Excavator mechanical arm trajectory tracking control method and device

Abstract

The invention relates to the technical field of electro-hydraulic position servo control systems of excavators, in particular to a trajectory tracking control method and device for a mechanical arm of an excavator, and the method comprises the following steps: S1, establishing a mathematical model of an electro-hydraulic position servo system of the mechanical arm; s2, identifying system parameters on line based on samples of a proportional pressure reducing valve and a multi-way valve of the excavator; s3, based on the mathematical model of the electro-hydraulic position servo system of the mechanical arm in the S1 and the identification parameters in the S2, a self-adaptive backstepping sliding mode controller based on a parameter layering strategy is designed, and tracking control is conducted on the track of the mechanical arm of the excavator through the self-adaptive backstepping sliding mode controller; and S4, a Lyapunov stability theory is used to carry out stability proving on the adaptive backstepping sliding mode controller in the S3, and an asymptotically stable system tracking error is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of excavator electro-hydraulic position servo control system, and particularly relates to a kind of excavator mechanical arm trajectory tracking control method and device. BACKGROUND

[0002] The excavator working device generally adopts electro-hydraulic servo system driving, and due to the inherent dead zone characteristics of hydraulic elements, time-varying of system parameters and external load disturbance and other factors, the system shows strong nonlinearity and uncertainty, which seriously restricts the improvement of trajectory tracking accuracy and becomes the main technical bottleneck of realizing high-precision automatic operation. At present, the research on trajectory tracking control of excavator electro-hydraulic servo system mainly develops in three directions: traditional control method, model-based control algorithm and intelligent control strategy. The traditional PID control is widely used in engineering practice due to its simple structure and intuitive parameter setting, but its control accuracy and robustness decrease significantly when facing system nonlinearity, parameter perturbation and external disturbance; advanced control methods based on model, such as sliding mode control, adaptive control and model predictive control, improve the tracking performance to some extent by introducing system dynamics information, however, this kind of method often depends too much on model accuracy, and generally has problems such as not fully considering high-order dynamic characteristics of the system, lack of targeted design of adaptive parameters, and difficulty in engineering implementation due to complex controller structure; intelligent control methods such as neural network control and fuzzy logic control have good nonlinear approximation ability and adaptability, but they usually need a large amount of training data support, and have inherent defects such as lack of real-time performance and difficulty in theoretically guaranteeing stability. It is particularly important to note that most of the existing researches separate the trajectory planning from the control link, lack the whole process optimization from trajectory generation to tracking execution, and fail to build a complete planning-control closed-loop system, which greatly limits the application effect of the control algorithm in actual working conditions. SUMMARY

[0003] The purpose of the present application is to establish a mathematical model of excavator mechanical arm electro-hydraulic servo system, considering the parameter uncertainty, uncertain nonlinearity and unknown disturbance existing in the system during the control process of hydraulic cylinder, and to design an adaptive backstepping sliding mode controller, so that the system obtains asymptotic tracking steady-state performance and realizes high-precision tracking of the planned trajectory of excavator mechanical arm.

[0004] The present application proposes a kind of excavator mechanical arm trajectory tracking control method, comprising the following steps: S1 establishes the mathematical model of mechanical arm electro-hydraulic position servo system; S2 on-line identifies system parameters based on excavator proportional pressure reducing valve and multi-way valve samples; S3, based on the mathematical model of the mechanical arm electro-hydraulic position servo system in S1 and the identified parameters in S2, designs an adaptive backstepping sliding mode controller based on a parameter hierarchical strategy, and controls the excavator mechanical arm trajectory to be tracked through the adaptive backstepping sliding mode controller; S4, using Lyapunov stability theory, proves the stability of the adaptive backstepping sliding mode controller in S3, and obtains an asymptotically stable system tracking error.

[0005] Preferably, the mathematical model in S1 is established specifically by the following steps: S1.1, the pressures in each working chamber of the hydraulic cylinder are equal, the hydraulic oil leakage of each element is laminar flow, the temperature and effective volume modulus of the hydraulic oil are constant values, the connecting pipeline between the valve and the hydraulic cylinder is symmetrical, and the load of the hydraulic cylinder is inertial load, a load-flow equation of the servo valve is established:

[0006] wherein is the load flow, represents the flow coefficient of the valve, is the area gradient of the valve port, is the displacement of the valve core, is the density of the hydraulic oil, is the supply pressure, is the load pressure; After linearizing the load-flow equation of the servo valve, the following equation is obtained:

[0007] wherein is the flow gain coefficient of the proportional valve, is the flow pressure coefficient of the proportional valve; S1.2, a load-flow equation of the hydraulic cylinder is established:

[0008] wherein is the leakage coefficient, is the total volume of the hydraulic cylinder chamber, is the area ratio of the two chambers of the hydraulic cylinder, is the effective volume modulus of the hydraulic oil, is the area of the rodless chamber of the hydraulic cylinder, is the displacement of the piston rod movement; The balance equation of the output force of the hydraulic cylinder and the load is:

[0009] wherein is the total mass of the piston and the load converted to the piston, viscous damping coefficient of the piston and load, spring stiffness of the load, external load force of the hydraulic cylinder, displacement, velocity and acceleration of the piston rod movement, respectively; S1.3 calculation of proportional amplification link: the output voltage signal of the controller is converted into a current signal through the resistance of the proportional pressure reducing valve:

[0010] wherein is the output current of the proportional pressure reducing valve, is the resistance of the proportional pressure reducing valve, is the output voltage of the controller; electro-hydraulic servo link: in the electro-hydraulic servo system of the excavator, this link is composed of a pilot valve and a main valve, combined with a proportional pressure reducing valve and a multi-way valve sample, this link is simplified as a proportional link:

[0011] wherein is the spool displacement, is the hydraulic valve servo coefficient; S1.4 calculation of displacement sensor link: the displacement sensor is responsible for measuring the stroke of the hydraulic cylinder, and the transfer function of this link is:

[0012] wherein is the transfer function of this link, is a complex frequency operator; S1.5 taking the displacement, velocity and acceleration of the piston as the state variables of the system, i.e. then the state space equation of the electro-hydraulic servo system is obtained as:

[0013] thus the mathematical model of the electro-hydraulic position servo system of the mechanical arm is established, wherein, , is the natural frequency of the system; is the damping ratio of the system, displacement, velocity and acceleration of the piston, respectively, is the control variable, is the system disturbance term, is the flow pressure coefficient of the proportional valve; is the flow pressure coefficient, is the flow gain coefficient of the proportional valve, is the valve servo coefficient of the system.

[0014] Preferably, the online identification of system parameters in step S2 specifically comprises the following steps: S2.1 Current compensation is performed on the dead zone of the pressure reducing valve, and a proportional relationship between the pilot pressure of the pressure reducing valve and the input current is obtained:

[0015] wherein P is the pilot pressure of the proportional pressure reducing valve, is the pilot pressure of the pressure reducing valve, is a proportional coefficient between the pilot pressure of the pressure reducing valve and the input current; S2.2 According to the valve core displacement and the pilot pressure of the proportional valve sample, the proportional relationship is expressed as:

[0016] In the formula: is a proportional coefficient between the valve core displacement and the pilot pressure, and the coefficient is is expressed as:

[0017] S2.3 When the boom, stick, and bucket of the mechanical arm make extension and retraction actions, different flow coefficients correspond thereto During the operation of the system, the flow coefficients under different working conditions are as follows: the flow coefficient corresponding to the extension of the boom is expressed as , the flow coefficient corresponding to the retraction is , the flow coefficient corresponding to the extension of the stick is expressed as , the flow coefficient corresponding to the retraction is , the flow coefficient corresponding to the extension of the bucket is expressed as , and the flow coefficient corresponding to the retraction is .

[0018] Preferably, the step S3 of designing the adaptive backstepping sliding mode controller based on the parameter hierarchical strategy specifically includes the following steps: S3.1 According to the state space equation set of the electro-hydraulic servo system, parameter adaptive processing is performed on the parameters , hierarchical design is realized, the actual values of the parameters are respectively , , , and the state space equation of the system is rewritten as:

[0019] S3.2 Assuming that the estimated values of the parameters , , are respectively , , , the error is

[0020] S3.3 According to the rewritten state space equation of the system as a mathematical model, the error is the state variable, is the expected displacement signal of the oil cylinder, is the system output displacement signal, the deviation of the system is represented as: Similarly, the deviation equation set is:

[0021] According to the design idea of backstepping method, the recursive control design method is used to decompose the high-order system into subsystems, and the virtual control quantity is gradually constructed. The in the deviation equation set is designed as a virtual quantity, respectively representing the displacement error, velocity error, and acceleration error of the system hydraulic cylinder; S3.4 The first Lyapunov function is defined, and the Lyapunov function is designed as:

[0022] Where is the Lyapunov function designed for the first error variable ; The first Lyapunov function is derived to obtain:

[0023] The virtual quantity is represented as

[0024] Where is the first proportional coefficient; S3.5 The second Lyapunov function is defined, and the Lyapunov function is designed as:

[0025] Where is the Lyapunov function containing two error variables and ; The second Lyapunov function is derived to obtain:

[0026] The virtual quantity is represented as:

[0027] Where is the second proportional coefficient; S3.6 Combined with the sliding mode control, the sliding surface is designed according to the system error state equation as follows:

[0028] wherein is the sliding surface, is the sliding surface coefficient; The exponential reaching law is selected as follows:

[0029] wherein is the reaching rate switching term gain, is the reaching rate exponential term gain, is the sign function; S3.7 The third Lyapunov function is defined, and the Lyapunov function is taken as:

[0030] wherein all are adaptive gains, is the total Lyapunov function of the whole system;

[0031] wherein is the third proportional coefficient, and the control rate is:

[0032] At this time:

[0033] In order to ensure negative, the parameter adaptive law is designed as:

[0034] In order to prevent the adaptive law from being too large to cause abnormal phenomenon of the control input signal, the adaptive mapping algorithm is used to correct the parameter adaptive law:

[0035] wherein is the derivative value of , and finally the control rate is expressed as: .

[0036] Preferably, in S4, Lyapunov stability theory is used to prove the stability of the adaptive backstepping sliding mode controller based on the parameter hierarchical strategy, which specifically includes the following steps: for the system, under the condition that the assumption is met, the adaptive mapping algorithm and the control rate are used, all signals in the closed-loop system are bounded, and the system is stably bounded, the parameter adaptive law is substituted into the total Lyapunov function of the derived system, and the following is obtained:

[0037] Therefore, it is confirmed that the control system is stable.

[0038] A trajectory tracking control device of an excavator mechanical arm adopts the trajectory tracking control method of the excavator mechanical arm as described above to track the trajectory of the excavator mechanical arm.

[0039] By adopting the above scheme, the present application has the following advantages and beneficial effects: the present application provides a mobile edge computing task offloading optimization method based on a graph state space and a causal reward mechanism. The method fundamentally innovates the traditional deep reinforcement learning framework in view of the high dynamics and uncertainty of the MEC environment: by constructing a heterogeneous graph model of users-tasks-servers, and using a graph neural network to encode the environment state, the problem of missing structured representation of the state space is solved; by designing a causal demand reward function based on counterfactual reasoning, the confusion bias in the reward signal is eliminated, and it is ensured that the policy learning is the real causal effect of the action. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions of the present application, the following will briefly introduce the drawings needed to be used in the specific embodiments of the present application. It should be understood that the following drawings only show some specific embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0041] Figure 1 is the adaptive backstepping sliding mode control principle diagram of the mechanical arm electro-hydraulic position servo system based on the parameter hierarchical strategy of the present application.

[0042] Figure 2 is the principle diagram of the excavator mechanical arm trajectory tracking control system of the present application.

[0043] Figure 3 is the excavator mechanical arm bucket end desired trajectory curve designed by the present application.

[0044] Figure 4 is the excavator mechanical arm bucket end desired digging curve and each controller tracking curve designed by the present application.

[0045] Figure 5 is the tracking error comparison curve of the system under the adaptive backstepping sliding mode control algorithm, the ordinary sliding mode control algorithm and the PID control designed in the application.

[0046] Figure 6 is the adaptive curve of the parameter of the boom electro-hydraulic servo system.

[0047] Figure 7 is the adaptive curve of the parameter of the boom electro-hydraulic servo system.

[0048] Figure 8 is the adaptive curve of the parameter of the boom electro-hydraulic servo system. DETAILED DESCRIPTION

[0049] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0050] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0051] In addition, the terms "first", "second", "third", etc. are used only for descriptive purposes and are not to be construed as indicating or implying relative importance or an ordered ranking of the indicated technical features. Thus, features defined with "first", "second" or "third" can include, explicitly or implicitly, one or more of such features. In the description of the application, the term "a plurality" means two or more, unless expressly specified and limited otherwise.

[0052] In the present application, unless expressly specified and limited otherwise, the terms "mounting", "connecting", "connecting", "fixing" and the like should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0053] The preferred embodiments of the present application are described in detail below with reference to the accompanying drawings, so that the advantages and features of the present application can be more easily understood by those skilled in the art, and the protection scope of the present application is more clearly and definitely defined.

[0054] The present application proposes Figure 1 and Figure 2 The excavator mechanical arm trajectory tracking control method described in the present application comprises the following steps: Step 1, establish a mathematical model of the mechanical arm electro-hydraulic position servo system, as follows: the pressure in each working chamber of the hydraulic cylinder is equal, the hydraulic oil leakage of each element is laminar flow, the temperature and effective volume modulus of the hydraulic oil are constant values, the connecting pipeline between the valve and the hydraulic cylinder is symmetrical, the load of the hydraulic cylinder is inertial load, and there is no elastic load.

[0055] Servo valve load-flow equation: (1) Wherein is the load flow, represents the flow coefficient of the valve, is the valve port area gradient, is the valve core displacement, is the density of the hydraulic oil, is the oil supply pressure, is the load pressure.

[0056] After linearizing formula (1), we get: (2) Wherein is the flow gain coefficient of the proportional valve, is the flow pressure coefficient of the proportional valve; Hydraulic cylinder load-flow equation: (3) where is the leakage coefficient, is the total volume of the hydraulic cylinder chamber, is the area ratio of the two chambers of the hydraulic cylinder, is the effective bulk modulus of the hydraulic oil, is the area of the rodless chamber of the hydraulic cylinder, is the displacement of the piston rod movement; According to Newton's second law, the balance equation of the output force of the hydraulic cylinder and the load is (4) where is the total mass of the piston and the load converted to the piston, is the viscous damping coefficient of the piston and the load, is the load spring stiffness, is the external load force of the hydraulic cylinder, are the displacement, velocity and acceleration of the piston rod movement, respectively; Proportional amplification link: the output voltage signal of the controller is converted into a current signal through the internal resistance of the proportional pressure reducing valve.

[0057] (5) where is the output current of the proportional pressure reducing valve, is the internal resistance of the proportional pressure reducing valve, is the output voltage of the controller; Electro-hydraulic servo link: in the electro-hydraulic servo system of the excavator, this link is generally composed of a pilot valve and a main valve, combined with the proportional pressure reducing valve and the multi-way valve sample, under the premise of not significantly reducing the model accuracy, this link can be simplified as a proportional link.

[0058] (6) where is the servo coefficient of the hydraulic valve; Displacement sensor link: the displacement sensor is responsible for measuring the stroke of the hydraulic oil cylinder, and the transfer function of this link is: (7) where is the transfer function of this link, is a complex frequency operator; Taking the displacement, velocity and acceleration of the piston as the state variables of the system, i.e. then the state space equation set of the steering system can be obtained from equations (1) to (7): (8) Thus, the mathematical model of the electro-hydraulic position servo system of the mechanical arm is established, wherein, , is the system natural frequency; is the system damping ratio, .

[0059] Go to Step 2 Step 2, based on the samples of the proportional pressure reducing valve and the multi-way valve of the excavator, the system part parameters are identified online According to the sample of the proportional pressure reducing valve used in the hydraulic excavator of this type, the internal resistance of the proportional pressure reducing valve is 17.5 ohms, and the dead zone current is 400 mA. At this time, the proportional relationship between the pilot pressure and the input current of the pressure reducing valve can be obtained by current compensation for the dead zone of the pressure reducing valve: (9) wherein is the pilot pressure output by the proportional pressure reducing valve, is the proportional coefficient between the pilot pressure and the input current of the pressure reducing valve.

[0060] According to the sample of the multi-way valve, the spool displacement and the pilot pressure can be approximately proportional, which is expressed as: (10) In the formula, is the proportional coefficient between the spool displacement and the pilot pressure, and the coefficient is is expressed as: (11) In the mechanical arm, the boom, the stick, and the bucket correspond to different flow coefficients when they make extension and retraction actions In the system running process, the flow coefficients under different working conditions; in the system running process, the flow coefficients under different working conditions can be regarded as determined values.

[0061] Go to Step 3.

[0062] Step 3, based on the mathematical model of the electro-hydraulic position servo system and the identified parameters, an adaptive backstepping sliding mode control method based on parameter hierarchical strategy is designed, Step 3-1 According to formula (8), the parameter can be obtained by online identification, therefore, the parameter hierarchical strategy only performs parameter adaptive processing on the parameter , realizes hierarchical design, and sets the actual values of each parameter as , , , and the state space equation of the system is rewritten as: (12) Step 3-2 Set parameters , , The estimated values of , , The error is represented as (13) Step 3-3 According to the mathematical model shown in formula (12), taking the error as the state variable, as the expected displacement signal of the oil cylinder, as the system output displacement signal, the deviation of the system is represented as: Similarly, the deviation equation set is obtained as: (14) According to the design idea of backstepping method, the recursive control design method is adopted to decompose the high-order system into subsystems, and the virtual control quantity is gradually constructed. The in formula (14) is designed as a virtual quantity, representing the displacement error, velocity error, and acceleration error of the system hydraulic cylinder, respectively; Step 3-4 Define the first Lyapunov function, and design the Lyapunov function as: (15) After derivation of formula (15), we get (16) The virtual quantity is represented as (17) Step 3-5 Define the second Lyapunov function, and design the Lyapunov function as: (18) After derivation of formula (18), we get (19) The virtual quantity is represented as: (20) Step 3-6 Combined with the sliding mode control, according to the system error state equation, the sliding surface is designed as: (21) The exponential approach law is selected as follows: (22) Step 3-7 Define the third Lyapunov function, and take the Lyapunov function as: (23) Let: (24) Control rate: (25) At this time: (26) To ensure Negative, the design parameter adaptive law is: (27) To prevent the adaptive law from being too large and causing abnormal phenomena of control input signal, the adaptive mapping algorithm is used to modify formula (27) to limit the adaptive law within a certain range.

[0063] (28) Finally, the control rate is expressed as: (29).

[0064] Go to step 4.

[0065] Step 4, use Lyapunov stability theory to prove the stability of the adaptive backstepping sliding mode controller based on parameter hierarchical strategy, and get the result that the system tracking error is asymptotically stable.

[0066] Substitute formula (27) into formula (26) to get: (30) From formula (30), the signal in the closed-loop system is uniformly ultimately bounded, and satisfies , the closed-loop system is stable. Therefore, the conclusion is that by adjusting the gain and other parameters, the designed adaptive backstepping sliding mode controller can be applied to the excavator arm electro-hydraulic servo system to obtain the result that the tracking error converges to 0, and then through the coordinated operation of the three electro-hydraulic servo systems on the excavator arm, the planned end-of-dipper digging trajectory can be tracked with high precision. The principle of adaptive backstepping sliding mode controller based on parameter hierarchical strategy is shown in Figure 1 .

[0067] Embodiment To evaluate the performance of the designed controller, the physical parameters of the excavator arm electro-hydraulic servo system in the simulation are shown in Table 1: Table 1 System physical parameters (take the dipper cylinder parameters as an example, the boom and dipper arm cylinders are similar)

[0068] The given system bucket end desired trajectory curve is as shown in Figure 3 .

[0069] The following controllers are taken in the simulation: The adaptive backstepping sliding mode controller of the boom hydraulic cylinder takes k1=k2=k3=1, ɛ=1.5, and k=250; Kq1 and Kq2 are 12.6 and 3.5 respectively during extension and retraction.

[0070] The adaptive backstepping sliding mode controller of the boom hydraulic cylinder takes k1=k2=k3=1, ɛ=1.0, and k=600; Kq3 and Kq4 are 16.5 and 13.5 respectively during extension and retraction.

[0071] The adaptive backstepping sliding mode controller of the boom hydraulic cylinder takes k1=k2=k3=1, ɛ=1.2, and k=300; Kq5 and Kq6 are 12.1 and 9.6 respectively during extension and retraction.

[0072] The PID controller parameters are set as follows: P=150, I=0.1, and D=0 for the boom, P=50, I=0.15, and D=0 for the stick, and P=70, I=0.21, and D=0 for the bucket.

[0073] The sliding mode controller parameters are set as follows: ɛ=1 and k=85 for the boom, ɛ=1.5 and k=64 for the stick, and ɛ=1.5 and k=71 for the bucket.

[0074] The tracking trajectory and tracking error are as shown in Figure 4 and Figure 5 It can be seen from Figure 5 that the adaptive backstepping sliding mode control (ABSMC) based on the parameter hierarchical strategy has great improvement in accuracy and stability compared with the PID control and the sliding mode control (SMC). The maximum error of the PID is 87 mm, the maximum error of the SMC is 22 mm, and the maximum error of the ABSMC is 10.8 mm. In terms of the root mean square error, the root mean square error of the PID control is 54.2 mm, the root mean square error of the SMC is 8.12 mm, and the root mean square error of the ABSMC is only 4.1 mm.

[0075] The above is the preferred embodiment of the present application, it should be noted that for those skilled in the art, without departing from the principles of the present application, can make a number of improvements and refinements, these improvements and refinements are also considered to be within the scope of the present application.

Claims

1. A method of excavator manipulator trajectory tracking control, characterized by, The method comprises the following steps: S1, establishing a mathematical model of an electro-hydraulic position servo system of a mechanical arm; S2, on-line identifying system parameters based on samples of a proportional pressure-reducing valve and a multi-way valve of the excavator; S3, designing an adaptive backstepping sliding mode controller based on a parameter hierarchical strategy based on the mathematical model of the electro-hydraulic position servo system of the mechanical arm in S1 and the identified parameters in S2, and tracking control of a trajectory of the mechanical arm of the excavator is performed through the adaptive backstepping sliding mode controller; S4, proving stability of the adaptive backstepping sliding mode controller in S3 by using Lyapunov stability theory, and obtaining an asymptotically stable system tracking error.

2. The excavator manipulator trajectory tracking control method of claim 1, wherein, The step S1 of establishing the mathematical model comprises the following steps: S1.1, establishing a servo valve load-flow equation under the conditions that pressures in each working chamber of a hydraulic cylinder are equal, hydraulic oil leakage of each element is laminar flow, temperature and effective volume modulus of the hydraulic oil are constant values, connecting pipelines between the valve and the hydraulic cylinder are symmetrical, and the load of the hydraulic cylinder is inertial load: wherein is the load flow, is the flow coefficient of the valve, is the valve port area gradient, is the spool displacement, is the density of the hydraulic fluid, is the supply pressure, is the load pressure; After linearization processing of the servo valve load-flow equation, the following equation is obtained: wherein is the flow gain coefficient of the proportional valve, is the flow pressure coefficient of the proportional valve; S1.2, establishing a hydraulic cylinder load-flow equation: wherein is the leakage coefficient, is the total volume of the hydraulic cylinder chamber, is the area ratio of the two chambers of the hydraulic cylinder, is the effective bulk modulus of the hydraulic oil, is the area of the rodless chamber of the hydraulic cylinder, is the displacement of the piston rod movement; A balance equation of the output force of the hydraulic cylinder and the load is: wherein is the total mass of the piston and the load reduced to the piston, is the viscous damping coefficient of the piston and the load, is the spring rate of the load, is the external load force of the hydraulic cylinder, are the displacement, velocity and acceleration of the piston rod motion, respectively; S1.3, calculating a proportional amplification link: a voltage signal output by a controller is converted into a current signal through resistance in a proportional pressure-reducing valve: wherein is the output current of the proportional pressure reducing valve, is the internal resistance of the proportional pressure reducing valve, is the output voltage of the controller; An electro-hydraulic servo link: in the electro-hydraulic servo system of the excavator, the link is composed of a pilot valve and a main valve, and the link is simplified as a proportional link in combination with the proportional pressure-reducing valve and the multi-way valve sample: wherein is the displacement of the valve core, is the hydraulic valve servo coefficient; S1.4, calculating a displacement sensor link: a displacement sensor is responsible for measuring a stroke of the hydraulic oil cylinder, and a transfer function of the link is: wherein is the transfer function of the link, is a complex frequency operator; S1.5 Take the displacement, velocity, acceleration of the piston as the system state variable, i.e. The state space equation set of the electro-hydraulic servo system is obtained as follows: Thus, the mathematical model of the electro-hydraulic position servo system of the robot arm is established, wherein, , is the system natural frequency; is the system damping ratio, respectively represent the displacement, velocity and acceleration of the piston, is the control variable, is the system disturbance term, is the flow-pressure coefficient of the proportional valve; is the flow-pressure coefficient, is the flow gain coefficient of the proportional valve, is the valve servo coefficient of the system.

3. The excavator manipulator trajectory tracking control method of claim 2, wherein, The step S2 of on-line identifying system parameters comprises the following steps: S2.1, performing current compensation on a dead zone of the pressure-reducing valve, and obtaining a proportional relationship between a pilot pressure of the pressure-reducing valve and an input current as: wherein is a proportional pressure reducing valve output, is a proportional coefficient between the pressure reducing valve pilot pressure and the input current; S2.2, according to the multi-way valve sample, a proportional relationship between a spool displacement and the pilot pressure of the multi-way valve is expressed as: In the formula: is the proportional coefficient between the spool displacement and the pilot pressure, and the coefficient is expressed as: S2.3 The boom, stick, and bucket in the mechanical arm correspond to different flow coefficients when they are extended and retracted During system operation, the flow coefficients in different working states are as follows: the flow coefficient corresponding to boom extension is represented as , the flow coefficient corresponding to boom retraction is , the flow coefficient corresponding to stick extension is represented as , the flow coefficient corresponding to stick retraction is , the flow coefficient corresponding to bucket extension is represented as , and the flow coefficient corresponding to bucket retraction is .

4. The excavator manipulator trajectory tracking control method of claim 3, wherein, The step S3 of designing the adaptive backstepping sliding mode controller based on the parameter hierarchical strategy comprises the following steps: S3.1 According to the state space equation set of electro-hydraulic servo system, parameter adaptive processing is carried out, hierarchical design is realized, and the actual values of each parameter are respectively , , The state space equation of the system is rewritten as: S3.2 Set parameters , , The estimated values of , , The error is S3.3 The state space equation of the modified system is taken as a mathematical model, with error as a state variable, as the desired displacement signal of the oil cylinder, as the system output displacement signal, the deviation of the system is represented as: Similarly, the deviation equation set is obtained as: According to the design idea of backstepping method, the recursive control design method is adopted to decompose the high-order system into subsystems, gradually build virtual control variables, and construct the error equation group of the system The design is a virtual variable, respectively represent the displacement error, velocity error and acceleration error of the system hydraulic cylinder S3.4, defining a first Lyapunov function, and designing the Lyapunov function as: wherein is a Lyapunov function designed for the first error variable ​ After derivation of the first Lyapunov function, the following equation is obtained: then the virtual quantity is represented as wherein is a first proportionality coefficient; S3.5, defining a second Lyapunov function, and designing the Lyapunov function as: wherein is a Lyapunov function comprising two error variables and ​ After derivation of the second Lyapunov function, the following equation is obtained: virtual quantity is represented as: wherein is a second proportionality coefficient; S3.6, in combination with a sliding mode control, designing a sliding mode surface according to a system error state equation as: wherein is the slide face, is the slide face coefficient; Selecting an exponential reaching law as follows: wherein is a rate of approach gain, is a rate of approach exponent gain, is a sign function; S3.7, defining a third Lyapunov function, and taking the Lyapunov function as: wherein all three are adaptive gains, V is the total Lyapunov function of the whole system; wherein is a third proportionality coefficient, the control rate is: At this time: To ensure negative, the design parameter adaptive law is: In order to prevent the adaptive law from being too large and causing abnormal phenomena of a control input signal, an adaptive mapping algorithm is used to correct the parameter adaptive law: wherein is the derivative value of the control rate is expressed as: 。 5. The excavator manipulator trajectory tracking control method of claim 4, wherein, In S4, Lyapunov stability theory is used to prove the stability of the adaptive backstepping sliding mode controller based on the parameter hierarchical strategy, which includes the following steps: for the system, under the condition that the assumption is met, the adaptive mapping algorithm and the control rate are used, all signals in the closed-loop system are bounded, the system is bounded and stable, the parameter adaptive law is substituted into the total Lyapunov function of the system after derivation, and the following is obtained: Therefore, it is confirmed that the control system is stable.

6. An excavator mechanical arm trajectory tracking control device characterized by comprising: The excavator mechanical arm trajectory tracking control method according to any one of claims 1-5 is used to track the trajectory of the excavator mechanical arm.

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