CN116460856A

CN116460856A - Hydraulic mechanical arm self-adaptive robust control method based on nonlinear state observation

Info

Publication number: CN116460856A
Application number: CN202310590367.2A
Authority: CN
Inventors: 周时钊; 沈翀; 夏杨修; 陈正; 梅德庆
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2023-05-24
Filing date: 2023-05-24
Publication date: 2023-07-21

Abstract

The invention discloses a hydraulic mechanical arm self-adaptive robust control method based on nonlinear state observation. Inputting the parameter estimation value of the dynamic parameter into an intermediate conversion state quantity model, outputting an intermediate conversion state quantity, and observing and outputting an observation state by a nonlinear state observer to obtain an estimation value of the joint angular velocity; inputting an estimated value of joint angular velocity and a target track, outputting a control signal of valve core displacement to control the operation of the multi-joint hydraulic mechanical arm, obtaining tracking error, outputting the tracking error to the self-adaptive robust control law, repeating the steps, and simultaneously, carrying out self-updating by the nonlinear state observer, thereby finally realizing the self-adaptive robust control. The method realizes real-time observation of the unmeasured state based on the uncertain model parameters, solves the problem that the feedback state is unmeasured due to the limitation of the sensor in the actual situation, reduces the tracking error of the tail end of the mechanical arm while ensuring the integral stability of the control system and the observation system, and improves the control performance.

Description

Hydraulic mechanical arm self-adaptive robust control method based on nonlinear state observation

Technical Field

The invention relates to a self-adaptive robust control method for a hydraulic mechanical arm, in particular to a self-adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation.

Background

The hydraulic mechanical arm is generally applied to severe operation tasks such as heavy load, but with the continuous forward development of industry and human exploration, the complexity of the operation tasks of the hydraulic mechanical arm is continuously increased, the requirement on the operation accuracy is also continuously increased, and the traditional proportional-integral-derivative PID control cannot meet the requirement of high control performance gradually because the factors such as uncertain mechanical arm dynamics model parameters are not considered. In this case, developing a full state feedback controller based on a multi-joint hydraulic robotic dynamics model is an effective solution. However, on the other hand, the working of the multi-joint hydraulic robot arm is becoming worse, and in most practical applications, only a position sensor with low accuracy is arranged in the hydraulic robot arm for safety and reliability. This results in a measurement signal that is noisy and that is not amenable to other state measurements, in particular speed measurements. The method of differentiating the position signal and adopting low-pass filtering is a common means of acquiring the velocity signal at the present stage. However, the presence of the low pass filter severely affects the closed loop bandwidth of the system, thereby limiting the control performance of the multi-joint hydraulic robotic arm. Therefore, the existing controller is difficult to comprehensively consider the problems of uncertain parameters, undetectable states and the like of the dynamic model of the multi-joint hydraulic mechanical arm in a severe and complex working environment, so that the problem that good control precision of the tail end of the mechanical arm is difficult to ensure and the working performance in specific occasions is influenced is caused.

Disclosure of Invention

In order to solve the problems in the background art, the self-adaptive robust control method for the hydraulic mechanical arm based on nonlinear state observation provided by the invention improves the tail end control precision of the multi-joint hydraulic mechanical arm under the conditions that the dynamic model parameters of the multi-joint hydraulic mechanical arm are uncertain and the feedback state is not measurable, reduces the tail end tracking error of the mechanical arm and enhances the control performance while guaranteeing the overall stability of a control system and an observation system.

The technical scheme adopted by the invention is as follows:

the self-adaptive robust control method of the hydraulic mechanical arm comprises the following steps:

step one: comprehensively considering the hydraulic characteristic and the multi-degree-of-freedom coupling characteristic, and establishing a nonlinear dynamics model of the multi-joint hydraulic mechanical arm under the constraint of the dynamics model; and designing an intermediate conversion state quantity model of the unmeasurable state of the multi-joint hydraulic mechanical arm and a nonlinear state space thereof, and establishing a nonlinear state observer by using a nonlinear state observation method according to the nonlinear state space.

Step two: inputting the parameter estimation value of the dynamic parameter of the nonlinear dynamic model into an intermediate conversion state quantity model, outputting an intermediate conversion state quantity by the intermediate conversion state quantity model, observing the intermediate conversion state quantity by a nonlinear state observer, outputting the observation state of the intermediate conversion state quantity, and obtaining the estimation value of the joint angular velocity of the multi-joint hydraulic mechanical arm according to the observation state of the intermediate conversion state quantity.

Step three: and designing an adaptive robust control law by using an adaptive robust control method according to the nonlinear dynamics model and the nonlinear state observer.

Step four: the nonlinear state space outputs an estimated value of the joint angular velocity of the multi-joint hydraulic mechanical arm to the adaptive robust control law, meanwhile, a target track of the multi-joint hydraulic mechanical arm is input to the adaptive robust control law, the adaptive robust control law outputs a control signal of valve core displacement of the multi-joint hydraulic mechanical arm to control the multi-joint hydraulic mechanical arm to operate, tracking errors are obtained through calculation of the target track of the multi-joint hydraulic mechanical arm and joint angles actually output during operation and are output to the adaptive robust control law, the adaptive robust control law outputs a parameter estimated value of dynamic parameters of a nonlinear dynamic model to an intermediate conversion state quantity model, the step two and the step four are repeated, and meanwhile, the nonlinear state observer is updated in a self-mode, so that the adaptive robust control of the multi-joint hydraulic mechanical arm is finally achieved.

In the first step, the nonlinear dynamics model of the multi-joint hydraulic mechanical arm is established as follows:

a) Connecting rod dynamics model:

τ _j ＝J _j (q)P _L

P _L ＝A _i P _i -A _o P _o

wherein q is, And->Respectively representing the joint angle, the joint angular velocity and the joint angular acceleration of the multi-joint hydraulic mechanical arm, and q and +.>n represents the joint number of the multi-joint hydraulic mechanical arm; m is M _j ()、C _j () And G _j () Respectively representing an inertia dynamic matrix, a coriolis force matrix and a gravity matrix of the multi-joint hydraulic mechanical arm, M _j ()、C _j ()、G _j ()∈R ^n×n ；τ _j Represents the driving torque of each joint of the multi-joint hydraulic mechanical arm, and tau _j ∈R ⁿ ；J _j () Representing a multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic mechanical arm; p (P) _L Representing the equivalent thrust of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, and P _L ∈R ⁿ ；A _i And A _o Respectively representing contact areas of oil inlet cavities and oil return cavities of hydraulic cylinders of joints of the multi-joint hydraulic mechanical arm, A _i 、A _o ∈R ^n×n ；P _i And P _o Oil pressure of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, and P _i 、P _o ∈R ⁿ The method comprises the steps of carrying out a first treatment on the surface of the l represents the elongation of a hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm, l epsilon R ⁿ The method comprises the steps of carrying out a first treatment on the surface of the Kinetic matrixIs obliquely symmetrical.

By setting the dynamics parameter theta of a proper connecting rod dynamics model _m The link dynamics model may be linearized into the following form:

wherein,,kinetic parameter θ representing a kinetic model of a connecting rod _m Is a regression matrix of (a).

b) In consideration of hydraulic drive characteristics, a hydraulic dynamics model is established on the premise of assuming that the hydraulic cylinder is free from leakage:

V _i ＝V _hi +A _i diag[l]

V _o ＝V _ho -A _o diag[l]

Wherein V is _i And V _o The volumes of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, V _i 、V _o ∈R ^n×n ；β _e Represents the bulk modulus of the hydraulic oil; v (V) _hi And V _ho The volumes of the oil inlet cavity and the oil return cavity of each hydraulic cylinder of each driving device under the initial condition that the push rod elongation l=0 of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented; diag []A diagonal matrix representing the principal element; q (Q) _i And Q _o Respectively representing actual flow of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, Q _id And Q _od The preset ideal flow rates of the oil inlet cavity and the oil return cavity of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, Q _id 、Q _od ∈R ⁿ ，And->The calculable flow difference and the +.A flow difference respectively representing the actual flow of the oil inlet cavity and the oil return cavity of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm>And->The flow difference and the +.A. Of the actual flow of the oil inlet cavity and the oil return cavity of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented by the non-calculable flow difference +.>And->Respectively express and verifyThe flow difference between the actual flow and the ideal flow; k (k) _qi And k _qo Flow gain constants of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented; x is x _v The valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm is represented; g ₁ () Oil pressure P of oil inlet cavity of hydraulic cylinder for indicating each joint of multi-joint hydraulic mechanical arm _i And spool displacement x of hydraulic control valve _v Nonlinear conversion function between g ₂ () Oil pressure P of oil return cavity of hydraulic cylinder for indicating each joint of multi-joint hydraulic mechanical arm _o And spool displacement x of hydraulic control valve _v Nonlinear conversion function between g ₁ ()、g ₂ ()∈R ^n×n 。

g ₁ ()、g ₂ () The method comprises the following steps:

wherein P is _s Is the supply pressure of the hydraulic pump, P _r Is the reference pressure of the hydraulic return tank.

By setting the dynamics parameters theta of a proper hydraulic dynamics model _p The hydrokinetic model can be linearized into the following form:

wherein,,kinetic parameter θ representing a hydrodynamic model _p Is a regression matrix of (a).

The dynamics model constraint is specifically as follows:

|Δ _j |≤δ _j

θ∈{θ:θ _min ≤θ≤θ _max }

wherein delta is _j Representing uncertain nonlinearities and disturbances, delta, in the motion of a multi-joint hydraulic robotic arm _j ∈R ⁿ ；δ _j Representing a preset constant vector; θ _max And theta _min Respectively represent the upper and lower bounds of the dynamic parameter theta of the nonlinear dynamic model, and theta= [ theta ] _m ；θ _p ]。

Valve core displacement x of hydraulic control valve of each joint of multi-joint hydraulic mechanical arm _v The method is characterized by comprising the following steps:

wherein Q is _L Represents the equivalent flow rate of the hydraulic cylinder chamber, Q _L ∈R ⁿ 。

In the first step, an intermediate transition state quantity model of the unmeasurable state of the multi-joint hydraulic mechanical arm is designed, and the model is specifically as follows:

s＝[s ₁ ；s ₂ ；s ₃ ]

s ₁ ＝q

Wherein s represents an intermediate transition state quantity, s ₁ 、s ₂ Sum s ₃ First, second and third state quantities representing intermediate transition state quantities s, respectively; q andrespectively representing the joint angle and the joint angular velocity of the multi-joint hydraulic mechanical arm;And->Respectively representing link dynamics parameters theta of link dynamics model _m Is provided with a first and a second element of (c),M _j and C _j Respectively representing an inertial dynamic matrix and a coriolis force matrix of the multi-joint hydraulic mechanical arm, wherein I represents a unit matrix; f (f) ₁ And f ₂ Simplified first and second equivalent matrices representing intermediate transition state quantities s, respectively; θ represents the kinetic parameters of the nonlinear kinetic model, +.>Parameter estimation representing the kinetic parameter θ of a non-linear kinetic model, +.>And parameter adaptive errors representing the dynamic parameters theta of the nonlinear dynamic model.

Joint angular velocity of multi-joint hydraulic mechanical armNamely, the non-measurable state of the multi-joint hydraulic mechanical arm.

In the first step, the nonlinear state space is specifically as follows:

wherein,,and->The first state quantity s respectively representing the intermediate transition state quantity s ₁ Second state quantity s ₂ And a third state quantity s ₃ Is a derivative of (2); θ _m3 Connecting rod dynamics parameter theta representing connecting rod dynamics model _m And θ _m3 ＝J _j ^-1 C _j ；Δ _j Indicating uncertain nonlinearity and interference in the movement process of the multi-joint hydraulic mechanical arm;And->Hydrodynamic parameters θ respectively representing the hydrodynamic model _p Is, +.>f ₃ 、f ₄ And f ₅ Simplified third, fourth and fifth equivalent matrices representing intermediate transition state quantities s, respectively; u (u) _v Control voltage, u, representing the actual output of the adaptive robust control law _v ＝k _v x _v ，u _v ∈R ⁿ ，x _v Valve core displacement, k of hydraulic control valve representing each joint of multi-joint hydraulic mechanical arm _v Representing the conversion scaling factor.

The simplified first-fifth equivalent matrix of the intermediate transition state quantity s is specifically as follows:

f ₁ ＝J _j P _L

in the first step, the nonlinear state observer is specifically as follows:

wherein,,observation state representing intermediate transition state quantity s, +.>And->Respectively represent the joint angular velocity of the multi-joint hydraulic mechanical arm +.>Is the first intermediate transition state quantity s of (2) ₁ Second intermediate transition state quantity s ₂ And a third intermediate transition state quantity s ₃ Is a measurement of the observed value of (2);And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i The first observer coefficient epsilon ₁ Is, +.>And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i Second observer coefficient epsilon ₂ Is, +.>And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i The third observer coefficient epsilon ₃ Is, +.> Anda second observer coefficient matrix phi representing respectively nonlinear state observers _i First observer coefficient phi ₁ Is, +.>And->A second observer coefficient matrix phi representing respectively nonlinear state observers _i Second observer coefficient phi ₂ Is, +.>And->A second observer coefficient matrix phi representing respectively nonlinear state observers _i And a third observer coefficient phi ₃ Is, +.>First and second observer coefficient matrices and uncertain kinetic model parameters θ _m And theta _p Related to;And->Respectively representing link dynamics parameters theta of link dynamics model _m Observations of first, second and third elements of (a);And->Hydrodynamic parameters θ respectively representing the hydrodynamic model _p Is a first and second element observation; v ₂ And v ₃ Representing the second and third observer adaptive characterization parameters, respectively; n represents the number of joints of the multi-joint hydraulic mechanical arm.

Observation state of intermediate transition state quantity s Third observer adaptive characterization parameter v in (a) ₃ Joint angular velocity as a multi-joint hydraulic manipulator +.>Estimate of +.>

In the third step, the designed adaptive robust control law is specifically as follows:

a) First order adaptive robust control law v _3d ：

v _3d ＝v _3da +v _3dr +v _3ds

v _3ds ＝v _3ds1 +v _3ds2

Wherein v is _3da Representing a first order adaptive model compensation control law, v _3dr Representing a first order linear robust control law, v _3ds Representing a first order nonlinear robust control law; z ₂ Represents the angle conversion error of the multi-joint hydraulic mechanical arm,z ₁ and->Respectively represent joint angle tracking error and differential, z of multi-joint hydraulic mechanical arm ₁ ＝q-q _d ，q _d The control target value of each joint angle of the multi-joint hydraulic mechanical arm is represented, namely the target track of the multi-joint hydraulic mechanical arm, and the angle conversion error z ₂ The aim of the establishment of the first nonlinear robust control law is also to ensure that the differential of the Lyapunov control function of the first nonlinear robust control law is smaller than or equal to zero, so that the overall nonlinear robust controller keeps stable; k (k) ₁ And k ₂ Representing a first and a second gain positive-definite diagonal matrix, k, respectively ₁ And k ₂ The differential of the Lyapunov control function of the first-order self-adaptive robust control law in the nonlinear robust controller is ensured to be smaller than or equal to zero, so that the stability of the whole nonlinear robust controller is kept; / >And->Respectively representing the angular velocity and the acceleration of each joint of the multi-joint hydraulic mechanical armControlling a target value; θ _1min Model parameter θ representing a nonlinear dynamics model of a multi-joint hydraulic robotic arm ₁ Is the minimum of (2); first order nonlinear robust control law v _3ds Divided into two parts, v _3ds1 And v _3ds2 Respectively represent a first-order nonlinear robust control law v _3d A first order parametric nonlinear robust control law and a first order observed nonlinear robust control law;Connecting rod dynamics parameter theta representing connecting rod dynamics model _m Is the first element of (a);Representing a second parametric regression matrix; θ _m Connecting rod dynamics parameter theta representing connecting rod dynamics model _m Parameter adaptive errors of (2);Sum epsilon ₂ Respectively representing first, second and third preset design parameters; z _ob Observer error representing a nonlinear state observer, < +.> An observation state representing an intermediate transition state quantity s; delta _ob Representing observer error integration.

And the uncertain nonlinear factors exist in the nonlinear dynamics model of the connecting rod mechanical arm, and the influence factors need to be compensated. As uncertainty compensation parameter, a first order nonlinear robust control law v _3ds Cannot be written as a specific formulation. First-order nonlinear robust control law v meeting conditions _3ds Can ensure a first-order self-adaptive robust control law v _3d Good control performance can be maintained in the presence of parameter uncertainty and uncertainty nonlinearities.

First order adaptive robustnessControl law v _3d The calculation process of (a) is specifically as follows:

joint angle tracking error z of multi-joint hydraulic mechanical arm ₁ The following are provided:

z ₁ ＝q-q _d

wherein q represents an actual measurement value of each joint angle of the multi-joint hydraulic mechanical arm.

Angle conversion error z of multi-joint hydraulic mechanical arm ₂ The following are provided:

differentiating the above formula gives the following form:

wherein,,indicating the angle conversion error z of the multi-joint hydraulic mechanical arm ₂ Is a derivative of (2);Indicating joint angle tracking error z of multi-joint hydraulic mechanical arm ₁ Is a second order derivative of (a).

Status of non-speedometerAnd acceleration state->Can be expressed in the following form:

the following equations can be obtained by combining the above equations:

because of v only in the above formula ₃ High-order term Q of nonlinear dynamics model of mechanical arm comprising connecting rod _L Therefore, based on the thought of order reduction, an inversion establishment method is adopted to provide a first-order adaptive robust control law v _3d As a linear robust control law of the multi-joint hydraulic mechanical arm, the tracking error of each joint angle is reduced while the transient performance of the system is ensured.

b) First-order adaptive robust control law v _3d Establishing a second order adaptive robust control law Q using an inversion establishment method _Ld ：

Q _Ld ＝Q _Lda +Q _Ldr +Q _Lds

Q _Ldr ＝-k _3r z ₃

Q _Lds ＝Q _Lds1 +Q _Lds2

Wherein Q is _Lda Represent the second order self-adaptive model compensation control law, Q _Ldr Represent a second order linear robust control law, Q _Lds Representing a second order nonlinear robust control law; omega ₂ And omega ₃ Respectively represent a first order adaptive robust control law v _3d And second order adaptive robust control law Q _Ld Is set in the constant of the preset proportion;indicating the angle conversion error z of the multi-joint hydraulic mechanical arm ₂ Is a function of the estimated value of (2); k (k) _ob1 Representing first order observer gain; v ₁ Representing a first observer adaptive characterization parameter;Representing a first order adaptive robust control law v _3d Is a derivative of the computable part of (a); k (k) _3r Representing a third gain positive-definite diagonal matrix, and ensuring the stability of the designed controller; z ₃ Representing equivalent flow tracking error, z of multi-joint hydraulic mechanical arm ₃ ＝v ₃ -v _3d The method comprises the steps of carrying out a first treatment on the surface of the Second order nonlinear robust control law Q _Lds Divided into two parts, Q _Lds1 And Q _Lds2 Q respectively representing second-order nonlinear robust control law _Lds A second order parametric nonlinear robust control law and a second order observation nonlinear robust control law;Representing a third parameter regression matrix;A parameter adaptive error representing a kinetic parameter θ of the nonlinear kinetic model;Sum epsilon ₃ Representing fourth, fifth and sixth preset design parameters, respectively.

Adapting the second orderRobust control law Q _Ld As a nonlinear robust control law for multi-joint hydraulic robotic arms. Second order adaptive robust control law Q _Ld The calculation process of (a) is specifically as follows:

equivalent flow tracking error z of multi-joint hydraulic mechanical arm ₃ The following are provided:

z ₃ ＝v ₃ -v _3d

differentiating the two sides of the above equal sign can obtain the following:

wherein,,represents the equivalent flow tracking error z of the multi-joint hydraulic mechanical arm ₃ Differential of->Representing a third observer adaptive characterization parameter v ₃ Is a derivative of (2);Representing a first order adaptive robust control law v _3d Is a derivative of (a).

According to a first order adaptive robust control law v _3d Design results and observer properties, v _3d Concerning joint angle q, time t, observer parameters eta, phi ₁ 、φ ₂ 、φ ₃ Parameter estimation valueSo a first order adaptive robust control law v _3d The differential form of (a) is as follows:

wherein v is _3dc Andrespectively represent v _3d Is a derivative of the calculable part of (v) _3du And->Respectively represent v _3d Is not calculable and its derivative; eta and->Observer parameters and derivatives thereof respectively representing the nonlinear state observer;And->Respectively representing the parameter estimation value and the derivative of the dynamic parameter theta of the nonlinear dynamic model.

Is a linear regression matrix, and is specifically as follows:

Establishing an auxiliary semi-positive definite matrix V as follows:

to the upper equal signDifferential on both sides and apply a first order adaptive robust control law v _3d Substitution may take the form:

wherein,,representing the differentiation of the auxiliary semi-positive definite matrix V.

On the basis of the above, a second-order adaptive robust control law Q is provided _Ld And the tracking error of each joint angle is reduced while the transient performance of the system is ensured.

c) Considering that the overall dynamics model of the hydraulic mechanical arm has model parameter uncertainty, constructing a parameter self-adaptive law to compensate, and the parameter self-adaptive law:

wherein,,connecting rod dynamics parameter theta representing connecting rod dynamics model _m Is determined by the method; τ ₂ And τ ₃ Respectively representing a first-order model parameter self-adaptive reference value and a second-order model parameter self-adaptive reference value;Differentiation of the estimated value of the kinetic parameter θ representing the nonlinear kinetic model;Parameter estimation value +.for the kinetic parameter θ representing the non-linear kinetic model>Is a self-adaptive mapping function of (a); Γ -shaped structure _c Representing a matrix of parameter adaptive gain coefficients Γ _c ＝[Γ _m ；Γ _p ]，Γ _m And Γ _p Respectively representing a matrix Γ of parameter adaptive gain coefficients _c Is a first and second element of (c).

Parameter estimation value of dynamic parameter theta of the nonlinear dynamic modelThe adaptive mapping function of (a) is specifically as follows:

Where x represents the input parameters of the adaptive mapping function.

The second parameter regression matrixThe method comprises the following steps:

wherein k is _e Representing the tracking error gain parameter.

The third parameter regression matrixThe method comprises the following steps:

wherein,,model parameter θ representing a nonlinear dynamics model of a multi-joint hydraulic robotic arm ₁ Is a function of the estimated value of (2);Representing a linear regression matrix.

The linear regression matrixThe method comprises the following steps:

in the fourth step, the nonlinear state observer performs self-updating, specifically, the first observer coefficient matrix epsilon of the nonlinear state observer _i A second observer coefficient matrix phi _i And the observer self-adaptive characterization parameter matrix v is self-updated at respective self-update rates, specifically as follows:

wherein v= [ v ] ₁ ；v ₂ ；v ₃ ]；And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i The first observer coefficient epsilon ₁ Second observer coefficient ε ₂ And a third observer coefficient epsilon ₃ Is a self-update rate of (2); a is that _ob And K _ob First and second gain factor matrices representing the nonlinear state observer, respectively; y and y _ob Respectively representing the theoretical and actual outputs of the observer; e, e ₁ 、e ₂ And e ₃ Representing the first, second and third three-dimensional characterization parameters, e, respectively ₁ ＝[1；0；0],e ₂ ＝[0；1；0],e ₃ ＝[0；0；1]；Representing the self-update rate of the observer self-adaptive characterization parameter matrix v; q (Q) _L Representing the equivalent flow of the hydraulic cylinder chamber;and->A second observer coefficient matrix phi representing respectively nonlinear state observers _i First observer coefficient phi ₁ Second observer coefficient phi ₂ And a third observer coefficient phi ₃ Is a self-update rate of (c).

The first gain coefficient matrix A of the nonlinear state observer _ob And a second gain coefficient matrix K _ob The method comprises the following steps:

Λ＝Λ ^T ＞0

wherein,,respectively represent a first gain coefficient matrix A _ob Elements 1, 2, … i … n;Respectively represent a second gain coefficient matrix K _ob Elements 1, 2, … i … n;and->Representing observer first, second and third gain parameters, respectively; Λ represents a semi-positive definite matrix; i represents an identity matrix.

The beneficial effects of the invention are as follows:

1. according to the invention, through constructing intermediate state observables and designing a nonlinear state observer, the real-time observation of the unmeasurable state based on the uncertainty of the model parameters of the multi-joint hydraulic mechanical arm is realized, and the problem that the feedback state is unmeasurable due to the limitation of the sensor in the actual situation is solved.

2. The invention provides a multi-joint hydraulic mechanical arm self-adaptive robust control method based on an unmeasurable state observation value, which reduces the tail end tracking error of the mechanical arm and improves the control performance while ensuring the overall stability of a control system and an observation system.

Drawings

FIG. 1 is a system block diagram of the method of the present invention;

FIG. 2 is a diagram of the hydraulic drive system of the multi-joint hydraulic robotic arm of the present invention;

FIG. 3 is a diagram of an example control object of the robotic arm of the present invention;

FIG. 4 is a graph of the signals from the hydraulic mechanical arm joint angle sensor and differential filtering results used in the present invention.

Fig. 5 is a graph comparing the control effect of the adaptive robust controller of the multi-joint hydraulic mechanical arm based on nonlinear state observation with that of the conventional PID controller.

Detailed Description

The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. The specific embodiments described herein are to be considered in an illustrative sense only and are not intended to limit the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.

As shown in fig. 1, the adaptive robust control method for the hydraulic mechanical arm of the present invention comprises the following steps:

a) Connecting rod dynamics model:

τ _j ＝J _j (q)P _L

P _L ＝A _i P _i -A _o P _o

wherein q is,And->Respectively representing the joint angle, the joint angular velocity and the joint angular acceleration of the multi-joint hydraulic mechanical arm, and q and +.>n represents the joint number of the multi-joint hydraulic mechanical arm; m is M _j ()、C _j () And G _j () Respectively representing an inertia dynamic matrix, a coriolis force matrix and a gravity matrix of the multi-joint hydraulic mechanical arm, M _j ()、C _j ()、G _j ()∈R ^n×n ；τ _j Represents the driving torque of each joint of the multi-joint hydraulic mechanical arm, and tau _j ∈R ⁿ ；J _j () Representing a multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic mechanical arm; p (P) _L Representing the equivalent thrust of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, and P _L ∈R ⁿ ；A _i And A _o Oil inlet cavity and oil return cavity of hydraulic cylinder respectively representing joints of multi-joint hydraulic mechanical armContact area A _i 、A _o ∈R ^n×n ；P _i And P _o Oil pressure of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, and P _i 、P _o ∈R ⁿ The method comprises the steps of carrying out a first treatment on the surface of the l represents the elongation of a hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm, l epsilon R ⁿ The method comprises the steps of carrying out a first treatment on the surface of the Kinetic matrix->Is obliquely symmetrical.

V _i ＝V _hi +A _i diag[l]

V _o ＝V _ho -A _o diag[l]

Q _id ＝k _qi g ₁ (P _i ,x _v )x _v

wherein V is _i And V _o The volumes of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, V _i 、V _o ∈R ^n×n ；β _e Represents the bulk modulus of the hydraulic oil; v (V) _hi And V _ho The volumes of the oil inlet cavity and the oil return cavity of each hydraulic cylinder of each driving device under the initial condition that the push rod elongation l=0 of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented; diag []A diagonal matrix representing the principal element; q (Q) _i And Q _o Respectively representing actual flow of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, Q _id And Q _od The preset ideal flow rates of the oil inlet cavity and the oil return cavity of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, Q _id 、Q _od ∈R ⁿ ，And->The calculable flow difference and the +.A flow difference respectively representing the actual flow of the oil inlet cavity and the oil return cavity of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm>And->The flow difference and the +.A. Of the actual flow of the oil inlet cavity and the oil return cavity of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented by the non-calculable flow difference +.>And->Respectively representing the flow difference between the actual flow and the ideal flow; k (k) _qi And k _qo Flow gain constants of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented; x is x _v The valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm is represented; g ₁ () Oil pressure P of oil inlet cavity of hydraulic cylinder for indicating each joint of multi-joint hydraulic mechanical arm _i And spool displacement x of hydraulic control valve _v Nonlinear conversion function between g ₂ () Oil pressure P of oil return cavity of hydraulic cylinder for indicating each joint of multi-joint hydraulic mechanical arm _o And spool displacement x of hydraulic control valve _v Nonlinear conversion function between g ₁ ()、g ₂ ()∈R ^n×n 。

g ₁ ()、g ₂ () The method comprises the following steps:

The kinetic model constraints are specifically as follows:

|Δ _j |≤δ _j

θ∈{θ:θ _min ≤θ≤θ _max }

In the first step, an intermediate transition state quantity model of the unmeasurable state of the designed multi-joint hydraulic mechanical arm is specifically as follows:

s＝[s ₁ ；s ₂ ；s ₃ ]

s ₁ ＝q

In the first step, the nonlinear state space is specifically as follows:

wherein,, And->The first state quantity s respectively representing the intermediate transition state quantity s ₁ Second state quantity s ₂ And a third state quantity s ₃ Is a derivative of (2); θ _m3 Connecting rod dynamics parameter theta representing connecting rod dynamics model _m And θ _m3 ＝J _j ^-1 C _j ；Δ _j Indicating uncertain nonlinearity and interference in the movement process of the multi-joint hydraulic mechanical arm;And->Hydrodynamic parameters θ respectively representing the hydrodynamic model _p And θ _P1 ＝1/β _e ，θ _P2 ＝Q _i /β _e ；f ₃ 、f ₄ And f ₅ Simplified third, fourth and fifth equivalent matrices representing intermediate transition state quantities s, respectively; u (u) _v Control voltage, u, representing the actual output of the adaptive robust control law _v ＝k _v x _v ，u _v ∈R ⁿ ，x _v Valve core displacement, k of hydraulic control valve representing each joint of multi-joint hydraulic mechanical arm _v Representing the conversion scaling factor.

The simplified first-fifth equivalent matrix of intermediate transition state quantities s is specifically as follows:

f ₁ ＝J _j P _L

in step one, the nonlinear state observer is specifically as follows:

wherein,,observation state representing intermediate transition state quantity s, +.>And->Respectively represent the joint angular velocity of the multi-joint hydraulic mechanical arm +.>Is the first intermediate transition state quantity s of (2) ₁ Second intermediate transition state quantity s ₂ And a third intermediate transition state quantity s ₃ Is a measurement of the observed value of (2);And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i The first observer coefficient epsilon ₁ Is, +.>And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i Second observer coefficient epsilon ₂ Is, +.>And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i The third observer coefficient epsilon ₃ Is, +.> And->A second observer coefficient matrix phi representing respectively nonlinear state observers _i First observer coefficient phi ₁ Phi of the second and third elements of (2) ₂₂ And phi ₂₃ A second observer coefficient matrix phi representing respectively nonlinear state observers _i Second observer coefficient phi ₂ Is, +.>And->A second observer coefficient matrix phi representing respectively nonlinear state observers _i And a third observer coefficient phi ₃ Is, +.>First and second observer coefficient matrices and uncertain kinetic model parameters θ _m And theta _p Related to;And->Respectively representing link dynamics parameters theta of link dynamics model _m Observations of first, second and third elements of (a);And->Hydrodynamic parameters θ respectively representing the hydrodynamic model _p Is a first and second element observation; v ₂ And v ₃ Representing the second and third observer adaptive characterization parameters, respectively; n represents the number of joints of the multi-joint hydraulic mechanical arm.

Observation state of intermediate transition state quantity sThird observer adaptive characterization parameter v in (a) ₃ Joint angular velocity as a multi-joint hydraulic manipulator +.>Estimate of +.>

a) First order adaptive robust control law v _3d ：

v _3d ＝v _3da +v _3dr +v _3ds

v _3ds ＝v _3ds1 +v _3ds2

Wherein v is _3da Representing a first order adaptive model compensation control law, v _3dr Representing a first order linear robust control law, v _3ds Representing a first order nonlinear robust control law; z ₂ Represents the angle conversion error of the multi-joint hydraulic mechanical arm, z ₁ And->Respectively represent joint angle tracking error and differential, z of multi-joint hydraulic mechanical arm ₁ ＝q-q _d ，q _d The control target value of each joint angle of the multi-joint hydraulic mechanical arm is represented, namely the target track of the multi-joint hydraulic mechanical arm, and the angle conversion error z ₂ The aim of the establishment of the first nonlinear robust control law is also to ensure that the differential of the Lyapunov control function of the first nonlinear robust control law is smaller than or equal to zero, so that the overall nonlinear robust controller keeps stable; k (k) ₁ And k ₂ Representing a first and a second gain positive-definite diagonal matrix, k, respectively ₁ And k ₂ Ensuring non-linearity robustnessThe differential of the Lyapunov control function of the first-order adaptive robust control law in the rod controller is smaller than or equal to zero, so that the whole nonlinear robust controller keeps stability;And->Respectively representing control target values of angular velocity and acceleration of each joint of the multi-joint hydraulic mechanical arm; θ _1min Model parameter θ representing a nonlinear dynamics model of a multi-joint hydraulic robotic arm ₁ Is the minimum of (2); first order nonlinear robust control law v _3ds Divided into two parts, v _3ds1 And v _3ds2 Respectively represent a first-order nonlinear robust control law v _3d A first order parametric nonlinear robust control law and a first order observed nonlinear robust control law;Connecting rod dynamics parameter theta representing connecting rod dynamics model _m Is the first element of (a);Representing a second parametric regression matrix; θ _m Connecting rod dynamics parameter theta representing connecting rod dynamics model _m Parameter adaptive errors of (2);Sum epsilon ₂ Respectively representing first, second and third preset design parameters; z _ob Observer error representing a nonlinear state observer, < +.> An observation state representing an intermediate transition state quantity s; delta _ob Representing observer error integration.

First order adaptive robust control law v _3d The calculation process of (a) is specifically as follows:

z ₁ ＝q-q _d

differentiating the above formula gives the following form:

the following equations can be obtained by combining the above equations:

Q _Ld ＝Q _Lda +Q _Ldr +Q _Lds

Q _Ldr ＝-k _3r z ₃

Q _Lds ＝Q _Lds1 +Q _Lds2

Second order adaptive robust control law Q _Ld As a nonlinear robust control law for multi-joint hydraulic robotic arms. Second order adaptive robust control law Q _Ld The calculation process of (a) is specifically as follows:

z ₃ ＝v ₃ -v _3d

differentiating the two sides of the above equal sign can obtain the following:

wherein,,represents the equivalent flow tracking error z of the multi-joint hydraulic mechanical arm ₃ Differential of->Representing a third observer adaptive characterization parameter v ₃ Is a derivative of (2); / >Representing a first order adaptive robust control law v _3d Is a derivative of (a).

According to a first order adaptive robust control law v _3d Design results and observer properties, v _3d Concerning joint angle q, time t, observer parameters eta, phi ₁ 、φ ₂ 、φ ₃ Parameter estimationMetering valueSo a first order adaptive robust control law v _3d The differential form of (a) is as follows:

Is a linear regression matrix, e.gThe following steps:

establishing an auxiliary semi-positive definite matrix V as follows:

differential the two sides of the above equal sign and apply a first order adaptive robust control law v _3d Substitution may take the form:

Parameter estimation of the kinetic parameter θ of a nonlinear kinetic modelThe adaptive mapping function of (a) is specifically as follows:

where x represents the input parameters of the adaptive mapping function.

Second parameter regression matrixThe method comprises the following steps:

wherein k is _e Representing the tracking error gain parameter.

Third parameter regression matrixThe method comprises the following steps:

Linear regression matrixThe method comprises the following steps:

First gain coefficient matrix A of nonlinear state observer _ob And a second gain coefficient matrix K _ob The method comprises the following steps:

Λ＝Λ ^T ＞0

As shown in fig. 2 and 3, the underwater multi-degree-of-freedom hydraulic mechanical arm comprises a multi-degree-of-freedom mechanical arm connecting rod mechanism and a hydraulic system, wherein the multi-degree-of-freedom mechanical arm connecting rod mechanism is provided with n degrees of freedom joints; the hydraulic system mainly comprises an oil tank, a hydraulic pump, a total oil supply pressure sensor, a total oil return pressure sensor and n driving devices, wherein each driving device is hinged with a corresponding freedom degree joint of the multi-freedom-degree mechanical arm connecting rod mechanism; hydraulic oil in the oil tank flows into each driving device after flowing through the hydraulic pump, so that each degree of freedom joint of the multi-degree-of-freedom mechanical arm connecting rod mechanism is driven to move, and the hydraulic oil flows back into the oil tank through each driving device; detecting a total supply pressure of the hydraulic pump, i.e., a supply pressure of the hydraulic pump, flowing out of the oil tank by a total supply pressure sensor; detecting the total return oil pressure flowing back to the oil tank through a total return oil pressure sensor, namely the reference pressure of the whole hydraulic system; the hydraulic system also comprises a one-way valve, two filters and a safety circuit; the hydraulic oil in the oil tank flows through the hydraulic pump through the total oil supply channel The one-way valve flows out and flows into each driving device through a filter; a safety loop is additionally arranged between the oil supply pressure sensor and the oil tank, so that the safety of the whole hydraulic system is ensured; the hydraulic oil in each driving device flows through the other filter through the total oil return passage and flows back to the oil tank. The total oil supply pressure sensor is arranged on a total oil supply channel of the oil tank between the one-way valve and one filter, and the total oil return pressure sensor is arranged on a total oil return channel between the other filter and a plurality of driving devices. Each driving device comprises a hydraulic cylinder, a hydraulic valve, an oil supply pressure sensor and an oil return pressure sensor, wherein a push rod of the hydraulic cylinder is hinged with a corresponding freedom degree joint of the multi-degree mechanical arm connecting rod mechanism, and the oil supply pressure and the oil return pressure of hydraulic oil flowing into and out of each driving device are respectively detected through the respective oil supply pressure sensor and the oil return pressure sensor. The hydraulic valve of the driving device is arranged on an oil supply channel for hydraulic oil flowing into the hydraulic cylinder and an oil return channel for hydraulic oil flowing out of the hydraulic cylinder, the oil supply pressure sensor is arranged on the oil supply channel between the hydraulic valve and the hydraulic cylinder, and the oil return pressure sensor is arranged on the oil return channel between the hydraulic valve and the hydraulic cylinder, wherein A is a valve _i And A _o The areas of the oil inlet cavity and the oil return cavity of each hydraulic cylinder of each driving device are respectively, areas of oil inlet cavities of the 1 st, 2 nd, 3 rd, … th and nth hydraulic cylinders respectively are>The areas of oil return cavities of the 1 st, 2 nd, 3 rd, … th and nth hydraulic cylinders are respectively; The displacement amounts of the valve cores of the 1 st, 2 nd, 3 rd, … th and nth hydraulic valves respectively; oil supply pressure of hydraulic oil flowing into 1 st, 2 nd, 3 rd, … th and nth driving devices, respectively, +.>The hydraulic oil outlet pressures of the hydraulic oil flowing out of the 1 st, the 2 nd, the 3 rd, the … th and the nth driving devices are respectively; the actual flow of the oil inlet cavity of the 1 st, the 2 nd, the 3 rd, the … th and the nth hydraulic cylinder is>The actual flow of the oil return cavity of the 1 st hydraulic cylinder, the 2 nd hydraulic cylinder, the 3 rd hydraulic cylinder, the … th hydraulic cylinder and the nth hydraulic cylinder respectively.

Experiments of the multi-degree-of-freedom hydraulic mechanical arm based on the non-configured speed sensor are carried out on the control method, and the control effect of the control method is verified by comparing the multi-degree-of-freedom hydraulic mechanical arm with a PID controller. At the time of verification, in the designed obARC controller, the controller gain parameters were selected as shown in table 1. The reason for some of the adaptive parameters in Γ being zero is: in practical applications, some parameters can be uniquely determined by known parameters, and the uncertainty is small, so that only parameters with large uncertainty can be adaptively adjusted in order to improve the efficiency of the controller.

Table 1 controller parameter selection

The sensing precision and differential filtering result of the multi-joint hydraulic mechanical arm corner sensor are shown in fig. 4, the original signal and the filtered speed signal in fig. 4 refer to the left ordinate, and the filtered angle signal refers to the right ordinate. As can be seen from FIG. 4, the first sub-graph is the original signal graph, and the second sub-graph is the filter passband frequency w _c Differential filtered signal result plot at 10rad/s, third sub-plot is filter passband frequency w _c Differential filtered signal result plot of =30rad/s, fourth sub-plot is filter passband frequency w _c The differential filtering signal result graph of =50rad/s shows that the multi-joint hydraulic mechanical arm corner sensor has lower precision, and differential filtering can introduce extra signal lag, so that control precision is limited.

The experimental results of the multi-joint hydraulic mechanical arm are shown in fig. 5, the first subgraph in fig. 5 is the tracking experimental results of the obARC and PID, the second subgraph is the control error of the PID controller, and the third subgraph is the control error of the obARC controller. The control effect subgraph shows that the adaptive robust controller of the multi-joint hydraulic mechanical arm based on nonlinear state observation designed by the invention can accurately and smoothly track a target track curve under the conditions that the dynamic model parameters are uncertain and the feedback state is not measurable, and meanwhile, the control tracking error curve shows that the angle tracking error of each joint keeps zero (the angular velocity and the acceleration keep unchanged) in a steady state in the whole motion process.

Compared with the traditional PID controller, the joint tracking error is greatly reduced, the transient response time is greatly shortened, the adaptive robust control method of the multi-joint hydraulic mechanical arm based on nonlinear state observation, which is designed by the invention, has more excellent transient response performance and better robustness, can effectively compensate the influence of uncertainty of the dynamic model parameters of the hydraulic mechanical arm and the partial state uncertainty on the control precision of the tail end of the mechanical arm, reduces the tracking error of the tail end of the mechanical arm while ensuring the stability of a control system, and improves the control performance.

The invention belongs to the field of motion control of multi-joint hydraulic mechanical arms, in particular to a motion control method for a complex operation environment under the condition that physical signals such as the motion speed of the multi-joint hydraulic mechanical arms are not measurable. The nonlinear observer is then designed to obtain intermediate state quantities related to the unmeasurable states. And then, based on the intermediate state quantity observation value, designing the adaptive robust controller of the multi-joint hydraulic mechanical arm. The adaptive robust control method obARC for the multi-joint hydraulic mechanical arm based on nonlinear state observation can effectively improve the end control precision of the multi-joint hydraulic mechanical arm under the conditions that the dynamic model parameters of the multi-joint hydraulic mechanical arm are uncertain and the feedback state is not measurable, reduce the tail end tracking error of the mechanical arm while guaranteeing the overall stability of a control system and an observation system, enhance the control performance, realize state observation under the conditions that the nonlinear state such as the movement speed is not measurable, ensure the stability of the control system, reduce the tail end movement tracking error of the multi-joint hydraulic mechanical arm and improve the control precision of a tail end actuator of the mechanical arm, thereby improving the working performance of the mechanical arm under a harsher working environment.

The above is only a technical idea of the present invention, and the protection scope of the present invention is not limited by the above, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims

1. A hydraulic mechanical arm self-adaptive robust control method based on nonlinear state observation is characterized by comprising the following steps of: the method comprises the following steps:

step one: establishing a nonlinear dynamics model of the multi-joint hydraulic mechanical arm under the constraint of the dynamics model; designing an intermediate conversion state quantity model of an unmeasurable state of the multi-joint hydraulic mechanical arm and a nonlinear state space thereof, and establishing a nonlinear state observer by using a nonlinear state observation method according to the nonlinear state space;

step two: inputting the parameter estimation value of the dynamic parameter of the nonlinear dynamic model into an intermediate conversion state quantity model, outputting an intermediate conversion state quantity by the intermediate conversion state quantity model, observing the intermediate conversion state quantity by a nonlinear state observer, outputting the observation state of the intermediate conversion state quantity, and obtaining the estimation value of the joint angular velocity of the multi-joint hydraulic mechanical arm according to the observation state of the intermediate conversion state quantity;

Step three: according to the nonlinear dynamics model and the nonlinear state observer, an adaptive robust control method is used for designing an adaptive robust control law;

step four: the nonlinear state space outputs an estimated value of the joint angular velocity of the multi-joint hydraulic mechanical arm to the adaptive robust control law, meanwhile, a target track of the multi-joint hydraulic mechanical arm is input to the adaptive robust control law, the adaptive robust control law outputs a control signal of valve core displacement of the multi-joint hydraulic mechanical arm to control the multi-joint hydraulic mechanical arm to operate, tracking errors are obtained through calculation of the target track of the multi-joint hydraulic mechanical arm and joint angles actually output during operation and are output to the adaptive robust control law, the adaptive robust control law outputs a parameter estimated value of dynamic parameters of a nonlinear dynamic model to an intermediate conversion state quantity model, the steps II and IV are repeated, and meanwhile, the nonlinear state observer performs self-updating, and finally continuous adaptive robust control of the multi-joint hydraulic mechanical arm is achieved.

2. The adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 1, wherein the method comprises the following steps: in the first step, the nonlinear dynamics model of the multi-joint hydraulic mechanical arm is established as follows:

a) Connecting rod dynamics model:

τ _j ＝J _j (q)P _L

P _L ＝A _i P _i -A _o P _o

wherein q is,And->Respectively represent the joint angle, the joint angular velocity and the joint angular acceleration of the multi-joint hydraulic mechanical arm, q,n represents the joint number of the multi-joint hydraulic mechanical arm; m is M _j ()、C _j () And G _j () Respectively representing an inertia dynamic matrix, a coriolis force matrix and a gravity matrix of the multi-joint hydraulic mechanical arm, M _j ()、C _j ()、G _j ( )∈R ^n×n ；τ _j Represents the driving torque of each joint of the multi-joint hydraulic mechanical arm, and tau _j ∈R ⁿ ；J _j () Representing a multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic mechanical arm; p (P) _L Representing the equivalent thrust of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, and P _L ∈R ⁿ ；A _i And A _o Respectively representing contact areas of oil inlet cavities and oil return cavities of hydraulic cylinders of joints of the multi-joint hydraulic mechanical arm, A _i 、A _o ∈R ^n×n ；P _i And P _o Oil pressure of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, and P _i 、P _o ∈R ⁿ The method comprises the steps of carrying out a first treatment on the surface of the l represents the elongation of a hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm, l epsilon R ⁿ ；

b) Hydraulic dynamics model:

wherein V is _i And V _o The volumes of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, V _i 、V _o ∈R ^n×n ；β _e Represents the bulk modulus of the hydraulic oil; v (V) _hi And V _ho The volumes of the oil inlet cavity and the oil return cavity of each hydraulic cylinder of each driving device under the initial condition that the push rod elongation l=0 of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented; diag [ ]A diagonal matrix representing the principal element; q (Q) _i And Q _o Respectively representing actual flow of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, Q _id And Q _od The preset ideal flow rates of the oil inlet cavity and the oil return cavity of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented, Q _id 、Q _od ∈R ⁿ ，And->The calculable flow difference and the +.A flow difference respectively representing the actual flow of the oil inlet cavity and the oil return cavity of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm>And->The method comprises the steps that the flow difference can not be calculated for the actual flow of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm respectively; k (k) _qi And k _qo Flow gain constants of an oil inlet cavity and an oil return cavity of a hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm are respectively represented; x is x _v The valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm is represented; g ₁ () Oil pressure P of oil inlet cavity of hydraulic cylinder for indicating each joint of multi-joint hydraulic mechanical arm _i And spool displacement x of hydraulic control valve _v Nonlinear conversion function between g ₂ () Oil pressure P of oil return cavity of hydraulic cylinder for indicating each joint of multi-joint hydraulic mechanical arm _o And spool displacement x of hydraulic control valve _v Nonlinear conversion function between g ₁ ()、g ₂ ()∈R ^n×n ；

The dynamics model constraint is specifically as follows:

|Δ _j |≤δ _j

θ∈{θ:θ _min ≤θ≤θ _max }

wherein delta is _j Representing uncertain nonlinearities and disturbances, delta, in the motion of a multi-joint hydraulic robotic arm _j ∈R ⁿ ；δ _j Representing a preset constant vector; θ _max And theta _min Respectively represent the upper and lower bounds of the dynamic parameter theta of the nonlinear dynamic model, and theta= [ theta ] _m ；θ _p ]；

3. The adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 2, wherein the method comprises the following steps: in the first step, an intermediate transition state quantity model of the unmeasurable state of the multi-joint hydraulic mechanical arm is designed, and the model is specifically as follows:

s＝[s ₁ ；s ₂ ；s ₃ ]

s ₁ ＝q

wherein s represents an intermediate transition state quantity, s ₁ 、s ₂ Sum s ₃ First, second and third state quantities representing intermediate transition state quantities s, respectively; q andrespectively representing the joint angle and the joint angular velocity of the multi-joint hydraulic mechanical arm;And->Respectively representing link dynamics parameters theta of link dynamics model _m Is, +.>M _j And C _j Respectively representing an inertial dynamic matrix and a coriolis force matrix of the multi-joint hydraulic mechanical arm, wherein I represents a unit matrix; f (f) ₁ And f ₂ First and second equivalent matrices representing intermediate transition state quantities s, respectively; θ represents the kinetic parameters of the nonlinear kinetic model, +. >Parameter estimation representing the kinetic parameter θ of a non-linear kinetic model, +.>A parameter adaptive error representing a kinetic parameter θ of the nonlinear kinetic model;

4. The adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 2, wherein the method comprises the following steps: in the first step, the nonlinear state space is specifically as follows:

wherein,,and->The first state quantity s respectively representing the intermediate transition state quantity s ₁ Second state quantity s ₂ And a third state quantity s ₃ Is a derivative of (2);Connecting rod dynamics parameter theta representing connecting rod dynamics model _m Is->Δ _j Indicating uncertain nonlinearity and interference in the movement process of the multi-joint hydraulic mechanical arm;And->Hydrodynamic parameters θ respectively representing the hydrodynamic model _p Is, +.>f ₃ 、f ₄ And f ₅ Third, fourth and fifth equal matrix representing intermediate transition state quantity s, respectively; u (u) _v Control voltage, u, representing the actual output of the adaptive robust control law _v ＝k _v x _v ，u _v ∈R ⁿ ，x _v Valve core displacement, k of hydraulic control valve representing each joint of multi-joint hydraulic mechanical arm _v Representing a conversion scaling factor;

the first-fifth equivalent matrix of the intermediate conversion state quantity s is specifically as follows:

f ₁ ＝J _j P _L

f ₃ ＝J _j V _i ^-1 A _i

5. the adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 2, wherein the method comprises the following steps: in the first step, the nonlinear state observer is specifically as follows:

wherein,,observation state representing intermediate transition state quantity s, +.>And->Respectively represent the joint angular velocity of the multi-joint hydraulic mechanical arm +.>Is the first intermediate transition state quantity s of (2) ₁ Second intermediate transition state quantity s ₂ And a third intermediate transition state quantity s ₃ Is a measurement of the observed value of (2);And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i The first observer coefficient epsilon ₁ Is, +.>And->First observers respectively representing nonlinear state observersCoefficient matrix epsilon _i Second observer coefficient epsilon ₂ Is, +.>And->First observer coefficient matrix epsilon respectively representing nonlinear state observers _i The third observer coefficient epsilon ₃ Is, +.> And->A second observer coefficient matrix phi representing respectively nonlinear state observers _i First observer coefficient phi ₁ Is, +.>And->A second observer coefficient matrix phi representing respectively nonlinear state observers _i Second observer coefficient phi ₂ Is, +.>And->A second observer coefficient matrix phi representing respectively nonlinear state observers _i And a third observer coefficient phi ₃ Is, +.> And->Respectively representing link dynamics parameters theta of link dynamics model _m Observations of first, second and third elements of (a);And->Hydrodynamic parameters θ respectively representing the hydrodynamic model _p Is a first and second element observation; v ₂ And v ₃ Representing the second and third observer adaptive characterization parameters, respectively; n represents the joint number of the multi-joint hydraulic mechanical arm;

6. The adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 4, wherein the method comprises the following steps: in the third step, the designed adaptive robust control law is specifically as follows:

a) First order adaptive robust control law v _3d ：

v _3d ＝v _3da +v _3dr +v _3ds

v _3ds ＝v _3ds1 +v _3ds2

Wherein v is _3da Representing a first order adaptive model compensation control law, v _3dr Representing a first order linear robust control law, v _3ds Representing a first order nonlinear robust control law; z ₂ Represents the angle conversion error of the multi-joint hydraulic mechanical arm,z ₁ and->Respectively represent joint angle tracking error and differential, z of multi-joint hydraulic mechanical arm ₁ ＝q-q _d ，q _d The control target value of each joint angle of the multi-joint hydraulic mechanical arm is represented, namely, the target track of the multi-joint hydraulic mechanical arm; k (k) ₁ And k ₂ Representing first and second gain positive definite diagonal matrices, respectively;And->Respectively representing control target values of angular velocity and acceleration of each joint of the multi-joint hydraulic mechanical arm; θ _1min Model parameter θ representing a nonlinear dynamics model of a multi-joint hydraulic robotic arm ₁ Is the minimum of (2); v _3ds1 And v _3ds2 Respectively represent a first-order nonlinear robust control law v _3d A first order parametric nonlinear robust control law and a first order observed nonlinear robust control law; θ _m1 Connecting rod dynamics parameter theta representing connecting rod dynamics model _m Is the first element of (a);Representing a second parametric regression matrix;connecting rod dynamics parameter theta representing connecting rod dynamics model _m Parameter adaptive errors of (2); Sum epsilon ₂ Respectively representing first, second and third preset design parameters; z _ob Observer error representing a nonlinear state observer, < +. > An observation state representing an intermediate transition state quantity s; delta _ob Representing observer error integration;

b) Second order adaptive robust control law Q _Ld ：

Q _Ld ＝Q _Lda +Q _Ldr +Q _Lds

Q _Ldr ＝-k _3r z ₃

Q _Lds ＝Q _Lds1 +Q _Lds2

Wherein Q is _Lda Represent the second order self-adaptive model compensation control law, Q _Ldr Represent a second order linear robust control law, Q _Lds Representing a second order nonlinear robust control law; omega ₂ And omega ₃ Respectively represent a first order adaptive robust control law v _3d And second order adaptive robust control law Q _Ld Is set in the constant of the preset proportion;indicating the angle conversion error z of the multi-joint hydraulic mechanical arm ₂ Is a function of the estimated value of (2); k (k) _ob1 Representing first order observer gain; v ₁ Representing a first observer adaptive characterization parameter;Representing a first order adaptive robust control law v _3d Is a derivative of the computable part of (a); k (k) _3r Representing a third gain positive diagonal matrix; z ₃ Representing equivalent flow tracking error, z of multi-joint hydraulic mechanical arm ₃ ＝v ₃ -v _3d ；Q _Lds1 And Q _Lds2 Q respectively representing second-order nonlinear robust control law _Lds A second order parametric nonlinear robust control law and a second order observation nonlinear robust control law;Representing a third parameter regression matrix;A parameter adaptive error representing a kinetic parameter θ of the nonlinear kinetic model;Sum epsilon ₃ Respectively representing fourth, fifth and sixth preset design parameters;

c) Parameter adaptive law:

7. The adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 6, wherein the adaptive robust control method is characterized in that: parameter estimation value of dynamic parameter theta of the nonlinear dynamic modelThe adaptive mapping function of (a) is specifically as follows:

where x represents the input parameters of the adaptive mapping function.

8. The adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 6, wherein the adaptive robust control method is characterized in that: the second parameter regression matrixThe method comprises the following steps:

wherein k is _e Representing a tracking error gain parameter;

the third parameter regression matrixThe method comprises the following steps:

Wherein,,model parameter θ representing a nonlinear dynamics model of a multi-joint hydraulic robotic arm ₁ Is a function of the estimated value of (2);Representing a linear regression matrix;

the linear regression matrixThe method comprises the following steps:

9. the adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 5, wherein the adaptive robust control method is characterized in that: in the fourth step, the nonlinear state observer performs self-updating, specifically, the first observer coefficient matrix epsilon of the nonlinear state observer _i A second observer coefficient matrix phi _i And the observer self-adaptive characterization parameter matrix v is self-updated at respective self-update rates, specifically as follows:

10. The adaptive robust control method for a hydraulic mechanical arm based on nonlinear state observation according to claim 9, wherein the method comprises the following steps: the first gain coefficient matrix A of the nonlinear state observer _ob And a second gain coefficient matrix K _ob The method comprises the following steps:

Λ＝Λ ^T ＞0