Adaptive model predictive pressure control method and system for pump-controlled electro-hydraulic actuators

Abstract

The application provides an adaptive model predictive pressure control method and system of a pump-controlled electro-hydraulic actuator, the method determines the load elasticity coefficient estimation value of the hydraulic system at time k according to the recursive least square method with genetic factors; the system matrix and the input matrix of the state space model of the hydraulic system are updated according to the load elasticity coefficient estimation value and the volume of the rodless cavity in the hydraulic system; the reference torque of the permanent magnet synchronous motor is determined according to the updated system matrix, the input matrix, the reference displacement of the hydraulic cylinder piston rod of the hydraulic system, the reference speed of the piston of the hydraulic system, the reference speed of the permanent magnet synchronous motor, the reference pressure of the rod cavity of the hydraulic cylinder of the hydraulic system and the constraints of the permanent magnet synchronous motor and the quantitative pump of the hydraulic system; and the permanent magnet synchronous motor is driven according to the reference torque. The method can avoid the dynamic performance attenuation caused by model mismatch, the torque driving can improve the response speed, and the excellent performance of the direct-drive pump-controlled electro-hydraulic actuator under different working conditions is ensured.

Description

Technical Field

[0001] This application relates to the field of electro-hydraulic servo control technology, and in particular to an adaptive model predictive pressure control method and system for a pump-controlled electro-hydraulic actuator. Background Technology

[0002] Stand-alone electro-hydraulic actuators are a promising technology that utilizes variable-speed motors and bidirectional servo pumps as the main control elements to regulate the movement of hydraulic cylinders. Compared to traditional valve-controlled systems, these pump-controlled actuators minimize throttling losses by eliminating proportional valves; compared to electromechanical actuators, hydraulic transmission still maintains the advantages of a high power-to-weight ratio, no backlash, and impact absorption capacity. Stand-alone electro-hydraulic actuators offer higher power-to-weight ratios, better maintainability, and stronger robustness. However, electro-hydraulic servo systems are typical nonlinear systems, exhibiting numerous nonlinear characteristics and model uncertainties. As industry demands increasingly higher control performance from electro-hydraulic servo systems, traditional classical PID control theory is no longer sufficient. Therefore, researching more advanced nonlinear control theories to address the nonlinear characteristics of electro-hydraulic servo systems is urgently needed. Moreover, in pump-controlled systems, the pressure of the hydraulic circuit, the speed of the pump and motor, and the torque provided by the permanent magnet synchronous motor are all limited by electromechanical hardware, resulting in slower dynamic response compared to valve-controlled systems, leading to dynamic performance degradation of electro-hydraulic actuators during use.

[0003] Therefore, there is an urgent need for a control method for regulating electro-hydraulic actuators to avoid dynamic performance degradation during use. Summary of the Invention

[0004] To address the aforementioned technical problems, this application provides an adaptive model predictive pressure control method and system for pump-controlled electro-hydraulic actuators, in order to avoid dynamic performance degradation of the electro-hydraulic actuators during use.

[0005] The first aspect of this application provides an adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator. This method is applied to the adaptive model predictive pressure control system of the pump-controlled electro-hydraulic actuator. The control system of the actuator includes a permanent magnet synchronous motor and a hydraulic system. The output terminal of the permanent magnet synchronous motor is connected to the input terminal of the hydraulic system. The adaptive model predictive pressure control method includes: determining the estimated load elasticity coefficient of the hydraulic system at time k using a recursive least squares method with genetic factors. Based on the estimated value of the load elasticity coefficient The system matrix A and input matrix B of the state-space model of the hydraulic system are updated based on the rodless cavity volume V1 in the hydraulic system; the updated system matrix A, input matrix B, and reference displacement of the hydraulic cylinder piston rod are then used to update the state-space model. Piston reference speed of hydraulic system The reference speed ω of a permanent magnet synchronous motor * Reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system Determine the reference torque of the permanent magnet synchronous motor based on the constraints of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system. According to the reference torque Drives a permanent magnet synchronous motor.

[0006] In some implementations, the estimated load elasticity coefficient of the hydraulic system at time k is determined using a recursive least squares method with genetic factors. Including: the displacement x of the hydraulic cylinder piston rod at time k+2. p(k+2) At time k+1, the displacement x of the hydraulic cylinder piston rod p(k+1) At time k, the displacement x of the hydraulic cylinder piston rod p(k) At time k, the rodless chamber p of the hydraulic cylinder 1(k) At time k, the rod chamber p of the hydraulic cylinder 2(k) Determine the output vector y of the hydraulic system at time k. (k) Input vector of hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) ; where the output vector y of the hydraulic system (k) Input vector of hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) satisfy:

[0007] Where m is the load mass, A a A represents the effective area of ​​the rodless chamber piston in a hydraulic cylinder. b b is the effective area of ​​the piston in the rod chamber of the hydraulic cylinder. v T is the viscous damping coefficient. s k is the sampling period. s The load elasticity coefficient is given by the output vector y of the hydraulic system. (k) Input vector of hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Determine the estimated load elasticity coefficient at time k.

[0008] In some implementations, based on the output vector y of the hydraulic system (k) Input vector of hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Determine the estimated load elasticity coefficient at time k. This includes: using recursive least squares with genetic factors, and based on the output vector y of the hydraulic system. (k) Input vector of hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Determine the observed values ​​of the unknown parameter vector Based on the observed values ​​of the unknown parameter vector Sampling period T s and viscous damping coefficient b v Determine the estimated value of the load elasticity coefficient

[0009] In some implementations, the estimated value of the load resilience coefficient is determined. Previously, the method also included: determining the state-space model of the hydraulic system; the state-space model was... x is the state variable of the state-space model. Let x be the first derivative of x, u be the input vector, and u = T e T e This refers to the torque of a permanent magnet synchronous motor.

[0010]

[0011] C is the output matrix of the state-space model, D is the direct transfer matrix of the state-space model, and β e For effective elastic modulus, V1 is the volume of the rodless chamber of the hydraulic cylinder, and C is the effective elastic modulus. i D is the internal leakage coefficient of the hydraulic cylinder. p Where J is the pump displacement, B is the moment of inertia, and J is the displacement of the pump. m It is the coefficient of viscous friction.

[0012] In some implementations, the state-space model of the hydraulic system is determined, including: determining the state-space model of the hydraulic system based on the motion equation of the permanent magnet synchronous motor, the hydraulic cylinder force balance equation of the hydraulic system, the fixed displacement pump flow equation of the hydraulic system, and the load torque of the fixed displacement pump.

[0013] In some implementations, the updated system matrix A, input matrix B, and reference displacement of the hydraulic cylinder piston rod of the hydraulic system are used as the basis. Piston reference speed of hydraulic system The reference speed ω of a permanent magnet synchronous motor * Reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system Determine the reference torque of the permanent magnet synchronous motor based on the constraints of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system. This includes: determining the incremental state-space model of the hydraulic system based on the updated system matrix A and input matrix B; wherein the incremental state-space model is:

[0014]

[0015] A oFor the system matrix of the incremental state-space model, B o C is the input matrix of the incremental state-space model. o The output matrix of the incremental state-space model is y. k Let z be the output variable of the incremental state-space model at time k. k Let z be the output variable at time k of the incremental state-space model. k+1 Let Δu be the output variable at time k+1 of the incremental state-space model. k The input variables are the system matrix A of the updated incremental state-space model. o Input matrix B o Output matrix C o Predicting the time domain N p and control time domain N c Determine the differential state matrix F and differential input matrix G of the hydraulic system; determine the relationship between the differential state matrix F, differential input matrix G, differential torque increment ΔU, and the torque reference increment Y at the next moment; based on the relationship, the differential torque increment ΔU, and the reference displacement of the hydraulic cylinder piston rod... Piston reference speed of hydraulic system Reference speed ω of permanent magnet synchronous motor * Reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system Determine the reference torque of the permanent magnet synchronous motor based on the constraints of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system.

[0016] In some implementations, based on the relational formula, the differential torque increment ΔU, and the reference displacement of the hydraulic cylinder piston rod... Piston reference speed of hydraulic system Reference speed ω of permanent magnet synchronous motor * Reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system Determine the reference torque of the permanent magnet synchronous motor based on the constraints of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system. This includes: determining the cost function J1 of the hydraulic system based on the relational expression and the differential torque increment ΔU; wherein the cost function J1 satisfies the fixed displacement pump constraint conditions of the permanent magnet synchronous motor and the hydraulic system, and the constraint conditions are:

[0017]

[0018] ω max Let ω(k) be the maximum mechanical angular velocity of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system at time k, and Δω(k+1) be the difference between the mechanical angular velocities at time k+1 and time k. emaxT represents the maximum torque limit of a permanent magnet synchronous motor. e (k) represents the torque of the permanent magnet synchronous motor at time k, ΔT e (k+1) is the difference in torque between time k+1 and time k, r tmax For ΔT e (k+1) Maximum limit; minimize the control cost function J1 to obtain the reference torque of the permanent magnet synchronous motor.

[0019] In some implementations, minimizing the control cost function J1 yields the reference torque of the permanent magnet synchronous motor. This includes: minimizing the control cost function J1 to determine the optimal differential torque increment ΔU; and determining the optimal input variable Δu of the incremental state-space model based on the optimal differential torque increment ΔU. k ;in,

[0020] In some implementations, the relation is Y = Fx k +GΔU;

[0021] in,

[0022]

[0023] C0 = [OI], where O is an empty matrix; B d =BT s ,

[0024] Let A be the system matrix after parameter updates, and I be the identity vector matrix.

[0025] The first aspect of this application provides an adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator. The pressure control employs adaptive model predictive control (AMPC) based on the torque output of a permanent magnet synchronous motor, which improves pressure control accuracy and response speed. It also incorporates a recursive least squares (FFRLS) design process with a forgetting factor. Online parameter identification uses FFRLS with a forgetting factor to estimate the unknown load elasticity coefficient, updating the system's volume parameters in real time. The parameter identification results and cavity volume parameters are used to update the model parameters, avoiding dynamic performance degradation caused by model mismatch. Torque drive further improves response speed.

[0026] The second aspect of this application provides an adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator, employing the method provided in the first aspect. The control system includes: a first determining module configured to determine an estimate of the load elasticity coefficient of the hydraulic system at time k using a recursive least squares method with genetic factors. The update module is configured to update based on the load resilience coefficient estimate. The system matrix A and input matrix B of the state space model of the hydraulic system are updated based on the rodless cavity volume V1 in the hydraulic system; the second determining module is configured to update the system matrix A and input matrix B of the state space model of the hydraulic system based on the updated system matrix A, input matrix B, and reference displacement of the hydraulic cylinder piston rod of the hydraulic system. Piston reference speed of hydraulic system The reference speed ω of a permanent magnet synchronous motor * Reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system Determine the reference torque of the permanent magnet synchronous motor based on the constraints of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system. The drive module is configured to operate based on a reference torque. Drives a permanent magnet synchronous motor.

[0027] The adaptive model predictive pressure control system for the pump-controlled electro-hydraulic actuator provided in the second aspect of this application adopts the adaptive model predictive pressure control method for the pump-controlled electro-hydraulic actuator provided in the first aspect. Therefore, its beneficial technical effects can be found in the first aspect, and will not be repeated here. Attached Figure Description

[0028] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a schematic diagram of the structure of an adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator provided in an embodiment of this application;

[0030] Figure 2 This is a flowchart illustrating an adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator provided in an embodiment of this application.

[0031] Figure 3 This is a schematic diagram of a permanent magnet synchronous motor in different quadrant rotation states provided in an embodiment of this application;

[0032] Figure 4 This is a general control block diagram of an adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator provided in an embodiment of this application;

[0033] Figure 5 This is a structural block diagram of an adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator provided in an embodiment of this application.

[0034] Illustration markings:

[0035] 1-Elastic load, 2-Hydraulic cylinder, 3-Relief valve, 4-Hydraulic check valve, 5-Measuring pump, 6-Permanent magnet synchronous motor, 7-Accumulator;

[0036] 100 - Control system; 101 - First determination module; 102 - Update module; 103 - Second determination module; 104 - Drive module. Detailed Implementation

[0037] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are all within the protection scope of this application.

[0038] In the following description, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this application, unless otherwise stated, "a plurality of" means two or more.

[0039] Furthermore, in this application, directional terms such as "upper," "lower," "inner," and "outer" are defined relative to the indicated placement of the components in the accompanying drawings. It should be understood that these directional terms are relative concepts, used for relative description and clarification, and can change accordingly depending on the placement of the components in the accompanying drawings.

[0040] Permanent Magnet Synchronous Motor (PMSM) drives are used across various industrial sectors, ranging from electromechanical actuators to electrohydraulic drives. Compared to electromechanical actuators, electrohydraulic drives offer significant advantages in terms of high power density, reliability, and robustness. Specifically, electrohydraulic actuators are the preferred choice for heavy machinery because they can apply large forces and absorb shocks and collisions. However, the energy efficiency of fluid transmission in traditional electrohydraulic systems is affected by throttling losses generated in fluid control valves. Therefore, pump-controlled hydraulic actuators, with their lower throttling losses and higher compactness, have been extensively studied. Pump-controlled direct-drive servo systems suffer from slow response rates and insufficient robustness, hindering their widespread adoption in civilian industries. Pump-controlled direct-drive actuators used in servo stamping and plastic forming CNC machine tools suffer from control model mismatch due to the difficulty in determining the elastic coefficient of the stamped parts and the variation in cavity volume during motion, significantly reducing the dynamic servo performance of the system.

[0041] Currently, most pump-controlled direct-drive solutions still use variable speed strategies to regulate system pressure. Pressure control in pump-controlled systems typically utilizes speed combined with pressure feedback to control system pressure, but this is difficult to achieve simultaneously with high-frequency response and zero overshoot. Traditional control methods (such as Proportion Integral Differential (PID)) struggle to achieve high-precision control for electro-hydraulic servo systems with parameter uncertainties. Model Predictive Control (MPC) relies on an accurate model of the controlled system, but model parameters are difficult to obtain in actual systems.

[0042] To improve the control accuracy and response speed of pump-controlled direct-drive electro-hydraulic actuators and avoid dynamic performance degradation caused by model mismatch, this application employs Adaptive Model Predictive Control (AMPC) based on motor torque output. Compared to traditional PID control, this improves control accuracy and response speed; compared to variable speed control, it reduces series control loops, thus improving response speed; and compared to traditional model predictive control, it uses Forgetting Factor Recursive Least Square (FFRLS) to identify unknown load elasticity coefficients online and update the system's volume parameters in real time. The parameter identification results and cavity volume parameters are used to update model parameters, thus avoiding dynamic performance degradation caused by model mismatch.

[0043] Figure 1 This is a schematic diagram of the structure of an adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator provided in an embodiment of this application.

[0044] like Figure 1 As shown, the electro-hydraulic actuator mainly uses a variable speed motor and a bidirectional servo pump as the main control elements to regulate the movement of the hydraulic cylinder. This system is a closed-loop pump-controlled direct-drive system, including an elastic load 1, an asymmetrical hydraulic cylinder 2, a relief valve 3, a hydraulically controlled check valve 4, a bidirectional fixed displacement pump 5, a permanent magnet synchronous motor 6, and an accumulator 7. The relief valve 3 serves as a safety protection mechanism in the system. The two ends of the bidirectional fixed displacement pump 5 are directly connected to the two chambers of the hydraulic cylinder 2. The permanent magnet synchronous motor 6 drives the fixed displacement pump 5 to control the flow and pressure of the hydraulic cylinder by adjusting its torque and speed. The asymmetrical flow is supplemented through the accumulator 7 and the hydraulically controlled check valve 4.

[0045] Figure 2 This is a schematic flowchart of an adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator provided in an embodiment of this application.

[0046] like Figure 2As shown, this method is applied to an adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator. The control system includes a permanent magnet synchronous motor and a hydraulic system. The output end of the permanent magnet synchronous motor is connected to the input end of the hydraulic system. The hydraulic system may include the other components mentioned above besides the permanent magnet synchronous motor 6. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator provided in this application embodiment can be implemented by the following steps S1 to S5.

[0047] Step S1: Determine the state-space model of the hydraulic system.

[0048] In step S1, the state-space model of the hydraulic system can be determined based on the motion equation of the permanent magnet synchronous motor, the hydraulic cylinder force balance equation of the hydraulic system, the flow equation of the fixed displacement pump, and the load torque of the fixed displacement pump.

[0049] 1. Permanent Magnet Synchronous Motor Model

[0050] The equation of motion for the permanent magnet synchronous motor is given by formula (1):

[0051]

[0052] In the formula: J is the moment of inertia, ω is the rotor's electrical angular velocity, and B... m T is the coefficient of viscous friction. e Motor torque; T L Load torque, t is time. θ is the rotor electrical angular displacement.

[0053] 2. Hydraulic Subsystem Model

[0054] Figure 3 This is a schematic diagram of a permanent magnet synchronous motor rotating in different quadrants, provided in an embodiment of this application.

[0055] like Figure 3 As shown, this invention takes the operation of a permanent magnet synchronous motor and a fixed displacement pump in quadrants I and III as the research object. Except for the change in the effective area of ​​the hydraulic cylinder, the dynamics of the motion quadrants II and IV are equivalent.

[0056] Mathematical model of asymmetric hydraulic cylinder

[0057] The force balance equation of the hydraulic cylinder is expressed as formula (2):

[0058]

[0059] In the formula: m is the load mass, A a A represents the effective area of ​​the rodless chamber piston in a hydraulic cylinder. b b is the effective area of ​​the piston in the rod chamber of the hydraulic cylinder. v k is the viscous damping coefficient. sF is the load elasticity coefficient. f For nonlinear loads and their disturbances, x p This refers to the displacement of the hydraulic cylinder piston rod. Let be the speed of the hydraulic cylinder piston rod (the derivative of the piston rod displacement). p1 is the acceleration of the hydraulic cylinder piston rod (the second derivative of the piston rod displacement), p2 is the pressure in the rodless chamber of the hydraulic cylinder, and p3 is the pressure in the rod chamber of the hydraulic cylinder.

[0060] Ignoring external leakage of the hydraulic cylinder, the pressure dynamics of the two chambers of the hydraulic cylinder can be modeled as formulas (3) to (4):

[0061]

[0062] In the formula: Q1 and Q2 are the flow rates of oil entering the rodless chamber of the hydraulic cylinder and exiting the rod chamber of the hydraulic cylinder, and C i V is the internal leakage coefficient of the hydraulic cylinder, V1 and V2 are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. 01 V 02 These represent the initial cavity volumes of the rodless and rod-side chambers of the hydraulic cylinder, respectively, β. e For effective elastic modulus, This is the derivative of the pressure in the rodless chamber of the hydraulic cylinder. This is the derivative of the pressure in the rod chamber of the hydraulic cylinder.

[0063] Fixed displacement pump flow rate Q P The equation is formula (5):

[0064] Q p =D p ω(5)

[0065] In the formula: D p This refers to the displacement of a fixed-displacement pump.

[0066] Ignoring the drive efficiency of the fixed displacement pump, the load torque T of the fixed displacement pump L For formula (6):

[0067] T L =D p p L (6)

[0068] In the formula: p L p represents the pressure difference between the two ends of the hydraulic cylinder. L =p1-p2.

[0069] Assuming the pressure in the rod cavity is p2 = 0, define the state variables. From equations (1) to (6), the state-space equations of the system can be obtained as follows:

[0070]

[0071] The state-space model of the hydraulic system can be derived from formula (7) and approximated as formula (8):

[0072]

[0073] In the formula: u is the input vector, u = T e A is the system matrix of the hydraulic system state space, B is the input matrix of the hydraulic system state space, C is the output matrix of the hydraulic system state space, and D is the direct transfer matrix of the state space model.

[0074]

[0075] The discrete state-space equation of the system obtained by forward Euler discretization of equation (8) is approximately expressed as equation (9):

[0076]

[0077] In the formula: x k Let x be the state variable at time k. k+1 Let y be the state variable at time k+1. k Let u be the output variable at time k. k The input vector T at time k e I is a unit vector matrix.

[0078] Algorithm design section

[0079] Figure 4 This is a general control block diagram of an adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator provided in an embodiment of this application.

[0080] Combination Figure 1 and Figure 4 As shown in the embodiments of this application, the adaptive model predictive pressure control method for pump-controlled electro-hydraulic actuators mainly includes online parameter identification design using recursive least squares with forgetting factor (FFRLS) and adaptive model predictive torque output control (AMPC) design for the hydraulic system. Among these, Figure 4 The Q shown includes Q1 and Q2.

[0081] Online parameter identification design for recursive least squares (FFRLS) with forgetting factor

[0082] Step S2: Determine the estimated load elasticity coefficient of the hydraulic system at time k using the recursive least squares method with a forgetting factor.

[0083] In the process of multi-parameter identification, the identification equation often faces the problem of underrank, which can lead to non-unique identification results. To address this underrank problem, considering that the load elastic coefficient has a more significant impact than the changes in the hydraulic cylinder area and viscous damping coefficient, this embodiment of the application adopts a method of fixing other parameters and only identifying the load elastic coefficient to ensure that the identification equation is full rank. The hydraulic cylinder force balance equation formula (2) is selected as the identification model, and the results are obtained by applying the formula (2) to the hydraulic cylinder force balance equation formula (2). Discretization is performed using the first-order and second-order forward Euler formulas (10).

[0084]

[0085] Step S2 may include the following steps S21 and S22.

[0086] Step S21: Based on the displacement x of the hydraulic cylinder piston rod at time k+2 p(k+2) At time k+1, the displacement x of the hydraulic cylinder piston rod p(k+1) At time k, the displacement x of the hydraulic cylinder piston rod p(k) At time k, the rodless chamber p of the hydraulic cylinder 1(k) At time k, the rod chamber p of the hydraulic cylinder 2(k) Determine the output vector y of the hydraulic system at time k. (k) Input vector of hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) .

[0087] The discretized formula is rewritten into a matrix form formula (12) for the identification model. The collected x is then used through formula (11). p(k+2) x p(k+1) x p(k) p 1(k) p 2(k) Calculate y at time k (k) , θ (k) .

[0088]

[0089] Step S22: Based on the output vector y of the hydraulic system (k) Input vector of hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Determine the estimated load elasticity coefficient at time k.

[0090] Step S22 can be achieved by steps S221 and S222.

[0091] Step S221: Using the recursive least squares method, based on the output vector y of the hydraulic system...(k) Input vector of hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Determine the observed values ​​of the unknown parameter vector

[0092] The k-th time was calculated using FFRLS formulas (12) and (13).

[0093]

[0094] In the formula: e (k) For the prediction error, y (k) For the system output vector, Let θ be the input vector. (k) K is the vector of unknown parameters of the model. (k) P is the weighting factor. (k) Let P be the positive definite covariance matrix at time k. (k-1) Let be the positive definite covariance matrix at time k-1, λ be the forgetting factor (0<λ<1), and T be the transpose.

[0095] Step S222: Based on the observed values ​​of the unknown vector Sampling period T s Viscous damping coefficient b v Determine the estimated value of the load elasticity coefficient

[0096] The estimated value of the load elasticity coefficient is calculated using formula (14).

[0097]

[0098] Step S3: Based on the estimated load elasticity coefficient The system matrix A and input matrix B of the discrete state-space equation of the hydraulic system are updated with the rodless cavity volume V1 in the hydraulic system.

[0099] Estimated load elasticity coefficient The volume V1 of the rodless chamber of the hydraulic cylinder is used to update the system state-space model formula (8) used by AMPC.

[0100] Adaptive Model Predictive Torque Output Control (AMPC) Design for Hydraulic Systems

[0101] Step S4: Based on the updated system matrix A, input matrix B, and the reference displacement of the hydraulic cylinder piston rod of the hydraulic system... Piston reference speed of hydraulic system The reference speed ω of a permanent magnet synchronous motor * Reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system Determine the reference torque of the permanent magnet synchronous motor based on the constraints of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system. Among them, the permanent magnet synchronous motor is controlled by an adaptive model predictive pressure control system.

[0102] AMPC is generally in discrete-time form, with a sampling period of T. s A discrete-time state-space model is established using a first-order forward Euler model. The incremental state equations of the state-space model are derived as follows:

[0103] Δx k+1 =A d Δx k +B d Δu k (15)

[0104] y k+1 =y k +C d A d Δx k +C d B d Δu k (16)

[0105] Δx k =x k -x k-1 (17)

[0106] Δu k =u k -u k-1 (18)

[0107] In the formula: B d =BT s C d =C. Let A be the system matrix after parameter updates. k-1 Let x be the state variable at time k-1. k Let u be the state variable at time k. k Let u be the input variable at time k. k-1 Let Δx be the input variable at time k-1. k+1 Let Δx be the difference between the state variables at time k+1 and time k. k Let Δu be the difference between the state variables at time k and time k-1. k Let y be the difference between the input variables at time k and time k-1. k Let y be the output variable of the incremental state-space model at time k. k+1Let k be the output variable at time k+1. Compared to conventional MPC, which uses a constant input state matrix A, AMPC updates the load resilience coefficient k in the state matrix in real time. s The cavity volume V1 improves the robustness of MPC parameters.

[0108] Step S4 can be achieved by steps S41 to S44.

[0109] Step S41: Determine the incremental state-space model of the hydraulic system based on the updated system matrix A and input matrix B.

[0110] Its incremental state-space model can be expressed as:

[0111]

[0112] In the formula: A o For the system matrix of the incremental state-space model, B o C is the input matrix of the incremental state-space model. o z is the output matrix of the incremental state-space model. k For the state variables of the incremental state-space model, Δu k For the input variables of the incremental state-space model, for The transpose of .

[0113] C0 = [OI]

[0114] O is an empty matrix.

[0115] Step S42: Based on the updated incremental state-space model system matrix A o Input matrix B o Output matrix C o Predicting the time domain N p and control time domain N c Determine the differential state matrix F and the differential input matrix G of the hydraulic system;

[0116] Step S43: Determine the relationship between the differential state matrix F, the differential input matrix G, the differential torque increment ΔU, and the torque reference increment Y at the next moment.

[0117] Through the prediction system in the prediction time domain N p The optimal output torque vector is calculated based on the dynamic characteristics within the torque vector. Therefore, we can derive the following relationship:

[0118] Y = Fx k +GΔU(20)

[0119] In the formula: Y represents the torque reference increment matrix at the next moment, F represents the state matrix after differentiation, G represents the input matrix after differentiation, and ΔU represents the torque increment after differentiation.

[0120]

[0121]

[0122] Step S44: Based on the relationship, the differential torque increment ΔU, and the reference displacement of the hydraulic cylinder piston rod... Piston reference speed Reference speed ω of permanent magnet synchronous motor * Reference pressure of the rod chamber of the hydraulic cylinder Determine the reference torque of the permanent magnet synchronous motor based on the constraints of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system.

[0123] Specifically, step S44 can be implemented by steps S441 and S442.

[0124] Step S441: Determine the cost function J1 of the hydraulic system based on the relation and the torque increment ΔU after differentiation.

[0125] In optimal control design, weighting coefficients are assigned to different variables, and corresponding factors are penalized. The cost function of model predictive control can be expressed as:

[0126] J1=(R m -Y) T Q(R m -Y)+ΔU T RΔU (21)

[0127] In the formula: R m Y is the reference vector, Q is the output weighting matrix, and R is the control weighting matrix, where R... m Including the reference displacement of the hydraulic cylinder piston rod Piston reference speed Reference speed ω of permanent magnet synchronous motor * .

[0128] Q = diag(Q0,Q0,L,Q0);

[0129]

[0130] Where: Q0 is the identity matrix of the reference output weights, It is the control weighting coefficient for the piston position of the hydraulic cylinder. It is the control weighting coefficient for the piston speed of the hydraulic cylinder. K is the control weighting coefficient for the controlled pressure in the piston chamber. ωR0 is the control weighting coefficient for the mechanical angular velocity of the permanent magnet synchronous motor, and R0 is the unit of control input weight. It is the control weighting coefficient for the output torque of the permanent magnet synchronous motor.

[0131] Step S442: Minimize the control cost function J1 to obtain the reference torque of the permanent magnet synchronous motor.

[0132] Step S442 can be implemented by steps S442a and S442b.

[0133] Step S442a: Minimize the control cost function J1 to determine the optimal differential torque increment ΔU;

[0134] Step S442b: Based on the optimal differential torque increment ΔU, determine the input variable Δu of the optimal incremental state-space model. k ;in,

[0135] The given signal in this invention is: piston position reference signal. Piston speed reference value and motor speed reference value ω * Reference pressure of the rod chamber of the hydraulic cylinder Reference signal of pressure in the rod chamber of the hydraulic cylinder As a step signal, and ω * Designed as a pulse signal, it provides excitation for state feedback and tests the dynamic characteristics of the closed-loop system.

[0136] The advantages of the MPC scheme include the ability to apply control constraints to algorithm development. These constraints represent the physical limitations of engineering applications, and the optimization of control performance and actuator efficiency is achieved through optimal control algorithms. In pump control systems, the speeds of the pump and permanent magnet synchronous motor in the hydraulic circuit, as well as the torque provided by the permanent magnet synchronous motor, are limited by electromechanical hardware. Furthermore, some pump suppliers recommend limiting the rotational shock of the pump to avoid component failure and shortened lifespan. Therefore, in this operating state variable, the cost function J1, the fixed displacement pump constraints of the permanent magnet synchronous motor and hydraulic system, the control input, and the control law are limited as follows:

[0137]

[0138] Where: ω max Let ω(k) be the maximum mechanical angular velocity of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system at time k, and T be the maximum mechanical angular velocity of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system at time k. emax T represents the maximum torque limit of a permanent magnet synchronous motor. e(k) represents the torque of the permanent magnet synchronous motor at time k, ΔT e (k+1) is the difference in torque between time k+1 and time k, r tmax For ΔT e (k+1) Maximum limit.

[0139] Step S5: Based on the reference torque Drives a permanent magnet synchronous motor.

[0140] The adaptive model predictive pressure control method for a direct-drive pump-controlled electro-hydraulic actuator provided in this application employs adaptive model predictive control (AMPC) based on the torque output of a permanent magnet synchronous motor. This improves pressure control accuracy and response speed, and incorporates a recursive least squares (FFRLS) design process with a forgetting factor. Online parameter identification uses FFRLS with a forgetting factor to estimate the unknown load elasticity coefficients and updates the system's volume parameters in real time. The parameter identification results and cavity volume parameters are then used to update the model parameters, avoiding dynamic performance degradation caused by model mismatch.

[0141] The control method, based on the adaptive model predictive pressure control (AMPC) method for permanent magnet synchronous motor torque output and the recursive least squares method with forgetting factor (FFRLS), is one of the key protection components. This encompasses the meticulous layout of each functional module, their organic connections, and rigorous execution logic. From the signal acquisition module, data processing and analysis module, control command generation module to the execution drive module, each link works closely together to form a complete and efficient control closed loop.

[0142] The implementation methods and processes of the innovative approaches: The specific implementation steps and detailed processes of the aforementioned core innovative methods, namely AMPC and FFRLS, are also key areas of protection. This includes the entire process from the initial system initialization settings, to the data acquisition variables and acquisition types during operation, to the selection and construction of the system model, prediction steps, controller parameter design, calculation and output of control quantities when using AMPC for pressure control, and the initial parameter settings, selection of forgetting factors, and specific implementation of iterative algorithms when using FFRLS for online parameter identification. These implementation methods and processes are all optimal solutions derived through extensive theoretical derivation and repeated simulation experiments, possessing extremely high technical content and innovation, ensuring the superior performance of the direct-drive pump-controlled electro-hydraulic actuator under different operating conditions.

[0143] Corresponding to the aforementioned embodiments of the adaptive model predictive pressure control method for pump-controlled electro-hydraulic actuators, this application also provides an embodiment of an adaptive model predictive pressure control system for pump-controlled electro-hydraulic actuators.

[0144] Figure 5This is a structural block diagram of an adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator provided in an embodiment of this application.

[0145] like Figure 5 As shown, the adaptive model predictive pressure control system 100 of the pump-controlled electro-hydraulic actuator includes a first determination module 101, an update module 102, a second determination module 103, and a drive module 104.

[0146] The first determining module 101 is configured to determine the estimated load elasticity coefficient of the hydraulic system at time k using a recursive least squares method with genetic factors. In other words, the first determining module 101 is used to perform the above step S2.

[0147] Update module 102 is configured to estimate the load resilience coefficient. The system matrix A and input matrix B of the state-space model of the hydraulic system are updated using the rodless cavity volume V1 in the hydraulic system. In other words, the update module 102 is used to perform the above step S3.

[0148] The second determining module 103 is configured to determine the system matrix A, the input matrix B, and the reference displacement of the hydraulic cylinder piston rod of the hydraulic system based on the updated system matrix A, the input matrix B, and the reference displacement of the hydraulic cylinder piston rod of the hydraulic system. Piston reference speed of hydraulic system The reference speed ω of a permanent magnet synchronous motor * Reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system Determine the reference torque of the permanent magnet synchronous motor based on the constraints of the fixed displacement pump in the permanent magnet synchronous motor and hydraulic system. In other words, the second determining module 103 is used to perform the above step S4.

[0149] Drive module 104 is configured to operate according to a reference torque. Drive the permanent magnet synchronous motor. That is, the drive module 104 is used to perform the above step S5.

[0150] This invention applies model predictive control to the control of permanent magnet synchronous motors and hydraulic systems. It fully leverages the flexibility, rapid response, and applicability of model predictive control to multiple control objectives, designing constraints required for the operation of the permanent magnet synchronous motor and pump. The pressure control employs adaptive model predictive control (AMPC) based on the torque output of the permanent magnet synchronous motor, which improves control accuracy and response speed.

[0151] Pump-controlled direct-drive actuators used in servo stamping and plastic forming CNC machine tools suffer from control model mismatch due to the difficulty in determining the elastic coefficient of the stamped parts and the variation of cavity volume during motion, significantly reducing the dynamic servo performance of the system. Online parameter identification uses a recursive least squares method with a forgetting factor to identify the unknown load elastic coefficient online. The parameter identification results and cavity volume parameters are then used to update the model parameters, providing an accurate system model for the AMPC and improving its parameter robustness.

[0152] It should be noted that, upon considering the specification and practicing the application disclosed herein, those skilled in the art will readily conceive of other embodiments of this application. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

[0153] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The true scope is indicated by this application.

Claims

1. An adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator, characterized in that, An adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator, the control system comprising a permanent magnet synchronous motor and a hydraulic system, wherein the output of the permanent magnet synchronous motor is connected to the input of the hydraulic system, and the adaptive model predictive pressure control method includes: The estimated load elasticity coefficient of the hydraulic system at time k is determined using the recursive least squares method with genetic factors. Based on the estimated load elasticity coefficient The system matrix A and input matrix B of the state space model of the hydraulic system are updated using the rodless cavity volume V1 in the hydraulic system. Based on the updated system matrix A, the input matrix B, and the reference displacement of the hydraulic cylinder piston rod of the hydraulic system. Piston reference speed of the hydraulic system The reference speed ω of the permanent magnet synchronous motor * The reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system The reference torque of the permanent magnet synchronous motor is determined by the constraints of the permanent magnet synchronous motor and the fixed displacement pump of the hydraulic system. According to the reference torque Drive the permanent magnet synchronous motor.

2. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator according to claim 1, characterized in that, The estimated load elasticity coefficient of the hydraulic system at time k is determined using the recursive least squares method with genetic factors. include: Based on the displacement x of the hydraulic cylinder piston rod at time k+2 p(k+2) At time k+1, the displacement x of the hydraulic cylinder piston rod p(k+1) At time k, the displacement x of the hydraulic cylinder piston rod p(k) At time k, the rodless chamber p of the hydraulic cylinder 1(k) At time k, the rod chamber p of the hydraulic cylinder 2(k) Determine the output vector y of the hydraulic system at time k. (k) The input vector of the hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Wherein, the output vector y of the hydraulic system (k) The input vector of the hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) satisfy: Where m is the load mass, A a A represents the effective area of ​​the rodless chamber piston in a hydraulic cylinder. b b is the effective area of ​​the piston in the rod chamber of the hydraulic cylinder. v T is the viscous damping coefficient. s k is the sampling period. s This is the load elasticity coefficient; According to the output vector y of the hydraulic system (k) The input vector of the hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Determine the estimated load elasticity coefficient at time k.

3. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator according to claim 2, characterized in that, The output vector y of the hydraulic system (k) The input vector of the hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Determine the estimated load elasticity coefficient at time k. include: Using the recursive least squares method with genetic factors, based on the output vector y of the hydraulic system (k) The input vector of the hydraulic system The unknown parameter vector θ of the state-space model of the hydraulic system (k) Determine the observed values ​​of the unknown parameter vector. Based on the observed values ​​of the unknown parameter vector The sampling period T s and the viscous damping coefficient b v Determine the estimated value of the load elasticity coefficient.

4. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator according to claim 3, characterized in that, Determine the estimated value of the load elasticity coefficient. Previously, the method also included: Determine the state-space model of the hydraulic system; The state-space model is as follows: x is the state variable of the state-space model. Let x be the first derivative of x, u be the input vector, and u = T e T e The torque of the permanent magnet synchronous motor; C is the output matrix of the state-space model, D is the direct transfer matrix of the state-space model, and β e For effective elastic modulus, V1 is the volume of the rodless chamber of the hydraulic cylinder, and C is the effective elastic modulus. i D is the internal leakage coefficient of the hydraulic cylinder. p Where J is the displacement of the fixed displacement pump, and B is the moment of inertia. m It is the coefficient of viscous friction.

5. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator according to claim 4, characterized in that, Determining the state-space model of the hydraulic system includes: The state-space model of the hydraulic system is determined based on the motion equation of the permanent magnet synchronous motor, the hydraulic cylinder force balance equation of the hydraulic system, the fixed displacement pump flow equation of the hydraulic system, and the load torque of the fixed displacement pump.

6. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator according to claim 5, characterized in that, The updated system matrix A, the input matrix B, and the reference displacement of the hydraulic cylinder piston rod of the hydraulic system are used as the basis. Piston reference speed of the hydraulic system The reference speed ω of the permanent magnet synchronous motor * The reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system The reference torque of the permanent magnet synchronous motor is determined by the constraints of the fixed displacement pump in the permanent magnet synchronous motor and the hydraulic system. include: The incremental state-space model of the hydraulic system is determined based on the updated system matrix A and the input matrix B; wherein the incremental state-space model is: A o Let B be the system matrix of the incremental state-space model. o Let C be the input matrix of the incremental state-space model. o Let y be the output matrix of the incremental state-space model. k Let z be the output variable of the incremental state-space model at time k. k Let z be the output variable at time k of the incremental state-space model. k+1 Let Δu be the output variable at time k+1 of the incremental state-space model. k These are the input variables for the incremental state-space model; Based on the updated system matrix A of the incremental state-space model o Input matrix B o Output matrix C o Predicting the time domain N p and control time domain N c Determine the differential state matrix F and the differential input matrix G of the hydraulic system; Determine the relationship between the differential state matrix F, the differential input matrix G, the differential torque increment ΔU, and the torque reference increment Y at the next moment; Based on the aforementioned relationship, the differential torque increment ΔU, and the reference displacement of the hydraulic cylinder piston rod... Piston reference speed of the hydraulic system The reference speed ω of the permanent magnet synchronous motor * The reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system The reference torque of the permanent magnet synchronous motor is determined by the constraints of the fixed displacement pump in the permanent magnet synchronous motor and the hydraulic system.

7. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator according to claim 6, characterized in that, The relationship, the differential torque increment ΔU, and the reference displacement of the hydraulic cylinder piston rod are used. Piston reference speed of the hydraulic system The reference speed ω of the permanent magnet synchronous motor * The reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system The reference torque of the permanent magnet synchronous motor is determined by the constraints of the fixed displacement pump in the permanent magnet synchronous motor and the hydraulic system. include: The cost function J1 of the hydraulic system is determined based on the aforementioned relationship and the differential torque increment ΔU; wherein, the cost function J1 satisfies the fixed displacement pump constraint condition of the permanent magnet synchronous motor and the hydraulic system, and the constraint condition is as follows: ω max Let ω(k) be the maximum mechanical angular velocity of the fixed displacement pump of the permanent magnet synchronous motor and hydraulic system at time k, and T be the mechanical angular velocity of the fixed displacement pump of the permanent magnet synchronous motor and hydraulic system at time k. emax T represents the maximum torque limit of the permanent magnet synchronous motor. e (k) represents the torque of the permanent magnet synchronous motor at time k, ΔT e (k+1) is the difference between the torque at time k+1 and time k, r tmax For ΔT e (k+1) Maximum limit; By minimizing the cost function J1, the reference torque of the permanent magnet synchronous motor is obtained.

8. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator according to claim 7, characterized in that, By minimizing the cost function J1, the reference torque of the permanent magnet synchronous motor is obtained. include: By minimizing the cost function J1, the optimal torque increment ΔU after differentiation is determined; Based on the optimal torque increment ΔU after differentiation, the input variable Δu of the optimal incremental state-space model is determined. k ;in, 9. The adaptive model predictive pressure control method for a pump-controlled electro-hydraulic actuator according to claim 8, characterized in that, The relationship is Y = Fx k +GΔU; in, C0 = [OI], where O is an empty matrix; B d =BT s C d =C, Let A be the system matrix after parameter updates, and I be the identity vector matrix.

10. An adaptive model predictive pressure control system for a pump-controlled electro-hydraulic actuator, employing the method as described in any one of claims 1 to 9, characterized in that, include: The first determining module is configured to determine the estimated load elasticity coefficient of the hydraulic system at time k using a recursive least squares method with genetic factors. The update module is configured to update the load resilience coefficient estimate. The system matrix A and input matrix B of the state space model of the hydraulic system are updated using the rodless cavity volume V1 in the hydraulic system. The second determining module is configured to determine the system based on the updated system matrix A, the input matrix B, and the reference displacement of the hydraulic cylinder piston rod of the hydraulic system. Piston reference speed of the hydraulic system The reference speed ω of a permanent magnet synchronous motor * The reference pressure of the rod chamber of the hydraulic cylinder in the hydraulic system The reference torque of the permanent magnet synchronous motor is determined by the constraints of the permanent magnet synchronous motor and the fixed displacement pump of the hydraulic system. The drive module is configured to operate according to the reference torque. Drive the permanent magnet synchronous motor.

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