Track correction and control method for multi-axis electro-hydraulic servo system of radial forging machine

Abstract

The invention discloses a track correction and control method for a multi-axis electro-hydraulic servo system of a radial forging machine, and provides a cooperative control scheme fusing an extended state observer and online iterative learning for the composite control problem of coexistence of random high-frequency forging impact and workpiece axial plastic extension accumulated deviation in the radial forging process. According to the method, by establishing and discretizing a system model, on one hand, real-time estimation and feed-forward compensation are carried out on total disturbance including random impact by using an extended state observer; on the other hand, multi-step state prediction is carried out based on the discrete model, an online iterative learning algorithm is adopted to carry out iterative correction on prediction errors caused by slow change factors such as workpiece extension, and track correction is generated. Finally, disturbance compensation and trajectory correction jointly act on a controller, synchronous suppression and compensation of high-frequency random interference and low-frequency trend deviation are achieved, and trajectory tracking precision and robustness of the multi-axis system under strong impact and nonlinear working conditions are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of electro-hydraulic servo control technology, specifically a trajectory correction and control method for a multi-axis electro-hydraulic servo system of a radial forging machine that integrates extended state observation and online iterative learning. Background Technology

[0002] Radial forging, a key metal plastic forming process, utilizes the synergistic effect of multi-directional radial concentrated forces to induce continuous localized plastic deformation in metal billets, ultimately yielding high-precision, high-strength, and high-performance shafts, tubes, and irregularly shaped parts. This technology is widely used in the precision forming of core components for high-end equipment such as aero-engine main shafts, heavy-duty vehicle drive shafts, and nuclear power plant main pipelines, and is an indispensable key process in modern manufacturing.

[0003] The core actuators of a radial forging machine typically consist of four main shaft systems: the hammer shaft, the position shaft, the clamping pressure shaft, and the core-pulling shaft. Driven by a multi-axis electro-hydraulic servo system, each shaft system must achieve highly coordinated and precise motion. The planning and control accuracy of its motion trajectory directly determines the geometric dimensions, shape accuracy, internal structure, and mechanical properties of the forging, making it a crucial element in ensuring the quality of the final product.

[0004] To meet the requirements of high-precision forging, modern radial forging machines generally adopt multi-axis closed-loop electro-hydraulic servo control systems. Trajectory planning and tracking control, as the core function of the system, is responsible for generating the ideal motion trajectory of each axis according to the process requirements, and ensuring that the actual motion accurately reproduces the trajectory through real-time feedback control. However, the working conditions of radial forging are extremely harsh, mainly in the following two aspects. (1) High-frequency, high-energy random forging impact: During the forging process, hundreds or even thousands of forging actions per minute generate huge impact loads in milliseconds. This load is transmitted to the entire electro-hydraulic servo system through the frame and hydraulic pipeline, causing strong pressure pulsation, vibration and nonlinear transient response of the valve control cylinder system, which constitutes dynamic interference with large amplitude, wide bandwidth and strong randomness. (2) Cumulative disturbance caused by axial plastic extension of the workpiece: As forging proceeds, the metal billet undergoes significant axial plastic flow, resulting in a continuous increase in its length. This load change caused by the "workpiece lengthening" is a deterministic, slow process, but the additional load it generates on the position axis often far exceeds the clamping force. If targeted trajectory compensation is not performed, the tracking error will continue to accumulate, seriously affecting dimensional consistency.

[0005] Traditional control and trajectory planning methods have significant limitations in the face of such complex disturbances.

[0006] At the trajectory planning level, traditional methods are mostly statically preset, such as using S-curves or polynomial curves to ensure trajectory smoothness, but they do not take into account the real-time dynamic disturbances during the forging process. Essentially, it is an "open-loop" feedforward planning method, which cannot adaptively adjust according to the actual operating state of the system (such as the impact it receives or the changes in load). As a result, the preset "ideal trajectory" is difficult to accurately track under actual high-frequency impact conditions, and the tracking error fluctuates significantly with the operating conditions.

[0007] At the control strategy level, a single advanced control algorithm is unlikely to effectively cope with the two types of interference with vastly different characteristics at the same time.

[0008] (1) Disturbance immunity control for random shocks: such as the model-free adaptive control method based on RBF neural network disturbance observer disclosed in Chinese patent application CN112925208A, and the intelligent self-learning PID control method disclosed in Chinese patent application CN113110037A. These data-driven or model-independent methods can estimate and compensate for unknown disturbances to a certain extent, but their design intention is more inclined to deal with parameter uncertainty and general external load disturbances. In the context of random shocks of up to hundreds of hertz in radial forging, the dynamic response speed and observation bandwidth of these methods may be insufficient, and their disturbance estimation model may be difficult to converge quickly or be inaccurate due to the strong randomness of the shock.

[0009] (2) Learning control for repetitive / cumulative deviations: For example, iterative learning control (ILC) can use repetitive running information to correct the trajectory, and theoretically can handle repetitive deviations such as workpiece extension. However, traditional ILC is highly dependent on the strict repeatability of the process and is extremely sensitive to non-repetitive random forging impacts in radial forging. Impact disturbances will act as "non-repetitive disturbances" to destroy the learning process, making it difficult for the algorithm to converge or even diverge.

[0010] (3) Prediction-based optimization control: such as the control method based on reinforcement learning and future trajectory prediction disclosed in Chinese patent application CN120686611A, which optimizes the current decision by predicting the future state. However, such methods are usually computationally complex and rely on a large amount of data for training, making them difficult to apply directly in forging control that requires millisecond-level real-time response. Moreover, if the prediction model is linear or a simple nonlinear model, it is difficult to accurately describe the complex dynamics of the valve-controlled cylinder system under strong impact.

[0011] In summary, the dilemma of existing technologies is that if a strong disturbance rejection controller (such as observer-based control) is used to suppress random shocks, its response to slow-changing and cumulative deviations such as workpiece extension may be insufficient, and it cannot actively correct the trajectory setpoint. If a learning or prediction method is used to correct the trajectory to cope with workpiece extension, it is easy for learning to fail or prediction to be inaccurate due to contamination by random shocks.

[0012] Therefore, how to design a trajectory correction and control method that can coordinate high-frequency random impacts and low-frequency cumulative deviations, and achieve high-precision and high-robust trajectory tracking of a multi-axis electro-hydraulic servo system under radial forging conditions with strong nonlinearity and strong interference, has become a long-standing and urgent core technical problem in this field. Summary of the Invention

[0013] In view of this, the purpose of this invention is to provide a trajectory correction and control method for a multi-axis electro-hydraulic servo system of a radial forging machine. By integrating an extended state observer to estimate and compensate for random disturbances in real time, and combining an online iterative learning algorithm based on model prediction to correct trend trajectory deviations, the method ultimately achieves high-precision and high-robust trajectory tracking of the multi-axis electro-hydraulic servo system under strong nonlinear impact conditions, thus ensuring the forming quality of forgings.

[0014] To achieve the above objectives, the present invention provides the following technical solution: A method for trajectory correction and control of a multi-axis electro-hydraulic servo system for a radial forging machine includes the following steps: S1: Collect the real operating data of the multi-axis electro-hydraulic servo system under forging conditions. The real operating data includes the pressure in the rod chamber of the hydraulic cylinder, the pressure in the rodless chamber, and the displacement of the piston rod. S2: Based on the real operating data collected in step S1, establish a nonlinear state-space equation model for the valve-controlled hydraulic cylinder, and simplify the model into a standard nonlinear state-space equation model. S3: Based on the real operating data collected in step S1, determine the steady-state operating point of the system, and at this steady-state operating point, linearize the standard nonlinear state-space equation model obtained in step S2 to obtain the linearized state-space equation. S4: Based on the linearized state-space equation obtained in step S3, derive the open-loop transfer function of the system, and introduce a PID controller to construct a closed-loop control system to obtain the closed-loop transfer function of the system. S5: Convert the closed-loop transfer function obtained in step S4 into a discrete state-space equation form; S6: Perform point-to-point ideal tracking trajectory planning for each axis of the multi-axis electro-hydraulic servo system; S7: Based on the discrete state-space equations obtained in step S5 and the ideal tracking trajectory planned in step S6, the recursive method is used to predict the system state at multiple future sampling times; S8: Based on the error between the system state predicted in step S7 and the ideal tracking trajectory at the corresponding time, the trajectory correction amount at future control times is calculated using an online iterative learning algorithm, and this correction amount is superimposed on the current output of the controller to generate the final control command. S9: Construct an extended state observer, which takes the actual displacement and control commands of the system as input, and estimates and outputs the total disturbance of the system in real time; The total disturbance estimate output by the expansion state observer is used to feedforward the control command to suppress random high-frequency forging impact interference; the online iterative learning algorithm in step S8 is used to compensate and correct the cumulative trajectory deviation caused by the axial plastic extension of the workpiece.

[0015] Furthermore, in step S2, the nonlinear state-space equation model of the valve-controlled hydraulic cylinder is expressed as: in: This represents the piston rod displacement, in meters (m). The speed of the piston rod is expressed in m / s. This refers to the pressure in the rod chamber of the hydraulic cylinder, expressed in Pa. This refers to the pressure in the rodless chamber of the hydraulic cylinder, expressed in Pa. The speed of the piston rod is expressed in m / s. The acceleration of the piston rod is expressed in m / s². 2 ; The pressure change rate in the rod chamber is expressed in Pa / s. The pressure change rate in the rodless chamber is expressed in Pa / s. Mass, unit is kg; This refers to the input voltage of the servo valve, measured in volts (V). The piston area of ​​the rod chamber is expressed in m². 2 ; The area of ​​the rodless chamber piston is expressed in m². 2 ; This refers to the external load force, expressed in N (N). This refers to the volume of the rodless cavity, in cubic meters (m³). 3 ;; This refers to the volume of the rod cavity, in meters (m). 3 ; This is the equivalent pressure square root term of the flow coefficient on the rod-side cavity, in units of... ; This is the equivalent pressure square root term of the flow coefficient on the rodless cavity side, in units of... ; This is the internal leakage coefficient, in meters (m). 3 / (s·Pa); The flow coefficient is expressed in units of 1000 ppm. ; This refers to the servo valve gain, expressed in m / V. This refers to the elastic modulus of hydraulic oil, expressed in Pa. Valve core displacement, in meters (m). The pressure is the hydraulic oil source pressure, measured in Pa.

[0016] Furthermore, the standard nonlinear state-space equation model is expressed as: in: These are the state variables of the open-loop system. The derivatives of the state variables of the open-loop system; These are the observed values; The state matrix of the open-loop system; The input matrix; This is the output matrix.

[0017] Further, in step S3, the linearization process specifically involves: controlling the electro-hydraulic servo system to perform a uniform motion test, collecting data on the rodless chamber pressure, rod chamber pressure, and servo valve spool displacement of the hydraulic cylinder during this stage, and calculating their arithmetic mean. This arithmetic mean is used as the steady-state operating point parameter to calculate the linearized constant input matrix B; for the rodless chamber volume in the system matrix A that varies with the piston displacement... and rod cavity volume The initial volume of the rodless chamber when the piston is in the middle of its stroke is used. and the initial volume of the rod cavity To make a substitution.

[0018] Furthermore, in step S4, the closed-loop transfer function It is obtained through the following method: First, perform a Laplace transform on the linearized state-space equations to obtain the open-loop transfer function. : in: The Laplace transform of the output value; The Laplace transform of the input values; The state matrix of the open-loop system; The input matrix; This is the output matrix; It is the identity matrix; This is the Laplace transform operator.

[0019] Select sampling step size The open-loop transfer function Transform into discrete open-loop transfer function : in: for Transformation operators; This is the z-transform operator.

[0020] Combined with PID controller transfer function : Finally, the closed-loop transfer function is obtained. : in: This is the proportionality coefficient; The integral coefficient; These are the differential coefficients; This is for tracking error.

[0021] Furthermore, in step S5, the discrete state-space equation is expressed as: in: Let be the discrete state variables of the closed-loop system at time k; For the observed variables of the closed-loop system at time k; Let be the observed variables of the closed-loop system at time k; This is the state matrix of the closed-loop system; The input matrix; This is the output matrix.

[0022] Furthermore, in step S7, a recursive method is used to calculate the future... The system state is predicted using a sampling step size, and the prediction formula is: in: for Predicted values ​​of system state variables at time 1; For the current moment Real-time acquisition of actual system state variables; In order to be in Ideal tracking trajectory at any given moment; for Predicted system disturbance values ​​at time 1; , This is the number of sampling steps for predicting the time domain.

[0023] Furthermore, in step S8, the process of calculating the trajectory correction amount by the online iterative learning algorithm specifically includes: Based on the predicted future Prediction output for each sampling step The predicted tracking error is obtained as follows: in: For the future Prediction tracking error per sampling step; In order to be in Ideal tracking trajectory at any given moment; For the current moment Real-time acquisition of actual system state variables; for Predicted system disturbance values ​​at time 1; The system disturbance at time k; This is the state matrix of the closed-loop system; The input matrix; This is the output matrix; For matrix of Power of 1.

[0024] The online iterative learning algorithm is used to obtain the first... Trajectory correction amount: in: For the future moment The first step in trajectory correction Secondary trajectory correction amount; The gain coefficient for trajectory correction; Track correction amount Overlay system in the current Input trajectory at any moment The corrected system output trajectory is obtained above: in: The corrected system input trajectory; The system input trajectory before correction.

[0025] Furthermore, the gain coefficient The value of needs to be determined by balancing convergence speed and convergence stability, and the prediction time domain The value of needs to cover the impact period of a single impact disturbance.

[0026] Furthermore, in step S9, the mathematical model of the extended state observer is: in: This is the observation error; This represents the actual displacement of the system. , and For observer state variables; , and The derivative of the observer's state variables; , , , and These are the coefficients that need to be tuned; This is the actual input to the system; The function is a piecewise function: in: For function variables; The shape factor; For transition bandwidth coefficient; It is a symbolic function.

[0027] The beneficial effects of this invention are as follows: The trajectory correction and control method of the multi-axis electro-hydraulic servo system of the radial forging machine of the present invention produces significant and synergistic technical effects by integrating an extended state observer and an online iterative learning collaborative control architecture.

[0028] (1) High-precision suppression of composite interference is achieved: The extended state observer can treat high-frequency random forging impact, model uncertainty, etc. as a "total disturbance" and perform millisecond-level real-time observation and dynamic feedforward compensation, which significantly improves the system's instantaneous anti-interference capability against nonlinear strong impacts. At the same time, the online iterative learning algorithm based on model prediction is specifically designed for slow-varying and cumulative deviations such as workpiece axial extension. Through multi-step prediction and iterative correction, it actively and accurately adjusts the trajectory setpoint, effectively avoiding the accumulation of tracking errors. The two work together to achieve synchronous optimization processing of two types of core interference with drastically different frequency and time domain characteristics.

[0029] (2) Improved overall performance of multi-axis system trajectory tracking: Under strong interference conditions, the present invention significantly reduces and stabilizes the system trajectory tracking error, thereby significantly improving the overall accuracy and synchronization of multi-axis coordinated motion. This not only directly ensures the dimensional consistency, shape accuracy and internal structure uniformity of forgings, but also provides a reliable control basis for the realization of high-speed and high-frequency forging processes.

[0030] (3) Enhanced system robustness and engineering practicality: Compared with methods that rely on accurate models or large amounts of data for training, this invention retains the advantage of accuracy based on model prediction while compensating for model errors through an extended state observer (ESO), reducing the stringent dependence on model accuracy. The overall scheme has a clear structure, clear physical meaning of parameters, and good engineering feasibility. It exhibits stronger adaptability and reliability when facing complex working conditions such as parameter perturbations and load changes, and has outstanding engineering application value. Attached Figure Description

[0031] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a schematic diagram of the trajectory correction and control method of the multi-axis electro-hydraulic servo system for radial forging machines according to the present invention; Figure 2 This is a flowchart of the trajectory correction and control method of the multi-axis electro-hydraulic servo system for radial forging machines according to the present invention; Figure 3 For the ideal trajectory curve; Figure 4 The diagram shows the applied strong interference force; Figure 5 The chart shows a comparison of tracking errors under conditions of no trajectory correction, trajectory correction, ESO correction, and a combination of trajectory correction and ESO, taking into account strong interference. Figure 6 This is a comparison chart of tracking errors before and after trajectory correction, without considering strong interference. Figure 7 Comparison of trajectories before and after correction. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0033] In this embodiment, the goal of trajectory correction and control of the radial forging machine's multi-axis servo system is to correct deviations in the trajectory tracking process based on the system's real-time operating status data, ensuring the accuracy and stability of force and position control during multi-axis coordinated motion. For example... Figure 1 As shown, specifically, the predictive model infers the tracking error of the system in the next instant by observing the current system state, and incorporates this error as a trajectory correction term into the closed-loop regulation logic of the control system. By correcting the control commands in advance to offset potential deviations, the system's tracking accuracy and response speed are improved.

[0034] like Figure 2As shown in the figure, the trajectory correction and control method of the multi-axis electro-hydraulic servo system of the radial forging machine in this embodiment includes the following steps.

[0035] S1: Collect the actual operating data of the multi-axis electro-hydraulic servo system under forging conditions. The actual operating data includes the pressure in the rod chamber of the hydraulic cylinder, the pressure in the rodless chamber, and the displacement of the piston rod.

[0036] Specifically, the steps for collecting real data on the operation of the electro-hydraulic servo system are as follows.

[0037] The test preparation work was completed on the forging hydraulic press platform, including system pressure adjustment, accumulator pre-charging, cooling device setting, motor speed adjustment, etc. At the same time, test parameters such as load pressure, frequency, and impact conditions were determined according to the predicted target.

[0038] Flow rate and pressure sensors are installed in the rod chamber and rodless chamber of the hydraulic cylinder, respectively. A displacement sensor is installed on the piston rod of the hydraulic cylinder, and flow rate and pressure sensors are installed at the valve core outlet to ensure that complete working signals can be collected and that valve core feedback signals can be read.

[0039] The collected signals include the pressure in the rod chamber and the rodless chamber, and the displacement of the piston rod.

[0040] Simultaneously, based on the samples of each component of the electro-hydraulic servo system, it is necessary to obtain the valve orifice flow coefficient, hydraulic oil density, fluid bulk modulus, effective area of ​​the rodless chamber of the hydraulic cylinder, effective area of ​​the rod chamber of the hydraulic cylinder, initial left chamber volume of the hydraulic cylinder, initial right chamber volume of the hydraulic cylinder, internal leakage coefficient of the hydraulic cylinder, and load mass.

[0041] S2: Based on the real operating data collected in step S1, establish a nonlinear state-space equation model for the valve-controlled hydraulic cylinder, and simplify the model into a standard nonlinear state-space equation model.

[0042] Specifically, when establishing and simplifying the nonlinear state-space equation model of a valve-controlled hydraulic cylinder, it is first necessary to clarify the core state variables of the valve-controlled hydraulic cylinder system. Combining the system's dynamic characteristics and control requirements, key parameters that can comprehensively reflect the system's dynamic behavior are selected as system state variables, including: the extension displacement of the hydraulic cylinder piston rod. The unit is meters (m); the piston rod speed. The unit is m / s; the pressure in the rod chamber of the hydraulic cylinder. The unit is Pa; and the rodless chamber pressure. The unit is Pa. Before solving the simultaneous equations, it is necessary to unify the parameter definitions of each equation to ensure that the units of all physical quantities are consistent.

[0043] The nonlinear state-space equation model of a valve-controlled hydraulic cylinder is expressed as follows: in: This represents the piston rod displacement, in meters (m). The speed of the piston rod is expressed in m / s. This refers to the pressure in the rod chamber of the hydraulic cylinder, expressed in Pa. This refers to the pressure in the rodless chamber of the hydraulic cylinder, expressed in Pa. The speed of the piston rod is expressed in m / s. The acceleration of the piston rod is expressed in m / s². 2 ; The pressure change rate in the rod chamber is expressed in Pa / s. The pressure change rate in the rodless chamber is expressed in Pa / s. Mass, unit is kg; This refers to the input voltage of the servo valve, measured in volts (V). The piston area of ​​the rod chamber is expressed in m². 2 ; The area of ​​the rodless chamber piston is expressed in m². 2 ; This refers to the external load force, expressed in N (N). This refers to the volume of the rodless cavity, in cubic meters (m³). 3 ;; This refers to the volume of the rod cavity, in meters (m). 3 ; This is the equivalent pressure square root term of the flow coefficient on the rod-side cavity, in units of... ; This is the equivalent pressure square root term of the flow coefficient on the rodless cavity side, in units of... ; This is the internal leakage coefficient, in meters (m). 3 / (s·Pa); The flow coefficient is expressed in units of 1000 ppm. ; This refers to the servo valve gain, expressed in m / V. This refers to the elastic modulus of hydraulic oil, expressed in Pa. Valve core displacement, in meters (m). The pressure is the hydraulic oil source pressure, measured in Pa.

[0044] The state equation primarily describes the nonlinear relationship between the rate of change of the state variables and the state variables and input quantities, where the input quantity is the servo valve input voltage. The output equation is determined based on control requirements. A parameter that directly reflects the system's operating state and is easy to detect is selected as the output quantity; typically, the piston rod displacement is chosen. As output, the inherent nonlinear characteristics of the system must be preserved, such as the square root term in the flow equation and the coupling relationship between pressure and displacement, without excessive linearization, to ensure that the model can accurately reflect the real dynamic response of the valve-controlled cylinder system under complex operating conditions.

[0045] When simplifying the nonlinear state-space equation model of a valve-controlled cylinder, the state-space equations need to be transformed into a standard form. To adapt to the subsequent trajectory correction model operations and logic, the simplification work focuses on converting the state-space equations into the standard form. While preserving the core dynamic characteristics of the system, the equation structure is standardized, providing a concise and accurate mathematical foundation for trajectory prediction and correction. All matrix elements are composed of integrated parameters, clearly reflecting the linear relationships between state variables and between state variables and input quantities.

[0046] Design the output matrix appropriately to ensure piston rod displacement. As a direct output. Specifically, the standard nonlinear state-space equation model is expressed as: In the formula: in: These are the state variables of the open-loop system. The derivatives of the state variables of the open-loop system; These are the observed values; The state matrix of the open-loop system; The input matrix; This is the output matrix.

[0047] S3: Based on the real operating data collected in step S1, determine the steady-state operating point of the system, and linearize the standard nonlinear state-space equation model obtained in step S2 at the steady-state operating point to obtain the linearized state-space equation.

[0048] In this embodiment, the specific execution of the state-space equation model for the personalized valve-controlled cylinder is as follows.

[0049] First, the electro-hydraulic servo system is controlled to perform uniform motion tests under actual working conditions, and real-time data of the rodless chamber pressure, rod chamber pressure, and servo valve core displacement of the hydraulic cylinder are collected simultaneously and their arithmetic average is calculated.

[0050] Secondly, the arithmetic mean of the data from the uniform motion phase is taken as the steady-state operating point parameter for system linearization. This parameter is then substituted into the relevant formula in step S5 to calculate... as well as Then, these two parameters are substituted into matrix B, thereby simplifying matrix B into a constant matrix.

[0051] As for the rodless cavity volume in matrix A and rod cavity volume Because its variation range is small within the local linearization range, the initial volume value (including the initial volume of the rodless chamber) when the hydraulic cylinder piston is in the middle position of its stroke is used. and the initial volume of the rod cavity The substitution can be simplified.

[0052] S4: Based on the linearized state-space equation obtained in step S3, derive the open-loop transfer function of the system, and introduce a PID controller to construct a closed-loop control system, thereby obtaining the closed-loop transfer function of the system.

[0053] Specifically, to build the closed-loop control mathematical framework required for trajectory correction, the core of this step is to transform the simplified linearized state-space equation into a closed-loop transfer function, establish a clear mapping relationship between the input signal and the output trajectory, and provide a convenient computational basis for subsequent discretization processing and trajectory prediction.

[0054] Based on the standard nonlinear state-space equation model obtained in step S2, and combined with the steady-state working characteristics of the radial forging machine multi-axis servo system, precise linearization is performed at the system equilibrium point. Since trajectory correction relies on the dynamic response law under the stable operating state of the system, the linearization process strictly uses the actual steady-state value of the working condition collected in step S1 as the benchmark to ensure that the linearization model can accurately reflect the core dynamic characteristics of the system in the working range and avoid distortion of the transfer function due to deviation from the actual working condition.

[0055] In this embodiment, the closed-loop transfer function It is obtained through the following method.

[0056] First, a Laplace transform is performed on the linearized state-space equations to eliminate time-domain variables, transforming them into a complex frequency-domain expression. Based on the definition of the transfer function, the open-loop transfer function is obtained. : in: The Laplace transform of the output value; The Laplace transform of the input values; For the system matrix; The input matrix; This is the output matrix; It is the identity matrix; This is the Laplace transform operator.

[0057] Substituting the linearized matrix from step S3 into this equation yields the complex frequency domain relationship between voltage and output displacement.

[0058] Select an appropriate sampling step size , usually take The sampling step size is set to 1 / 5 to 1 / 10 of the system's minimum time constant. A zero-order hold is used to transform it into a discrete open-loop transfer function. This hold maintains a constant input signal within the sampling interval, closely matching the output characteristics of the digital controller and ensuring the integrity of the system's dynamic information during discretization. In this embodiment, the sampling step size is selected as... The open-loop transfer function Transform into discrete open-loop transfer function ,get: in: for Transformation operators; This is the z-transform operator.

[0059] Subsequently, a PID controller was introduced to construct a closed-loop control system. Based on the high-frequency impact conditions and trajectory tracking accuracy requirements of radial forging, the structure and core parameters of the PID controller were determined: proportional coefficient. Integral coefficient and differential coefficients In this embodiment, the transfer function of the PID controller is defined as: It is important to note that when tuning PID parameters, it is necessary to ensure system stability, high tracking accuracy, fast response speed, and a certain bandwidth. This can further reduce the impact of inaccurate models after linearization of the valve-controlled cylinder nonlinear system.

[0060] Based on the PID controller transfer function, the closed-loop transfer function can be finally obtained. : in: This is the proportionality coefficient; The integral coefficient; These are the differential coefficients; This is for tracking error.

[0061] S5: Convert the closed-loop transfer function obtained in step S4 into a discrete state-space equation form. Specifically, the discrete state-space equation is expressed as: in: Let be the discrete state variables of the closed-loop system at time k; For the observed variables of the closed-loop system at time k; Let be the observed variables of the closed-loop system at time k; This is the state matrix of the closed-loop system; The input matrix; This is the output matrix.

[0062] S6: Perform point-to-point ideal tracking trajectory planning for each axis of the multi-axis electro-hydraulic servo system. For example... Figure 3 As shown in this embodiment, the ideal trajectory planning from point to point can be performed using traditional methods, such as seven-segment S-curve planning, polynomial planning, etc., which will not be elaborated further.

[0063] S7: Based on the discrete state-space equations obtained in step S5 and the ideal tracking trajectory planned in step S6, the system state at multiple future sampling times is predicted using a recursive method.

[0064] The core of this step is to accurately predict the dynamic state of the system in the future time period based on the established closed-loop discrete state space equation and the planned target trajectory. This provides a reliable predictive basis for subsequent error calculation and trajectory correction determination, ensuring that trajectory correction can cope with dynamic disturbances such as high-frequency impacts in advance.

[0065] Multi-step state prediction based on recursion: From the current time step Begin by collecting real-time status data. With input Substituting into the discrete state-space equations, the predicted state variables for the next time step are calculated. Later As a new input state, combined with the target trajectory in Expected input at time Recursively obtained Predicted state at time ; and so on, to obtain the final predicted time in the time domain. The state prediction. In summary, this embodiment uses a recursive method to predict the future state. The system state is predicted using a sampling step size, and the prediction formula is: in: for Predicted values ​​of system state variables at time 1; For the current moment Real-time acquisition of actual system state variables; In order to be in Ideal tracking trajectory at any given moment; for Predicted system disturbance values ​​at time 1; , This is the number of sampling steps for predicting the time domain.

[0066] It should be noted that due to the inaccuracy of the prediction model, To obtain the smallest possible value, generally take This ensures that the prediction covers the impact period of a single shock disturbance, while avoiding error accumulation due to an excessively long prediction time domain.

[0067] Finally, the output at the final prediction time is calculated using the output equation, as shown in the following formula: Meanwhile, based on the assumption of gradual change in perturbation, the perturbation prediction in this embodiment is as follows: in: For the predicted future Predicted output for each sampling step; In order to be in The ideal tracking trajectory at any given moment; For the current moment Real-time acquisition of actual system state variables; for Predicted system disturbance values ​​at time 1; The system disturbance at time k; For matrix of Power of 1.

[0068] S8: Based on the error between the system state predicted in step S7 and the ideal tracking trajectory at the corresponding time, the trajectory correction amount for future control times is calculated using an online iterative learning algorithm, and this correction amount is superimposed on the current output of the controller to generate the final control command.

[0069] The core of this step is to accurately calculate the trajectory correction amount through iterative calculation based on the multi-step state prediction results of step S7, and to transform the prediction error into a correction command that can be directly applied to the control system, thereby achieving predictive cancellation of high-frequency impact interference and ensuring the force position control accuracy and trajectory tracking stability of the multi-axis servo system.

[0070] In this embodiment, the process of calculating the trajectory correction amount by the online iterative learning algorithm is as follows.

[0071] Based on the predicted future Prediction output for each sampling step The predicted tracking error is obtained as follows: in: For the future Prediction tracking error per sampling step; In order to be in Ideal tracking trajectory at any given moment; For the predicted future The predicted output for each sampling step.

[0072] The corresponding trajectory correction for the first iteration is: in: For the future moment The amount of the first trajectory correction; The gain coefficient for trajectory correction; The larger the value, the faster the convergence, but the more sensitive it is to noise and the worse the convergence stability.

[0073] The tracking error after the first correction is: in: For the future moment The tracking error after the first trajectory correction; The coefficients are calculated from the matrix; For matrix of Power of 1.

[0074] The second trajectory correction is equal to: in: For the future moment The second trajectory correction amount.

[0075] For the future moment When performing trajectory correction, it is important to note that In this embodiment, because Therefore, it is generally taken .

[0076] By analogy, an online iterative learning algorithm can be used to obtain the first... Trajectory correction amount: in: For the future moment The first step in trajectory correction Secondary trajectory correction amount.

[0077] Finally, the total correction amount is incorporated into the closed-loop logic of the control system: Superimposed on the original system input trajectory The corrected system input trajectory is obtained: in: The corrected system input trajectory; The system input trajectory before correction.

[0078] By adjusting the servo valve action in advance through this correction command, deviations caused by dynamic interference such as high-frequency impacts and changes in workpiece deformation resistance are offset, continuously ensuring the accuracy of force and position control and the stability of trajectory tracking in multi-axis coordinated motion, and ultimately meeting the dimensional consistency and forming quality requirements of high-end forgings.

[0079] If the prediction model is accurate enough, the final tracking error of the system will be: Finally, the total trajectory correction is obtained through iterative accumulation. When the prediction model has high enough accuracy and When the system tracking error gradually converges to 0, it achieves accurate trajectory correction.

[0080] In this embodiment, the gain coefficient The value of needs to be determined by balancing convergence speed and convergence stability, and the prediction time domain The value of needs to cover the impact period of a single impact disturbance.

[0081] S9: Construct an extended state observer, which takes the actual displacement and control commands of the system as input, and estimates and outputs the total disturbance of the system in real time.

[0082] In this embodiment, the mathematical model of the extended state observer is defined as follows: in: This is the observation error; This represents the actual displacement of the system. , and For observer state variables; , and The derivative of the observer's state variables; , , , and These are the coefficients that need to be tuned; This is the actual input to the system; The function is a piecewise function: in: For function variables; The shape factor; For transition bandwidth coefficient; It is a symbolic function.

[0083] like Figure 3 The image shown is a graph of the ideal trajectory. Figure 4 The diagram shown is a diagram of the applied strong interference force. Figure 5 This chart compares the tracking errors under conditions of strong interference: no trajectory correction, trajectory correction, ESO correction, and a combination of trajectory correction and ESO. Figure 6 This is a comparison curve of tracking error before and after trajectory correction, without considering strong interference. Figure 7 This is a comparison chart of the ideal trajectory before and after correction. (From...) Figure 3-7 Therefore, the trajectory correction and control method for the multi-axis electro-hydraulic servo system of the radial forging machine proposed in this embodiment integrates expansion state observation and online iterative learning. Compared with existing methods, the core advantage of this embodiment lies in achieving high-precision trajectory tracking of the position control axis under complex impact conditions by suppressing forging impact interference and performing trajectory correction in conjunction with workpiece deformation. By introducing an expansion state observer (ESO), the external random forging impact of the electro-hydraulic servo system is regarded as a "total disturbance" for real-time observation and compensation, which significantly improves the system's anti-interference capability under nonlinear conditions. At the same time, combined with the online iterative learning algorithm, dynamic learning and trajectory correction are performed on the cumulative position deviation caused by the axial plastic extension of the workpiece during forging, reducing the trajectory tracking error caused by high-frequency impact interference and changes in workpiece deformation resistance, and improving the response speed and anti-dynamic interference capability of the multi-axis servo system.

[0084] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A trajectory correction and control method for a multi-axis electro-hydraulic servo system of a radial forging machine, characterized in that: Includes the following steps: S1: Collect the real operating data of the multi-axis electro-hydraulic servo system under forging conditions. The real operating data includes the pressure in the rod chamber of the hydraulic cylinder, the pressure in the rodless chamber, and the displacement of the piston rod. S2: Based on the real operating data collected in step S1, establish a nonlinear state-space equation model for the valve-controlled hydraulic cylinder, and simplify the model into a standard nonlinear state-space equation model. S3: Based on the real operating data collected in step S1, determine the steady-state operating point of the system, and at this steady-state operating point, linearize the standard nonlinear state-space equation model obtained in step S2 to obtain the linearized state-space equation. S4: Based on the linearized state-space equation obtained in step S3, derive the open-loop transfer function of the system, and introduce a PID controller to construct a closed-loop control system to obtain the closed-loop transfer function of the system. S5: Convert the closed-loop transfer function obtained in step S4 into a discrete state-space equation form; S6: Perform point-to-point ideal tracking trajectory planning for each axis of the multi-axis electro-hydraulic servo system; S7: Based on the discrete state-space equations obtained in step S5 and the ideal tracking trajectory planned in step S6, the recursive method is used to predict the system state at multiple future sampling times; S8: Based on the error between the system state predicted in step S7 and the ideal tracking trajectory at the corresponding time, the trajectory correction amount at future control times is calculated using an online iterative learning algorithm, and this correction amount is superimposed on the current output of the controller to generate the final control command. S9: Construct an extended state observer, which takes the actual displacement and control commands of the system as input, and estimates and outputs the total disturbance of the system in real time; The total disturbance estimate output by the expansion state observer is used to feedforward the control command to suppress random high-frequency forging impact interference; the online iterative learning algorithm in step S8 is used to compensate and correct the cumulative trajectory deviation caused by the axial plastic extension of the workpiece.

2. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of a radial forging machine according to claim 1, characterized in that: In step S2, the nonlinear state-space equation model of the valve-controlled hydraulic cylinder is expressed as: in: This represents the piston rod displacement, in meters (m). The speed of the piston rod is expressed in m / s. This refers to the pressure in the rod chamber of the hydraulic cylinder, expressed in Pa. This refers to the pressure in the rodless chamber of the hydraulic cylinder, expressed in Pa. The speed of the piston rod is expressed in m / s. The acceleration of the piston rod is expressed in m / s². 2 ; The pressure change rate in the rod chamber is expressed in Pa / s. The rate of change of pressure in the rodless chamber is expressed in Pa / s. Mass, unit is kg; This refers to the input voltage of the servo valve, measured in volts (V). The piston area of ​​the rod chamber is expressed in m². 2 ; The area of ​​the rodless chamber piston is expressed in m². 2 ; This refers to the external load force, expressed in N (N). This refers to the volume of the rodless cavity, in cubic meters (m³). 3 ;; This refers to the volume of the rod cavity, in meters (m). 3 ; This is the equivalent pressure square root term of the flow coefficient on the rod-side cavity, in units of... ; This is the equivalent pressure square root term of the flow coefficient on the rodless cavity side, in units of... ; This is the internal leakage coefficient, in meters (m). 3 / (s·Pa); The flow coefficient is expressed in units of 1000 ppm. ; This refers to the servo valve gain, expressed in m / V. This refers to the elastic modulus of hydraulic oil, expressed in Pa. Valve core displacement, in meters (m). The pressure is the hydraulic oil source pressure, measured in Pa.

3. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of the radial forging machine according to claim 2, characterized in that: The standard nonlinear state-space equation model is expressed as: in: These are the state variables of the open-loop system. The derivatives of the state variables of the open-loop system; These are the observed values; The state matrix of the open-loop system; The input matrix; This is the output matrix.

4. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of a radial forging machine according to claim 1, characterized in that: In step S3, the linearization process specifically involves: controlling the electro-hydraulic servo system to perform a uniform motion test, collecting data on the rodless chamber pressure, rod chamber pressure, and servo valve spool displacement of the hydraulic cylinder during this stage, and calculating their arithmetic mean. This arithmetic mean is used as the steady-state operating point parameter to calculate the linearized constant input matrix B; for the rodless chamber volume in system matrix A that varies with piston displacement... and rod cavity volume The initial volume of the rodless chamber when the piston is in the middle of its stroke is used. and the initial volume of the rod cavity To make a substitution.

5. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of a radial forging machine according to claim 1, characterized in that: In step S4, the closed-loop transfer function It is obtained through the following method: First, perform a Laplace transform on the linearized state-space equations to obtain the open-loop transfer function. : in: The Laplace transform of the output value; The Laplace transform of the input values; For the system matrix; The input matrix; This is the output matrix; It is the identity matrix; For the Laplace transform operator; Select sampling step size The open-loop transfer function Transform into discrete open-loop transfer function : in: for Transformation operators; For z-transform operators; Combined with PID controller transfer function : Finally, the closed-loop transfer function is obtained. : in: This is the proportionality coefficient; The integral coefficient; These are the differential coefficients; This is for tracking error.

6. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of a radial forging machine according to claim 1, characterized in that: In step S5, the discrete state-space equation is expressed as: in: Let be the discrete state variables of the closed-loop system at time k; For the observed variables of the closed-loop system at time k; Let be the observed variables of the closed-loop system at time k; This is the state matrix of the closed-loop system; The input matrix; This is the output matrix.

7. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of a radial forging machine according to claim 1, characterized in that: In step S7, a recursive method is used to calculate the future... The system state is predicted using a sampling step size, and the prediction formula is: in: for Predicted values ​​of system state variables at time 1; For the current moment Real-time acquisition of actual system state variables; In order to be in Ideal tracking trajectory at any given moment; for Predicted system disturbance values ​​at time 1; , This is the number of sampling steps for predicting the time domain.

8. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of a radial forging machine according to claim 1, characterized in that: In step S8, the process of calculating the trajectory correction amount by the online iterative learning algorithm specifically includes: Based on the predicted future Prediction output for each sampling step The predicted tracking error is obtained as follows: in: For the future Prediction tracking error per sampling step; In order to be in Ideal tracking trajectory at any given moment; For the current moment Real-time acquisition of actual system state variables; for Predicted system disturbance values ​​at time 1; The system disturbance at time k; This is the state matrix of the closed-loop system; The input matrix; This is the output matrix; For matrix of Power; The online iterative learning algorithm is used to obtain the first... Trajectory correction amount: in: For the future moment The first step in trajectory correction Secondary trajectory correction amount; The gain coefficient for trajectory correction; Track correction amount Overlay onto the system in the current Input trajectory at any moment The corrected system input trajectory is obtained above: in: The corrected system input trajectory; The system input trajectory before correction.

9. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of a radial forging machine according to claim 8, characterized in that: The gain coefficient The value of needs to be determined by balancing convergence speed and convergence stability, and the prediction time domain The value of needs to cover the impact period of a single impact disturbance.

10. The trajectory correction and control method for the multi-axis electro-hydraulic servo system of a radial forging machine according to claim 1, characterized in that: In step S9, the mathematical model of the extended state observer is: in: This is the observation error; This represents the actual displacement of the system. , and For observer state variables; , and The derivative of the observer's state variables; , , , and These are the coefficients that need to be tuned; This is the actual input to the system; The function is a piecewise function: in: For function variables; The shape factor; Transition bandwidth coefficient; It is a symbolic function.

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