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

Abstract

The invention discloses an adaptive robust control method of a hydraulic mechanical arm based on nonlinear state observation. The estimated value of the dynamic parameters is input into the intermediate transition state quantity model, the intermediate transition state quantity is output, the nonlinear state observer observes and outputs the observed state, and obtains the estimated value of the joint angular velocity; the estimated value of the joint angular velocity and the target trajectory are input, and the control signal of the valve core displacement is output to control the operation of the multi-joint hydraulic manipulator, and the tracking error is obtained and output to the adaptive robust control law. Repeat the steps while the nonlinear state observer performs self-update, and finally realizes adaptive robust control. The method of the present invention realizes real-time observation of unmeasurable states based on uncertain model parameters, solves the situation of unmeasurable feedback states caused by sensor limitations in actual situations, and while ensuring the overall stability of the control system and the observation system, reduces the tracking error at the end of the mechanical arm and improves control performance.

Description

Adaptive robust control method for hydraulic manipulator based on nonlinear state observation

Technical Field

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

Background Art

Hydraulic manipulators are usually used for demanding operation tasks such as heavy loads. However, with the development of industry and the continuous advancement of human exploration, the complexity of hydraulic manipulators' operation tasks has continued to increase, and the requirements for operation accuracy have also continued to increase. The traditional proportional-integral-differential PID control has gradually failed to meet the high control performance requirements because it does not consider the uncertainty of the parameters of the manipulator's dynamic model. In this case, developing a full-state feedback controller based on the dynamic model of a multi-joint hydraulic manipulator is an effective solution. On the other hand, the working environment of a multi-joint hydraulic manipulator has become increasingly harsh. In most practical applications, for safety and reliability reasons, hydraulic manipulators are only equipped with low-precision position sensors. This results in large noise in the measurement signal and the inability to perform other state measurements, especially speed measurement. The method of differentiating the position signal and using a low-pass filter is a common means of obtaining the speed signal at this stage. However, the existence of the low-pass filter seriously affects the closed-loop bandwidth of the system, thereby limiting the control performance of the multi-joint hydraulic manipulator. Therefore, it is difficult for existing controllers to comprehensively consider problems such as uncertainty in the dynamic model parameters and unpredictable state of multi-joint hydraulic robotic arms in harsh and complex working environments, which makes it difficult to ensure good robotic arm end control accuracy and affects the operating performance in specific situations.

Summary of the invention

In order to solve the problems existing in the background technology, the present invention provides an adaptive robust control method for a hydraulic manipulator arm based on nonlinear state observation, which improves the end control accuracy of a multi-joint hydraulic manipulator arm when the parameters of the dynamic model are uncertain and the feedback state is unmeasurable, and reduces the end tracking error of the manipulator arm while ensuring the overall stability of the control system and the observation system, thereby enhancing the control performance.

The technical solution adopted by the present invention is:

The hydraulic mechanical arm adaptive robust control method of the present invention comprises the following steps:

Step 1: Comprehensively consider the hydraulic characteristics and multi-degree-of-freedom coupling characteristics, and establish a nonlinear dynamic model of the multi-joint hydraulic robotic arm under the constraints of the dynamic model; design the intermediate conversion state quantity model of the unmeasurable state of the multi-joint hydraulic robotic arm and its nonlinear state space, and establish a nonlinear state observer based on the nonlinear state space using the nonlinear state observation method.

Step 2: Input the parameter estimation values of the dynamic parameters of the nonlinear dynamic model into the intermediate conversion state quantity model, the intermediate conversion state quantity model outputs the intermediate conversion state quantity, the nonlinear state observer observes the intermediate conversion state quantity and outputs the observation state of the intermediate conversion state quantity, and obtains the estimated value of the joint angular velocity of the multi-joint hydraulic robot arm according to the observation state of the intermediate conversion state quantity.

Step 3: Based on the nonlinear dynamic model and nonlinear state observer, use the adaptive robust control method to design the adaptive robust control law.

Step 4: The nonlinear state space outputs the estimated value of the joint angular velocity of the multi-joint hydraulic mechanical arm to the adaptive robust control law, and at the same time inputs the target trajectory of the multi-joint hydraulic mechanical arm into the adaptive robust control law. The adaptive robust control law outputs the control signal of the valve core displacement of the multi-joint hydraulic mechanical arm to control the operation of the multi-joint hydraulic mechanical arm. The tracking error is obtained by calculating the target trajectory of the multi-joint hydraulic mechanical arm and the joint angle actually output during operation and output it to the adaptive robust control law. The adaptive robust control law outputs the parameter estimation value of the dynamic parameters of the nonlinear dynamic model to the intermediate conversion state quantity model and repeats steps 2 and 4. At the same time, the nonlinear state observer is self-updated to finally realize the adaptive robust control of the multi-joint hydraulic mechanical arm.

In the step 1, the nonlinear dynamic 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

Among them, q, and They represent the joint angle, joint angular velocity and joint angular acceleration of the multi-joint hydraulic manipulator, q, n represents the number of joints of the multi-joint hydraulic mechanical arm; M _j (), C _j () and G _j () represent the inertial dynamics matrix, Coriolis force matrix and gravity matrix of the multi-joint hydraulic mechanical arm respectively, 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, τ _j ∈R ⁿ ; J _j () represents the multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic mechanical arm; _PL represents the equivalent thrust of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _PL ∈R ⁿ ; _Ai and Ao represent the contact areas of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm respectively, _Ai , _Ao ∈R ^n×n ; _Pi and P _o represent the oil pressures of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm respectively, _Pi , P _o ∈R ⁿ ; _l represents the extension of the hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm, l∈R ⁿ ; dynamic matrix It is obliquely symmetrical.

By setting appropriate dynamic parameters θ _m of the connecting rod dynamic model, the connecting rod dynamic model can be linearized into the following form:

in, Represents the regression matrix of the dynamic parameters _θm of the connecting rod dynamic model.

b) Considering the hydraulic drive characteristics, a hydraulic dynamics model is established under the assumption that the hydraulic cylinder has no leakage:

V _i = V _hi + A _i diag[l]

V _o =V _ho -A _o diag[l]

Wherein, _Vi and _Vo represent the volume of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Vi , _Vo ∈Rn ^×n ; _βe represents the bulk modulus of the hydraulic oil; _Vhi and _Vho represent the volume of the oil inlet chamber and oil return chamber of each hydraulic cylinder of each driving device under the initial condition that the extension of the hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm is l=0; diag[·] represents a diagonal matrix with · as the main element; _Qi and _Qo represent the actual flow of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Qid and _Qod represent the preset ideal flow of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Qid , _Qod ^∈Rn , and The calculable flow difference of the actual flow of the hydraulic cylinder oil inlet chamber and oil return chamber of each joint of the multi-joint hydraulic mechanical arm is respectively represented. and They represent the uncalculated flow difference of the actual flow of the oil inlet chamber and the oil return chamber of each joint of the multi-joint hydraulic mechanical arm, and They respectively represent the flow difference between the actual flow and the ideal flow; k _qi and k _qo respectively represent the flow gain constants of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm; x _v represents the valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm; g ₁ () represents the nonlinear conversion function between the oil pressure _Pi of the oil inlet chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm and the valve core displacement x _v of the hydraulic control valve, g ₂ () represents the nonlinear conversion function between the oil pressure _Po of the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm and the valve core displacement x _v of the hydraulic control valve, g ₁ (), g ₂ ()∈R ^n×n .

g ₁ () and g ₂ () are as follows:

Among them, _Ps is the supply pressure of the hydraulic pump and _Pr is the reference pressure of the hydraulic return tank.

By setting appropriate dynamic parameters θ _p of the hydraulic dynamic model, the hydraulic dynamic model can be linearized into the following form:

in, Represents the regression matrix of the dynamic parameters _θp of the hydraulic dynamic model.

The constraints of the dynamic model are as follows:

|Δ _j |≤δ _j

θ∈{θ:θ _min ≤θ≤θ _max }

Among them, Δ _j represents the uncertain nonlinearity and interference in the motion process of the multi-joint hydraulic manipulator, Δ _j ∈R ⁿ ; δ _j represents the preset constant vector; θ _max and θ _min represent the upper and lower bounds of the dynamic parameter θ of the nonlinear dynamic model, respectively, θ＝[θ _m ; θ _p ].

The valve core displacement x _v of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm is as follows:

Wherein, Q _L represents the equivalent flow rate of the hydraulic cylinder chamber, Q _L ∈R ⁿ .

In the step 1, the intermediate conversion state quantity model of the unmeasurable state of the multi-joint hydraulic mechanical arm is designed, which is as follows:

s＝[s ₁ ；s ₂ ；s ₃ ]

s ₁ =q

Where s represents the intermediate conversion state quantity, _s1 , _s2 and _s3 represent the first, second and third state quantities of the intermediate conversion state quantity s respectively; q and They represent the joint angles and joint angular velocities of the multi-joint hydraulic manipulator respectively; and denote the first and second elements of the connecting rod dynamics parameter _θm of the connecting rod dynamics model, respectively. _Mj and _Cj represent the inertial dynamic matrix and Coriolis force matrix of the multi-joint hydraulic manipulator, respectively; I represents the unit matrix; _f1 and _f2 represent the simplified first and second equal-quantity matrices of the intermediate conversion state quantity s, respectively; θ represents the dynamic parameter of the nonlinear dynamic model, represents the parameter estimate of the kinetic parameter θ of the nonlinear kinetic model, Represents the parameter adaptation error of the dynamic parameter θ of the nonlinear dynamic model.

Joint angular velocity of multi-joint hydraulic manipulator That is the unpredictable state of the multi-joint hydraulic robotic arm.

In the step 1, the nonlinear state space is specifically as follows:

in, and They represent the differentials of the first state quantity s ₁ , the second state quantity s ₂ and the third state quantity s ₃ of the intermediate conversion state quantity s respectively; θ _m3 represents the third element of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model, θ _m3 =J _j ^-1 C _j ; Δ _j represents the uncertain nonlinearity and interference in the motion process of the multi-joint hydraulic manipulator; and denote the first and second elements of the hydrodynamic parameter _θp of the hydrodynamic model, respectively, _f3 , _f4 and _f5 represent the simplified third, fourth and fifth equal-quantity matrices of the intermediate conversion state quantity s respectively; _uv represents the control voltage actually output by the adaptive robust control law, _uv = _kvxv , _uv∈Rn , _xv represents the ^valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm, _{and kv represents} the conversion proportional coefficient.

The simplified first to fifth equal quantity matrices of the intermediate conversion state quantity s are as follows:

f ₁ = J _j P _L

In the step 1, the nonlinear state observer is specifically as follows:

in, represents the observed state of the intermediate conversion state quantity s, and Represent the joint angular velocity of the multi-joint hydraulic manipulator observed values of the first intermediate conversion state quantity s ₁ , the second intermediate conversion state quantity s ₂ and the third intermediate conversion state quantity s ₃ ; and denote the second and third elements of the first observer coefficient ε ₁ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the second observer coefficient ε ₂ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the third observer coefficient ε ₃ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the first observer coefficient φ ₁ in the second observer coefficient matrix φ _i of the nonlinear state observer, respectively, and denote the second and third elements of the second observer coefficient φ ₂ in the second observer coefficient matrix φ _i of the nonlinear state observer, respectively, and denote the second and third elements of the third observer coefficient φ ₃ in the second observer coefficient matrix φ _i of the nonlinear state observer, respectively, The first and second observer coefficient matrices are related to the uncertain dynamic model parameters θ _m and θ _p ; and denote the observed values of the first, second and third elements of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model respectively; and They respectively represent the observed values of the first and second elements of the hydraulic dynamic parameter θ _p of the hydraulic dynamic model; v ₂ and v ₃ respectively represent the second and third observer adaptive characterization parameters; n represents the number of joints of the multi-joint hydraulic manipulator.

The observed state of the intermediate conversion state quantity s The third observer adaptive characterization parameter v ₃ in is used as the joint angular velocity of the multi-joint hydraulic manipulator Estimated value of

In step 3, the designed adaptive robust control law is 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

Among them, v _3da represents the first-order adaptive model compensation control law, v _3dr represents the first-order linear robust control law, v _3ds represents the first-order nonlinear robust control law; z ₂ represents the angle conversion error of the multi-joint hydraulic manipulator, z ₁ and They represent the joint angle tracking error and its differential of the multi-joint hydraulic manipulator, z ₁ =qq _d , q _d represents the control target value of each joint angle of the multi-joint hydraulic manipulator, that is, the target trajectory of the multi-joint hydraulic manipulator, and the purpose of establishing the angle conversion error z ₂ is also to ensure that the differential of the Lyapunov control function of the first nonlinear robust control law is less than or equal to zero, so that the overall nonlinear robust controller maintains stability; k ₁ and k ₂ represent the first and second gain positive definite diagonal matrices, respectively, k ₁ and k ₂ ensure that the differential of the Lyapunov control function of the first-order adaptive robust control law in the nonlinear robust controller is less than or equal to zero, so that the entire nonlinear robust controller maintains stability; and They represent the control target values of the angular velocity and acceleration of each joint of the multi-joint hydraulic manipulator respectively; θ _1min represents the minimum value of the model parameter θ ₁ of the nonlinear dynamic model of the multi-joint hydraulic manipulator; the first-order nonlinear robust control law v _3ds is divided into two parts, v _3ds1 and v _3ds2 represent the first-order parameter nonlinear robust control law and the first-order observation nonlinear robust control law of the first-order nonlinear robust control law v _3d respectively; The first element of the connecting rod dynamics parameter θ _m representing the connecting rod dynamics model; represents the second parameter regression matrix; θ _m represents the parameter adaptive error of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model; and ∈ ₂ represent the first, second and third preset design parameters respectively; z _ob represents the observer error of the nonlinear state observer, represents the observed state of the intermediate conversion state quantity s; δ _ob represents the observer error integration.

Considering that there are still uncertain nonlinear factors in the nonlinear dynamics model of the connecting rod manipulator, it is necessary to compensate for these influencing factors. As an uncertainty compensation parameter, the first-order nonlinear robust control law v _{3ds cannot be expressed as a specific formula. The first-order nonlinear robust control law v 3ds that} meets the conditions can ensure that the first-order adaptive robust control law v _3d can maintain good control performance when there are parameter uncertainties and uncertainty nonlinearities.

The calculation process of the first-order adaptive robust control law v _3d is as follows:

The joint angle tracking error _z1 of the multi-joint hydraulic manipulator is as follows:

z ₁ = qq _d

Where q represents the actual measured value of each joint angle of the multi-joint hydraulic manipulator.

The angle conversion error _z2 of the multi-joint hydraulic manipulator is as follows:

Differentiating the above formula, we can get the following form:

in, represents the differential of the angle conversion error z ₂ of the multi-joint hydraulic manipulator; Represents the second-order differential of the joint angle tracking error _z1 of the multi-joint hydraulic manipulator.

Unmeasured speed status With acceleration state It can be expressed as follows:

Combining the above formulas, we can get the following equation:

Because only v ₃ in the above formula contains the high-order term Q _L of the nonlinear dynamic model of the connecting rod manipulator, based on the idea of order reduction, the back-stepping method is adopted to propose a first-order adaptive robust control law v _3d as the linear robust control law of the multi-joint hydraulic manipulator, which reduces the tracking error of each joint angle while ensuring the transient performance of the system.

b) Based on the first-order adaptive robust control law v _3d , the second-order adaptive robust control law Q _Ld is established using the inverse establishment method:

Q _Ld = Q _Lda + Q _Ldr + Q _Lds

Q _Ldr = -k _3r z ₃

Q _Lds = Q _Lds1 + Q _Lds2

Wherein, Q _Lda represents the second-order adaptive model compensation control law, Q _Ldr represents the second-order linear robust control law, Q _Lds represents the second-order nonlinear robust control law; ω ₂ and ω ₃ represent the preset proportional balance constants of the first-order adaptive robust control law v _3d and the second-order adaptive robust control law Q _Ld , respectively; represents the estimated value of the angle conversion error _z2 of the multi-joint hydraulic manipulator; k _ob1 represents the first-order observer gain; v ₁ represents the first observer adaptive characterization parameter; represents the differential of the computable part of the first-order adaptive robust control law v _3d ; k _3r represents the third gain positive definite diagonal matrix, which ensures the stability of the designed controller; z ₃ represents the equivalent flow tracking error of the multi-joint hydraulic manipulator, z ₃ =v ₃ -v _3d ; the second-order nonlinear robust control law Q _Lds is divided into two parts, Q _Lds1 and Q _Lds2 represent the second-order parameter nonlinear robust control law and the second-order observation nonlinear robust control law of Q _Lds of the second-order nonlinear robust control law respectively; represents the third parameter regression matrix; represents the parameter adaptation error of the dynamic parameter θ of the nonlinear dynamic model; and ∈ ₃ represent the fourth, fifth and sixth preset design parameters respectively.

The second-order adaptive robust control law Q _Ld is used as the nonlinear robust control law of the multi-joint hydraulic manipulator. The calculation process of the second-order adaptive robust control law Q _Ld is as follows:

The equivalent flow tracking error z ₃ of the multi-joint hydraulic manipulator is as follows:

z ₃ = v ₃ - v _3d

Differentiating both sides of the above equation, we can get the following:

in, represents the differential of the equivalent flow tracking error z ₃ of the multi-joint hydraulic manipulator, represents the differential of the adaptive characterization parameter v ₃ of the third observer; represents the derivative of the first-order adaptive robust control law v _3d .

According to the design results of the first-order adaptive robust control law v _3d and the properties of the observer, v _3d is related to the joint angle q, time t, observer parameters η, φ ₁ , φ ₂ , φ ₃ and parameter estimates function, so the differential form of the first-order adaptive robust control law v _3d is as follows:

Among them, v _3dc and denote the computable part of v _3d and its derivative, v _3du and denote the incalculable part of v _3d and its differential respectively; η and denote the observer parameters and their derivatives of the nonlinear state observer respectively; and They represent the parameter estimate and its differential of the kinetic parameter θ of the nonlinear kinetic model respectively.

is the linear regression matrix, as follows:

Establish the auxiliary semi-positive definite matrix V as:

Differentiating both sides of the above equation and substituting the first-order adaptive robust control law v _3d into it, we can get the following form:

in, represents the differential of the auxiliary positive semidefinite matrix V.

Based on the above equation, a second-order adaptive robust control law Q _Ld is proposed to reduce the tracking error of each joint angle while ensuring the transient performance of the system.

c) Considering the uncertainty of model parameters in the overall dynamics model of the hydraulic manipulator, a parameter adaptive law is constructed to compensate for it. The parameter adaptive law is:

in, represents the differential of the estimated value of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model; τ ₂ and τ ₃ represent the first-order and second-order model parameter adaptive reference values respectively; represents the differential of the estimated value of the kinetic parameter θ of the nonlinear kinetic model; Represents the parameter estimate of the kinetic parameter θ of the nonlinear kinetic model Adaptive mapping function; Γ _c represents a parameter adaptive gain coefficient matrix, Γ _c =[Γ _m ; Γ _p ], Γ _m and Γ _p represent the first and second elements of the parameter adaptive gain coefficient matrix Γ _c, respectively.

The parameter estimate of the kinetic parameter θ of the nonlinear kinetic model is The adaptive mapping function is as follows:

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

The second parameter regression matrix The details are as follows:

Where _ke represents the tracking error gain parameter.

The third parameter regression matrix The details are as follows:

in, represents the estimated value of the model parameter θ ₁ of the nonlinear dynamic model of the multi-joint hydraulic manipulator; represents the linear regression matrix.

The linear regression matrix The details are as follows:

In the step 4, the nonlinear state observer performs self-update, specifically, the first observer coefficient matrix ε _i , the second observer coefficient matrix φ _i and the observer adaptive characterization parameter matrix v of the nonlinear state observer are self-updated at their respective self-update rates, as follows:

Wherein, v = [v ₁ ; v ₂ ; v ₃ ]; and denote the self-update rates of the first observer coefficient ε ₁ , the second observer coefficient ε ₂ and the third observer coefficient ε ₃ in the first observer coefficient matrix ε _i of the nonlinear state observer respectively; A _ob and K _ob denote the first and second gain coefficient matrices of the nonlinear state observer respectively; y and y _ob denote the theoretical and actual outputs of the observer respectively; e ₁ , e ₂ and e ₃ denote the first, second and third dimensional characterization parameters respectively, e ₁ = [1; 0; 0], e ₂ = [0; 1; 0], e ₃ = [0; 0; 1]; represents the self-update rate of the observer adaptive characterization parameter matrix v; Q _L represents the equivalent flow rate of the hydraulic cylinder chamber; and They respectively represent the self-update rates of the first observer coefficient φ ₁ , the second observer coefficient φ ₂ and the third observer coefficient φ ₃ in the second observer coefficient matrix φ _i of the nonlinear state observer.

The first gain coefficient matrix A _ob and the second gain coefficient matrix K _ob of the nonlinear state observer are specifically as follows:

Λ＝Λ ^T ＞0

in, Respectively represent the 1st, 2nd, ...i...nth elements in the first gain coefficient matrix A _ob ; Respectively represent the 1st, 2nd, ...i...nth elements in the second gain coefficient matrix K _ob ; and denote the first, second and third gain parameters of the observer respectively; Λ denotes a semi-positive definite matrix; I denotes an identity matrix.

The beneficial effects of the present invention are:

1. The present invention realizes real-time observation of unmeasurable states with uncertain parameters of a multi-joint hydraulic mechanical arm model by constructing intermediate state observation quantities and designing a nonlinear state observer, thereby solving the problem of unmeasurable feedback states caused by sensor limitations in actual situations.

2. The present invention proposes an adaptive robust control method for a multi-joint hydraulic manipulator based on unmeasurable state observation values, which reduces the tracking error of the manipulator end and improves the control performance while ensuring the overall stability of the control system and the observation system.

BRIEF DESCRIPTION OF THE DRAWINGS

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

FIG2 is a diagram of a hydraulic drive system of a multi-joint hydraulic mechanical arm of the present invention;

3 is a structural diagram of an example of a robot arm control object of the present invention;

FIG. 4 is a diagram showing the joint angle sensor signal and differential filtering result of the hydraulic mechanical arm used in the present invention.

FIG5 is a comparison diagram of the control effects of the multi-joint hydraulic mechanical arm adaptive robust controller based on nonlinear state observation designed by the present invention and the traditional PID controller.

DETAILED DESCRIPTION

In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other.

As shown in FIG1 , the hydraulic mechanical arm adaptive robust control method of the present invention comprises the following steps:

Step 1: Comprehensively consider the hydraulic characteristics and multi-degree-of-freedom coupling characteristics, and establish a nonlinear dynamic model of the multi-joint hydraulic robotic arm under the constraints of the dynamic model; design the intermediate conversion state quantity model of the unmeasurable state of the multi-joint hydraulic robotic arm and its nonlinear state space, and establish a nonlinear state observer based on the nonlinear state space using the nonlinear state observation method.

In step 1, the nonlinear dynamic model of the multi-joint hydraulic manipulator 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

Among them, q, and They represent the joint angle, joint angular velocity and joint angular acceleration of the multi-joint hydraulic manipulator, q, n represents the number of joints of the multi-joint hydraulic mechanical arm; M _j (), C _j () and G _j () represent the inertial dynamics matrix, Coriolis force matrix and gravity matrix of the multi-joint hydraulic mechanical arm respectively, 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, τ _j ∈R ⁿ ; J _j () represents the multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic mechanical arm; _PL represents the equivalent thrust of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _PL ∈R ⁿ ; _Ai and Ao represent the contact areas of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm respectively, _Ai , _Ao ∈R ^n×n ; _Pi and P _o represent the oil pressures of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm respectively, _Pi , P _o ∈R ⁿ ; _l represents the extension of the hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm, l∈R ⁿ ; dynamic matrix It is obliquely symmetrical.

By setting appropriate dynamic parameters θ _m of the connecting rod dynamic model, the connecting rod dynamic model can be linearized into the following form:

in, Represents the regression matrix of the dynamic parameters _θm of the connecting rod dynamic model.

b) Considering the hydraulic drive characteristics, a hydraulic dynamics model is established under the assumption that the hydraulic cylinder has no leakage:

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, _Vi and _Vo represent the volume of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Vi , _Vo ∈Rn ^×n ; _βe represents the bulk modulus of the hydraulic oil; _Vhi and _Vho represent the volume of the oil inlet chamber and oil return chamber of each hydraulic cylinder of each driving device under the initial condition that the extension of the hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm is l=0; diag[·] represents a diagonal matrix with · as the main element; _Qi and _Qo represent the actual flow of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Qid and _Qod represent the preset ideal flow of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Qid , _Qod ^∈Rn , and The calculable flow difference of the actual flow of the hydraulic cylinder oil inlet chamber and oil return chamber of each joint of the multi-joint hydraulic mechanical arm is respectively represented. and They represent the uncalculated flow difference of the actual flow of the oil inlet chamber and the oil return chamber of each joint of the multi-joint hydraulic mechanical arm, and They respectively represent the flow difference between the actual flow and the ideal flow; k _qi and k _qo respectively represent the flow gain constants of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm; x _v represents the valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm; g ₁ () represents the nonlinear conversion function between the oil pressure _Pi of the oil inlet chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm and the valve core displacement x _v of the hydraulic control valve, g ₂ () represents the nonlinear conversion function between the oil pressure _Po of the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm and the valve core displacement x _v of the hydraulic control valve, g ₁ (), g ₂ ()∈R ^n×n .

g ₁ () and g ₂ () are as follows:

Among them, _Ps is the supply pressure of the hydraulic pump and _Pr is the reference pressure of the hydraulic return tank.

By setting appropriate dynamic parameters θ _p of the hydraulic dynamic model, the hydraulic dynamic model can be linearized into the following form:

in, Represents the regression matrix of the dynamic parameters _θp of the hydraulic dynamic model.

The dynamic model constraints are as follows:

|Δ _j |≤δ _j

θ∈{θ:θ _min ≤θ≤θ _max }

Among them, Δ _j represents the uncertain nonlinearity and interference in the motion process of the multi-joint hydraulic manipulator, Δ _j ∈R ⁿ ; δ _j represents the preset constant vector; θ _max and θ _min represent the upper and lower bounds of the dynamic parameter θ of the nonlinear dynamic model, respectively, θ＝[θ _m ; θ _p ].

The valve core displacement x _v of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm is as follows:

Wherein, Q _L represents the equivalent flow rate of the hydraulic cylinder chamber, Q _L ∈R ⁿ .

In step 1, the intermediate conversion state quantity model of the unmeasurable state of the multi-joint hydraulic manipulator is designed as follows:

s＝[s ₁ ；s ₂ ；s ₃ ]

s ₁ =q

Where s represents the intermediate conversion state quantity, _s1 , _s2 and _s3 represent the first, second and third state quantities of the intermediate conversion state quantity s respectively; q and They represent the joint angles and joint angular velocities of the multi-joint hydraulic manipulator respectively; and denote the first and second elements of the connecting rod dynamics parameter _θm of the connecting rod dynamics model, respectively. _Mj and _Cj represent the inertial dynamic matrix and Coriolis force matrix of the multi-joint hydraulic manipulator, respectively; I represents the unit matrix; _f1 and _f2 represent the simplified first and second equal-quantity matrices of the intermediate conversion state quantity s, respectively; θ represents the dynamic parameter of the nonlinear dynamic model, represents the parameter estimate of the kinetic parameter θ of the nonlinear kinetic model, Represents the parameter adaptation error of the dynamic parameter θ of the nonlinear dynamic model.

Joint angular velocity of multi-joint hydraulic manipulator That is the unpredictable state of the multi-joint hydraulic robotic arm.

In step 1, the nonlinear state space is as follows:

in, and They represent the differentials of the first state quantity s ₁ , the second state quantity s ₂ and the third state quantity s ₃ of the intermediate conversion state quantity s respectively; θ _m3 represents the third element of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model, θ _m3 =J _j ^-1 C _j ; Δ _j represents the uncertain nonlinearity and interference in the motion process of the multi-joint hydraulic manipulator; and represent the first and second elements of the hydraulic dynamic parameter θ _p of the hydraulic dynamic model, θ _P1 =1/β _e , θ _P2 =Q _i /β _e ; f ₃ , f ₄ and f ₅ represent the simplified third, fourth and fifth equal matrices of the intermediate conversion state quantity s, respectively; _uv represents the control voltage actually output by the adaptive robust control law, _uv =k _v x _v , _uv ∈R ⁿ , x _v represents the valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm, and k _v represents the conversion proportional coefficient.

The simplified first-fifth equal quantity matrix of the intermediate conversion state quantity s is as follows:

f ₁ = J _j P _L

In step 1, the nonlinear state observer is as follows:

in, represents the observed state of the intermediate conversion state quantity s, and Represent the joint angular velocity of the multi-joint hydraulic manipulator observed values of the first intermediate conversion state quantity s ₁ , the second intermediate conversion state quantity s ₂ and the third intermediate conversion state quantity s ₃ ; and denote the second and third elements of the first observer coefficient ε ₁ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the second observer coefficient ε ₂ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the third observer coefficient ε ₃ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the first observer coefficient φ ₁ in the second observer coefficient matrix φ _i of the nonlinear state observer, φ ₂₂ and φ ₂₃ denote the second and third elements of the second observer coefficient φ ₂ in the second observer coefficient matrix φ _i of the nonlinear state observer, and denote the second and third elements of the third observer coefficient φ ₃ in the second observer coefficient matrix φ _i of the nonlinear state observer, respectively, The first and second observer coefficient matrices are related to the uncertain dynamic model parameters θ _m and θ _p ; and denote the observed values of the first, second and third elements of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model respectively; and They respectively represent the observed values of the first and second elements of the hydraulic dynamic parameter θ _p of the hydraulic dynamic model; v ₂ and v ₃ respectively represent the second and third observer adaptive characterization parameters; n represents the number of joints of the multi-joint hydraulic manipulator.

The observed state of the intermediate conversion state quantity s The third observer adaptive characterization parameter v ₃ in is used as the joint angular velocity of the multi-joint hydraulic manipulator Estimated value of

Step 2: Input the parameter estimation values of the dynamic parameters of the nonlinear dynamic model into the intermediate conversion state quantity model, the intermediate conversion state quantity model outputs the intermediate conversion state quantity, the nonlinear state observer observes the intermediate conversion state quantity and outputs the observation state of the intermediate conversion state quantity, and obtains the estimated value of the joint angular velocity of the multi-joint hydraulic robot arm according to the observation state of the intermediate conversion state quantity.

Step 3: Based on the nonlinear dynamic model and nonlinear state observer, use the adaptive robust control method to design the adaptive robust control law.

In step 3, the designed adaptive robust control law is 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

Among them, v _3da represents the first-order adaptive model compensation control law, v _3dr represents the first-order linear robust control law, v _3ds represents the first-order nonlinear robust control law; z ₂ represents the angle conversion error of the multi-joint hydraulic manipulator, z ₁ and They represent the joint angle tracking error and its differential of the multi-joint hydraulic manipulator, z ₁ =qq _d , q _d represents the control target value of each joint angle of the multi-joint hydraulic manipulator, that is, the target trajectory of the multi-joint hydraulic manipulator, and the purpose of establishing the angle conversion error z ₂ is also to ensure that the differential of the Lyapunov control function of the first nonlinear robust control law is less than or equal to zero, so that the overall nonlinear robust controller maintains stability; k ₁ and k ₂ represent the first and second gain positive definite diagonal matrices, respectively, k ₁ and k ₂ ensure that the differential of the Lyapunov control function of the first-order adaptive robust control law in the nonlinear robust controller is less than or equal to zero, so that the entire nonlinear robust controller maintains stability; and They represent the control target values of the angular velocity and acceleration of each joint of the multi-joint hydraulic manipulator respectively; θ _1min represents the minimum value of the model parameter θ ₁ of the nonlinear dynamic model of the multi-joint hydraulic manipulator; the first-order nonlinear robust control law v _3ds is divided into two parts, v _3ds1 and v _3ds2 represent the first-order parameter nonlinear robust control law and the first-order observation nonlinear robust control law of the first-order nonlinear robust control law v _3d respectively; The first element representing the connecting rod dynamics parameter θ _m of the connecting rod dynamics model; represents the second parameter regression matrix; θ _m represents the parameter adaptive error of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model; and ∈ ₂ represent the first, second and third preset design parameters respectively; z _ob represents the observer error of the nonlinear state observer, represents the observed state of the intermediate conversion state quantity s; δ _ob represents the observer error integration.

Considering that there are still uncertain nonlinear factors in the nonlinear dynamics model of the connecting rod manipulator, it is necessary to compensate for these influencing factors. As an uncertainty compensation parameter, the first-order nonlinear robust control law v _{3ds cannot be expressed as a specific formula. The first-order nonlinear robust control law v 3ds that} meets the conditions can ensure that the first-order adaptive robust control law v _3d can maintain good control performance when there are parameter uncertainties and uncertainty nonlinearities.

The calculation process of the first-order adaptive robust control law v _3d is as follows:

The joint angle tracking error _z1 of the multi-joint hydraulic manipulator is as follows:

z ₁ = qq _d

Where q represents the actual measured value of each joint angle of the multi-joint hydraulic manipulator.

The angle conversion error _z2 of the multi-joint hydraulic manipulator is as follows:

Differentiating the above formula, we can get the following form:

in, represents the differential of the angle conversion error z ₂ of the multi-joint hydraulic manipulator; Represents the second-order differential of the joint angle tracking error _z1 of the multi-joint hydraulic manipulator.

Unmeasured speed status With acceleration state It can be expressed as follows:

Combining the above formulas, we can get the following equation:

Because only v ₃ in the above formula contains the high-order term Q _L of the nonlinear dynamic model of the connecting rod manipulator, based on the idea of order reduction, the back-stepping method is adopted to propose a first-order adaptive robust control law v _3d as the linear robust control law of the multi-joint hydraulic manipulator, which reduces the tracking error of each joint angle while ensuring the transient performance of the system.

b) Based on the first-order adaptive robust control law v _3d , the second-order adaptive robust control law Q _Ld is established using the inverse establishment method:

Q _Ld = Q _Lda + Q _Ldr + Q _Lds

Q _Ldr = -k _3r z ₃

Q _Lds = Q _Lds1 + Q _Lds2

Wherein, Q _Lda represents the second-order adaptive model compensation control law, Q _Ldr represents the second-order linear robust control law, Q _Lds represents the second-order nonlinear robust control law; ω ₂ and ω ₃ represent the preset proportional balance constants of the first-order adaptive robust control law v _3d and the second-order adaptive robust control law Q _Ld , respectively; represents the estimated value of the angle conversion error _z2 of the multi-joint hydraulic manipulator; k _ob1 represents the first-order observer gain; v ₁ represents the first observer adaptive characterization parameter; represents the differential of the computable part of the first-order adaptive robust control law v _3d ; k _3r represents the third gain positive definite diagonal matrix, which ensures the stability of the designed controller; z ₃ represents the equivalent flow tracking error of the multi-joint hydraulic manipulator, z ₃ =v ₃ -v _3d ; the second-order nonlinear robust control law Q _Lds is divided into two parts, Q _Lds1 and Q _Lds2 represent the second-order parameter nonlinear robust control law and the second-order observation nonlinear robust control law of Q _Lds of the second-order nonlinear robust control law respectively; represents the third parameter regression matrix; represents the parameter adaptation error of the dynamic parameter θ of the nonlinear dynamic model; and ∈ ₃ represent the fourth, fifth and sixth preset design parameters respectively.

The second-order adaptive robust control law Q _Ld is used as the nonlinear robust control law of the multi-joint hydraulic manipulator. The calculation process of the second-order adaptive robust control law Q _Ld is as follows:

The equivalent flow tracking error z ₃ of the multi-joint hydraulic manipulator is as follows:

z ₃ = v ₃ - v _3d

Differentiating both sides of the above equation, we can get the following:

in, represents the differential of the equivalent flow tracking error z ₃ of the multi-joint hydraulic manipulator, represents the differential of the adaptive characterization parameter v ₃ of the third observer; represents the derivative of the first-order adaptive robust control law v _3d .

According to the design results of the first-order adaptive robust control law v _3d and the properties of the observer, v _3d is related to the joint angle q, time t, observer parameters η, φ ₁ , φ ₂ , φ ₃ and parameter estimates function, so the differential form of the first-order adaptive robust control law v _3d is as follows:

Among them, v _3dc and denote the computable part of v _3d and its derivative, v _3du and denote the incalculable part of v _3d and its differential respectively; η and denote the observer parameters and their derivatives of the nonlinear state observer respectively; and They represent the parameter estimation value and its differential of the kinetic parameter θ of the nonlinear kinetic model respectively.

is the linear regression matrix, as follows:

Establish the auxiliary semi-positive definite matrix V as:

Differentiating both sides of the above equation and substituting the first-order adaptive robust control law v _3d into it, we can get the following form:

in, represents the differential of the auxiliary positive semidefinite matrix V.

Based on the above equation, a second-order adaptive robust control law Q _Ld is proposed to reduce the tracking error of each joint angle while ensuring the transient performance of the system.

c) Considering the uncertainty of model parameters in the overall dynamics model of the hydraulic manipulator, a parameter adaptive law is constructed to compensate for it. The parameter adaptive law is:

in, represents the differential of the estimated value of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model; τ ₂ and τ ₃ represent the first-order and second-order model parameter adaptive reference values respectively; represents the differential of the estimated value of the kinetic parameter θ of the nonlinear kinetic model; Represents the parameter estimate of the kinetic parameter θ of the nonlinear kinetic model Adaptive mapping function; Γ _c represents a parameter adaptive gain coefficient matrix, Γ _c =[Γ _m ; Γ _p ], Γ _m and Γ _p represent the first and second elements of the parameter adaptive gain coefficient matrix Γ _c, respectively.

Parameter estimates of the kinetic parameters θ of the nonlinear kinetic model The adaptive mapping function is as follows:

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

The second parameter regression matrix The details are as follows:

Where _ke represents the tracking error gain parameter.

The third parameter regression matrix The details are as follows:

in, represents the estimated value of the model parameter θ ₁ of the nonlinear dynamic model of the multi-joint hydraulic manipulator; represents the linear regression matrix.

Linear Regression Matrix The details are as follows:

Step 4: The nonlinear state space outputs the estimated value of the joint angular velocity of the multi-joint hydraulic mechanical arm to the adaptive robust control law, and at the same time inputs the target trajectory of the multi-joint hydraulic mechanical arm into the adaptive robust control law. The adaptive robust control law outputs the control signal of the valve core displacement of the multi-joint hydraulic mechanical arm to control the operation of the multi-joint hydraulic mechanical arm. The tracking error is obtained by calculating the target trajectory of the multi-joint hydraulic mechanical arm and the joint angle actually output during operation and output it to the adaptive robust control law. The adaptive robust control law outputs the parameter estimation value of the dynamic parameters of the nonlinear dynamic model to the intermediate conversion state quantity model and repeats steps 2 and 4. At the same time, the nonlinear state observer is self-updated to finally realize the adaptive robust control of the multi-joint hydraulic mechanical arm.

In step 4, the nonlinear state observer performs self-update, specifically, the first observer coefficient matrix ε _i , the second observer coefficient matrix φ _i and the observer adaptive characterization parameter matrix v of the nonlinear state observer are self-updated at their respective self-update rates, as follows:

Wherein, v = [v ₁ ; v ₂ ; v ₃ ]; and denote the self-update rates of the first observer coefficient ε ₁ , the second observer coefficient ε ₂ and the third observer coefficient ε ₃ in the first observer coefficient matrix ε _i of the nonlinear state observer respectively; A _ob and K _ob denote the first and second gain coefficient matrices of the nonlinear state observer respectively; y and y _ob denote the theoretical and actual outputs of the observer respectively; e ₁ , e ₂ and e ₃ denote the first, second and third dimensional characterization parameters respectively, e ₁ = [1; 0; 0], e ₂ = [0; 1; 0], e ₃ = [0; 0; 1]; represents the self-update rate of the observer adaptive characterization parameter matrix v; Q _L represents the equivalent flow rate of the hydraulic cylinder chamber; and They respectively represent the self-update rates of the first observer coefficient φ ₁ , the second observer coefficient φ ₂ and the third observer coefficient φ ₃ in the second observer coefficient matrix φ _i of the nonlinear state observer.

The first gain coefficient matrix A _ob and the second gain coefficient matrix K _ob of the nonlinear state observer are specifically as follows:

Λ＝Λ ^T ＞0

in, Respectively represent the 1st, 2nd, ...i...nth elements in the first gain coefficient matrix A _ob ; Respectively represent the 1st, 2nd, ...i...nth elements in the second gain coefficient matrix K _ob ; and denote the first, second and third gain parameters of the observer respectively; Λ denotes a semi-positive definite matrix; I denotes an identity matrix.

As shown in Figures 2 and 3, the underwater multi-degree-of-freedom hydraulic manipulator includes a multi-degree-of-freedom manipulator linkage mechanism and a hydraulic system. The multi-degree-of-freedom manipulator linkage mechanism has n degrees-of-freedom joints in total; the hydraulic system mainly includes an oil tank, a hydraulic pump, a total oil supply pressure sensor, a total oil return pressure sensor and n drive devices, each drive device is hinged to a corresponding degree-of-freedom joint of the multi-degree-of-freedom manipulator linkage mechanism; the hydraulic oil in the oil tank flows through the hydraulic pump and then flows into each drive device, thereby driving the various degrees-of-freedom joints of the multi-degree-of-freedom manipulator linkage mechanism to move, and the hydraulic oil then flows back to the oil tank through each drive device; through the total The oil supply pressure sensor detects the total oil supply pressure flowing out of the oil tank, that is, the supply pressure of the hydraulic pump; the total return oil pressure flowing back to the oil tank is detected by the total return oil pressure sensor, that is, the reference pressure of the entire hydraulic system; the hydraulic system also includes a one-way valve, two filters and a safety circuit; the hydraulic oil in the oil tank flows through the total oil supply channel through the hydraulic pump and then flows out through the one-way valve, and flows into each drive device through a filter; a safety circuit is also provided between the oil supply pressure sensor and the oil tank to ensure the safety of the entire hydraulic system; the hydraulic oil in each drive device flows through the total return oil channel through another filter and returns to the oil tank. The total oil supply pressure sensor is set on the total oil supply channel of the oil tank between the one-way valve and a filter, and the total return oil pressure sensor is set on the total return oil channel between another filter and several drive devices. Each drive device includes a hydraulic cylinder, a hydraulic valve, an oil supply pressure sensor and an oil return pressure sensor. The push rod of the hydraulic cylinder is hinged to a corresponding degree of freedom joint of the multi-degree-of-freedom mechanical arm linkage mechanism. The oil supply pressure and oil return pressure of the hydraulic oil flowing into and out of each drive device are detected by respective oil supply pressure sensors and oil return pressure sensors. The hydraulic valve of the drive device is arranged on the oil supply channel for the hydraulic oil to flow into the hydraulic cylinder and the oil return channel for the hydraulic oil to flow 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. Among them, _Ai and _Ao are the areas of the oil inlet chamber and the oil return chamber of each hydraulic cylinder of each drive device, respectively. are the areas of the oil inlet chambers of the first, second, third, ..., and nth hydraulic cylinders, respectively. are the areas of the oil return chambers of the first, second, third, ..., nth hydraulic cylinders respectively; are the displacements of the valve cores of the first, second, third, ..., nth hydraulic valves respectively; are the supply pressures of the hydraulic oil flowing into the first, second, third, ..., nth drive units, respectively, are respectively the outlet pressures of the hydraulic oil flowing out of the first, second, third, ..., nth driving device; are the actual flow rates of the oil inlet chambers of the first, second, third, ..., and nth hydraulic cylinders, respectively. They are the actual flow rates of the oil return chambers of the 1st, 2nd, 3rd, …, nth hydraulic cylinders respectively.

The control method of the present invention is experimented with a multi-degree-of-freedom hydraulic manipulator without a speed sensor, and compared with a PID controller to verify the control effect of the control method proposed by the present invention. During verification, in the designed obARC controller, the controller gain parameter selection is shown in Table 1. The reason why some adaptive parameters in Γ are zero is that in practical applications, some parameters can be uniquely determined by known parameters, and their uncertainty is small. Therefore, in order to improve the efficiency of the controller, only parameters with large uncertainty can be adaptively adjusted.

Table 1 Controller parameter selection

The sensing accuracy and differential filtering results of the multi-joint hydraulic mechanical arm angle sensor are shown in Figure 4. In Figure 4, the original signal and the filtered speed signal are both referred to the left ordinate, and the filtered angle signal is referred to the right ordinate. It can be seen from Figure 4 that the first sub-graph is the original signal graph, the second sub-graph is the differential filtering signal result graph when the filter passband frequency w _c = 10 rad/s, the third sub-graph is the differential filtering signal result graph when the filter passband frequency w _c = 30 rad/s, and the fourth sub-graph is the differential filtering signal result graph when the filter passband frequency w _c = 50 rad/s, indicating that the multi-joint hydraulic mechanical arm angle sensor has low accuracy, and differential filtering will introduce additional signal lag, thereby limiting the control accuracy.

The experimental results of the multi-joint hydraulic manipulator are shown in Figure 5. The first sub-graph in Figure 5 is the tracking experimental results of obARC and PID, the second sub-graph is the control error of the PID controller, and the third sub-graph is the control error of the obARC controller. It can be seen from the control effect sub-graph that the multi-joint hydraulic manipulator adaptive robust controller based on nonlinear state observation designed by the present invention can accurately and smoothly track the target trajectory curve when the dynamic model parameters are uncertain and the feedback state is unmeasurable. At the same time, the control tracking error curve shows that the angle tracking error of each joint remains zero in the steady state during the entire movement process (the angular velocity and acceleration remain unchanged).

Compared with the traditional PID controller, the joint tracking error is greatly reduced and the transient response time is greatly shortened, which shows that the adaptive robust control method of the multi-joint hydraulic manipulator arm based on nonlinear state observation designed in the present invention has superior transient response performance and better robustness, and can effectively compensate for the influence of the uncertainty of the hydraulic manipulator arm dynamics model parameters and the unmeasurable state of some states on the control accuracy of the manipulator end. While ensuring the stability of the control system, it reduces the tracking error of the manipulator end and improves the control performance.

The present invention belongs to the field of multi-joint hydraulic mechanical arm motion control, specifically, a motion control method for multi-joint hydraulic mechanical arm in a complex working environment when physical signals such as motion speed are unmeasurable. The present invention comprehensively considers factors such as parameter uncertainty and multi-joint coupling, and establishes a nonlinear dynamic model of underwater multi-joint hydraulic mechanical arm. Then, a nonlinear observer is designed to obtain an intermediate state quantity related to the unmeasurable state. Then, based on the observed value of the intermediate state quantity, an adaptive robust controller of the multi-joint hydraulic mechanical arm is designed. The proposed multi-joint hydraulic mechanical arm adaptive robust control method obARC based on nonlinear state observation can effectively improve the terminal control accuracy of the multi-joint hydraulic mechanical arm under the condition of uncertain parameters of the dynamic model and unmeasurable feedback state, and reduce the tracking error of the terminal of the mechanical arm while ensuring the overall stability of the control system and the observation system, enhance the control performance, and realize state observation when nonlinear states such as motion speed are unmeasurable, and ensure the stability of the control system, reduce the motion tracking error of the terminal of the multi-joint hydraulic mechanical arm, and improve the control accuracy of the end actuator of the mechanical arm, thereby improving the working performance of the mechanical arm in a more severe working environment.

The above contents are only the technical ideas of the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical ideas proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims (10)

1. A method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation, characterized in that the method comprises the following steps: Step 1: Establish a nonlinear dynamic model of the multi-joint hydraulic manipulator under the constraints of the dynamic model; design the intermediate conversion state quantity model of the unmeasurable state of the multi-joint hydraulic manipulator and its nonlinear state space, and establish a nonlinear state observer based on the nonlinear state space using the nonlinear state observation method; Step 2: Inputting the parameter estimation value of the dynamic parameter of the nonlinear dynamic model into the intermediate conversion state quantity model, the intermediate conversion state quantity model outputs the intermediate conversion state quantity, the nonlinear state observer observes the intermediate conversion state quantity and outputs the observation state of the intermediate conversion state quantity, and obtaining the estimated value of the joint angular velocity of the multi-joint hydraulic manipulator according to the observation state of the intermediate conversion state quantity; Step 3: Based on the nonlinear dynamic model and nonlinear state observer, an adaptive robust control law is designed using the adaptive robust control method; Step 4: The nonlinear state space outputs the estimated value of the joint angular velocity of the multi-joint hydraulic mechanical arm to the adaptive robust control law, and at the same time inputs the target trajectory of the multi-joint hydraulic mechanical arm into the adaptive robust control law. The adaptive robust control law outputs the control signal of the valve core displacement of the multi-joint hydraulic mechanical arm to control the operation of the multi-joint hydraulic mechanical arm. The tracking error is obtained by calculating the target trajectory of the multi-joint hydraulic mechanical arm and the joint angle actually output during operation and output it to the adaptive robust control law. The adaptive robust control law outputs the parameter estimation value of the dynamic parameters of the nonlinear dynamic model to the intermediate conversion state quantity model and repeats steps 2 and 4. At the same time, the nonlinear state observer is self-updated, and finally the continuous adaptive robust control of the multi-joint hydraulic mechanical arm is realized. 2. According to the method for adaptive robust control of hydraulic mechanical arm based on nonlinear state observation of claim 1, it is characterized in that: in the step 1, the nonlinear dynamic model of the multi-joint hydraulic mechanical arm established is as follows: a) Connecting rod dynamics model: τ _j =J _j (q)P _L P _L =A _i P _i -A _o P _o Among them, q, and They represent the joint angle, joint angular velocity and joint angular acceleration of the multi-joint hydraulic manipulator, q, n represents the number of joints of the multi-joint hydraulic mechanical arm; M _j (), C _j () and G _j () represent the inertial dynamic matrix, Coriolis force matrix and gravity matrix of the multi-joint hydraulic mechanical arm, respectively, 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, τ _j ∈R ⁿ ; J _j () represents the multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic mechanical arm; _PL represents the equivalent thrust of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _PL ∈R ⁿ ; _Ai and Ao represent the contact areas of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Ai , _Ao ∈R ^n×n ; _Pi and P _o represent the oil pressures of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Pi , P _o ∈R ⁿ ; _l represents the extension of the hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm, l∈R ⁿ ; b) Hydrodynamic model: Wherein, _Vi and _Vo represent the volume of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Vi , _Vo ∈Rn ^×n ; _βe represents the bulk modulus of the hydraulic oil; _Vhi and _Vho represent the volume of the oil inlet chamber and oil return chamber of each hydraulic cylinder of each driving device under the initial condition that the extension of the hydraulic cylinder push rod of each joint of the multi-joint hydraulic mechanical arm is l=0; diag[·] represents a diagonal matrix with · as the main element; _Qi and _Qo represent the actual flow of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Qid and _Qod represent the preset ideal flow of the oil inlet chamber and oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic mechanical arm, _Qid , _Qod ^∈Rn , and The calculable flow difference of the actual flow of the hydraulic cylinder oil inlet chamber and oil return chamber of each joint of the multi-joint hydraulic mechanical arm is respectively represented. and Respectively represent the uncalculated flow difference of the actual flow of the hydraulic cylinder oil inlet chamber and the oil return chamber of each joint of the multi-joint hydraulic mechanical arm; k _qi and k _qo represent the flow gain constants of the hydraulic cylinder oil inlet chamber and the oil return chamber of each joint of the multi-joint hydraulic mechanical arm; x _v represents the valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm; g ₁ () represents the nonlinear conversion function between the oil pressure _Pi of the hydraulic cylinder oil inlet chamber of each joint of the multi-joint hydraulic mechanical arm and the valve core displacement x _v of the hydraulic control valve, g ₂ () represents the nonlinear conversion function between the oil pressure _Po of the hydraulic cylinder oil return chamber of each joint of the multi-joint hydraulic mechanical arm and the valve core displacement x _v of the hydraulic control valve, g ₁ (), g ₂ ()∈R ^n×n ; The constraints of the dynamic model are as follows: |Δ _j |≤δ _j θ∈{θ:θ _min ≤θ≤θ _max } Wherein, Δ _j represents the uncertain nonlinearity and interference in the motion process of the multi-joint hydraulic manipulator, Δ _j ∈ R ⁿ ; δ _j represents the preset constant vector; θ _max and θ _min represent the upper and lower bounds of the dynamic parameter θ of the nonlinear dynamic model, respectively, θ = [θ _m ; θ _p ]; The valve core displacement x _v of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm is as follows: Wherein, Q _L represents the equivalent flow rate of the hydraulic cylinder chamber, Q _L ∈R ⁿ . 3. According to claim 2, a method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation is characterized in that: in the step 1, the intermediate conversion state quantity model of the unmeasurable state of the multi-joint hydraulic mechanical arm is designed as follows: s＝[s ₁ ；s ₂ ；s ₃ ] s ₁ =q Where s represents the intermediate conversion state quantity, _s1 , _s2 and _s3 represent the first, second and third state quantities of the intermediate conversion state quantity s respectively; q and They represent the joint angles and joint angular velocities of the multi-joint hydraulic manipulator respectively; and denote the first and second elements of the connecting rod dynamics parameter _θm of the connecting rod dynamics model, respectively. _Mj and _Cj represent the inertial dynamic matrix and Coriolis force matrix of the multi-joint hydraulic manipulator, respectively; I represents the unit matrix; _f1 and _f2 represent the first and second equal-quantity matrices of the intermediate conversion state quantity s, respectively; θ represents the dynamic parameter of the nonlinear dynamic model, represents the parameter estimate of the kinetic parameter θ of the nonlinear kinetic model, represents the parameter adaptation error of the dynamic parameter θ of the nonlinear dynamic model; Joint angular velocity of multi-joint hydraulic manipulator That is the unpredictable state of the multi-joint hydraulic robotic arm. 4. The method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation according to claim 2 is characterized in that: in the step 1, the nonlinear state space is specifically as follows: in, and They represent the differentials of the first state quantity s ₁ , the second state quantity s ₂ and the third state quantity s ₃ of the intermediate conversion state quantity s respectively; The third element of the connecting rod dynamics parameter θ _m representing the connecting rod dynamics model, Δ _j represents the uncertain nonlinearity and disturbance during the motion of the multi-joint hydraulic manipulator; and denote the first and second elements of the hydrodynamic parameter _θp of the hydrodynamic model, respectively, _f3 , _f4 and _f5 represent the third, fourth and fifth equal-quantity matrices of the intermediate conversion state quantity s, respectively; _uv represents the control voltage actually output by the adaptive robust control law, _uv = _kvxv , _uv∈Rn , _xv represents the valve core displacement of the hydraulic control valve of each joint of the multi-joint hydraulic mechanical arm, ^and _kv represents the conversion proportional _coefficient ; The first to fifth equal quantity matrices of the intermediate conversion state quantity s are specifically as follows: f ₁ = J _j P _L f ₃ = J _j V _i ^-1 A _i 5. The method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation according to claim 2 is characterized in that: in the step 1, the nonlinear state observer is specifically as follows: in, represents the observed state of the intermediate conversion state quantity s, and Represent the joint angular velocity of the multi-joint hydraulic manipulator observed values of the first intermediate conversion state quantity s ₁ , the second intermediate conversion state quantity s ₂ and the third intermediate conversion state quantity s ₃ ; and denote the second and third elements of the first observer coefficient ε ₁ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the second observer coefficient ε ₂ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the third observer coefficient ε ₃ in the first observer coefficient matrix ε _i of the nonlinear state observer, respectively, and denote the second and third elements of the first observer coefficient φ ₁ in the second observer coefficient matrix φ _i of the nonlinear state observer, respectively, and denote the second and third elements of the second observer coefficient φ ₂ in the second observer coefficient matrix φ _i of the nonlinear state observer, respectively, and denote the second and third elements of the third observer coefficient φ ₃ in the second observer coefficient matrix φ _i of the nonlinear state observer, respectively, and denote the observed values of the first, second and third elements of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model respectively; and denote the observed values of the first and second elements of the hydraulic dynamics parameter θ _p of the hydraulic dynamics model, respectively; v ₂ and v ₃ denote the second and third observer adaptive characterization parameters, respectively; n denotes the number of joints of the multi-joint hydraulic manipulator; The observed state of the intermediate conversion state quantity s The third observer adaptive characterization parameter v ₃ in is used as the joint angular velocity of the multi-joint hydraulic manipulator Estimated value of 6. The method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation according to claim 4 is characterized in that: in the step 3, the adaptive robust control law designed is 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 Among them, v _3da represents the first-order adaptive model compensation control law, v _3dr represents the first-order linear robust control law, v _3ds represents the first-order nonlinear robust control law; z ₂ represents the angle conversion error of the multi-joint hydraulic manipulator, z ₁ and denote the joint angle tracking error and its differential of the multi-joint hydraulic mechanical arm, respectively; z ₁ =qq _d , q _d denotes the control target value of each joint angle of the multi-joint hydraulic mechanical arm, i.e., the target trajectory of the multi-joint hydraulic mechanical arm; k ₁ and k ₂ denote the first and second gain positive definite diagonal matrices, respectively; and They represent the control target values of the angular velocity and acceleration of each joint of the multi-joint hydraulic manipulator respectively; θ _1min represents the minimum value of the model parameter θ ₁ of the nonlinear dynamic model of the multi-joint hydraulic manipulator; v _3ds1 and v _3ds2 represent the first-order parameter nonlinear robust control law and the first-order observation nonlinear robust control law of the first-order nonlinear robust control law v _3d respectively; θ _m1 represents the first element of the connecting rod dynamic parameter θ _m of the connecting rod dynamic model; represents the second parameter regression matrix; represents the parameter adaptation error of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model; and ∈ ₂ represent the first, second and third preset design parameters respectively; z _ob represents the observer error of the nonlinear state observer, represents the observed state of the intermediate conversion state quantity s; δ _ob represents the 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 _Lda represents the second-order adaptive model compensation control law, Q _Ldr represents the second-order linear robust control law, Q _Lds represents the second-order nonlinear robust control law; ω ₂ and ω ₃ represent the preset proportional balance constants of the first-order adaptive robust control law v _3d and the second-order adaptive robust control law Q _Ld , respectively; represents the estimated value of the angle conversion error _z2 of the multi-joint hydraulic manipulator; k _ob1 represents the first-order observer gain; v ₁ represents the first observer adaptive characterization parameter; represents the differential of the computable part of the first-order adaptive robust control law v _3d ; k _3r represents the third gain positive definite diagonal matrix; z ₃ represents the equivalent flow tracking error of the multi-joint hydraulic manipulator, z ₃ =v ₃ -v _3d ; Q _Lds1 and Q _Lds2 represent the second-order parameter nonlinear robust control law and the second-order observation nonlinear robust control law of Q _Lds of the second-order nonlinear robust control law, respectively; represents the third parameter regression matrix; represents the parameter adaptation error of the dynamic parameter θ of the nonlinear dynamic model; and ∈ ₃ represent the fourth, fifth and sixth preset design parameters respectively; c) Parameter Adaptive Law: in, represents the differential of the estimated value of the connecting rod dynamics parameter θ _m of the connecting rod dynamics model; τ ₂ and τ ₃ represent the first-order and second-order model parameter adaptive reference values respectively; represents the differential of the estimated value of the kinetic parameter θ of the nonlinear kinetic model; Represents the parameter estimate of the kinetic parameter θ of the nonlinear kinetic model Adaptive mapping function; Γ _c represents a parameter adaptive gain coefficient matrix, Γ _c =[Γ _m ; Γ _p ], Γ _m and Γ _p represent the first and second elements of the parameter adaptive gain coefficient matrix Γ _c, respectively. 7. The method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation according to claim 6 is characterized in that: the parameter estimation value of the dynamic parameter θ of the nonlinear dynamic model The adaptive mapping function is as follows: Where x represents the input parameter of the adaptive mapping function. 8. The method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation according to claim 6, characterized in that: the second parameter regression matrix The details are as follows: Where, _ke represents the tracking error gain parameter; The third parameter regression matrix The details are as follows: in, represents the estimated value of the model parameter θ ₁ of the nonlinear dynamic model of the multi-joint hydraulic manipulator; represents the linear regression matrix; The linear regression matrix The details are as follows: 9. The method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation according to claim 5, characterized in that: in the step 4, the nonlinear state observer performs self-update, specifically, the first observer coefficient matrix ε _i , the second observer coefficient matrix φ _i and the observer adaptive characterization parameter matrix v of the nonlinear state observer are self-updated at their respective self-update rates, specifically as follows: Wherein, v = [v ₁ ; v ₂ ; v ₃ ]; and denote the self-update rates of the first observer coefficient ε ₁ , the second observer coefficient ε ₂ and the third observer coefficient ε ₃ in the first observer coefficient matrix ε _i of the nonlinear state observer respectively; A _ob and K _ob denote the first and second gain coefficient matrices of the nonlinear state observer respectively; y and y _ob denote the theoretical and actual outputs of the observer respectively; e ₁ , e ₂ and e ₃ denote the first, second and third dimensional characterization parameters respectively, e ₁ = [1; 0; 0], e ₂ = [0; 1; 0], e ₃ = [0; 0; 1]; represents the self-update rate of the observer adaptive characterization parameter matrix v; Q _L represents the equivalent flow rate of the hydraulic cylinder chamber; and They respectively represent the self-update rates of the first observer coefficient φ ₁ , the second observer coefficient φ ₂ and the third observer coefficient φ ₃ in the second observer coefficient matrix φ _i of the nonlinear state observer. 10. The method for adaptive robust control of a hydraulic mechanical arm based on nonlinear state observation according to claim 9, characterized in that: the first gain coefficient matrix A _ob and the second gain coefficient matrix K _ob of the nonlinear state observer are specifically as follows: Λ＝Λ ^T ＞0 in, Respectively represent the 1st, 2nd, ...i...nth elements in the first gain coefficient matrix A _ob ; Respectively represent the 1st, 2nd, ...i...nth elements in the second gain coefficient matrix K _ob ; and denote the first, second and third gain parameters of the observer respectively; Λ denotes a semi-positive definite matrix; I denotes an identity matrix.