An adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system

Abstract

The application discloses a kind of self-adapting loading control methods of distributed pump control direct drive electro-hydraulic system, S1, the nonlinear state space model of each execution unit is established;S2, the distributed hierarchical control architecture is constructed;S3, switching function is constructed;S4, output updated parameter estimate;S5, construct loading force nonlinear observer, real-time estimate external time-varying load force;S6, generate comprehensive control instruction and output to servo motor driver;S7, the global performance index is the dimensionless comprehensive evaluation index after normalizing to each sub-item.Processing.The application organically fuses sliding mode control, adaptive control and feedforward compensation into three-channel composite control architecture, three control quantities correspond to the transient response stage, steady-state operation stage and disturbance response stage of system respectively, which are naturally decoupled in time scale and complementary in function, and the sliding mode control ensures global stability and transient response quality under wide range of working conditions.

Description

Technical Field

[0001] This application belongs to the field of electro-hydraulic servo control technology, specifically relating to an adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system. Background Technology

[0002] Pump-controlled direct drive (also known as volumetric speed control) technology directly drives a fixed-displacement pump to supply oil to the hydraulic cylinder via a servo motor. This replaces the throttling control in traditional valve-controlled systems with motor speed regulation, fundamentally eliminating throttling and overflow losses. It offers significant advantages such as high efficiency, low heat generation, and compact structure. As electro-hydraulic systems evolve towards multi-actuator and high integration, distributed pump-controlled direct drive electro-hydraulic systems, where each actuator is driven by an independent servo motor-fixed-displacement pump assembly, have become an important development direction in the field of electro-hydraulic transmission.

[0003] However, existing distributed pump-controlled direct-drive electro-hydraulic systems and their control methods still have the following technical shortcomings:

[0004] First, traditional centralized control architectures struggle to meet the real-time, reliability, and scalability requirements of multi-actuator systems. Current technologies for multi-actuator electro-hydraulic systems often employ a single controller for centralized control. In a centralized architecture, the controller must simultaneously handle signal acquisition, control calculations, and command output from all actuators. As the number of actuators increases, the controller's computational load rises sharply, easily leading to computational delays and data congestion. More critically, centralized architectures suffer from single-point-of-failure risks; if the main controller fails, the entire system will be paralyzed, resulting in low reliability and scalability.

[0005] Second, pump-controlled direct-drive electro-hydraulic systems exhibit strong nonlinearity and time-varying parameter characteristics, making it difficult for traditional fixed-parameter controllers to maintain high-precision control across the entire operating range. During system operation, the effective bulk modulus of the oil changes significantly with oil temperature and air ingress, the leakage coefficient drifts with piston wear and operating pressure fluctuations, and the viscous damping coefficient exhibits nonlinear time-varying characteristics with oil viscosity. These parameter perturbations cause a persistent deviation between the system's mathematical model and the actual system, which conventional PID controllers, due to their fixed parameters, cannot adapt to. While existing research has attempted to address parameter uncertainty using adaptive backstepping methods, these approaches are mostly limited to single-actuator systems and fail to solve the problems of parameter differentiation and collaborative estimation in multi-actuator scenarios.

[0006] Third, external load disturbances are one of the most significant sources of disturbance affecting system control accuracy, and existing methods lack efficient real-time load estimation and active compensation mechanisms. In actual operation, the external load force borne by each actuator in a distributed pump-controlled direct-drive electro-hydraulic system fluctuates in real time with changes in operating conditions and is difficult to measure directly using sensors. Installing additional force sensors on each actuator would not only significantly increase hardware costs but also introduce additional measurement noise and latency. Existing technologies mostly employ error-based feedback control to passively suppress disturbances, meaning corrections are only made after the disturbance has caused position or pressure deviations, which is insufficient to meet the demands of high-precision control.

[0007] Fourth, the coordination and control problem among multiple actuators has not yet been effectively solved. In distributed pump-controlled direct-drive electro-hydraulic systems, each actuator is driven by an independent servo motor-displacement pump assembly. While this eliminates the throttling losses of centralized hydraulic systems, it also introduces new challenges regarding how the actuators can work collaboratively and achieve displacement synchronization and load balancing. When an actuator experiences a large displacement deviation due to sudden changes in external load or parameter perturbations, the lack of effective information transmission and collaborative correction mechanisms leads to a decline in overall coordination performance.

[0008] In summary, existing distributed pump-controlled direct-drive electro-hydraulic systems have significant shortcomings in terms of control architecture, parameter adaptation, load disturbance suppression, and multi-actuator coordination. There is an urgent need for a comprehensive control scheme that can balance system robustness, adaptability, and global coordination performance. Summary of the Invention

[0009] This application provides an adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system, aiming to solve the problems of low reliability of the existing centralized control architecture, decreased control accuracy due to time-varying parameters, lack of active compensation for external load disturbances, and difficulty in coordinating multiple actuators.

[0010] An adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system, the method being applied to a distributed hierarchical control architecture consisting of a central coordinator and multiple local controllers, the method comprising:

[0011] S1. Establish a nonlinear state-space model for each execution unit. The model takes the servo motor speed as the control input and the piston displacement, motion speed and two-chamber pressure as state variables. The model is rewritten into a strict feedback form that satisfies the design conditions of the adaptive backstepping method. The model parameter set and nonlinear function matrix of each execution unit are output.

[0012] S2, construct the distributed hierarchical control architecture, establish a data communication link between each local controller and the central coordinator, the central coordinator broadcasts the desired displacement signal and desired loading force signal to each local controller, each local controller uploads the real-time collected state variables of its execution unit to the central coordinator, the central coordinator calculates the global coordination error based on the state variables of each execution unit and feeds it back to each local controller, each local controller corrects the desired trajectory based on the global coordination error and outputs the corrected desired displacement signal and desired loading force signal;

[0013] S3, each local controller calculates the displacement tracking error and its rate of change based on the corrected expected displacement signal and the piston displacement signal fed back by the execution unit in real time, constructs the sliding mode switching function, and determines whether the sliding mode arrival condition is met. If it is not met, the fuzzy control softening module is triggered to intervene and outputs the displacement tracking error and the sliding mode switching function and its derivative.

[0014] S4, each local controller constructs a Lyapunov function based on the strict feedback state space model using an adaptive backstepping method, and derives the real-time online adaptive law of the system uncertainty parameters according to the displacement tracking error, updates and limits the parameters to be estimated for each execution unit online, and outputs the updated parameter estimates.

[0015] S5, each local controller constructs a loading force nonlinear observer based on the two-chamber pressure signals of its execution unit and the estimated parameter value, estimates the external time-varying load force in real time, and compares the estimated value with the expected loading force signal. When the loading force tracking error exceeds the preset threshold, the loading compensation module is triggered to output the feedforward compensation amount.

[0016] S6, each local controller integrates the sliding mode control quantity, the adaptive compensation quantity, and the feedforward compensation quantity to generate a comprehensive control command and output it to the servo motor driver. At the same time, it uploads the current control quantity and all state variables of the execution unit to the central coordinator.

[0017] S7, the central coordinator calculates the global performance index based on the displacement tracking error, loading force tracking error and control quantity uploaded by each execution unit. The global performance index is a dimensionless comprehensive evaluation index after normalizing each sub-item.

[0018] When the global performance index exceeds the preset threshold, the sliding mode control parameters, adaptive gain coefficient and / or feedforward compensation gain of the corresponding local controller are adjusted in a targeted manner according to the error distribution of each execution unit, and the updated controller parameters are sent to each local controller to realize online adaptive iterative optimization of the controller parameters.

[0019] The performance evaluation and parameter optimization process of the central coordinator is executed in parallel with the real-time control process of each local controller, and the triggering period of the performance evaluation and parameter optimization process is longer than the sampling period of the real-time control process.

[0020] Optionally, in S1, to address the flow asymmetry problem caused by the unequal effective areas of the two chambers of the asymmetric hydraulic cylinder, the nonlinear state-space model is established based on configuring an oil replenishment module composed of a hydraulically controlled check valve and a check valve, and a safety pressure stabilizing module composed of an overflow valve in each execution unit.

[0021] The established model was transformed and rewritten into a strict feedback form, which contains five system parameters, laying the model foundation for the subsequent design of the adaptive backstepping controller.

[0022] Optionally, in S2, the distributed hierarchical control architecture adopts a two-layer structure of "central coordinator-local controller", and the central coordinator forms a star-topology real-time data communication network with each local controller through industrial Ethernet.

[0023] The central coordinator broadcasts the desired signal to each local controller at a fixed sampling period, and each local controller uploads the state variables in an aperiodic asynchronous transmission manner.

[0024] The global coordination error reflects the average deviation of the displacement of each execution unit relative to the expected value. Each local controller corrects its own expected displacement based on the global coordination error. The corrected expected displacement signal is the difference between the broadcast expected displacement signal and the product of the coordination gain coefficient and the global coordination error.

[0025] Optionally, in S3, each local controller performs numerical differentiation processing on the displacement tracking error using backward differential combined with low-pass filtering, and performs amplitude limiting processing on the calculated error change rate.

[0026] The sliding mode switching function is the sum of the sliding surface slope coefficient and the displacement tracking error, plus the error change rate;

[0027] The sliding mode arrival condition is that the product of the sliding mode switching function and its derivative is less than zero.

[0028] Optionally, in step S4, the parameters to be estimated include the ratio of viscous damping coefficient to load mass, the effective bulk elastic modulus of the oil, and the product of the effective bulk elastic modulus of the oil and the leakage coefficient.

[0029] Each local controller defines a virtual control quantity, a velocity tracking error, and a third error variable based on the displacement tracking error, and then constructs a Lyapunov candidate function that includes a system error state energy term and a parameter estimation error penalty term;

[0030] The parameter adaptive law for each parameter to be estimated is obtained by taking the derivative of the Lyapunov candidate function and setting the coefficient of the cross term containing the parameter estimation error to zero. The parameter adaptive law is discretized by the Euler forward difference method for each local controller, and the parameter estimate is constrained after each update.

[0031] Optionally, in S5, the loading force nonlinear observer estimates the external load force based on the driving force generated by the pressure difference between the two chambers of the hydraulic cylinder after deducting the remaining part used to overcome inertial force, viscous damping force and elastic force.

[0032] Each local controller uses a tracking differentiator for filtering when calculating piston acceleration;

[0033] The loading compensation module calculates the feedforward compensation amount based on the magnitude and direction of the loading force tracking error. The feedforward compensation amount is the product of the feedforward compensation gain coefficient and the loading force tracking error.

[0034] Optionally, in step S6, the sliding mode control quantity is calculated based on the sliding mode switching function, and a saturation function is used instead of the standard sign function to suppress high-frequency chattering;

[0035] The adaptive compensation term performs reverse compensation on the unknown parameter terms in the state equation based on the parameter estimate value of S4, in order to eliminate the impact of internal parameter uncertainty on control accuracy.

[0036] The feedforward compensation is superimposed on the sliding mode control and adaptive compensation to suppress external time-varying load disturbances.

[0037] The three control quantities are combined into a comprehensive control command according to the principle of linear superposition. The comprehensive control command is then processed by amplitude limiting and rate of change limiting before being output to the servo motor driver.

[0038] Optionally, in S7, the global performance index is the weighted sum of the square of the displacement tracking error, the square of the loading force tracking error, and the square of the control quantity of each execution unit. After normalization, each item is a dimensionless pure value, and the global performance index is a dimensionless comprehensive evaluation index.

[0039] The central coordinator compares the global performance metrics with preset thresholds. When the thresholds are exceeded, it further analyzes the error distribution uploaded by each execution unit, identifies the execution unit and error type that caused the performance degradation, and executes a multi-condition branch parameter adjustment strategy accordingly.

[0040] For execution units with large displacement tracking errors, branch determination is based on the magnitude of the displacement tracking error:

[0041] (1) If the absolute value of the displacement tracking error is greater than the first preset threshold, it is determined that the control quantity is too large because the system has not yet converged, and the sliding mode control parameters and adaptive gain coefficient of the execution unit are increased.

[0042] (2) If the absolute value of the displacement tracking error is less than the second preset threshold and the control quantity exhibits high-frequency oscillation characteristics, it is determined that the system is close to the target position but there is chattering, and the sliding mode control parameters of the execution unit are reduced.

[0043] (3) If the absolute value of the displacement tracking error is between the second preset threshold and the first preset threshold, then the current parameters are kept unchanged;

[0044] Meanwhile, a monitoring criterion for the rate of change of the control quantity is added: if the rate of change of the control quantity exceeds the preset rate of change threshold, the boundary layer thickness in the sliding mode switching function is reduced first to enhance the ability to suppress high-frequency disturbances.

[0045] For execution units with large force tracking errors, increase the feedforward compensation gain;

[0046] After the central coordinator completes the parameter adjustment, it sends the updated controller parameter set to each local controller through the data communication link. Each local controller applies the updated parameters to the control law calculation in the next control cycle, thereby realizing online adaptive iterative optimization of the controller parameters.

[0047] When the global performance index is lower than the preset threshold for a predetermined number of consecutive sampling periods, the central coordinator determines that the system has entered a stable operating state and stops parameter iterative updates; when the system receives a stop command or the system is powered off, the entire control process terminates.

[0048] The performance evaluation and parameter optimization process of the central coordinator is executed in parallel with the real-time control process of each local controller. The performance evaluation and parameter optimization process is triggered at a period lower than the sampling frequency of the real-time control process.

[0049] Optionally, when each local controller executes the parameter adaptive law, it stores the adaptive gain coefficients in logarithmic coordinates, and the adaptive gain coefficients are restored through logarithmic mapping when participating in the calculation;

[0050] The error state vector is preprocessed by normalization before participating in the parameter adaptive law operation;

[0051] The central coordinator uses the normalized dimensionless gain coefficient as the object of parameter optimization and distribution. The dimensionless gain coefficient is linearly mapped to the actual gain coefficient value range in logarithmic coordinates.

[0052] Compared with the prior art, this application has at least the following beneficial effects:

[0053] This application adopts a two-layer distributed architecture of "central coordinator-local controller," where each execution unit is equipped with an independent local controller. Control computation tasks are completely distributed across these local controllers for parallel execution, eliminating the computational bottleneck of centralized architectures and avoiding the single point of failure risk that could paralyze the entire system. Furthermore, increasing or decreasing the number of execution units only requires adding or removing local controller nodes accordingly, without affecting the overall system operation, demonstrating excellent scalability. The central coordinator, through real-time calculation and feedback of global coordination errors, enables each execution unit to achieve displacement convergence while maintaining independent control, overcoming the difficulties in coordinating multiple execution units in distributed architectures.

[0054] This application, based on a rigorous feedback state-space model, employs an adaptive backstepping method to perform real-time online estimation of key uncertainty parameters such as the viscous damping coefficient, effective bulk modulus of the oil, and leakage coefficient. It continuously tracks parameter drift caused by factors such as oil temperature changes, piston wear, and working pressure fluctuations. The parameter estimates are recursively updated using an adaptive law constrained by Lyapunov functions, ensuring the stability and convergence of the estimation process. The central coordinator differentiates the adaptive gain coefficients of each actuator based on their operating conditions, enabling the same control framework to adapt to the load characteristics and parameter variation ranges of different actuators, thus solving the problems of parameter differentiation and collaborative estimation in multi-actuator scenarios.

[0055] The nonlinear load observer constructed in this application utilizes only the existing displacement and pressure sensor signals in the system. By calculating the difference between the hydraulic cylinder driving force and the inertial force, viscous damping force, and elastic force in real time, it achieves soft measurement of the external time-varying load force. Accurate load estimates can be obtained without the need for additional force sensors, avoiding increased hardware costs and the introduction of additional measurement noise. The feedforward compensation mechanism based on the observer can generate corresponding control quantity corrections in advance based on the estimated value before disturbances significantly affect the system output, thus offsetting the disturbances before they significantly impact the system output. This overcomes the limitation of traditional feedback control, which can only correct after the fact.

[0056] This application organically integrates sliding mode control, adaptive control, and feedforward compensation into a three-channel composite control architecture. The three control variables correspond to the transient response stage, steady-state operation stage, and disturbance response stage of the system, respectively. They are naturally decoupled in terms of time scale and complementary in terms of function. Sliding mode control ensures global stability and transient response quality under a wide range of operating conditions; adaptive compensation eliminates steady-state deviations caused by uncertainties in internal parameters; and load feedforward compensation suppresses the impact of rapidly time-varying loads on the system output. The three control strategies work collaboratively within the same framework without interfering with each other, achieving a unity of high precision, strong robustness, and adaptive capability in the system.

[0057] This application constructs a dimensionless comprehensive evaluation index in the central coordinator, comprehensively reflecting the displacement tracking accuracy, loading force tracking accuracy, and control energy consumption of each execution unit. It also identifies the execution units and error types causing performance degradation through multi-condition branching criteria, and accordingly adjusts sliding mode control parameters, adaptive gain coefficients, or feedforward compensation gains. The performance evaluation and parameter optimization process is executed in parallel with the real-time control process of the local controller, with a longer trigger cycle, avoiding the adverse effects of high-frequency parameter adjustments on system stability. This forms a collaborative operation mechanism of "local real-time control—global slow optimization," enabling the system to maintain excellent control performance throughout its entire lifecycle. Attached Figure Description

[0058] Figure 1 This is a flowchart illustrating an adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system, as provided in one embodiment of this application. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments.

[0060] This application provides an adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system, such as... Figure 1 As shown, it includes the following steps:

[0061] S1: Establish a nonlinear state-space model of the distributed pump-controlled direct-drive electro-hydraulic system. The system uses a servo motor directly driving a bidirectional fixed-displacement piston pump as its power source. Each actuator is driven by an independent servo motor-fixed-displacement pump group, which in turn drives its corresponding asymmetric hydraulic cylinder, forming a closed-loop volumetric control circuit. Because the effective areas of the two chambers of the asymmetric hydraulic cylinder are unequal, the flow rates in the two chambers are asymmetrical during the piston's forward and reverse movements. A replenishment circuit is needed to achieve flow balance.

[0062] In response to this structural feature, this step configures each execution unit with an oil replenishment module consisting of a hydraulic control check valve and a check valve, as well as a safety pressure stabilizing module consisting of an overflow valve. Based on this, a nonlinear state-space model that can fully describe the dynamic characteristics of the system is established.

[0063] Collect hydraulic cylinder piston displacement signal y and speed signal from each actuator. Rodless chamber pressure signal and rod chamber pressure signal Construct the system state vector Simultaneously, the servo motor speed signals corresponding to each execution unit are collected. As the system control input u, the following simplifications are made when establishing the mathematical models of each execution unit: external leakage of the hydraulic cylinder is ignored, and only internal leakage is considered; the effective volumetric elastic modulus of the oil is assumed to be constant; pressure loss in the pipeline and valve chamber is ignored; the servo motor speed control module is simplified to a proportional element.

[0064] Based on the above assumptions, the flow continuity equations for the two chambers of an asymmetric cylinder are first established. Taking the piston moving to the right (oil entering the rodless chamber and returning to the rod chamber) as an example, and neglecting external leakage, the flow equations for the rodless and rod chambers are as follows:

[0065]

[0066]

[0067] in, The effective area of ​​the rodless cavity (m²) 2 ), The effective area of ​​the rod cavity (m²) 2 ), The initial volume of the rodless cavity side (including the pipes and pump cavity) (m 3 ), The initial volume of the rod-side cavity (including the pipe and pump cavity) (m 3 ), This represents the effective bulk modulus of the oil (Pa). The total leakage coefficient of the hydraulic cylinder (m 3 / s) / Pa);

[0068] The force balance equation for the piston is given by Newton's second law of motion, neglecting nonlinear factors such as static friction:

[0069]

[0070] Where m is the equivalent total mass of the load and piston (kg), B is the oil viscosity damping coefficient (N / (m / s)), and K is the equivalent elastic stiffness coefficient of the system (N / m). External load force (N);

[0071] The flow equation for a fixed displacement pump is:

[0072]

[0073] in, The displacement of a fixed displacement pump (m³) 3 / r), u is the servo motor speed (r / s), and the positive or negative sign indicates the direction of oil flow;

[0074] Considering the compensation requirement for the flow imbalance between the two chambers of an asymmetric cylinder in a closed loop, a mathematical model of a hydraulically controlled check valve and a check valve is introduced. The conduction state of the check valve is determined by the pressure difference across its two ends, defined as:

[0075]

[0076] in, , These represent the pressures (Pa) at both ends of the check valve. The opening pressure of the check valve (Pa). The flow rate of the check valve is a piecewise function: when When, the check valve is fully open; when When, the check valve is fully closed; when At this time, the check valve is in a partially open state. The check valve compensates for the flow. , Based on this calculation;

[0077] As a safety protection component, the flow rate of the relief valve can be simplified as a piecewise function: when the pressure difference across the relief valve... Less than the opening pressure When the overflow valve is closed, the flow rate is zero; when At that time, the overflow valve opens, and the overflow flow... Where G is the liquid conductivity ((m³ / s) / Pa);

[0078] Based on the flow continuity equations of the two chambers of the hydraulic cylinders of each actuator, the piston force balance equation, the flow equation of the fixed displacement pump, and the flow models of the check valve and relief valve, the nonlinear state-space model of each actuator is established as follows:

[0079]

[0080]

[0081]

[0082]

[0083] In the above model, state variables Let be the piston displacement (m). The piston speed is (m / s). The pressure in the rodless chamber is (Pa). The pressure in the rod chamber (Pa);

[0084] To facilitate the subsequent design of the adaptive backstepping controller, the above model is rewritten in a strictly feedback form. Vectors are introduced. and order The state-space model described above can then be rewritten as:

[0085]

[0086]

[0087]

[0088] The system parameter set is defined as follows:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] After the above transformation, the original fourth-order state-space model is rewritten in a strictly feedback form, where , , , This is the parameter set containing system uncertainty parameters. This strict feedback form satisfies the design conditions of the adaptive backstepping controller, allowing the control law and parameter adaptation law of the system to be derived step by step by recursively constructing Lyapunov functions.

[0096] The output of this step is the parameter set of the strict feedback state-space model for each execution unit. and the corresponding nonlinear function matrix , , The model parameters of each actuator differ due to variations in hydraulic cylinder structure dimensions, load conditions, and oil state. The central coordinator in S2 performs global coordination control based on the model parameters uploaded by each actuator.

[0097] S2: Construct a distributed hierarchical control architecture and establish data communication links between each execution unit and the central coordinator. In order to overcome the computing power bottleneck and single point of failure risk of traditional centralized controllers when facing multi-actuator systems, this step constructs a distributed hierarchical control architecture based on a two-layer structure of "central coordinator - local controller".

[0098] This architecture separates system-level coordination functions from the independent control functions of each execution unit. The central coordinator is responsible for global task allocation and synchronization coordination, while each local controller independently completes the force / position servo control of its own execution unit, thereby taking into account both the real-time response capability and global coordination accuracy of the system.

[0099] Each execution unit is equipped with an independent local controller. Each local controller adopts an embedded industrial control platform, equipped with a real-time operating system, and includes an adaptive backstepping control module and a loading force observation module. The adaptive backstepping control module is used to calculate the servo motor speed control command based on the desired displacement signal and the state variables fed back in real time by the execution unit; the loading force observation module is used to estimate the external load force in real time based on the pressure signals of the two chambers of the hydraulic cylinder.

[0100] Each local controller is also equipped with an analog input interface (for connecting displacement and pressure sensor signals), an analog / digital output interface (for driving servo motor drivers), and an industrial Ethernet communication interface. Each local controller connects to the central coordinator via an industrial Ethernet switch, forming a star-topology real-time data communication network. The communication protocol uses the EtherCAT industrial real-time Ethernet protocol, which supports a distributed clock synchronization mechanism, ensuring that data acquisition and control command issuance between each local controller and the central coordinator are completed within sub-millisecond time deviations.

[0101] A central coordinator is set up. The central coordinator uses a high-performance industrial control computer, runs coordination control software, and establishes real-time data communication links with each local controller via industrial Ethernet;

[0102] The main functions of the central coordinator include: broadcasting the desired displacement signal and desired applied force signal to each local controller; receiving the real-time state variables of the execution unit uploaded by each local controller; calculating the global coordination error of the system and feeding it back to each local controller; and iteratively optimizing the control parameters of each local controller based on the global performance indicators.

[0103] The central coordinator uses a fixed sampling period Broadcast the desired displacement signal to each local controller and expected load signal Broadcast data frames are sent in a periodic synchronous manner. Each data frame contains a timestamp, the expected displacement value of each execution unit, and the expected loading force value. After receiving the broadcast data frame, each local controller extracts the expected value corresponding to its execution unit and corrects it by combining it with the global coordination error fed back by the central coordinator, which serves as the control target for the current control cycle.

[0104] At the same time, each local controller will collect the state variables of its execution unit in real time, including piston displacement y and velocity. rodless chamber pressure and rod chamber pressure The data is uploaded to the central coordinator via a data communication link. The uploaded data uses an aperiodic asynchronous transmission method, and each data frame contains a timestamp, execution unit number, and the current values ​​of the four status variables mentioned above, ensuring that the central coordinator can obtain the latest operating status of each execution unit.

[0105] The central coordinator calculates the system's global coordination error based on the state variables uploaded by each execution unit. Assume there are N execution units in the system, and the current displacement of each execution unit is... The central coordinator calculates the global coordination error using the following formula:

[0106]

[0107] in, The desired displacement signal broadcast by the central coordinator. Global coordination error. This reflects the average deviation of the displacement of each execution unit relative to the desired value. The central coordinator will... The adaptive backstepping control module, fed back through the data communication link to each local controller, corrects the desired trajectory of its respective execution unit accordingly. The corrected desired displacement signal is:

[0108]

[0109] Where η is the coordination gain coefficient (0 < η ≤ 1), used to adjust the correction strength of the global coordination error on the expected trajectory of a single execution unit. This correction mechanism ensures that when an execution unit experiences a large displacement deviation due to external load changes or parameter perturbations, the central coordinator can transmit this deviation information to all execution units, enabling each execution unit to achieve coordinated convergence of global displacement while maintaining its independent control.

[0110] The output of this step is the corrected desired displacement signal received by each local controller. and expected load signal The input is sent to S3. The corrected expected displacement signal of each execution unit is affected by global coordination errors. The system dynamically adjusts to real-time changes, thereby achieving displacement synchronization and load balancing among multiple execution units in subsequent steps.

[0111] S3: Each local controller calculates the displacement tracking error and its rate of change for its execution unit, constructs a sliding mode switching function, and receives the corrected displacement signal from S2. Then, it is compared with the piston displacement signal acquired in real time by the displacement sensor of this execution unit. Compare and calculate displacement tracking error Simultaneously, each local controller uses numerical differentiation to perform differential calculations on the displacement tracking error, obtaining the error change rate. ,in This is the real-time feedback value of the piston's movement speed. The first derivative of the desired displacement signal;

[0112] To improve the accuracy of error rate calculation and suppress the amplification effect of measurement noise, this step uses a backward differential method combined with low-pass filtering, namely:

[0113]

[0114] Where k is the current sampling time number. The sampling period is defined. The calculated error rate of change is limited to prevent excessive error rate of change due to sensor noise or signal abrupt changes from affecting the stability of the controller.

[0115] Based on the above error information, each local controller constructs a sliding mode switching function in the following form:

[0116]

[0117] Where c is the sliding surface slope coefficient, taken as a positive constant c=15. This coefficient determines the convergence speed of the sliding surface; the larger the value of c, the faster the system state approaches the sliding surface, but an excessively large value of c may lead to control saturation and system oscillation. Each execution unit can fine-tune the value of c within the range of c=10 to c=20 according to the actual operating conditions of its unit to adapt to the dynamic response requirements under different load characteristics;

[0118] The physical meaning of the sliding mode switching function s is the signed distance from the system state in the phase plane to the sliding surface s=0. When the system state is above the sliding surface, s>0; when it is below the sliding surface, s<0. Each local controller simultaneously calculates the derivative of the sliding mode switching function. Used to determine the motion trend of the system state relative to the sliding surface:

[0119]

[0120] in The second derivative of the error is obtained by... The numerical difference is obtained;

[0121] Each local controller determines the sliding mode arrival condition in real time during each sampling period. Is it satisfied? This condition is the arrival condition for sliding mode variable structure control; its fulfillment means that the system state is approaching the sliding surface.

[0122] like The establishment of this condition indicates that the system has entered the sliding mode approach stage, and each local controller directly outputs control quantities according to the sliding mode control law in S6.

[0123] like If the condition is not met, it indicates that the system state deviates from the sliding surface or is in a divergent trend, at which point the fuzzy control softening module is triggered to intervene.

[0124] The fuzzy control softening module uses the sliding mode switching function s and its derivative. As input, a softening compensation amount is output through fuzzy inference. This is superimposed on the control law in subsequent steps to replace the discontinuous symbolic function terms in traditional sliding mode control, thereby effectively reducing the high-frequency chattering of control quantities during sliding mode switching while ensuring that the system state can reach the sliding surface.

[0125] The output of this step is the displacement tracking error of each execution unit. Sliding mode switching function s and its derivative Input to S4 and S5. Construction of Lyapunov functions and derivation of adaptive parameter laws for adaptive backstepping controllers in S4, s and Used for determining the state of the loading force observer in S5 and calculating the sliding mode control law in S6;

[0126] In addition, each local controller will also upload the sliding mode switching function s value calculated in this step to the central coordinator through the data communication link, as one of the reference bases for the central coordinator to evaluate the control status of each execution unit;

[0127] S4: Based on the adaptive backstepping method, an adaptive law for parameter design is used to estimate the system's uncertainty parameters in real time online. Each local controller, based on the rigorous feedback state-space model established in S1, uses the adaptive backstepping method to estimate the system's uncertainty parameters in real time online. In a direct-drive pump-controlled electro-hydraulic system, the effective bulk elastic modulus of the oil... The leakage coefficient changes significantly with oil temperature and the amount of air mixed in. The viscous damping coefficient BB drifts with piston wear and working pressure fluctuations, exhibiting nonlinear time-varying characteristics as the oil viscosity changes.

[0128] The above parameters are difficult to determine precisely through offline identification; therefore, an adaptive algorithm must be used to continuously track their changes during system operation. This step involves the S1 parameter set. The most significantly affected by parameter perturbations , and As the object to be estimated, and will Treating it as a known constant (the load mass in mm can be obtained through offline weighing or calibration), In It is considered a known constant (the displacement of a fixed displacement pump is determined by the pump's model parameters);

[0129] This approach effectively reduces the computational burden of the adaptive estimator and covers the sources of uncertainty in the system that have the greatest impact on control accuracy.

[0130] To derive the parameter adaptive law, each local controller first defines the displacement tracking error in S3. Virtual control quantity Based on the recursive design principle of the backstep method, let:

[0131]

[0132] in These are design parameters used to adjust the convergence rate of the displacement tracking process. The velocity tracking error is defined accordingly.

[0133]

[0134] Furthermore, in the rigorous feedback model rewritten from S1 Substitute the expression and combine it with the definition in S3. ,get The dynamic equation is:

[0135]

[0136] It contains unknown parameters To compensate for the influence of this unknown parameter, a virtual control variable α is introduced in the second step of the backstepping method, which is designed to be an estimate of α. Functions:

[0137]

[0138] in For design parameters. Define a third error variable:

[0139]

[0140] At this point, the system's error state is... , , All definitions are complete, including It is a two-dimensional vector;

[0141] Each local controller selects a Lyapunov candidate function of the following form:

[0142]

[0143] in For parameter estimation error, For parameters Real-time estimated value; These are adaptive gain coefficients, used to adjust the convergence speed of the three parameters to be estimated.

[0144] The structure design of this Lyapunov function follows the general principle of backstepping. The first half contains the energy term of the system error state, and the second half contains the penalty term of the parameter estimation error, ensuring that the parameter estimation can be compensated by feedback control when there is a deviation.

[0145] Differentiating the Lyapunov function along the system trajectory and substituting the strict feedback state equation of S1 into it, after simplification and combining like terms, we obtain the following expression:

[0146]

[0147] In order to make For a negative definite expression, the parameter estimation error contained in the above expression must be eliminated. , , The cross terms. Setting the coefficients of each cross term to zero, we obtain the adaptive law for the three parameters as follows:

[0148]

[0149]

[0150]

[0151] In the above adaptive law, The update rate for each parameter to be estimated is determined by the current error state and the adaptive gain coefficient. When the system tracking error is large, the adaptive law provides a large parameter correction, accelerating parameter convergence; as the system state approaches the sliding surface and the error gradually returns to zero, the parameter update rate decreases, and the parameter estimates tend to stabilize.

[0152] Each local controller in each sampling period The adaptive law described above is discretized using the Euler forward difference method:

[0153]

[0154]

[0155]

[0156] Where k is the current sampling time number;

[0157] To ensure that the parameter estimates remain within a reasonable physical range, each local controller applies a limiting constraint to the estimates after each update: Set a lower limit and upper limit ;

[0158] right Set a lower limit and upper limit ;

[0159] right Set a lower limit and upper limit ;

[0160] The limiting process avoids the parameter estimates from diverging due to excessive initial errors or noise interference, and ensures that the parameter update direction always conforms to the physical constraints of the system.

[0161] It should be noted that, Dimensions and different, The physical quantity is much smaller than In a typical hydraulic system, the total leakage coefficient is... The order of magnitude is to m 3 / (Pa·s), therefore The numerical range usually falls within to Between. In this specific embodiment, take , This covers the vast majority of parameter variations encountered in actual engineering projects. Each actuator can further determine its own characteristics during the commissioning phase through offline identification, based on the sealing structure and wear condition of its hydraulic cylinder. Personalized amplitude limit boundaries;

[0162] Adaptive gain coefficient , , The value of the gain coefficient determines the convergence speed and steady-state fluctuation amplitude of the parameter estimation. A larger gain coefficient makes the parameter estimation converge quickly, but amplifies the estimation fluctuations caused by measurement noise; a smaller gain coefficient makes the estimation process smoother, but the convergence speed is slower.

[0163] Based on theoretical analysis and extensive simulation verification, the preferred value range in this step is: Due to differences in load characteristics and operating conditions, the gain coefficients of each execution unit can be adjusted differentially within the above range by the central coordinator based on the global performance evaluation results of S7;

[0164] It is important to note that , , The numerical range is extremely large, and there is a risk of numerical overflow when implementing it in an embedded system. Therefore, the following process should be adopted:

[0165] The adaptive gain coefficients are stored using logarithmic coordinates. The controller does not directly store them. , Instead of storing the original value, it stores its base-10 logarithmic value. In actual computation, the data is restored through table lookup or shift operations. At this point, the parameters issued by the central coordinator are distributed to the following recipients: , Instead , The parameter adjustment step size is also expressed in logarithmic coordinates as an increment;

[0166] For the error vector Normalization preprocessing is performed before calculating the adaptive law. The components are normalized: ,in This represents the maximum permissible amplitude of the error component (which can be preset according to the system range). The normalized error has a single dimension, and its amplitude is limited to the range of [-1, 1], thus significantly reducing the reasonable range of values ​​for the adaptive gain coefficient, typically down to [-1, 1]. Magnitude;

[0167] Floating-point arithmetic is employed, and parameter change rate limiting is set. On embedded platforms with floating-point units (such as ARM Cortex-M4 / M7 and above), adaptive law calculation is performed directly using double-precision floating-point numbers. Simultaneously, the change in the parameter estimate is limited in each sampling period. To prevent excessive single-step update from causing the estimated values ​​to diverge;

[0168] Add an adaptive gain coefficient normalization mapping to the parameter optimization logic of the central coordinator. Replace the variables actually optimized and stored by the central coordinator in S7 with normalized dimensionless gain coefficients. The gain coefficient actually used for adaptive law calculation is obtained by mapping the following formula:

[0169]

[0170] This involves linear interpolation in logarithmic coordinates. This mapping ensures that the actual value of the gain coefficient always falls within a preset range. Within the interval, and the parameter optimization process of the central coordinator is carried out in the normalized [0,1] interval, the numerical sensitivity problem caused by directly optimizing large numerical gain coefficients is avoided.

[0171] The output of S4 is the real-time updated system parameter estimates for each local controller. , , The input is sent to S6 to calculate the adaptive compensation term in the integrated control command;

[0172] Meanwhile, each local controller uploads the change curve of the parameter estimate to the central coordinator through the data communication link, so that operators can view the parameter convergence trend on the monitoring interface and determine whether the system has entered a steady state and whether there is any abnormal parameter drift.

[0173] S5: Construct a nonlinear load observer to estimate external time-varying load disturbances in real time. In the actual operation of a direct-drive pump-controlled electro-hydraulic servo system, external load force is one of the main sources of disturbance affecting the system's control accuracy. The magnitude of the load force fluctuates in real time with changes in operating conditions and is difficult to measure directly by sensors. If additional force sensors are installed on each actuator, it will not only significantly increase the system hardware cost, but also introduce additional measurement noise and delay due to the limitations of the sensor installation location.

[0174] Therefore, this step constructs a nonlinear load force observer based on the system dynamics model in each local controller, and uses existing displacement and pressure sensor signals to perform real-time soft measurement of time-varying load force.

[0175] Each local controller operates based on the pressure signals from the two chambers of the hydraulic cylinder in its respective actuator unit. and Combining the piston force balance equation in S1 and the parameter estimates updated in real time in S4 Construct the following force observer:

[0176]

[0177] in The real-time estimated value of the applied force (N); , The effective areas (m²) of the rodless cavity and the rod cavity are respectively. 2 ); , The pressures of the two chambers are (Pa); m is the equivalent total mass of the load and piston (kg). Piston acceleration (m / s²) 2 ), by analyzing the velocity state variable in S1 Numerical differentiation is performed to obtain B, which is the viscous damping coefficient (N / (m / s)), estimated from S4. The result is obtained by reverse calculation, i.e. ; Where is the piston speed (m / s); K is the system's equivalent elastic stiffness coefficient (N / m); For piston displacement (m);

[0178] The physical meaning of this observer is clear: the driving force generated by the pressure difference between the two chambers of the hydraulic cylinder. Deducting the force used to overcome inertia Viscous damping force and elastic force The remaining portion is the external load force. ;

[0179] Due to the observer The term involves numerical differentiation of acceleration. Direct difference operations will severely amplify the high-frequency noise in the pressure and displacement sensors, affecting the calculations of each local controller. A tracking differentiator is used for filtering to avoid noise amplification that could cause drastic fluctuations in the observed values.

[0180] Each local controller in each sampling period Internal completed loading force estimation value The real-time calculation is performed and compared with the expected loading force signal transmitted from S2. By comparison, the force tracking error is obtained:

[0181]

[0182] Each local controller performs sampling in each sampling period. Perform real-time judgment. If Exceeding the preset threshold If the system is in a state of strong load disturbance, it is determined that the external load has undergone significant sudden changes or periodic fluctuations, and the load compensation module is triggered to intervene.

[0183] The loading compensation module calculates the feedforward compensation amount according to the magnitude and direction of the loading force tracking error, following these rules:

[0184]

[0185] in This is the feedforward compensation gain coefficient, and its value determines the strength of the applied force compensation. If the value is too small, the compensation will be insufficient, and the system will have a weak ability to suppress external load disturbances. If the value is too high, it may lead to overcompensation and cause system oscillations;

[0186] Based on theoretical analysis and simulation verification, in this step The preferred range is to Each execution unit can perform differentiated tuning of KFKF within the above range according to its actual load characteristics. The sign of the compensation amount is... The signs are consistent when the actual load force is greater than the expected value ( When the compensation is positive, the motor speed is increased to provide greater driving force; when the actual load force is less than the expected value ( When the compensation is negative, the motor speed is reduced to decrease the driving force.

[0187] like If the system is in a state of weak loading disturbance or steady-state operation, and the loading force tracking error is within an acceptable range, then there is no need to trigger the loading compensation module. This is to avoid introducing additional control disturbances through unnecessary compensation actions. Threshold The value of balances the robustness and sensitivity of the control. It is less than the maximum force deviation allowed in the steady state of the system (usually 5% of the desired loading force) and greater than the typical amplitude of sensor noise and observer estimation error, ensuring that the compensation module intervenes only when it is really needed.

[0188] The essence of load feedforward compensation is an active suppression strategy based on disturbance estimation: unlike traditional feedback control which can only be corrected after the disturbance has caused position or pressure deviation, feedforward compensation generates the corresponding control quantity correction based on the observer estimate within the same sampling period when the disturbance occurs, thereby offsetting the disturbance before it significantly affects the system output.

[0189] This "estimation-compensation" mechanism complements the parameter adaptive law in S4. The parameter adaptive law deals with the slow time-varying nature of internal system parameters (oil elastic modulus, leakage coefficient, etc.), while the load observer deals with the rapid abrupt changes in external load. There is a natural decoupling between the two in terms of time scale: internal parameter changes are typically slow (seconds to minutes), while external load disturbances often change rapidly (milliseconds to hundreds of milliseconds). This difference in time scale allows the two compensation mechanisms to work in parallel within the same control framework without interfering with each other.

[0190] The output of this step is an estimated loading force. and its compensation signal Input to S6. Among them... It is also uploaded to the central coordinator via a data communication link, so that the central coordinator can refer to the load distribution of each execution unit when performing global performance evaluation in S7, so as to reasonably redistribute tasks to execution units with excessive load.

[0191] S6: Integrate sliding mode control quantity, adaptive compensation quantity, and loading force feedforward compensation quantity to generate comprehensive control instructions for each execution unit. After completing the sliding mode switching function calculation in S3, the online estimation of system parameters in S4, and the loading force observation in S5, each local controller integrates the outputs of the above three modules to generate the final comprehensive control instructions that act on the servo motor driver.

[0192] Sliding mode control ensures the system's robustness to parameter perturbations and external disturbances, adaptive compensation eliminates steady-state deviations caused by uncertain parameters within the system, and load feedforward compensation actively suppresses rapidly time-varying loads. The three functions complement each other and are decoupled in time scale, together forming a complete three-channel composite control architecture.

[0193] Each local controller calculates the sliding mode control quantity based on the sliding mode switching function s of S3, according to the proportional switching sliding mode control law:

[0194]

[0195] Where α>0 and β>0 are sliding mode control parameters. The physical meaning of the α term is to make the sliding mode control quantity follow the displacement error. The magnitude of the linear adjustment means that when the error is large, the system is far from the target position and a larger control action is required to accelerate the approach process; the β term is a constant term, which ensures that the system state can still maintain sufficient control force to overcome static friction and external disturbances and maintain the motion of the system on the sliding surface when the error approaches zero. The sign function takes the following values: +1 when s > 0, -1 when s < 0, and 0 when s = 0. The introduction of the sign function allows the sliding mode control variable to switch only on both sides of the sliding surface, thus maintaining the sliding motion of the system state on the sliding surface.

[0196] To fundamentally suppress the high-frequency chattering phenomenon caused by sign function switching, each local controller, in its actual implementation, uses a saturation function. Alternative standard symbolic functions:

[0197]

[0198] Where Φ>0 represents the boundary layer thickness, and its value determines the trade-off between chattering suppression and control accuracy. When the value of Φ is too small, the chattering suppression effect is not obvious; when the value of Φ is too large, the system state no longer converges to the sliding surface within the boundary layer, and the steady-state error increases.

[0199] Through simulation verification and experimental debugging, the preferred range of Φ in this step is 0.01 to 0.1. Each execution unit can be tuned within the above range according to the actual tracking accuracy requirements.

[0200] Each local controller superimposes an adaptive compensation term (S4) onto the sliding mode control input to eliminate the impact of internal system parameter uncertainties on control accuracy. The complete adaptive compensation term is expressed as:

[0201]

[0202] in Used to compensate for the effects of uncertainties in the viscous damping coefficient and load-mass ratio on the velocity loop. Given a constant term, The term representing the driving force generated by the pressure difference between the two chambers of the hydraulic cylinder. The impact of changes in the elastic modulus of the compensating oil on pressure dynamics. The impact of the uncertainty of the compensation leakage coefficient on flow continuity;

[0203] It should be pointed out that, The expression and the state equation in S1 There is a strict correspondence, that is, the adaptive term is essentially the reverse compensation of the unknown parameter term in the state equation. Its physical meaning is: the controller actively injects a control action into the system that is equal in quantity but opposite in direction to the uncertain term based on the latest estimate of the system parameters, so that the actual system is equivalent to a nominal system with known parameters in the eyes of the controller.

[0204] Each local controller, based on the sliding mode control quantity and the adaptive compensation quantity, further superimposes the loading force feedforward compensation term of S5. This is to suppress the impact of external time-varying load disturbances on the system position output.

[0205] The three control variables are synthesized into the final integrated control command according to the principle of linear superposition:

[0206]

[0207] The dimension of the comprehensive control command u is the speed command (r / s), and its physical meaning is the desired servo motor speed.

[0208] Since actual servo motor drivers can only accept analog voltage signals within a limited range, each local controller performs amplitude limiting on u before outputting control commands. This limiting process involves two steps: first, amplitude limiting, which sets an upper limit based on the servo motor's rated speed. and lower limit , usually take The corresponding rotational speed value ensures that the control command does not exceed the mechanical load-bearing capacity of the motor; secondly, the rate of change is limited, that is, the change range of the control command is limited within two adjacent sampling periods. To prevent sudden changes in control commands from impacting the system. The typical value is 50 r / s;

[0209] After being limited, the integrated control command u is output to the servo motor driver in the form of a standard analog voltage signal of ±10V through the analog output channels of each local controller. The speed loop of the driver controls the actual speed and direction of the servo motor accordingly. Positive voltage corresponds to the motor rotating forward and the hydraulic cylinder piston moving forward; negative voltage corresponds to the motor rotating in reverse and the hydraulic cylinder piston moving in the opposite direction; the absolute value of the voltage corresponds to the speed.

[0210] At the same time, each local controller will input the current control quantity u and all state variables of its execution unit, including displacement y and velocity. Two-chamber pressure and The data is uploaded to the central coordinator via a data communication link. Upon receiving the data from each execution unit, the central coordinator uses it for global coordination error calculation in the next sampling period. The calculation (see S2) is performed, and the result is stored in the historical database as the data basis for global performance evaluation and controller parameter iterative update in S7.

[0211] The output of this step is the speed control command u(t) of the servo motor of each execution unit, which is input to S7;

[0212] It should be noted that the three compensation channels have significantly different functional roles: sliding mode control quantity. It is the main control channel, responsible for ensuring the global stability of the system under a wide range of operating conditions; adaptive compensation term It serves as a steady-state accuracy guarantee channel, responsible for eliminating residuals caused by uncertainties in internal parameters; the loading force feedforward compensation term It is a dynamic response enhancement channel, responsible for suppressing the impact of rapidly changing loads on the system output;

[0213] The time scales of the three control variables correspond to the transient response stage, steady-state operation stage, and disturbance response stage of the system, respectively. The coordination relationship between the three is uniformly adjusted by the central coordinator in S7 through global performance evaluation and parameter optimization.

[0214] S7: The central coordinator performs global performance evaluation and iterative updates of controller parameters. At the end of each control cycle, the central coordinator collects the displacement tracking error uploaded by each execution unit through the data communication link. Force tracking error and control quantity The superscript i = 1, 2, ..., N represents the sequence number of the execution unit;

[0215] The central coordinator calculates the system's overall performance index based on the above data. This index is designed to reflect the system's comprehensive performance in three aspects: tracking accuracy, anti-interference capability, and energy consumption. Its expression is:

[0216]

[0217] in , , These are weighting coefficients, used to adjust the relative importance of displacement tracking accuracy, loading force tracking accuracy, and energy consumption in the overall performance indicators. The three weighting coefficients can be constrained as follows: ;

[0218] , and These are the maximum allowable amplitudes for displacement tracking error, loading force tracking error, and control quantity, respectively, preset according to system design specifications. Each component, after normalization, is a dimensionless pure numerical value, making J a truly dimensionless comprehensive evaluation index; the components can be directly added together.

[0219] The selection principle for the normalization benchmark value is as follows: Take the maximum position deviation allowed by the system (e.g., 1% of full scale). Take the maximum allowable load force deviation of the system (e.g., 5% of the rated load force). The maximum permissible input voltage or speed command limit value of the servo motor driver is obtained. Once determined, each normalized reference value remains unchanged during system operation.

[0220] The values ​​of the three weighting coefficients need to be determined based on the actual needs of the specific application scenario: in precision positioning scenarios that pursue high positioning accuracy, the weighting coefficients should be appropriately increased. ;

[0221] In force servo scenarios requiring precise control of output force, the output force should be appropriately increased. ;

[0222] In energy-saving scenarios with strict constraints on system energy consumption, the energy consumption should be appropriately increased. ;

[0223] The weighting coefficients must meet the dimension matching condition, that is... The dimension of is meter (m). The dimension of J is Newton (N), and the dimension of u is revolutions per second (r / s) – making J a dimensionless comprehensive evaluation index.

[0224] Based on engineering experience, the recommended range for selecting weighting coefficients in this step is: Use a value of 0.4 to 0.8 (for scenarios where positional accuracy is prioritized). Take a value of 0.1 to 0.4 (for scenarios where force control accuracy is prioritized). The value is set to 0.05~0.2 (for scenarios where energy consumption constraints are prioritized), and the sum of the three is 1. The value of the threshold Jth is also adjusted accordingly to the dimensionless range of 0.01~0.1.

[0225] The central coordinator compares the calculated global performance index J with a preset threshold. Compare them. The value of reflects the minimum acceptable level of the system's overall performance. If the current control performance of the system already meets the requirements, there is no need to adjust the controller parameters, and the existing parameters can be maintained and the system can continue to operate. If the system performance degrades beyond the threshold, the parameter optimization process is triggered.

[0226] It is usually determined based on system design specifications, and its typical value is taken as 1.5 to 2.0 times the J value of the system under rated operating conditions in steady state. When J exceeds... At that time, the central coordinator further analyzes the error distribution uploaded by each execution unit, identifies the execution unit and the main error type that cause the performance degradation, whether it is that the position tracking error of a certain execution unit is too large, the loading force tracking deviation of a certain execution unit is serious, or the overall control energy consumption is too high—and adjusts the corresponding controller parameters accordingly.

[0227] The parameter adjustment strategy is as follows: when the central coordinator detects a control input from a certain execution unit... When the amplitude is consistently large or fluctuates drastically, first consider the displacement tracking error. Determine the cause based on the amplitude:

[0228] (1) If ( Take 5 times the system's allowable steady-state error, for example. If the control input is too large, it is determined that the system has not yet converged. In this case, the sliding mode control parameters should be appropriately increased. and (A single increase shall not exceed 10% of the current value) in order to strengthen control and accelerate the convergence process;

[0229] (2) If ( Take 0.5 times the system's allowable steady-state error, for example. Furthermore, the control quantity exhibits high-frequency oscillation characteristics (determined by calculating the sum of the absolute values ​​of adjacent differences in the control quantity). ,in If the preset threshold is set to 5% of the rated control value, then the system is determined to be close to the target position but chattering exists. In this case, the sliding mode control parameters should be appropriately reduced. and (The single reduction shall not exceed 10% of the current value) in order to weaken the high-frequency switching of the control quantity and reduce the oscillation amplitude;

[0230] (3) If If the current parameters remain unchanged, continue to observe. Make a decision only after understanding the changing trends.

[0231] Simultaneously, add a monitoring criterion for the rate of change of the control quantity: if the rate of change of the control quantity... ( Taking 10% of the rated control quantity per sampling period indicates a drastic change in the control quantity, thus prioritizing reducing the boundary layer thickness in step three. To enhance the ability to suppress high-frequency disturbances, rather than directly adjusting... and ;

[0232] The above multi-condition branching logic ensures that the direction of parameter adjustment matches the actual response state of the system, avoiding the adoption of a single adjustment strategy under all operating conditions.

[0233] The central coordinator distributes the newly generated controller parameter set to each local controller via the industrial Ethernet data communication link. After receiving the new parameter set, each local controller applies it to the control law calculations for S3 to S6 of the next control cycle, realizing online adaptive iterative optimization of the controller parameters.

[0234] Parameter delivery adopts a non-periodic event-triggered method, sending data frames only when the parameter set changes, in order to save communication bandwidth. Each parameter delivery data frame contains a timestamp, the target execution unit number, and the new values ​​of the five controller parameters, ensuring the timing consistency and traceability of parameter updates;

[0235] The entire control process is executed repeatedly according to the cyclical structure of "S3→S4→S5→S6→S7→S3".

[0236] The central coordinator calculates the global performance index J in real time after each control cycle. If J remains below a threshold for 100 consecutive sampling cycles (0.1 seconds), the performance index is determined. When the system is determined to have entered a stable operating state, parameter iterative updates are stopped to reduce the computational load on the central coordinator; when the system receives an external stop command or the system is powered off, the entire control process terminates.

[0237] Under normal operating conditions, the above loop runs continuously with a sampling period of 1ms. The performance evaluation and parameter optimization process of the central coordinator is executed in parallel with the real-time control process of each local controller. The local controller is forced to perform real-time control calculations from S3 to S6 in each sampling period, while the performance evaluation and parameter optimization process of the central coordinator is triggered at a low frequency (once every 100 control cycles) to avoid the adverse effects of high-frequency parameter adjustments on system stability.

[0238] Thus, all seven steps of the adaptive loading control method for the distributed pump-controlled direct-drive electro-hydraulic system proposed in this invention have been completed. This method, through the organic combination of S1 to S7, constructs a complete adaptive loading control scheme for a multi-actuator pump-controlled direct-drive electro-hydraulic system. S1 establishes an accurate nonlinear state-space model as the basis for the control algorithm; S2 constructs a distributed hierarchical control architecture to achieve coordinated communication among multiple actuators; S3 to S6 complete the real-time control calculation of the local controller at four levels: error calculation, parameter estimation, disturbance observation, and control quantity fusion, respectively; and S7 achieves adaptive iterative optimization of the controller parameters at the global level. The seven steps are tightly connected through strict data flow transmission relationships, jointly achieving high-precision, robust, and adaptive coordinated control of the distributed pump-controlled direct-drive electro-hydraulic system.

[0239] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. An adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system, characterized in that, The method is applied to a distributed hierarchical control architecture consisting of a central coordinator and multiple local controllers, and the method includes: S1. Establish a nonlinear state-space model for each execution unit. The model takes the servo motor speed as the control input and the piston displacement, motion speed and two-chamber pressure as state variables. The model is rewritten into a strict feedback form that satisfies the design conditions of the adaptive backstepping method. The model parameter set and nonlinear function matrix of each execution unit are output. S2, construct the distributed hierarchical control architecture, establish a data communication link between each local controller and the central coordinator, the central coordinator broadcasts the desired displacement signal and desired loading force signal to each local controller, each local controller uploads the real-time collected state variables of its execution unit to the central coordinator, the central coordinator calculates the global coordination error based on the state variables of each execution unit and feeds it back to each local controller, each local controller corrects the desired trajectory based on the global coordination error and outputs the corrected desired displacement signal and desired loading force signal; S3, each local controller calculates the displacement tracking error and its rate of change based on the corrected expected displacement signal and the piston displacement signal fed back by the execution unit in real time, constructs the sliding mode switching function, and determines whether the sliding mode arrival condition is met. If it is not met, the fuzzy control softening module is triggered to intervene and outputs the displacement tracking error and the sliding mode switching function and its derivative. S4, each local controller constructs a Lyapunov function based on the strict feedback state space model using an adaptive backstepping method, and derives the real-time online adaptive law of the system uncertainty parameters according to the displacement tracking error, updates and limits the parameters to be estimated for each execution unit online, and outputs the updated parameter estimates. S5, each local controller constructs a loading force nonlinear observer based on the two-chamber pressure signals of its execution unit and the estimated parameter value, estimates the external time-varying load force in real time, and compares the estimated value with the expected loading force signal. When the loading force tracking error exceeds the preset threshold, the loading compensation module is triggered to output the feedforward compensation amount. S6, each local controller integrates the sliding mode control quantity, the adaptive compensation quantity, and the feedforward compensation quantity to generate a comprehensive control command and output it to the servo motor driver. At the same time, it uploads the current control quantity and all state variables of the execution unit to the central coordinator. S7, the central coordinator calculates the global performance index based on the displacement tracking error, loading force tracking error and control quantity uploaded by each execution unit. The global performance index is a dimensionless comprehensive evaluation index after normalizing each sub-item. When the global performance index exceeds the preset threshold, the sliding mode control parameters, adaptive gain coefficient and / or feedforward compensation gain of the corresponding local controller are adjusted in a targeted manner according to the error distribution of each execution unit, and the updated controller parameters are sent to each local controller to realize online adaptive iterative optimization of the controller parameters. The performance evaluation and parameter optimization process of the central coordinator is executed in parallel with the real-time control process of each local controller, and the triggering period of the performance evaluation and parameter optimization process is longer than the sampling period of the real-time control process.

2. The adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system according to claim 1, characterized in that, In S1, to address the flow asymmetry problem caused by the unequal effective areas of the two chambers of the asymmetric hydraulic cylinder, the nonlinear state space model is established based on the configuration of an oil replenishment module consisting of a hydraulically controlled check valve and a check valve, and a safety pressure stabilizing module consisting of an overflow valve in each execution unit. The established model was transformed and rewritten into a strict feedback form, which contains five system parameters, laying the model foundation for the subsequent design of the adaptive backstepping controller.

3. The adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system according to claim 1, characterized in that, In S2, the distributed hierarchical control architecture adopts a two-layer structure of "central coordinator-local controller". The central coordinator forms a star-topology real-time data communication network with each local controller through industrial Ethernet. The central coordinator broadcasts the desired signal to each local controller at a fixed sampling period, and each local controller uploads the state variables in an aperiodic asynchronous transmission manner. The global coordination error reflects the average deviation of the displacement of each execution unit relative to the expected value. Each local controller corrects its own expected displacement based on the global coordination error. The corrected expected displacement signal is the difference between the broadcast expected displacement signal and the product of the coordination gain coefficient and the global coordination error.

4. The adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system according to claim 1, characterized in that, In S3, each local controller performs numerical differentiation processing on the displacement tracking error using backward differential combined with low-pass filtering, and performs amplitude limiting processing on the calculated error change rate. The sliding mode switching function is the sum of the sliding surface slope coefficient and the displacement tracking error, plus the error change rate; The sliding mode arrival condition is that the product of the sliding mode switching function and its derivative is less than zero.

5. The adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system according to claim 1, characterized in that, In S4, the parameters to be estimated include the ratio of viscous damping coefficient to load mass, the effective bulk elastic modulus of the oil, and the product of the effective bulk elastic modulus of the oil and the leakage coefficient. Each local controller defines a virtual control quantity, a velocity tracking error, and a third error variable based on the displacement tracking error, and then constructs a Lyapunov candidate function that includes a system error state energy term and a parameter estimation error penalty term; By differentiating the Lyapunov candidate function and setting the coefficient of the cross term, which includes the parameter estimation error, to zero, the parameter adaptive law for each parameter to be estimated is obtained. Each local controller implements the parameter adaptive law by discretizing it using the Euler forward difference method, and applies amplitude constraints to the parameter estimates after each update.

6. The adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system according to claim 1, characterized in that, In S5, the loading force nonlinear observer estimates the external load force based on the driving force generated by the pressure difference between the two chambers of the hydraulic cylinder, after deducting the remaining part used to overcome inertial force, viscous damping force and elastic force. Each local controller uses a tracking differentiator for filtering when calculating piston acceleration; The loading compensation module calculates the feedforward compensation amount based on the magnitude and direction of the loading force tracking error. The feedforward compensation amount is the product of the feedforward compensation gain coefficient and the loading force tracking error.

7. The adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system according to claim 1, characterized in that, In step S6, the sliding mode control quantity is calculated based on the sliding mode switching function, and a saturation function is used to replace the standard sign function to suppress high-frequency chattering. The adaptive compensation term performs reverse compensation on the unknown parameter terms in the state equation based on the parameter estimate value of S4, in order to eliminate the impact of internal parameter uncertainty on control accuracy. The feedforward compensation is superimposed on the sliding mode control and adaptive compensation to suppress external time-varying load disturbances. The three control quantities are combined into a comprehensive control command according to the principle of linear superposition. The comprehensive control command is then processed by amplitude limiting and rate of change limiting before being output to the servo motor driver.

8. The adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system according to claim 1, characterized in that, In S7, the global performance index is the weighted sum of the square of the displacement tracking error, the square of the loading force tracking error, and the square of the control quantity of each execution unit. After normalization, each item is a dimensionless pure value. The global performance index is a dimensionless comprehensive evaluation index. The central coordinator compares the global performance metrics with preset thresholds. When the thresholds are exceeded, it further analyzes the error distribution uploaded by each execution unit, identifies the execution unit and error type that caused the performance degradation, and executes a multi-condition branch parameter adjustment strategy accordingly. For execution units with large displacement tracking errors, branch determination is based on the magnitude of the displacement tracking error: (1) If the absolute value of the displacement tracking error is greater than the first preset threshold, it is determined that the control quantity is too large because the system has not yet converged, and the sliding mode control parameters and adaptive gain coefficient of the execution unit are increased. (2) If the absolute value of the displacement tracking error is less than the second preset threshold and the control quantity exhibits high-frequency oscillation characteristics, it is determined that the system is close to the target position but there is chattering, and the sliding mode control parameters of the execution unit are reduced. (3) If the absolute value of the displacement tracking error is between the second preset threshold and the first preset threshold, then the current parameters are kept unchanged; Meanwhile, a monitoring criterion for the rate of change of the control quantity is added: if the rate of change of the control quantity exceeds the preset rate of change threshold, the boundary layer thickness in the sliding mode switching function is reduced first to enhance the ability to suppress high-frequency disturbances. For execution units with large force tracking errors, increase the feedforward compensation gain; After the central coordinator completes the parameter adjustment, it sends the updated controller parameter set to each local controller through the data communication link. Each local controller applies the updated parameters to the control law calculation in the next control cycle, thereby realizing online adaptive iterative optimization of the controller parameters. When the global performance index is lower than the preset threshold for a predetermined number of consecutive sampling periods, the central coordinator determines that the system has entered a stable operating state and stops parameter iterative updates; when the system receives a stop command or the system is powered off, the entire control process terminates. The performance evaluation and parameter optimization process of the central coordinator is executed in parallel with the real-time control process of each local controller. The performance evaluation and parameter optimization process is triggered at a period lower than the sampling frequency of the real-time control process.

9. The adaptive loading control method for a distributed pump-controlled direct-drive electro-hydraulic system according to claim 5, characterized in that, When each local controller executes the parameter adaptive law, the adaptive gain coefficients are stored in logarithmic coordinates, and the adaptive gain coefficients are restored through logarithmic mapping when participating in the calculation. The error state vector is preprocessed by normalization before participating in the parameter adaptive law operation; The central coordinator uses the normalized dimensionless gain coefficient as the object of parameter optimization and distribution. The dimensionless gain coefficient is linearly mapped to the actual gain coefficient value range in logarithmic coordinates.

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