An active balance high-efficiency high-precision liquid-electric hybrid driving pitch servo system and a control method thereof

Abstract

The application discloses an active balance high-efficiency high-precision liquid-electric hybrid driving pitching servo system and a control method thereof, and belongs to the technical field of servo control of mechatronic hydraulic systems. The servo system comprises an EHA driving system, a rotary shaft electric servo system and a heavy rocker, the EHA driving system and the rotary shaft electric servo system are connected with the heavy rocker, the EHA driving system adopts a three-hinge-point direct pushing type layout, the rotary shaft electric servo system is directly arranged on a rotary shaft of the heavy rocker, and the EHA driving system and the rotary shaft electric servo system cooperatively drive the heavy rocker to complete a task as two independent subsystems. The adaptive active disturbance rejection composite control strategy is adopted, the problem of the system under the action of parameter uncertainty and unmodeled disturbance is effectively solved, and the angle tracking accuracy in the turning process of the servo system is improved.

Description

Technical Field

[0001] This invention belongs to the field of electromechanical-hydraulic system servo control technology, specifically a high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system with active balancing and its control method. Background Technology

[0002] As modern industrial automation continues to develop towards intelligence, high precision, and high reliability, the operating mode of heavy-duty rocker arm equipment has undergone fundamental changes. Traditional heavy-duty rocker arm systems are mainly used for fixed-position, low-speed, heavy-load operations, with relatively low requirements for real-time motion response and multi-task adaptability. However, in current intelligent manufacturing and flexible production lines, heavy-duty rocker arms often need to complete material handling, precise positioning, and multi-axis collaborative operations under conditions of frequent starts and stops, changes in direction, or high dynamic loads, significantly accelerating the production cycle and placing higher demands on the position control, dynamic response, and load adaptability of the actuators. Hydraulic drives have high thrust density and strong load-bearing capacity, but in low-speed precision control, problems such as internal leakage and frictional nonlinearity make it difficult to balance high precision and high response. Moreover, traditional valve control systems use throttling control, resulting in low energy efficiency. While pump-controlled cylinders (EHA) significantly improve the energy efficiency of hydraulic systems, their control response and precision cannot meet the requirements of high dynamics. Applying all-electric drive to the rotating axis has advantages such as convenient control and compact structure, but under conditions of high inertia and high load, problems such as insufficient power density and susceptibility to overload damage exist, limiting reliability. Both of these driving methods have their advantages, but they also have obvious technical shortcomings. Summary of the Invention

[0003] The purpose of this invention is to provide an active balancing, high-efficiency, high-precision hydraulic-electric hybrid drive pitch servo system. In terms of configuration, it integrates the high efficiency and high load capacity of the EHA system with the high response and high precision performance of the rotary axis electric servo. The functions and performance complement each other, realizing agile control of heavy-duty rocker arm servo.

[0004] The technical solution to achieve the purpose of this invention is: an active balancing, high-efficiency, high-precision hydraulic-electric hybrid drive pitch servo system, comprising: an EHA drive system, a rotary axis electric servo system, and a heavy-duty rocker arm. Both the EHA drive system and the rotary axis electric servo system are connected to the heavy-duty rocker arm. The EHA drive system adopts a three-hinge point direct-drive layout. The rotary axis electric servo system is directly arranged on the rotation axis of the heavy-duty rocker arm. The EHA drive system and the rotary axis electric servo system work together as two independent subsystems to drive the heavy-duty rocker arm to complete the task.

[0005] Preferably, the EHA drive system includes an EHA servo motor, an EHA bidirectional constant displacement pump, a hydraulic oil tank, a pneumatic accumulator group, and an EHA asymmetric single-rod hydraulic cylinder; the EHA servo motor is coaxially connected to the EHA bidirectional constant displacement pump, which has two working ports, A and B. When the EHA servo motor rotates forward, port A is the inlet and port B is the outlet; when the EHA servo motor rotates in reverse, port A is the outlet and port B is the inlet. Port A of the EHA bidirectional constant displacement pump is connected to... The pipeline connects to the rod-side port of the EHA asymmetric single-rod hydraulic cylinder to provide the pressure and flow required by the EHA drive system. The B port of the EHA bidirectional constant displacement pump is connected to the hydraulic oil tank through a pipeline. The hydraulic oil tank serves to store hydraulic oil. The bladder accumulator group is connected to the rodless port of the EHA asymmetric single-rod hydraulic cylinder through a pipeline to provide the pressure and flow required by the EHA drive system. The rod end of the EHA asymmetric single-rod hydraulic cylinder is hinged to the pitch servo system base, and the cylinder end of the EHA asymmetric single-rod hydraulic cylinder is hinged to the heavy-duty rocker arm.

[0006] Preferably, the EHA drive system further includes a rod chamber pressure sensor and a rodless chamber pressure sensor; the rod chamber pressure sensor is installed on the connecting pipeline between the EHA bidirectional constant displacement pump and the EHA asymmetric single-rod hydraulic cylinder, and is used to monitor the real-time pressure of the rod chamber of the EHA asymmetric single-rod hydraulic cylinder; the rodless chamber pressure sensor is installed on the connecting pipeline between the air bladder accumulator group and the EHA asymmetric single-rod hydraulic cylinder, and is used to monitor the real-time pressure of the rodless chamber of the EHA asymmetric single-rod hydraulic cylinder.

[0007] Preferably, the rotary axis electric servo system includes a rotary axis servo motor, a rotary axis reducer, and a rotary axis absolute encoder; the rotary axis servo motor is connected to the input end of the rotary axis reducer via a mechanical shaft, the output end of the rotary axis reducer is connected to the transmission structure at the rotary shaft of the heavy-duty rocker arm via a mechanical shaft, and the rotary axis absolute encoder is connected to the transmission mechanism at the rotary shaft of the heavy-duty rocker arm via a mechanical shaft for monitoring the real-time angle of the heavy-duty rocker arm.

[0008] This invention also addresses the complex configuration characteristics of the aforementioned systems, proposing a control method for an actively balanced, efficient, and high-precision hydroelectric hybrid drive pitch servo system under conditions of parameter uncertainty and unmodeled disturbances. The method includes the following steps:

[0009] Step 1: Establish a mathematical model for the hydraulic-electric hybrid drive heavy-duty rocker arm pitch servo system;

[0010] Step 2: Design a discontinuous projection mapping function to achieve bounded adaptive parameter learning results. Based on the discontinuous projection mapping function, design an adaptive law function so that the controller can learn the unknown parameters of the system online while running.

[0011] Step 3: Based on active disturbance rejection control theory, extended state observers are designed for the equivalent single-degree-of-freedom pitch servo system load motor system and the hydraulic cylinder rod chamber pressure system, respectively. The extended state observers are used to estimate the system's uncertainty disturbances.

[0012] Step 4: Based on the estimation of system uncertainty disturbances and unknown system parameters in Steps 2 and 3, design the control law according to the backstepping framework, and adopt the feedforward method to compensate for system disturbances; based on the driving characteristics of the hydraulic cylinder and the rotary shaft motor, perform task planning and controller design for both, and use the controller to achieve the system's tracking effect on arbitrary smooth position commands.

[0013] Compared with the prior art, the significant advantages of this invention are: (1) This invention adopts a hydraulic-electric hybrid drive method that fully combines the advantages of hydraulic system and electromechanical direct drive system. Under the premise of meeting the servo performance of servo system, the power of drive components can be further reduced; (2) This invention rationally allocates tasks based on the inherent differences between electro-hydraulic transmission system and electromechanical direct drive system. The hydraulic cylinder counteracts the load torque of pitch servo system, and the rotary axis rotary motor completes the system position servo, reducing the internal coupling influence of electromechanical-hydraulic system; (3) This invention adopts an adaptive self-disturbance rejection composite control strategy, which effectively solves the problem of system under the simultaneous presence of parameter uncertainty and unmodeled disturbance, improves the angle tracking accuracy during servo system adjustment, and obtains good tracking performance. Simulation results verify its effectiveness. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of an active balancing, high-efficiency, and high-precision hydraulic-electric hybrid drive pitch servo system.

[0015] Figure 2 This is a schematic diagram of an experimental platform for an active balancing, high-efficiency, and high-precision hydraulic-electric hybrid drive pitch servo system.

[0016] Figure 3 This is a schematic diagram illustrating the principle of an active balancing, high-efficiency, and high-precision hydraulic-electric hybrid drive pitch servo system control method.

[0017] Figure 4 This is a diagram illustrating the process by which the system output tracks the desired command under the action of a Composite Adaptive Robust Controller (CARC).

[0018] Figure 5 This is a graph showing the change of the system's tracking error over time under the action of the CARC controller.

[0019] Figure 6 This is a comparison curve of the tracking error of the system under the action of the CARC controller and the model-based velocity feedforward proportional-integral (MBVFPI) controller.

[0020] Figure 7 These are CARC controller parameters. A graph showing how the estimated value changes over time.

[0021] Figure 8 These are CARC controller parameters. A graph showing how the estimated value changes over time. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0023] The following section will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention, using this design example as an example.

[0024] A highly efficient and high-precision hydroelectric hybrid drive pitch servo system with active balancing, such as Figure 1 and Figure 2 As shown, it includes an EHA drive system 1, a rotary axis electric servo system 2, and a heavy-duty rocker arm 3. Both the EHA drive system 1 and the rotary axis electric servo system 2 are connected to the heavy-duty rocker arm 3. The EHA drive system 1 adopts a three-hinge point direct-drive layout. The rotary axis electric servo system 2 is directly arranged on the rotation axis of the heavy-duty rocker arm 3. The EHA drive system 1 and the rotary axis electric servo system 2 work together as two independent subsystems to drive the heavy-duty rocker arm 3 to complete the predetermined task.

[0025] The EHA drive system 1 includes an EHA servo motor 11, an EHA bidirectional constant displacement pump 12, a hydraulic oil tank 13, a pneumatic accumulator group 14, and an EHA asymmetric single-rod hydraulic cylinder 16. The EHA servo motor 11 is coaxially connected to the EHA bidirectional constant displacement pump 12. The EHA bidirectional constant displacement pump 12 has two working ports, A and B. When the EHA servo motor 11 rotates forward, port A of the EHA bidirectional constant displacement pump 12 is the inlet and port B is the outlet. When the EHA servo motor 11 rotates in reverse, port A of the EHA bidirectional constant displacement pump 12 is the outlet and port B is the inlet. Port A of the EHA bidirectional constant displacement pump 12 is connected to... The rod-side port of the EHA asymmetric single-rod hydraulic cylinder 16 is connected to provide the pressure and flow required by the EHA drive system 1. The B port of the EHA bidirectional constant displacement pump 12 is connected to the hydraulic oil tank 13 through a pipeline. The hydraulic oil tank 13 serves to store hydraulic oil. The air bladder accumulator group 14 is connected to the rodless port of the EHA asymmetric single-rod hydraulic cylinder 16 through a pipeline to provide the pressure and flow required by the EHA drive system 1. The rod end of the EHA asymmetric single-rod hydraulic cylinder 16 is hinged to the pitch servo system base at the lower support lug, and the cylinder end of the EHA asymmetric single-rod hydraulic cylinder 16 is hinged to the heavy-duty rocker arm 3 at the upper support lug.

[0026] The EHA pressure sensor group 15 includes a rod chamber pressure sensor 151 and a rodless chamber pressure sensor 152. The rod chamber pressure sensor 151 is installed on the pipeline connecting the EHA bidirectional constant displacement pump 12 and the EHA asymmetric single rod hydraulic cylinder 16, near the rod chamber port of the EHA asymmetric single rod hydraulic cylinder 16, and is used to monitor the real-time pressure of the rod chamber of the EHA asymmetric single rod hydraulic cylinder 16. The rodless chamber pressure sensor 152 is installed on the pipeline connecting the airbag accumulator group 14 and the EHA asymmetric single rod hydraulic cylinder 16, near the rodless chamber port of the EHA asymmetric single rod hydraulic cylinder 16, and is used to monitor the real-time pressure of the rodless chamber of the EHA asymmetric single rod hydraulic cylinder 16.

[0027] The rotary axis electric servo system 2 includes a rotary axis servo motor 21, a rotary axis reducer 22, and a rotary axis absolute encoder 23. The rotary axis servo motor 21 is connected to the input end of the rotary axis reducer 22 via a mechanical shaft. The output end of the rotary axis reducer 22 is connected to the left transmission structure at the rotary shaft of the heavy-duty rocker arm 3 via a mechanical shaft. The rotary axis servo motor 21 provides the torque required for the pitch servo system load through the reduction mechanism. The rotary axis absolute encoder 23 is connected to the right transmission mechanism at the rotary shaft of the heavy-duty rocker arm 3 via a mechanical shaft and is used to monitor the real-time angle of the heavy-duty rocker arm 3.

[0028] The heavy-duty rocker arm 3 is driven by the EHA drive system 1 and the rotary axis electric servo system 2. This system is based on an adaptive self-disturbance rejection composite control method and can achieve agile and high-precision servo function in the pitch direction.

[0029] Combination Figure 3 A control method for an active balancing, high-efficiency, and high-precision hydraulic-electric hybrid drive pitch servo system includes the following steps:

[0030] Step 1: Establish a mathematical model for the hydraulic-electric hybrid drive heavy-duty rocker arm pitch servo system. The steps are as follows:

[0031] Step 1.1: The heavy-duty rocker arm pitch servo system adopts a pump-controlled hydraulic cylinder and a rotary shaft motor for combined drive. The hydraulic cylinder adopts a three-hinged direct-push layout. The torque balance equation of the heavy-duty rocker arm pitch servo system is established according to Newton's second law:

[0032]

[0033] Mode middle, This represents the equivalent moment of inertia of the pitch servo system load relative to the rotation axis. , , These are the load angle, angular velocity, and angular acceleration of the pitch servo system; This indicates the driving torque exerted on the rotating shaft by the rotary motor via a reducer. This refers to the driving force of the hydraulic cylinder acting on the pitch servo system, i.e., the hydraulic cylinder thrust. This refers to the lever arm length relative to the rotation axis when the hydraulic cylinder exerts thrust. For the pitch servo system load torque; The frictional resistance torque experienced by the pitch servo system during rotary motion; This represents the total disturbance term consisting of other unmodeled terms and external disturbances. It is a time variable;

[0034] The method for determining the parameters in the torque balance equation of a heavy-duty rocker arm pitch servo system is as follows:

[0035] Based on the geometric relationship between the load of the pitch servo system and the hydraulic cylinder, the distance between the upper and lower pivot points of the hydraulic cylinder in the system's working state is calculated using the law of cosines:

[0036]

[0037] Mode middle The distance between the upper and lower fulcrum points of the hydraulic cylinder during system operation; This is the distance from the upper fulcrum of the hydraulic cylinder to the rotating shaft. This is the distance from the lower fulcrum of the hydraulic cylinder to the rotating shaft; The horizontal angle between the lower fulcrum of the hydraulic cylinder and the rotating shaft; The angle between the line connecting the upper fulcrum of the hydraulic cylinder to the rotation axis and the axis of the cylinder body;

[0038] Similarly, we can obtain

[0039]

[0040] Mode middle The distance between the upper and lower fulcrums of the hydraulic cylinder in the initial state of the system; The initial angle of the pitch servo system load.

[0041] According to the formula , Calculations yielded

[0042]

[0043] Mode middle This refers to the displacement of the piston in the hydraulic cylinder.

[0044] By adjusting the formula The displacement of the piston in the hydraulic cylinder relative to the load angle of the pitch servo system By taking the partial derivative, we can obtain the lever arm length relative to the rotation axis when the hydraulic cylinder thrusts. for

[0045]

[0046] Write out the specific formula The pitch servo system load gravity torque as follows:

[0047]

[0048] Mode middle The total mass of the pitch servo system load; It is the acceleration due to gravity; This is the distance from the center of mass of the load in the pitch servo system to the rotation axis; The angle between the line connecting the load center of mass of the pitch servo system to the rotation axis and the axis of the body tube.

[0049] Considering viscous friction and Coulomb friction effects, the specific formula is written as follows: Frictional resistance torque experienced by the pitch servo system during rotational motion as follows:

[0050]

[0051] Mode middle The coefficient of viscous friction representing the pitch motion of the pitch servo system; This represents the Coulomb friction torque of the pitch servo system during pitch motion, where... Let be the Coulomb friction amplitude. To approximate the sign function The continuous approximate Coulomb friction shape function.

[0052] Ignoring the transmission efficiency of the transmission components between the rotary motor shaft and the load rotary shaft of the heavy-duty rocker arm pitch servo system, we can obtain the driving torque that the rotary motor, through the reduction mechanism, acts on the rotary shaft. for:

[0053]

[0054] Mode middle, The reduction ratio at the load end of the rotary axis rotary motor and the heavy-duty rocker arm pitch servo system; This provides the output torque for the rotary motor rotating the shaft.

[0055] Ignoring the effects of the hydraulic cylinder piston's inertial force and friction on the system's motion, the driving force of the hydraulic cylinder acting on the pitch servo system is obtained. for:

[0056]

[0057] Mode middle, This is the hydraulic cylinder driving force coefficient, representing the number of parallel hydraulic cylinders in the heavy-duty rocker arm pitch servo system; The pressure in the rodless chamber of the hydraulic cylinder. The pressure in the rod chamber of the hydraulic cylinder; This refers to the piston working area of ​​the rodless chamber in the hydraulic cylinder. This refers to the piston working area of ​​the rod chamber in the hydraulic cylinder.

[0058] Step 1.2: Establish the motion equations for the rotary motor on the rotating shaft, as follows:

[0059] The rotary motor of the rotary axis directly drives the load of the heavy-duty rocker arm pitch servo system through a rigid reduction mechanism. Considering that the electromagnetic time constant is much smaller than the mechanical time constant, and the current loop response speed is much greater than the speed and position response speed, the dynamics of the current loop can be ignored. The control strategy of zero d-axis current commonly used in industry can be adopted, and the q-axis current of the rotary motor of the rotary axis can be regarded as the ideal control input.

[0060] Therefore, according to Newton's second law, the equation of motion for the rotary motor with a rotating shaft is as follows:

[0061]

[0062] Mode middle, This represents the moment of inertia of a rotary motor with a rotating shaft. , , These are the rotation angle, angular velocity, and angular acceleration of the rotary motor on the rotating shaft, respectively. This indicates the torque coefficient of a rotary motor with a rotating shaft. It is the control input q-axis current of the rotary motor; This represents the coefficient of viscous friction of a rotary motor with a rotating shaft. This is the output torque of the rotary motor shaft.

[0063] Step 1.3: Based on the torque balance equation of the heavy-duty rocker arm pitch servo system and the motion equation of the rotary axis rotary motor, establish the equivalent single-degree-of-freedom heavy-duty rocker arm pitch servo system torque balance equation, as follows:

[0064] Treating all transmission devices in the entire heavy-duty rocker arm pitch servo system as rigid bodies, meaning they do not undergo any elastic deformation when transmitting torque, and ignoring the influence of backlash characteristics on the motion relationship between the rotary axis motor and the load of the heavy-duty rocker arm pitch servo system throughout the entire transmission process, the rotation angle of the rotary axis motor can be obtained. Rotary shaft motor rotational angular velocity Rotary shaft motor angular acceleration With the load angle of the heavy-duty rocker arm pitch servo system Pitch servo system load angular velocity Pitch servo system load angular acceleration The relationship between them is as follows:

[0065]

[0066] According to the formula , , , , , , The torque balance equations for the equivalent single-degree-of-freedom heavy-load rocker arm pitch servo system are obtained as follows:

[0067]

[0068] Mode middle, , is the equivalent rotational inertia of a single-degree-of-freedom system; , is the equivalent moment coefficient; , is the equivalent viscous friction coefficient of a single-degree-of-freedom system.

[0069] Step 1.4: Establish the dynamic equation for hydraulic cylinder pressure, as follows:

[0070] To facilitate the establishment of the dynamic equation for hydraulic cylinder pressure, the following assumptions are made:

[0071] Assumption 1: Neglect internal and external leakage in the hydraulic cylinder;

[0072] Assumption 2: Neglect pipeline pressure loss and hydraulic cylinder port pressure drop;

[0073] Assumption 3: The bulk modulus of the oil is constant, and the elastic deformation of the oil in the rodless chamber of the hydraulic cylinder is ignored;

[0074] Assumption 4: The pressure at the oil port connecting the oil pump and the oil tank is one standard atmosphere;

[0075] The rodless chamber of the hydraulic cylinder used in this hydraulic-electric hybrid drive heavy-duty rocker arm pitch servo system is connected to the oil port of the air bladder accumulator through a pipeline, and the rod chamber is connected to the oil port of the motor direct drive pump. The pressure of the two working chambers can be obtained through feedback from pressure sensors.

[0076] set up( , This represents the initial state of the accumulator airbag. This represents the initial pressure of the accumulator airbag. Let (the initial volume of the accumulator airbag; let () , This indicates the operating status of the accumulator airbag. The pressure of the accumulator airbag during operation. The working volume of the accumulator airbag; during rapid turning of the heavy-duty rocker arm pitch servo system, the gas inside the accumulator airbag can be considered an adiabatic process, according to the gas state equation...

[0077]

[0078] Mode middle, Indicates the gas index; Represents a constant;

[0079] Based on existing assumptions, the pressure in the rodless chamber of the hydraulic cylinder can be determined. With accumulator airbag pressure Since the accumulator airbag volume increment is equal to the sum of the hydraulic cylinder rodless chamber volume increments, the working volume of the accumulator airbag can be obtained as follows:

[0080]

[0081] In the electro-hydraulic system, the servo motor has a higher response bandwidth than other components, therefore its rotational speed can be approximated as an ideal control input. Based on existing assumptions, ignoring the influence of external leakage from the oil pump, the rod chamber pressure P of the hydraulic cylinder is established. B The dynamic equations are as follows:

[0082]

[0083] Mode middle, It is the total control volume of the rod-side chamber of the hydraulic cylinder. It is the initial volume of the rod chamber of the hydraulic cylinder; The effective bulk modulus of hydraulic oil; It is the displacement of the fixed displacement pump; It is the rotational speed of the pump-controlled servo motor; It is the internal leakage coefficient of the oil pump; This is to account for the dynamic modeling error of hydraulic cylinder pressure caused by factors such as unmodeled dynamics.

[0084] The torque balance equation of the equivalent single-degree-of-freedom heavy-load rocker arm pitch servo system and the pressure dynamic equation of the hydraulic cylinder constitute the hydraulic-electric hybrid pitch servo system model.

[0085] Step 1.5: Rewrite the hydraulic-electric hybrid pitch servo system model into a state-space equation, i.e., the mathematical model of the hydraulic-electric hybrid drive heavy-duty rocker arm pitch servo system, as follows:

[0086] Define system state variables: ,in For the pitch servo system load angle position variables, For the pitch servo system load angular velocity variable, The thrust variable in the rod chamber of the hydraulic cylinder can be described by the system's state equation as follows:

[0087]

[0088] Mode middle, Intermediate variable function intermediate variable function intermediate variable function intermediate variable function intermediate variable function intermediate variable function ; Function of intermediate variables regarding system disturbance terms , ; , All are intermediate variables.

[0089] Step 2, Design the projection mapping function and the adaptive parameter law function: Design the adaptive law function so that the controller can learn unknown system parameters online while running, and design the projection mapping function to ensure that the adaptive parameter learning results are bounded; specifically including the following steps:

[0090] Step 2.1: Define the unknown system parameter vector Unknown system parameters The estimated value is defined as , This indicates the parameter estimation error.

[0091] Step 2.2: To facilitate subsequent controller design, based on practical engineering experience, the following assumptions are made:

[0092] Assumption 1: Desired position command trajectory Third-order continuously differentiable; the current output of the rotary shaft motor is within the limiting range; the pressure in both chambers of the hydraulic cylinder is within the limiting range;

[0093] Assumption 2: Defined unknown system parameter vector It is bounded. ,in , yes The known upper and lower bounds, and Parameters The minimum and maximum values, .

[0094] Assumption 3: System disturbance , They are all bounded, that is... , , , , is a positive constant.

[0095] Step 2.3: Define a discontinuous projection mapping function to ensure that the adaptive parameter result is bounded.

[0096]

[0097] in , Representing vectors The Each component.

[0098] Step 2.4: Design an adaptive law function based on the discontinuous projection mapping function.

[0099]

[0100] in ; It is a positive definite diagonal adaptive parameter gain matrix; This is an adaptive function that will be designed later. For any adaptive function... The following conditions must be met:

[0101] ;

[0102] ;

[0103] Step 3, Dual-channel extended state observer design: Based on active disturbance rejection control theory, extended state observers are designed for the equivalent single-degree-of-freedom pitch servo system load-motor system and the hydraulic cylinder rod chamber pressure system, respectively, to estimate system uncertainty disturbances and facilitate feedforward compensation for subsequent control. This includes the following steps:

[0104] Disturbance of the system , Each is expanded into an extended state of the system. , .make , They represent , The rate of change, i.e. , Hypothesis function , It is unknown but bounded. Then, based on the system model... Design two linearly extended state observers as follows:

[0105]

[0106]

[0107] Mode , middle, , , These are the system states. , , The estimated value; , These are the expansion states. , Estimates of (system disturbances); This indicates the estimation error of the above estimates; and These are parameters that need to be tuned, and can be considered as the bandwidth of two linearly extended state observers.

[0108] According to the formula , , The dynamics of the state estimation error can be given by the following equation.

[0109]

[0110]

[0111] Mode , middle, , ,

[0112] ,

[0113] , , Due to the matrix and Since it is a Herwitz matrix, there must exist two positive definite matrices. and They respectively satisfy the following properties related to the Lyapunov equations. , ,in Represents the identity matrix. Matrix and It can be solved from the above formula.

[0114] , ;

[0115] Step 4, Controller Design: Based on the estimations of system uncertainties and unknown system parameters from Steps 2 and 3, a control law is designed using the backstepping framework, employing a feedforward approach to compensate for system disturbances. The controller aims to achieve excellent tracking performance for arbitrary smooth position commands. Based on the driving characteristics of the hydraulic cylinder and the rotary shaft motor, task planning and controller design are performed for both, as detailed below:

[0116] Step 4.1: Design of the hydraulic cylinder pump control motor speed controller

[0117] Based on the characteristic differences between the hydraulic cylinder and the rotary motor of the rotary axis in the hydraulic-electric hybrid drive pitch servo system, the hydraulic cylinder has a lower natural frequency than the servo motor, but a higher power-to-weight ratio. Therefore, the task of the hydraulic cylinder is to balance the load torque of the pitch servo system in real time. Based on the above description, the ideal hydraulic cylinder rod chamber thrust command can be obtained as follows:

[0118]

[0119] Mode middle, It is the desired thrust command for the rod chamber of the hydraulic cylinder; the pressure for the rodless chamber of the hydraulic cylinder. The change is continuous and bounded, and can be obtained through feedback from a pressure sensor; the load angle position variable of the pitch servo system. This can be obtained through feedback from an angle sensor; the changes are continuous and bounded. As mentioned earlier... It is a bounded, continuously differentiable thrust command signal that is related to the real-time state of the system.

[0120] definition To address the tracking error of the thrust in the rod chamber of the hydraulic cylinder, according to formula... The third equation in the equation, for Regarding time Taking the derivative, we get:

[0121]

[0122] Mode middle, For the thrust command of the rod chamber of the hydraulic cylinder, the time... The derivative;

[0123] According to the formula The hydraulic cylinder pump control motor speed controller is designed as follows:

[0124]

[0125] Mode middle, For linear robust feedback terms, A positive adjustable feedback gain. For unknown parameters of the system A lower bound on the given numerical value; This is a feedforward compensation term based on the thrust model of the rod chamber of a hydraulic cylinder. Unknown parameters of the system The estimated value, Unknown parameters of the system The estimated value;

[0126] Step 4.2: Design of the virtual control law for the angular velocity of the load-motor system of the equivalent single-degree-of-freedom pitch servo system.

[0127] definition This refers to the system's angular position tracking error; The desired angle and position command. For the desired angular velocity command, similarly, The desired angular acceleration command;

[0128] According to the formula The first equation in the equation, for Regarding time Taking the derivative, we get

[0129]

[0130] Select As a virtual control object, let for The virtual control law is defined. The tracking error between the two is substituted into the formula. achievable

[0131]

[0132] According to the formula ,design The virtual control law is as follows:

[0133]

[0134] Mode middle, For a positive adjustable feedback gain, the equation is... Substitution We can obtain:

[0135]

[0136] because In the formula It is a stable transfer function, when When it approaches 0, It will inevitably approach 0, so the following design goal is to make Approaching 0;

[0137] Step 4.3: Design of the current controller for the rotary shaft motor

[0138] According to the formula The second equation in the equation, with respect to z2 with respect to time Taking the derivative, we get

[0139]

[0140] Mode middle, System status Virtual control law about time The derivative;

[0141] According to the formula The current controller for the rotary shaft motor is designed as follows:

[0142]

[0143] Mode middle, For linear robust feedback terms, A positive adjustable feedback gain; For model-based feedforward compensation terms;

[0144] Given an adaptive function with unknown system parameters:

[0145]

[0146] Mode middle, and The positive parameter is the coordination coefficient of the adaptive function. , where is the parameter adaptive regression function; in summary, the design of the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system controller is completed. The desired angle command of the pitch servo system load, the real-time feedback of the pitch servo system load angle and angular velocity values ​​from the rotary axis absolute encoder, and the real-time feedback of the pressure values ​​from the rodless and rod-side pressure sensors of the hydraulic cylinder are input to the controller. The controller internally generates accurate model-based feedforward compensation terms based on the system's unknown parameter adaptive mechanism and dual-channel state observer disturbance estimation. It utilizes command tracking errors to construct feedback robust terms, generating current commands for the rotary axis motor and speed commands for the hydraulic cylinder pump-controlled motor as control inputs for both. The rotary axis motor outputs driving torque, and the EHA system outputs hydraulic driving force; both act together on the pitch servo system load, achieving hydraulic-electric system drive control of the pitch servo system.

[0147] This invention balances high load-bearing capacity and high dynamic response performance, proposing a novel pitch servo system that integrates the advantages of both: an EHA-driven support cylinder and a hybrid drive system using a rotary axis motor. The EHA system actively compensates for the weight balance and static support of the barrel, and the volumetric control-based servo cylinder system significantly reduces energy consumption compared to traditional valve-controlled hydraulic systems with throttling control. Simultaneously, the rotary axis motor provides rapidly changing pitch torque, achieving high-precision attitude control.

[0148] Due to its configuration characteristics, the aforementioned hybrid drive servo system is subject to multiple disturbances and uncertainties during operation, such as changes in gravitational torque, frictional nonlinearity, hydraulic pressure fluctuations, gear meshing fluctuations, and external impacts. These factors lead to continuous deviations in the system model, which are the main sources affecting attitude accuracy and control stability. Therefore, considering the unique characteristics of this special drive system, including complex multiple disturbances and uncertainties, a multi-channel extended state observer needs to be designed to achieve hierarchical estimation and decoupling compensation of disturbances at each level. On the other hand, considering the time-varying and uncertain nature of system parameters, an adaptive law for dynamic error driving is established to achieve online identification and dynamic updating of key parameters, thereby mitigating the impact of model mismatch on the performance of the hybrid drive. By integrating observation and adaptive mechanisms into the control law design, the disturbance estimation and parameter update processes share state information, reducing the observer's burden and improving the system's identification accuracy and dynamic robustness. This method can maintain high-precision and robust attitude control performance of the heavy-duty rocker arm pitch servo system under complex disturbances and time-varying parameter conditions.

[0149] Example

[0150] To verify the performance of the designed controller, the following physical parameters were used in the simulation to model the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system:

[0151] Table 1. Overview of Modeling Physical Parameters

[0152]

[0153] The system expects the position command to be selected as follows: .

[0154] The following controller is used for comparison in the simulation:

[0155] Composite Adaptive Robust Controller (CARC) based on extended state observer: The control gain is set to k1=10, k2=2, k4=20; the extended state observer gain is set to... , Take the approximate Coulomb friction shape function as: Take the initial values ​​of the parameter estimates. ; range of unknown system parameters , Take the parameter adaptive gain matrix Take the adaptive function coordination coefficient. , .

[0156] Model-Based Velocity Feedforward PI Controller (MBVFPI): Based on the geometric relationship between the pitch servo system load and the drive components, it calculates in real time the desired speed of the rotary axis motor and the desired flow compensation speed of the pump-controlled motor according to the system's desired position command. These speed feedforward commands are used as the speed feedforward commands for both motors. The rotary axis motor, combined with the position loop proportional controller and the speed loop proportional-integral controller, provides the final command current. The pump-controlled motor, combined with the pressure loop proportional-integral controller, provides the final command speed. The selected controller parameters are as follows: rotary axis motor position loop gain k... TP =2; Rotary shaft motor speed loop gain k WP =2.17, k WI =1.26; Pump-controlled motor pressure loop gain k PP =2,k PI =1.

[0157] The system output tracking effect of the CARC controller on the desired instruction is as follows: Figure 4 As shown, the tracking error of the CARC controller is as follows: Figure 5 As shown, the tracking comparison between the CARC controller and the MBVFPI controller is as follows: Figure 6 As shown. By Figure 4 and Figure 5 It can be seen that, under the action of the CARC controller, the actively balanced, high-efficiency, high-precision hydraulic-electric hybrid drive pitch servo system achieved good tracking accuracy, with a steady-state tracking error amplitude of approximately 2.218 × 10⁻⁶. -4 rad, from Figure 6 The comparison of the tracking errors of the two controllers shows that the tracking error of the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system proposed in this invention is much smaller under the action of the CARC controller than that of the MBVFPI controller. Due to the online adaptive parameter adjustment and the feedforward compensation of the output disturbance of the extended state observer in the control law, the impact of structural uncertainty and other uncertainty disturbances caused by the system model parameter error on the system control performance can be effectively reduced.

[0158] Figure 7 and Figure 8 These are the system unknown parameters. and The curves showing how the estimated values ​​change over time demonstrate that the estimated parameters in the CARC controller can converge well over time.

[0159] In summary, the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system and its composite adaptive robust control method described in this invention can achieve high-precision and agile turning of heavy-duty rocker arms.

Claims

1. A high-efficiency, high-precision, actively balanced hydraulic-electric hybrid drive pitch servo system, characterized in that, include: The system consists of an EHA drive system (1), a rotary axis electric servo system (2), and a heavy-duty rocker arm (3). Both the EHA drive system (1) and the rotary axis electric servo system (2) are connected to the heavy-duty rocker arm (3). The EHA drive system (1) adopts a three-hinge direct-drive layout. The rotary axis electric servo system (2) is directly arranged on the rotation axis of the heavy-duty rocker arm (3). The EHA drive system (1) and the rotary axis electric servo system (2) work together as two independent subsystems to drive the heavy-duty rocker arm (3) to complete the task.

2. The active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system according to claim 1, characterized in that, The EHA drive system (1) includes an EHA servo motor (11), an EHA bidirectional constant displacement pump (12), a hydraulic oil tank (13), a pneumatic accumulator group (14), and an EHA asymmetric single-rod hydraulic cylinder (16). The EHA servo motor (11) is coaxially connected to the EHA bidirectional constant displacement pump (12). The EHA bidirectional constant displacement pump (12) includes two working oil ports, A and B. When the EHA servo motor (11) rotates forward, port A of the EHA bidirectional constant displacement pump (12) is the oil inlet and port B is the oil outlet. When the EHA servo motor (11) rotates in reverse, port A of the EHA bidirectional constant displacement pump (12) is the oil outlet and port B is the oil inlet. Port A is connected to the rod chamber port of the EHA asymmetric single-rod hydraulic cylinder (16) via a pipeline to provide the pressure and flow required by the EHA drive system (1). Port B of the EHA bidirectional constant displacement pump (12) is connected to the hydraulic oil tank (13) via a pipeline. The hydraulic oil tank (13) serves to store hydraulic oil. The airbag accumulator group (14) is connected to the rodless chamber port of the EHA asymmetric single-rod hydraulic cylinder (16) via a pipeline to provide the pressure and flow required by the EHA drive system (1). The rod end of the EHA asymmetric single-rod hydraulic cylinder (16) is hinged to the pitch servo system base. The cylinder end of the EHA asymmetric single-rod hydraulic cylinder (16) is hinged to the heavy-duty rocker arm (3).

3. The active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system according to claim 2, characterized in that, The EHA drive system (1) also includes a rod chamber pressure sensor (151) and a rodless chamber pressure sensor (152). The rod chamber pressure sensor (151) is installed on the connecting pipeline between the EHA bidirectional constant displacement pump (12) and the EHA asymmetric single rod hydraulic cylinder (16) to monitor the real-time pressure of the rod chamber of the EHA asymmetric single rod hydraulic cylinder (16). The rodless chamber pressure sensor (152) is installed on the connecting pipeline between the airbag accumulator group (14) and the EHA asymmetric single rod hydraulic cylinder (16) to monitor the real-time pressure of the rodless chamber of the EHA asymmetric single rod hydraulic cylinder (16).

4. The active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system according to claim 1, characterized in that, The rotary axis electric servo system (2) includes a rotary axis servo motor (21), a rotary axis reducer (22), and a rotary axis absolute encoder (23). The rotary axis servo motor (21) is connected to the input end of the rotary axis reducer (22) through a mechanical shaft. The output end of the rotary axis reducer (22) is connected to the transmission structure at the rotary shaft of the heavy-duty rocker arm (3) through a mechanical shaft. The rotary axis absolute encoder (23) is connected to the transmission mechanism at the rotary shaft of the heavy-duty rocker arm (3) through a mechanical shaft and is used to monitor the real-time angle of the heavy-duty rocker arm (3).

5. A control method for an active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system as described in any one of claims 1 to 4, characterized in that, Includes the following steps: Step 1: Establish a mathematical model for the hydraulic-electric hybrid drive heavy-duty rocker arm pitch servo system; Step 2: Design a discontinuous projection mapping function to achieve bounded adaptive parameter learning results. Based on the discontinuous projection mapping function, design an adaptive law function so that the controller can learn the unknown parameters of the system online while running. Step 3: Based on active disturbance rejection control theory, extended state observers are designed for the equivalent single-degree-of-freedom pitch servo system load motor system and the hydraulic cylinder rod chamber pressure system, respectively. The extended state observers are used to estimate the system's uncertainty disturbances. Step 4: Based on the estimation of system uncertainty disturbances and unknown system parameters in Steps 2 and 3, design the control law according to the backstepping framework, and adopt the feedforward method to compensate for system disturbances; based on the driving characteristics of the hydraulic cylinder and the rotary shaft motor, perform task planning and controller design for both, and use the controller to achieve the system's tracking effect on arbitrary smooth position commands.

6. The control method for the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system according to claim 5, characterized in that, The specific method for establishing the mathematical model of the hydraulic-electric hybrid drive heavy-duty rocker arm pitch servo system is as follows: Step 1.1: Establish the torque balance equation for the heavy-duty rocker arm pitch servo system based on Newton's second law, specifically: In the formula, This represents the equivalent moment of inertia of the pitch servo system load relative to the rotation axis. , , These are the load angle, angular velocity, and angular acceleration of the pitch servo system; This indicates the driving torque exerted on the rotating shaft by the rotary motor via a reducer. The driving force of the hydraulic cylinder acting on the pitch servo system; This refers to the lever arm length relative to the rotation axis when the hydraulic cylinder exerts thrust. For the pitch servo system load torque; The frictional resistance torque experienced by the pitch servo system during rotary motion; This represents the total disturbance term consisting of other unmodeled terms and external disturbances. It is a time variable; Step 1.2: Establish the motion equations for the rotary motor on the rotating shaft, specifically as follows: In the formula, This represents the moment of inertia of a rotary motor with a rotating shaft. , , These are the rotation angle, angular velocity, and angular acceleration of the rotary motor on the rotating shaft, respectively. This indicates the torque coefficient of a rotary motor with a rotating shaft. It is the control input q-axis current of the rotary motor; This represents the coefficient of viscous friction of a rotary motor with a rotating shaft. The output torque of the rotary motor shaft is for the rotating shaft; Step 1.3: Based on the torque balance equation of the heavy-duty rocker arm pitch servo system and the motion equation of the rotary axis rotary motor, establish the equivalent torque balance equation of the single-degree-of-freedom heavy-duty rocker arm pitch servo system, specifically as follows: In the formula, It is the equivalent rotational inertia of a single-degree-of-freedom system. These are the equivalent moment coefficients. It is the equivalent viscous friction coefficient of a single-degree-of-freedom system. This is the hydraulic cylinder driving force coefficient, representing the number of parallel hydraulic cylinders in the heavy-duty rocker arm pitch servo system; The pressure in the rodless chamber of the hydraulic cylinder. The pressure in the rod chamber of the hydraulic cylinder; This refers to the piston working area of ​​the rodless chamber in the hydraulic cylinder. This refers to the piston working area of ​​the rod chamber in a hydraulic cylinder. The total mass of the pitch servo system load; It is the acceleration due to gravity; This is the distance from the center of mass of the load in the pitch servo system to the rotation axis; The angle between the line connecting the load center of mass of the pitch servo system to the rotation axis and the axis of the body tube; This represents the Coulomb friction torque of the pitch servo system during pitch motion, where... Let be the Coulomb friction amplitude. To approximate the sign function A continuous approximate Coulomb friction shape function; Step 1.4: Establish the dynamic equation for hydraulic cylinder pressure, specifically as follows: It is the total control volume of the rod-side chamber of the hydraulic cylinder. It is the initial volume of the rod chamber of the hydraulic cylinder; The effective bulk modulus of hydraulic oil; It is the displacement of the fixed displacement pump; It is the rotational speed of the pump-controlled servo motor; It is the internal leakage coefficient of the oil pump; Errors in dynamic modeling of hydraulic cylinder pressure; The torque balance equation of the equivalent single-degree-of-freedom heavy-load rocker arm pitch servo system and the pressure dynamic equation of the hydraulic cylinder constitute the hydraulic-electric hybrid pitch servo system model. Step 1.5: Rewrite the hydraulic-electric hybrid pitch servo system model into a state-space equation, that is, the mathematical model of the hydraulic-electric hybrid drive heavy-duty rocker arm pitch servo system, specifically as follows: Define system state variables: ,in For the load angle position variables of the pitch servo system, For the pitch servo system load angular velocity variable, The thrust variable in the rod chamber of the hydraulic cylinder is described by the system's state equation as follows: In the formula, Intermediate variable function intermediate variable function intermediate variable function intermediate variable function intermediate variable function intermediate variable function ; Intermediate variable function of the system disturbance term , ; , All of these are intermediate variables.

7. The control method for the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system according to claim 6, characterized in that, The method for determining the parameters in the torque balance equation of a heavy-duty rocker arm pitch servo system is as follows: Based on the geometric relationship between the load of the pitch servo system and the hydraulic cylinder, the distance between the upper and lower pivot points of the hydraulic cylinder in the system's working state is calculated using the law of cosines: In the formula The distance between the upper and lower fulcrum points of the hydraulic cylinder during system operation; This is the distance from the upper fulcrum of the hydraulic cylinder to the rotating shaft. This is the distance from the lower fulcrum of the hydraulic cylinder to the rotating shaft; The horizontal angle between the lower fulcrum of the hydraulic cylinder and the rotating shaft; The angle between the line connecting the upper fulcrum of the hydraulic cylinder to the rotation axis and the axis of the cylinder body; The initial distance between the upper and lower fulcrums of the hydraulic cylinder is: In the formula The distance between the upper and lower fulcrums of the hydraulic cylinder in the initial state of the system; Initial angle of load for pitch servo system The calculated displacement of the hydraulic cylinder piston is as follows: In the formula, This refers to the displacement of the hydraulic cylinder piston. By controlling the displacement of the hydraulic cylinder piston relative to the load angle of the pitch servo system By taking the partial derivative, we can obtain the lever arm length relative to the rotation axis when the hydraulic cylinder thrust is applied. for Pitch servo system load torque Specifically: In the formula, The total mass of the pitch servo system load; It is the acceleration due to gravity; This is the distance from the center of mass of the load in the pitch servo system to the rotation axis; The angle between the line connecting the load center of mass of the pitch servo system to the rotation axis and the axis of the body tube; Frictional resistance torque experienced by the pitch servo system during rotational motion as follows: In the formula, The coefficient of viscous friction representing the pitch motion of the pitch servo system; This represents the Coulomb friction torque of the pitch servo system during pitch motion, where... Let be the Coulomb friction amplitude. To approximate the sign function A continuous approximate Coulomb friction shape function; Ignoring the transmission efficiency of the transmission components between the rotary motor shaft and the load rotary shaft of the heavy-duty rocker arm pitch servo system, we obtain the driving torque that the rotary motor, transmitted through the reduction mechanism, acts on the rotary shaft. for: In the formula, The reduction ratio at the load end of the rotary axis rotary motor and the heavy-duty rocker arm pitch servo system; The output torque of the rotary motor is for the rotating shaft; Ignoring the effects of the hydraulic cylinder piston's inertial force and friction on the system's motion, the driving force of the hydraulic cylinder acting on the pitch servo system is obtained. for: In the formula, This is the hydraulic cylinder driving force coefficient, representing the number of parallel hydraulic cylinders in the heavy-duty rocker arm pitch servo system; The pressure in the rodless chamber of the hydraulic cylinder. The pressure in the rod chamber of the hydraulic cylinder; This refers to the piston working area of ​​the rodless chamber in the hydraulic cylinder. This refers to the piston working area of ​​the rod chamber in a hydraulic cylinder.

8. The control method for the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system according to claim 6, characterized in that, The design of a discontinuous projection mapping function to achieve bounded adaptive parameter learning results, and the design of an adaptive law function based on the discontinuous projection mapping function to enable the controller to learn unknown system parameters online while running are as follows: Step 2.1: Define the unknown system parameter vector Unknown system parameters The estimated value is defined as , This indicates the parameter estimation error. Step 2.2, set the following assumptions: Assumption 1: Desired position command trajectory Third-order continuously differentiable; the current output of the rotary shaft motor is within the limiting range; the pressure in both chambers of the hydraulic cylinder is within the limiting range; Assumption 2: Defined unknown system parameter vector It is bounded. ,in , yes The known upper and lower bounds, and Parameters The minimum and maximum values, ; Assumption 3: Function of intermediate variables regarding the system disturbance term , They are all bounded, that is... , , , A positive constant that is set; Step 2.3: Design a discontinuous projection mapping function to ensure that the adaptive parameter result is bounded. in , Representing vectors The One component; Step 2.4: Design the adaptive law function based on the discontinuous projection mapping function: in ; It is a positive definite diagonal adaptive parameter gain matrix; It is an adaptive function; for any adaptive function It meets the following conditions: ； 。 9. The control method for the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system according to claim 8, characterized in that, Based on active disturbance rejection control theory, extended state observers are designed for the equivalent single-degree-of-freedom pitch servo system load motor system and the hydraulic cylinder rod chamber pressure system, respectively. The specific method is as follows: The intermediate variable function of the system disturbance term , Each is expanded into an extended state of the system. , ;make , They represent , The rate of change, i.e. , Hypothesis function , It is unknown but bounded. Based on the system's state equations, two linearly extended state observers are designed as follows: In the formula, , , They are , , The estimated value; , These are two linearly extended state observers, representing the extended states. , The estimated value; Indicates the estimation error; and These are the bandwidths of the two linearly extended state observers; The dynamics of the state estimation error are determined as follows: In the formula, , , , , , Due to the matrix and Since it is a Herwitz matrix, there must exist two positive definite matrices. and They respectively satisfy the following properties related to the Lyapunov equations. , ,in Represents the identity matrix; Solve the matrix and They are respectively: ， It is an identity matrix.

10. The control method for the active balancing high-efficiency and high-precision hydraulic-electric hybrid drive pitch servo system according to claim 9, characterized in that, Based on the estimation of system uncertainties and unknown system parameters in steps 2 and 3, a control law is designed according to the backstepping framework, and a feedforward approach is adopted to compensate for system disturbances. Based on the driving characteristics of the hydraulic cylinder and the rotary shaft motor, task planning and controller design are performed for both, respectively. The controller is used to achieve the system's tracking effect on arbitrary smooth position commands, specifically including: Step 4.1: Design the speed controller for the hydraulic cylinder pump control motor. The specific method is as follows: Based on the characteristic differences between the hydraulic cylinder and the rotary motor of the rotary axis in the hydraulic-electric hybrid drive pitch servo system, the thrust command of the rod chamber of the ideal hydraulic cylinder is obtained as follows: In the formula, It is the desired thrust command for the rod chamber of the hydraulic cylinder; This refers to the pressure in the rodless chamber of the hydraulic cylinder. For the load angle position variable of the pitch servo system, It is a bounded, continuously differentiable, and real-time state-dependent thrust command for the rod chamber of an ideal hydraulic cylinder. definition To address the tracking error of the thrust in the rod chamber of the hydraulic cylinder, Regarding time Differentiate: In the formula, For the thrust command of the rod chamber of the hydraulic cylinder, the time... The derivative; The hydraulic cylinder pump control motor speed controller is designed as follows: In the formula, For linear robust feedback terms, A positive adjustable feedback gain. For unknown parameters of the system A lower bound on the given numerical value; This is a feedforward compensation term based on the thrust model of the rod chamber of a hydraulic cylinder. Unknown parameters of the system The estimated value, Unknown parameters of the system The estimated value; Step 4.2: Design the virtual control law for the angular velocity of the load-motor system of the equivalent single-degree-of-freedom pitch servo system. The specific method is as follows: definition This refers to the system's angular position tracking error; The desired angle and position command. For the desired angular velocity command, similarly, The desired angular acceleration command; right Regarding time Differentiate: Select As a virtual control object, let for The virtual control law is defined. The tracking error between the two is obtained. design The virtual control law is as follows: In the formula, For a positive adjustable feedback gain, we get: Step 4.3: Design the current controller for the rotary shaft motor. The specific method is as follows: Regarding z2 with respect to time Differentiate: In the formula, System status Virtual control law regarding time The derivative; The current controller for the rotary shaft motor is designed as follows: In the formula, For linear robust feedback terms, A positive adjustable feedback gain; For model-based feedforward compensation terms; Given an adaptive function with unknown system parameters: In the formula, and The positive parameter is the coordination coefficient of the adaptive function. For parameterized adaptive regression functions.

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