Track following control method for complex and uncertain hydraulic mechanical arm system

Abstract

The invention discloses a track following control method for a complex and uncertain hydraulic mechanical arm system, which adopts a self-adaptive robust constraint control strategy based on a kinetic model to control in a top layer and a bottom layer according to the complex, non-linear, uncertain and high-precision track following requirements of the hydraulic mechanical arm system. The top layer control adopts servo constraint and dynamics modeling, a self-adaptive control law is designed through position, speed and acceleration constraint, and parameter uncertainty and external disturbance influence are dealt with. The bottom layer control aims at the uncertainty of the pressure-flow relation, and the stability and precision are improved by combining a disturbance observer through an adaptive robust control method. According to the method, high-precision track following of the hydraulic mechanical arm under parameter uncertainty and external disturbance is achieved, theoretical analysis and simulation verification show that robustness and precision are high in fixed value and sine track following tasks, the problems of a traditional control method are solved, and the method is suitable for actual requirements of multiple fields.

Description

Technical Field

[0001] The invention relates to the technical field of hydraulic mechanical arm system control, and in particular to an adaptive robust constraint following control method of a hydraulic mechanical arm containing complex uncertainties. Background Art

[0002] Hydraulic manipulators are widely used in many fields such as industrial automation, aerospace, and marine engineering. However, the hydraulic manipulator system itself has strong nonlinearity and complex uncertainty. The nonlinearity of the hydraulic manipulator system is mainly manifested in the compressibility of the hydraulic oil, the flow characteristics of the valve port, and friction factors, which makes accurate modeling and control face huge challenges. At the same time, in the actual working environment, the hydraulic manipulator will have complex uncertainties such as the moment of inertia, friction coefficient, hydraulic oil bulk modulus, and flow rate. These will seriously affect the trajectory following accuracy and stability of the manipulator.

[0003] Traditional control methods, such as PID control, are simple and practical, but they are difficult to handle complex uncertainty problems, such as fast time-varying and unknown boundaries, which results in the hydraulic manipulator system being unable to meet the high-precision trajectory following requirements. Model predictive control relies on an accurate system model, and the complexity of the hydraulic manipulator system makes it difficult to avoid modeling errors, which in turn affects the control effect. Neural network control requires a large amount of training data and is computationally complex, while fuzzy control lacks an accurate theoretical basis and systematic design method. Therefore, there is an urgent need for a new control method to effectively solve the trajectory following problem of complex and uncertain hydraulic manipulator systems.

[0004] Therefore, in order to solve the problem that the hydraulic manipulator system is difficult to meet high-precision trajectory following, the uncertainties of the time-varying and unknown boundaries of the dynamic model parameters, the bulk modulus of the hydraulic oil and the flow rate are considered, and an adaptive robust constrained following control method is proposed, which includes top-level control (input force control) and bottom-level control (flow rate control). Summary of the invention

[0005] The present invention provides an adaptive robust constraint following control method for a hydraulic mechanical arm system. This method is based on a dynamic model and can meet high-precision control requirements. The specific steps are as follows:

[0006] 1. Top-level control

[0007] Step 1: Build a dynamic model of the hydraulic manipulator

[0008] The dynamic equation of the hydraulic manipulator is as follows:

[0009]

[0010] M(q) is the inertia matrix, symmetric and positive definite;

[0011] is the centrifugal and Coriolis force matrix;

[0012] G(q) is the effect of gravity on the joint;

[0013] τ is the control input, which is the output force of the hydraulic cylinder;

[0014] σ(t) is the uncertainty.

[0015] Assumption 1: For constraints is consistent, for a given A and b, there is at least one solution This consistency condition is the most basic in any constrained motion, otherwise the constraint is unrealistic and cannot be achieved.

[0016] Assumption 2: For every (q, t)∈R n ×R, σ∈∑, inertia matrix M(q, σ, t)>0, M, C and G can be decomposed into:

[0017]

[0018] in The nominal part, At the same time, ΔM, ΔC, and ΔG represent the uncertain part. ΔM, ΔC, All ΔG are continuous. Therefore ΔD(q,σ,t)=D(q,t)E(q,σ,t).

[0019] Step 2: Design the Servo Constraints

[0020] Represent the trajectory of the robot as constraints

[0021] Set the target trajectory of the robotic arm system to qd(t), in

[0022] q d (t) is the expected position trajectory;

[0023] is the expected velocity trajectory;

[0024] is the expected acceleration trajectory;

[0025] Tracking Error Definition:

[0026] Position error: e q (t) = q(t) - q d (t);

[0027] Speed ​​error:

[0028] First-order constraint (speed constraint)

[0029]

[0030] Where k1 is a constant > 0

[0031] Further expressed as

[0032]

[0033] A is the constraint matrix, c is the objective function

[0034] Second-order constraint (acceleration constraint)

[0035]

[0036] The constraints can be further expressed in the form of servo constraints

[0037]

[0038] A is the constraint matrix and b is the objective function

[0039] Theorem 1 Consider the constraint The constraint is consistent if and only if AA + =b“+” represents the generalized inverse matrix

[0040] Step 3: Design of control method for hydraulic manipulator system without uncertainty

[0041] Assumption 3: For every (q, t)∈R n ×R, A(q, t) is full rank, which means that A(q, t)A T (q, t) is reversible.

[0042] Assumption 4: Given P∈R according to Assumption 3 m×m , P>0,

[0043] set up:

[0044]

[0045] There is a constant ρ E >-1 so that all (q, t)∈R n ×R,

[0046]

[0047] where λ min Represents the minimum eigenvalue

[0048] when In the special case of (i.e. no uncertainty), then E = 0, W = 0, so we can choose ρ E = 0 is greater than -1. Therefore, through continuity, this assumption imposes uncertainty on M and The effect of possible deviations of the control within a certain threshold is unidirectional. That is, the threshold is bounded in one direction but unbounded in the other. This assumption means that the uncertainty in the connection between the control and the system should not change the direction of the control.

[0049] For all set up:

[0050]

[0051] τ=p1+p2

[0052] Where A is the constraint matrix, c is the objective function, b is the target function, (same as above), "+" represents the generalized inverse matrix k2>0 control coefficient, and τ is the control input;

[0053] Step 4: Design of control method for hydraulic manipulator system with uncertainty

[0054] According to the previous assumptions based on the continuity of the function and the boundedness of σ, there exists a function Φ(·): R n ×R n ×R→R + is known or unknown so that each

[0055]

[0056] Assumption 5: There exists a constant vector α∈(0,∞) k and a known function Π(·): (0, ∞) k ×R n ×R n ×R→R + For each

[0057]

[0058] This assumption means that the function Φ The exact value of the function Π is equal to the same The value of is determined by the parameter α. can be interpreted as a total bound on uncertainty.

[0059] Assumption 6: In Assumption 5, for each The function Π(·) can linearly decompose α. There exists a function Make

[0060]

[0061] To estimate the uncertainty bound, an adaptive parameter Adaptive Law

[0062]

[0063] ( yes , i=1...,k, is the design parameter

[0064]

[0065] in

[0066]

[0067] in ∈ ∈R, ∈ >0, is a constant

[0068] τ=p1+p2+p3

[0069] Step 5: Stability Analysis

[0070] Theorem 2: Let According to the previous assumptions 1-6, the control input τ now exhibits the following performance

[0071] (1) Uniform boundedness: For any r>0, there exists a d(r)<∞ such that Then for all t ≥ t0, we have

[0072] (2) Eventually uniformly bounded For any r>0, when There is a d >0, so For any when Head

[0073] Proof According to Lyapunov stability theory

[0074] Take the Lyapunov function:

[0075]

[0076] Then the derivative of V is:

[0077]

[0078] For ||μ||>∈

[0079]

[0080] For ||μ||≤∈

[0081]

[0082] According to hypothesis 6

[0083]

[0084] For all ||μ||

[0085]

[0086] According to the designed adaptive law, we can get

[0087]

[0088]

[0089] Substituting the above two final formulas with 1+ρ E Multiplication can As shown below, (Note )

[0090]

[0091] Furthermore, uniformly bounded

[0092]

[0093] 2. Bottom-level control part

[0094] According to the top-level control method, the control torque required by the manipulator can be obtained. In actual work, the torque is provided by the hydraulic cylinder. Considering the uncertainty of temperature on flow and bulk modulus, an adaptive robust control method with a disturbance observer is designed, namely the bottom-level control. The main function of the disturbance observer is to estimate the uncertainty of the hydraulic system. The hydraulic system control can be divided into rod cavity flow control and rodless cavity flow control.

[0095] 1. Rod cavity pressure control

[0096] Step 1. Determine the relationship between pressure and flow:

[0097]

[0098] Where V 02 is the initial volume of the rod chamber, A2 is the effective area of ​​the piston in the rod chamber, x l is the piston displacement, is the piston speed, Q2 is the flow rate, β(t) and λ(t) are uncertain quantities, Rod cavity pressure

[0099] Step 2. Error change rate between pressure and reference pressure

[0100]

[0101] in The reference pressure

[0102] Let α: =V 02 -A2x l , β(t): = β m Δβ(t), β m is a constant

[0103]

[0104] make

[0105]

[0106] make

[0107]

[0108] The designed flow rate is

[0109] Q2=Q eq +Q n +Q s

[0110]

[0111] Let σ: = P2-P 2d , sat(σ) is defined as

[0112]

[0113] make

[0114]

[0115] Step 3. Build the observer

[0116]

[0117] The derivative of

[0118]

[0119] Substituting the previous formula into

[0120]

[0121] make

[0122]

[0123] Assumptions

[0124] Step 4: Stability Analysis

[0125]

[0126] according to

[0127]

[0128] According to the uniformly eventually bounded criterion, The boundary is

[0129]

[0130] The boundary of |σ| is

[0131]

[0132] 2. Rodless cavity pressure control

[0133] Step 1. Determine the relationship between pressure and flow

[0134]

[0135] Where V 01 is the initial volume of the rodless chamber, A1 is the effective area of ​​the rodless chamber piston, x l is the piston displacement, is the piston speed, Q1 is the flow rate, β(t) and δ(t) are uncertain quantities, P2 is the rod chamber pressure, is the reference rodless chamber pressure, P 1d is the expected rodless chamber pressure F l is the hydraulic cylinder output force

[0136] Step 2. Error change rate between pressure and reference pressure

[0137] make β(t):=β m Δβ(t), β m is a constant

[0138]

[0139] make

[0140]

[0141] make

[0142]

[0143] The designed flow rate is

[0144] Q1=Q eq +Q n +Q s

[0145]

[0146]

[0147] Let k: =P1-P 1d , sat(k) is defined as

[0148]

[0149] make

[0150]

[0151] Step 3. Construct the observer

[0152]

[0153] The derivative of

[0154]

[0155] Substituting the previous formula into

[0156]

[0157] make

[0158]

[0159] Assumptions Step 4: Stability Analysis

[0160]

[0161] according to

[0162]

[0163] According to the uniformly eventually bounded criterion, The boundary is

[0164]

[0165] |κ| boundary is

[0166]

[0167] Compared with the prior art, the beneficial effects of the present invention are: (1) a trajectory following control method for a complex uncertain hydraulic manipulator system is proposed. By combining top-level control with bottom-level control, the complex uncertainty of the hydraulic manipulator system can be effectively handled, so that the output of the manipulator system can track the desired trajectory with high precision.

[0168] (2) In the top-level control, by building a dynamic model and establishing servo constraints, a hydraulic manipulator constraint following control method is designed under both uncertainty-free and uncertainty-containing conditions, and stability analysis is performed. This control can handle time-varying and unknown boundary parameter uncertainties such as inertia matrix, centrifugal force and Coriolis force matrix, and gravity effect, and has good adaptability to uncertainty factors such as parameter changes within the system.

[0169] (3) The underlying control takes into account the uncertainty of temperature on flow and bulk modulus, designs an adaptive robust control method with a disturbance observer, and performs stability analysis. The flow of the rod cavity and the rodless cavity are controlled separately, which improves the control accuracy of the system when facing external uncertainties (such as temperature changes) in the actual working environment. Figure 2-Figure 5 The control effect under various reference trajectories is visible and the tracking error is small, which verifies the effectiveness of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0170] Figure 1 Uncertain hydraulic manipulator system trajectory following control flow chart

[0171] Figure 2 Control effect of the robotic arm system without uncertainty under constant reference trajectory

[0172] Figure 3 Control effect of a robotic arm system without uncertainty under a sinusoidal reference trajectory

[0173] Figure 4 Control effect of uncertain manipulator system under constant reference trajectory

[0174] Figure 5 Control effect of uncertain manipulator system under sinusoidal reference trajectory DETAILED DESCRIPTION

[0175] In order to better understand the present invention, the content of the present invention is further explained below with reference to the accompanying drawings and examples, but the content of the present invention is not limited to the following embodiments.

[0176] Example 1

[0177] See also Figure 1 This embodiment proposes a trajectory following control method for a complex uncertain hydraulic manipulator system, and the specific implementation steps are as follows:

[0178] 1. Top-level control part

[0179] Step 1: Establish the dynamic model of the robotic arm system

[0180]

[0181] Where M(q) is the inertia matrix, symmetric and positive definite; is the centrifugal force and Coriolis force matrix; G(q) is the effect of gravity on the joint; τ is the control input; σ(t) is the uncertainty, M(q, σ, t), G(q,σ,t) all depends on the uncertainty σ.

[0182] Assumption 1: For every (q, t)∈R n ×R, σ∈∑, inertia matrix M(q, σ, t)>0, M, C and G can be decomposed into:

[0183]

[0184] in Belongs to the nominal part, ΔM, ΔC, ΔG belong to the uncertain part

[0185] Step 2 Design Servo Constraints

[0186] Set the target trajectory of the robotic arm system to qd(t),

[0187] q d (t) is the expected position trajectory;

[0188] is the expected velocity trajectory;

[0189] is the expected acceleration trajectory

[0190] Tracking Error Definition:

[0191] Position error: e q (t) = q(t) - q d (t);

[0192] Speed ​​error:

[0193] First-order constraint (speed constraint)

[0194]

[0195] Where k1 is a constant > 0

[0196] Further expressed as

[0197]

[0198] Second-order constraint (acceleration constraint)

[0199]

[0200] The constraints can be further expressed in the form of servo constraints

[0201]

[0202] Where A is the constraint matrix, c and b are the objective functions

[0203] Assumption 2: For every (q, t)∈R n ×R, A(q, t) is full rank, which means that A(q, t)A T (q, t) is reversible.

[0204] Assumption 3: Given P∈R according to Assumption 2 m×m , P>0,

[0205] set up:

[0206]

[0207] There is a constant ρ E >-1 so that all (q, t)∈R n ×R,

[0208]

[0209] Step 3 Design of control method for robotic arm system without uncertainty

[0210] Assumption 4: For every (q, t)∈R n ×R, A(q, t) is full rank, which means that A(q, t)A T (q, t) is reversible.

[0211] Assumption 5: Given P∈R according to Assumption 2 m×m , P>0,

[0212] set up:

[0213]

[0214] There is a constant ρ E >-1 so that all (q, t)∈R n ×R,

[0215]

[0216] where λ min Represents the minimum eigenvalue

[0217] when In the special case of (i.e. no uncertainty), then E = 0, W = 0, so we can choose ρ E = 0 is greater than -1. Therefore, through continuity, this assumption imposes uncertainty on M and The effect of possible deviations of the control within a certain threshold is unidirectional. That is, the threshold is bounded in one direction but unbounded in the other. This assumption means that the uncertainty in the connection between the control and the system should not change the direction of the control.

[0218] For all set up:

[0219]

[0220] τ=p1+p2

[0221] Where A is the constraint matrix, c is the objective function, b is the target function, (same as above), "+" represents the generalized inverse matrix k2>0 control coefficient, and τ is the control input;

[0222] Step 4: Design of control method for robotic arm system with uncertainty

[0223] According to the previous assumptions 1-5, based on the continuity of the function and the boundedness of σ, there exists a function Φ(·): R n ×R n ×R→R + is known or unknown so that each

[0224]

[0225] Assumption 6: There exists a constant vector α∈(0,∞) k and a known function Π(·): (0, ∞) k ×R n ×R n ×R→R + For each

[0226]

[0227]

[0228] Verify assumptions 2-5 and construct the adaptive law based on assumption 6

[0229]

[0230] At this time, the control input of the hydraulic manipulator system is

[0231] τ=p1+p2+p3

[0232] in

[0233] Step 5: Stability Analysis

[0234] Take the Lyapunov function

[0235]

[0236] The derivative of V is:

[0237]

[0238] For all ||μ||

[0239]

[0240] According to the designed adaptive law, we can get

[0241]

[0242] Combine the above two equations with 1+ρ E Multiplication can As shown below, (Note

[0243]

[0244] in

[0245] According to the uniform boundedness, we have

[0246]

[0247] Consistently eventually bounded, there are

[0248]

[0249] 2. Bottom-level control part

[0250] According to the top-level control method, the control torque required by the manipulator can be obtained. In actual work, the torque is provided by the hydraulic cylinder. Considering the uncertainty of temperature on flow and bulk modulus, an adaptive robust control method with a disturbance observer is designed, namely the bottom-level control. The main function of the disturbance observer is to estimate the uncertainty of the hydraulic system. The hydraulic system control can be divided into rod cavity flow control and rodless cavity flow control.

[0251] 1. Rod cavity pressure control

[0252] Step 1. Determine the relationship between pressure and flow

[0253]

[0254] Where V 02 is the initial volume of the rod chamber, A2 is the effective area of ​​the piston in the rod chamber, x l is the piston displacement, is the piston speed, Q2 is the flow rate, β(t) and λ(t) are uncertain quantities, Rod cavity pressure

[0255] Step 2. Error change rate between pressure and reference pressure

[0256]

[0257] in The reference pressure

[0258] Let α: =V 02 -A2x l , β(t): = β m Δβ(t), β m is a constant

[0259]

[0260] make

[0261]

[0262] make

[0263]

[0264] The designed flow rate is

[0265] Q2=Q eq +Q n +Q s

[0266]

[0267] Let σ: = P2-P2d, sat(σ) is defined as

[0268]

[0269] make

[0270]

[0271] Step 3. Build the observer

[0272]

[0273] The derivative of

[0274]

[0275] Substituting the previous formula into

[0276]

[0277] make

[0278]

[0279] Assumptions

[0280] Step 4: Stability Analysis

[0281]

[0282] according to

[0283]

[0284] According to the uniformly eventually bounded criterion, The boundary is

[0285]

[0286] The boundary of |σ| is

[0287]

[0288] 2. Rodless cavity pressure control

[0289] Step 1. Determine the relationship between pressure and flow

[0290]

[0291] Where V 01 is the initial volume of the rodless chamber, A1 is the effective area of ​​the rodless chamber piston, xl is the piston displacement, is the piston speed, Q1 is the flow rate, β(t) and δ(t) are uncertain quantities, P2 is the rod chamber pressure, is the reference rodless chamber pressure, P 1d is the expected rodless chamber pressure F l is the hydraulic cylinder output force

[0292] Step 2. Error change rate between pressure and reference pressure

[0293] make β(t):=β m Δβ(t), β m is a constant

[0294]

[0295] make

[0296]

[0297] make

[0298]

[0299] The designed flow rate is

[0300] Q1=Q eq +Q n +Q s

[0301]

[0302] Let κ: =P1-P 1d , sat(k) is defined as

[0303]

[0304] make

[0305]

[0306] Step 3. Construct the observer

[0307]

[0308] The derivative of

[0309]

[0310] Substituting the previous formula into

[0311]

[0312] make

[0313]

[0314] Assumptions Step 4: Stability Analysis

[0315]

[0316] according to

[0317]

[0318] According to the uniformly eventually bounded criterion, The boundary is

[0319]

[0320] |κ| boundary is

[0321]

[0322] Through the effective combination of top-level control and bottom-level control, the output of the hydraulic manipulator system can follow the desired position with high precision.

[0323] Control method effect: Figure 2 , Figure 3 , Figure 4 , Figure 5 They are the control effect of the robotic arm system without uncertainty under the constant reference trajectory, the control effect of the robotic arm system without uncertainty under the sine reference trajectory, the control effect of the robotic arm system with uncertainty under the constant reference trajectory, and the control effect of the robotic arm system with uncertainty under the sine reference trajectory. It can be seen from the figure that the tracking error has a high tracking accuracy, which verifies the effectiveness of this method.

[0324] The above content is merely an illustration and explanation of a trajectory following control method for a complex uncertain hydraulic manipulator system. In addition, the above implementation methods are only examples. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are included in the protection scope of the present invention.

Claims

1. A complex uncertain hydraulic manipulator system trajectory following control method, characterized in that The top-level control and the bottom-level control are divided into two parts. The top-level control proposes an adaptive robust constraint following control method based on the dynamic model. The bottom-level control considers the uncertainty of temperature on flow and bulk modulus, and designs an adaptive robust control method with disturbance observer.

2. The adaptive robust constraint following control method of top-level control according to claim 1 is characterized in that: The following steps are involved: Step 1: Establish the dynamic model of the hydraulic manipulator: Step 2, expressing the trajectory of the hydraulic manipulator as a constraint; Step 3, design of control method for hydraulic manipulator system without uncertainty; Step 4, design of control method for hydraulic manipulator system with uncertainty; Step 5: Stability analysis.

3. Establish the dynamic model of the hydraulic mechanical arm system according to claim 2: in: M(q) is the inertia matrix, symmetric and positive definite; is the centrifugal and Coriolis force matrix; G(q) is the effect of gravity on the joint; τ is the control input; the force output by the hydraulic cylinder; σ(t) is the uncertainty parameter, M(q, σ, t), G(qσ,t) depends on the uncertainty parameter σ. Assumption 1: For every (q, t)∈R n ×R, σ∈∑, inertia matrix M(q, σ, t)>0, M, C and G can be decomposed into: G(q,σ,t)=G(q,t)+ΔG(q,σ,t); in C, G represent the nominal part, At the same time, ΔM, ΔC, and ΔG represent the uncertain part. ΔM, ΔC, ΔG is continuous. Therefore ΔD(q,σ,t)=D(q,t)E(q,σ,t).

4. According to claim 2, the trajectory of the hydraulic manipulator is expressed as a constraint and the target trajectory of the manipulator system is set as q d (t), where q d (t), They represent the expected position trajectory, expected velocity trajectory, and expected acceleration trajectory respectively. Definition of tracking error Position error: e q (t) = q(t) - q d (t); Speed ​​error: Servo Constraint Where A is the constraint matrix b and c is the objective function 5. Design of a control method for a hydraulic manipulator system without uncertainty according to claim 2 Assumption 2: For every (q, t)∈R n ×R, A(q, t) is full rank, which means that A(q, t)A T (q, t) is reversible. Assumption 3: Given P∈R according to Assumption 2 m×m , P>0, set up: There is a constant ρ E >-1 so that all (q, t)∈R n ×R λ min Represents the minimum eigenvalue when In the special case of (i.e. no uncertainty), then E = 0, W = 0, so we can choose ρ E = 0 is greater than -1. Therefore, through continuity, this assumption imposes uncertainty on M and The effect of possible deviations of the control within a certain threshold is unidirectional. That is, the threshold is bounded in one direction, but unbounded in the other. This assumption means that the uncertainty connecting the control and the system should not change the direction of the control (for example, an external push will not become a pull due to uncertainty). In fact, all control theory requires an assumption of similar nature (maybe in different mathematical form) For all set up: τ=p1+p2 Where A is the constraint matrix, c is the objective function, b is the target function (same as above), "+" represents the generalized inverse matrix k2>0 control coefficient, and τ is the control input.

6. Design of control method for hydraulic manipulator system with uncertainty according to claim 2 According to the previous assumptions based on the continuity of the function and the boundedness of σ, there exists a function Φ(·): R n ×R n ×R→R + is known or unknown so that each have Assumption 4: There exists a constant vector α∈(0,∞) k and a known function Π(·): (0, ∞) k ×R n ×R n ×R→R + For each This assumption means that the function Φ The exact value of the function Π is equal to the same The value of is determined by the parameter a. can be interpreted as the overall bound on uncertainty. Assumption 5: In Assumption 4, for each The function Π(·) can linearly decompose a. There exists a function Make In order to simulate unknown situations, adaptive parameters are proposed Adaptive Law ( yes , i=1...,k, is the design parameter in where ∈ ∈R, ∈>0, is a constant τ=p1+p2+p 3。 7. Stability analysis according to claim 2: Theorem 2: Let According to the previous assumptions 1-5, the control input τ exhibits the following performance Uniform boundedness: For any r>0, there exists a d(r)<∞ such that Then for all t ≥ t0, we have Eventually uniformly bounded: For any r>0, when There is a d >0, so For any when Head Take the Lyapunov function: The derivative of V is: For all By the adaptive law we have: Multiplying the above two equations by 1+ρε gives As shown below, (Note ) in Uniform Boundedness: Eventually Uniformly Bounded 8. The adaptive robust control method with a disturbance observer in the bottom layer control according to claim 1 is characterized in that: The following steps are included Step 1. Determine the relationship between pressure and flow; Step 2. Error change rate between pressure and reference pressure; Step 3. Build the observer; Step 4. Stability analysis.

9. According to claim 8: Step 9.1 Determine the relationship between the flow rate and pressure of the rod chamber: Where V 02 is the initial volume of the rod chamber, A2 is the effective area of ​​the piston in the rod chamber, x l is the piston displacement, is the piston speed, Q2 is the flow rate, β(t) and λ(t) are uncertain quantities, There is rod cavity pressure. Step 9.2, error change rate between pressure and reference pressure: in The reference pressure Let α := V 02 -A2x l , and let β(t) := β m Δβ(t), β m be constants make make Let σ: = P2-P 2d , sat(σ) is defined as Step 9.3, build the observer The derivative of Substituting the previous formula into make Assumptions Step 9.4 Stability analysis according to According to Corless and Leitmann, The boundary is The boundary of |σ| is By combining top-level control with bottom-level control, the complex uncertainty of the hydraulic manipulator system can be effectively handled, so that the output of the manipulator system can track the desired trajectory with high precision.

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