurate, and the hydraulic parameter β e It is difficult to obtain accurate results, and the parameter estimation matrix can be reduced. The adverse effects caused.

[0175] The corresponding working mode needs to be defined to determine the working state of EHA. The working mode selection is based on the given tracking trajectory and real-time position tracking error. The working mode selection method is shown in Table 1 below, where is the preset error tolerance threshold, and e is the trajectory tracking error of EHA.

[0176] Table 1 Working mode selection scheme

[0177]

[0178] Finally, the control method of the present invention is simulated by MATLAB / Simulink based on the electric hydrostatic actuator, and compared with the traditional adaptive control method to verify the control effect of the control method proposed by the present invention. Figure 2 shown.

[0179] In terms of establishing the controller gain coefficient, the gain parameters of the proposed control cover all the gain parameters of the traditional adaptive controller. Therefore, the selection of the traditional adaptive control parameters can be the same as that of the proposed controller. The gain parameters of the established adaptive controller are: k1 = k2 = k3 = 30, Γ = diag[2000; 10; 5; 10 9 ; 5×10 -11 ], l=1, κ2=20, κ3=0.1.

[0180] The specific simulation parameters of the electric hydrostatic actuator are shown in Table 2

[0181] Table 2 Simulation model parameters

[0182]

[0183] The position tracking results of the adaptive controller established by the present invention are as follows: Figure 3 As shown, the dotted line represents the target tracking trajectory, the solid line represents the actual actuator position under the adaptive control established during the simulation process, and the dotted line represents the actual actuator position under the traditional adaptive control during the simulation process.

[0184] The position tracking results of the established adaptive controller are shown in Figure 4 As shown, the solid line represents the position tracking error under the adaptive control established during the simulation process, and the dotted line represents the position tracking error under the traditional adaptive control during the simulation process.

[0185] Finally, the online parameter estimation results of the electro-hydrostatic actuation are shown in Figure 5 As shown, Figure 5It can be divided into two sub-figures on the left and right. The left figure is the parameter estimation result of the established adaptive controller, in which the dotted lines represent the actual parameter values, and the solid lines represent the estimated parameter values; the right figure is the parameter estimation result of the traditional adaptive controller, in which the dotted lines represent the actual parameter values, and the dotted lines represent the estimated parameter values.

[0186] It can be seen from the above simulation result diagram that the parameter estimation effect and convergence ability of the established adaptive controller are better, and it can converge the unknown parameters to the actual values ​​faster and more accurately, while the traditional adaptive controller has poor parameter convergence ability, and some parameters cannot converge to the actual values; observing the trajectory tracking and tracking error diagram, it can be seen that compared with the traditional adaptive controller, the error transient response of the established adaptive controller is better, and it can track the target trajectory faster and better, thereby improving the control performance of the system.

Claims

1. An adaptive control method for an electro-hydrostatic actuator with guaranteed parameter estimation, characterized in that: The method comprises the following steps: 1) Establishing a system dynamics model of the electric hydrostatic actuator; Based on the system dynamics model, a hydraulic nonlinear dynamics model of the electric hydrostatic actuator is established using the modeling method of the Newton-Euler equation and the flow continuity equation; 2) Based on the hydraulic nonlinear dynamic model of the electric hydrostatic actuator, an adaptive backstepping controller is established using an adaptive backstepping control method, wherein the adaptive backstepping controller includes a first adaptive controller and a second adaptive controller; 3) inputting the tracking desired displacement of the actuating rod of the electrostatic hydrostatic actuator into the first adaptive controller, the first adaptive controller outputting the first adaptive control law, controlling the displacement tracking of the actuating rod of the electrostatic hydrostatic actuator by the first adaptive control law to track the desired displacement, thereby realizing the position tracking of the actuating rod of the electrostatic hydrostatic actuator; 4) establishing a second coefficient regression matrix of each unknown parameter in the parameter estimation matrix in the second adaptive controller, and inputting the first adaptive control law into the second adaptive controller, the second adaptive controller outputs the second adaptive control law, and the output force of the electric hydrostatic actuator is controlled by the second adaptive control law to track the first adaptive control law, thereby realizing force tracking of the electric hydrostatic actuator; 5) Use the parameter online adaptive estimation method to adaptively iterate the first adaptive controller and the second adaptive controller. In each adaptive iteration, the unknown parameter matrices in the first adaptive controller and the second adaptive controller are updated and steps 3)-5) are repeated, thereby achieving continuous tracking of the position of the actuator rod of the electric hydrostatic actuator and continuous tracking of the force of the electric hydrostatic actuator, and finally achieving adaptive control of the electric hydrostatic actuator.

2. The method for adaptive control of an electro-hydrostatic actuator with guaranteed parameter estimation according to claim 1, characterized in that: In the step 1), the system dynamics model of the electro-hydrostatic actuator established is as follows: F L =P1A1-P2A2 ||D d ||≤e d ,he d >0 Among them, m L represents the total mass of the hydraulic cylinder piston and the unknown inertial load of the electrohydrostatic actuator; x L , and They represent the displacement, velocity and acceleration of the actuator rod of the electro-hydrostatic actuator respectively; F L Indicates the output force of the electric hydrostatic actuator; B m Indicates the piston viscous friction coefficient; A f Represents the piston Coulomb friction coefficient; S f () represents the switching function sgn() of smooth transition; d() represents the lumped uncertain nonlinear term of the electro-hydrostatic actuator due to external interference, unmodeled friction and other disturbances that are difficult to model; P1 and P2 represent the pressure of the rodless cavity and the rod cavity of the electro-hydrostatic actuator respectively; A1 and A2 represent the piston area of ​​the rodless cavity and the piston area of ​​the rod cavity of the electro-hydrostatic actuator respectively; d n The nominal value of the lumped uncertain nonlinear term d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model; Δ d The uncertain nonlinear terms in the lumped uncertain nonlinear terms d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model; d M Represents a preset constant; ε d Represents the maximum value of the uncertain nonlinear term.

3. The method for adaptive control of an electro-hydrostatic actuator with guaranteed parameter estimation according to claim 2, characterized in that: In the step 1), based on the system dynamics model, the hydraulic nonlinear dynamics model of the electric hydrostatic actuator is established using the modeling method of the flow continuity equation, which is as follows: V1=V 01 +A1x L <h2 style=";text-align:left;direction:ltr">V2=V<h2 style=";text-align:left;direction:ltr"> 02 <h2 style=";text-align:left;direction:ltr"> -A2x<h2 style=";text-align:left;direction:ltr"> L Where V1 and V2 represent the volumes of the two connected chambers of the hydraulic cylinder of the electro-hydrostatic actuator, V 01 and V 02 They represent the initial values ​​of the volumes V1 and V2 of the two chambers of the hydraulic cylinder of the electro-hydrostatic actuator respectively; β e represents the effective elastic modulus; represents the derivative of the pressure P1 of the rodless chamber of the electrostatic hydrostatic actuator; Q1 and Q2 represent the flow rates of the two chambers of the electrostatic hydrostatic actuator respectively; C i Indicates the internal leakage coefficient of the hydraulic cylinder of the electro-hydrostatic actuator; Represents the derivative of the pressure P2 in the rod chamber of the electrohydrostatic actuator.

4. The method for adaptive control of an electro-hydrostatic actuator with guaranteed parameter estimation according to claim 3, characterized in that: The flow rates Q1 and Q2 of the two chambers of the electrostatic hydrostatic actuator under the extension condition of the electrostatic hydrostatic actuator are as follows: Q1=Q p ,Q2=Q p -Q c Q p =D p w-C p (P p -P t ) Among them, Q p Indicates the pump flow rate of the electro-hydrostatic actuator; Q c Indicates the flow compensation amount of the electric hydrostatic actuator; D p represents the preset pump displacement of the electrostatic hydraulic actuator; w represents the rotation speed of the pump of the electrostatic hydraulic actuator; C p Indicates the pump leakage flow coefficient of the electrostatic actuator; P p and P t Respectively represent the pump outlet pressure and pump inlet pressure of the electro-hydrostatic actuator; The flow rates Q1 and Q2 of the two chambers of the electrostatic hydraulic actuator under the retracted condition of the electrostatic hydraulic actuator are as follows: Q1=Q p +Q c ,Q2=Q p 。 5. The method for adaptive control of an electro-hydrostatic actuator with guaranteed parameter estimation according to claim 2, characterized in that: In the step 2), the first adaptive controller is specifically as follows: θ=[B m / m L ,A f / m L ,d n / m L ,b e ,b e C] T F Ld =F Lda +F Ldr F Ldr =-m L k2z2 Where τ2 represents the first adaptive function; Φ2() represents the parameter estimation matrix The first coefficient regression matrix of each unknown parameter in the first adaptive controller; z2 represents the position conversion error of the electrostatic actuator; W2 represents the auxiliary term of the first adaptive parameter estimation error law; κ2 represents the positive definite gain for constructing the auxiliary term W2 of the first adaptive parameter estimation error law; W2(t) represents the auxiliary term of the first adaptive parameter estimation error law at time t; M2(t) and They represent the value of the auxiliary variable M2 introduced at time t and its derivative value; N2(t) and represents the value of the auxiliary variable N2 and its derivative at time t; N2(0) represents the value of the auxiliary variable M2 at the initial time 0; the unknown parameter matrix includes several unknown parameters of the electrostatic actuator, θ and denote the unknown parameter matrix and parameter estimation matrix of the electro-hydrostatic actuator, respectively. represents the parameter estimation error between the unknown parameter matrix of the electro-hydrostatic actuator and its parameter estimation matrix; ψ2 represents a bounded matrix, ||ψ2||≤ε ψ , ε ψ >0,ε ψ represents the maximum value of the bounded matrix ψ2; C = C i +C p It represents the equivalent total leakage coefficient of the sum of the internal leakage coefficient of the hydraulic cylinder of the electric hydrostatic actuator and the pump leakage flow coefficient; l represents an adjustable parameter, l>0; Φ 2f The first coefficient regression matrix Φ2() representing each unknown parameter in the filtered parameter estimation matrix in the first adaptive controller; Indicates the velocity of the actuator rod of the electro-hydrostatic actuator after filtering F 2f Represents the first equivalent force F2 after filtering, F2 = F L / m L ; k represents the constant filter parameter, k>0; N2(0) represents the value of the auxiliary variable N2 at the initial time 0; F Ld represents the first adaptive control law, F Lda represents the compensation parameter term of the first adaptive control law, F Ldr represents a first robust feedback term of the first adaptive control law; represents the parameter estimate of the piston's viscous friction coefficient; represents the parameter estimate of the piston Coulomb friction coefficient; The nominal quantity d represents the lumped uncertain nonlinear term d() of the electro-hydrostatic actuator due to external disturbances, unmodeled friction, and other disturbances that are difficult to model. n Parameter estimates of ; represents the preset acceleration of the actuator rod of the electric hydrostatic actuator; k2 represents the positive feedback gain coefficient of the position conversion error z2 of the electric hydrostatic actuator.

6. The method for adaptive control of an electro-hydrostatic actuator with guaranteed parameter estimation according to claim 5, characterized in that: The position conversion error z2 of the electro-hydrostatic actuator is as follows: z1=x L -x 1d where z1 and They represent the actual displacement x of the actuator rod of the electro-hydrostatic actuator. L and the error between tracking the expected displacement and its derivative; k1 represents the actual displacement x of the actuator rod of the electro-hydrostatic actuator L The positive feedback gain coefficient of the error z1 between the tracking desired displacement; x 2eq Indicates the preset speed of the actuator rod of the electro-hydrostatic actuator; x 1d and They are the tracking expected displacement and its derivative of the actuator rod of the electro-hydrostatic actuator, respectively.

7. The method for adaptive control of an electro-hydrostatic actuator with guaranteed parameter estimation according to claim 2, characterized in that: In the step 2), the second adaptive controller is specifically as follows: in=in a +in r Where τ3 represents the second adaptive function; Φ3() represents the parameter estimation matrix The second coefficient regression matrix of each unknown parameter in the second adaptive controller; z3 represents the pressure parameter error of the electric hydrostatic actuator; W3 represents the auxiliary term of the second adaptive parameter estimation error law; κ3 represents the positive definite gain for constructing the auxiliary term W3 of the second adaptive parameter estimation error law; W3(t) represents the auxiliary term of the second adaptive parameter estimation error law at time t; M3(t) and Respectively represent the value of auxiliary variable M3 and its derivative at time t; N3(t) and They represent the auxiliary flow variable and its derivative at time t respectively; Φ 3f represents the second coefficient regression matrix Φ3 after filtering; M3(0) represents the value of the auxiliary variable M3 at the initial time 0; F 3f Represents the second equivalent force F3 after filtering, F3 = β e D p A v w r ; N3(0) represents the value of the auxiliary variable N3 at the initial time 0; w represents the second adaptive control law, w a represents the compensation parameter term of the adaptive control law, w r represents a second robust feedback term of the second adaptive control law; represents the effective elastic modulus β e The parameter estimates of v Represents the equivalent variable related to the area and volume of the two chambers of the hydraulic cylinder; D p Indicates the pump displacement of the hydraulic pump; β e C represents the effective elastic modulus β e The estimated value of the parameter w of the product of the equivalent total leakage coefficient C; Denotes the first adaptive control law F Ld Differential The calculable part; k3 represents the positive feedback gain coefficient of the pressure parameter error z3 of the electric hydrostatic actuator.

8. The method for adaptive control of an electro-hydrostatic actuator with guaranteed parameter estimation according to claim 7, characterized in that: The pressure parameter error z3 of the electric hydrostatic actuator is as follows: z3=F L -F Ld 。 9. The method for adaptive control of an electro-hydrostatic actuator with guaranteed parameter estimation according to claim 2, characterized in that: In the step 5), the unknown parameter matrix is ​​adaptively iterated using the parameter online adaptive estimation method, and an updated unknown parameter matrix is ​​obtained in each adaptive iteration, as follows: τ=τ2+τ3 in, represents the parameter estimation matrix The initial value of Represents the parameter estimation matrix The differential of t s represents the sampling time of the adaptive backstepping controller; Γ represents the preset parameter adaptive gain matrix; τ represents the adaptive function, including the first adaptive function τ2 and the second adaptive function τ3.

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