A backlash elimination control method for a high-order valve-controlled cylinder system

Abstract

This invention discloses a backlash elimination control method for a high-order valve-controlled cylinder system, belonging to the field of electro-hydraulic position servo control technology. The method first performs mechanistic modeling of the high-order valve-controlled cylinder system; then, based on the established mathematical model and relevant servo system operation data, it identifies the backlash model parameters; and, based on obtaining the backlash value of the transmission mechanism, designs a backlash elimination control method based on model adaptive compensation and high-order active disturbance rejection. This control method enables backlash nonlinear control of the high-order valve-controlled cylinder system. This invention improves the robustness and stability of the electro-hydraulic servo control unit, achieving high-precision position tracking control of the valve-controlled cylinder system under the influence of backlash nonlinearity and unknown external disturbance torques.

Description

Technical Field

[0001] This invention relates to the field of electro-hydraulic position servo control technology, and in particular to a backlash elimination control method for a high-order valve-controlled cylinder system. Background Technology

[0002] With the development and innovation of science and technology, electro-hydraulic position servo systems, as a very important branch in the field of hydraulic technology, combine the advantages of both hydraulics and electricity. They have excellent power density ratio, speed range and response speed, and have been widely used in many fields such as military industry, energy, aviation and ships. At the same time, the requirements for the control performance of servo systems are also increasing.

[0003] Valve-controlled cylinder systems are typical nonlinear systems. In practical engineering applications, factors such as time delay, strong coupling, and parameter perturbations reduce the system's efficiency and response speed. To meet the requirements of intelligent control, the control system design must fully consider nonlinear factors to ensure the stability and accuracy of the servo control system. In actual operation, when the hydraulic cylinder begins to drive the load device to move left and right, the connecting mechanism must be in a clearance fit. Considering the influence of manufacturing errors, mechanical wear, installation errors, and multiple disassemblies and reassemblies of the load mechanism, there will inevitably be mechanical clearance between the moving pairs. Under the influence of clearance and parameter perturbations, traditional control methods cannot guarantee good dynamic and static characteristics. Therefore, it is essential to study the clearance characteristics of the transmission mechanism and its compensation methods.

[0004] Current research on reducing or eliminating backlash characteristics on the control accuracy of servo systems mainly falls into two categories: one is through mechanical structure solutions. Mechanical structure solutions primarily include backlash elimination mechanisms, synchronous drives, or double-chain drives, mainly considering the physical space aspect. While these solutions offer high control accuracy in engineering, issues such as the elastic connection of the transmission remain unresolved; the complexity of structural design and adjustment costs also increase. Before determining a specific backlash elimination solution, it is necessary to analyze the causes, manifestations, and structural characteristics of backlash nonlinearity in conjunction with the servo system's mechanical structure and connection methods, comprehensively considering cost and implementation difficulty, and constructing a suitable servo system backlash nonlinearity control strategy. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a backlash elimination control method for a high-order valve-controlled cylinder system, so as to solve the adverse effects of backlash nonlinearity and uncertain disturbances on control quality in the valve-controlled cylinder system and achieve high-precision position tracking control.

[0006] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0007] A backlash elimination control method for a high-order valve-controlled cylinder system includes the following steps:

[0008] Step 1: Perform mechanism modeling of the high-order valve-controlled cylinder system;

[0009] Step 2: Identify the gap model parameters based on the established mathematical model and relevant data from the servo system operation;

[0010] Step 3: Based on the obtained backlash value of the transmission mechanism, design a backlash elimination control method based on model adaptive compensation and high-order active disturbance rejection.

[0011] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0012] 1) The gap elimination control method for the high-order valve-controlled cylinder system designed in this invention constructs a gap model suitable for the high-order valve-controlled cylinder system and introduces it into the dynamic model of the servo system. The nonlinear mathematical model of the overall system is derived, which is closer to the actual state of the system than the traditional model used in previous work, laying the foundation for the design of the controller.

[0013] 2) The backlash elimination control method for the high-order valve-controlled cylinder system designed in this invention combines the whale optimization algorithm to identify backlash model parameters and improves the accuracy of the system model based on the discrete sampling points of the output signal in actual application. It fully describes the relationship between the hydraulic power mechanism and the load device and solves the problem of difficult modeling of valve-controlled cylinder systems.

[0014] 3) The backlash elimination control method of the high-order valve-controlled cylinder system designed in this invention considers the hysteresis caused by backlash nonlinearity and proposes a model-based adaptive compensation method to eliminate the adverse effects of backlash on system function before giving drive commands. Based on the main loop control, a high-order linear active disturbance rejection controller is introduced, which can effectively estimate the unmeasurable state and uncertain disturbance of the system and perform timely disturbance compensation, thereby improving the robustness and stability of the electro-hydraulic servo control unit. Attached Figure Description

[0015] Figure 1 Flowchart of the backlash elimination control method for a high-order valve-controlled cylinder system;

[0016] Figure 2 This is a schematic diagram of the valve-controlled cylinder system.

[0017] Figure 3 This is a schematic diagram of gap model parameter identification in an embodiment of the present invention;

[0018] Figure 4 This is the position response curve based on a sinusoidal input in an embodiment of the present invention;

[0019] Figure 5 This is the position response curve based on a step input in an embodiment of the present invention. Detailed Implementation

[0020] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The following examples are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0021] Combination Figure 1 This invention provides a backlash elimination control method for a high-order valve-controlled cylinder system, comprising the following steps:

[0022] Step 1: Perform mechanism modeling of the high-order valve-controlled cylinder system;

[0023] Step 2: Identify the gap model parameters based on the established mathematical model and relevant data from the servo system operation;

[0024] Step 3: Based on the obtained backlash value of the transmission mechanism, design a backlash elimination control method based on model adaptive compensation and high-order active disturbance rejection.

[0025] Example

[0026] Using the above method, the specific process of step 1 includes:

[0027] Step 1.1: Model the mechanism of the high-order valve-controlled cylinder system using a two-step method. First, ignore the relevant nonlinearities and construct the transfer function of the high-order valve-controlled cylinder system.

[0028] Step 1.2: Design the nonlinear model of the valve-controlled cylinder system clearance.

[0029] Furthermore, the specific process of step 1.1 is as follows:

[0030] Combination Figure 2 Based on the valve core position with the lowest natural frequency, the servo valve flow equation, the hydraulic cylinder load flow continuity equation, and the valve-controlled cylinder system torque balance equation are established. Irrelevant intermediate variables are eliminated, and related nonlinear factors such as equivalent viscous damping are ignored. The transfer function of the high-order valve-controlled cylinder system is derived, and its mathematical expression is as follows:

[0031]

[0032] In the formula, This refers to the gain coefficient of the servo amplifier. This is the displacement gain coefficient. This refers to the flow gain coefficient of the servo valve. The effective area of ​​the hydraulic cylinder. For the servo valve's natural frequency, , For effective fluid bulk modulus, For the total equivalent mass, This refers to the volume of the hydraulic cylinder cavity. For the damping ratio of the servo valve, For the servo valve's natural frequency, , The pressure coefficient of the total system flow. is the viscous damping coefficient.

[0033] Furthermore, the specific process of step 1.2 is as follows:

[0034] The load device and the hydraulic power mechanism are connected by a kinematic pair. The clearance nonlinearity is mainly transmitted to the system in the form of position disturbances, and has a certain degree of coupling effect on the control performance. The actual output displacement of the load device It can be described as:

[0035]

[0036] In the formula, and These represent the clearance values ​​on the left and right sides of the hinge joint between the piston rod and the load device, respectively. This represents the actual output displacement of the piston rod. and These are the maximum input values ​​for the gap amplitude on both sides. and This is the transmission ratio between the piston rod and the load device.

[0037] To simplify the description, we will first introduce an indicator function to quasi-linearize the piecewise function:

[0038]

[0039] The indicator function of the gap hysteresis nonlinear model is extended as follows:

[0040]

[0041] Clearly, the indicator function satisfies the following expression:

[0042]

[0043] The actual output displacement of the load device can be described as follows:

[0044]

[0045] Furthermore, the specific process of step 2 is as follows:

[0046] Data is acquired based on the high-order valve-controlled cylinder system. The sampled data undergoes preprocessing to eliminate trend terms, achieve zero mean, and remove DC components and interference signals. The resulting data is then stored. The whale optimization algorithm parameters are initialized, and the individual whale dimension for the gap model to be identified is:

[0047]

[0048] In the formula, This refers to the size of the whale population.

[0049] The gap identification value can be obtained by the following formula:

[0050]

[0051] From this, the identification value of the gap model can be obtained, and the identification error is:

[0052]

[0053] The optimal whale location is determined based on the identification error value. The distance between the individual whale and the optimal whale location is:

[0054]

[0055] In the formula, The location of the whale with the lowest identification error in the t-th iteration. This is the oscillation factor.

[0056] Then, a position update operation is performed based on the updated optimal position, and its expression is:

[0057]

[0058] In the formula, This represents the location of a random whale in the current population. The convergence factor is A random number in (-1, 1). It is a constant. As a determinant of search strategy, , , The maximum number of iterations, It is a random number in (0, 1).

[0059] Based on experimental data obtained from piston rod displacement and load device displacement, the whale population size was set to 200, the maximum number of iterations to 500, and the search space for the parameters to be identified was set to [0, 10]. Algorithm parameters were also set accordingly. Repeat the above steps until the optimal identification value is obtained. The gap model parameter identification curve is shown below. Figure 3 As shown.

[0060] Furthermore, the specific process of step 3 includes:

[0061] Step 3.1: In order to offset the effects of gap nonlinearity, a model adaptive compensation structure design is carried out to eliminate the adverse effects of gap on system function before the controller gives the drive command, so as to ensure accurate tracking of the given signal.

[0062] Step 3.2: Introduce a high-order linear active disturbance rejection controller on the basis of the main control loop to improve the overall robustness of the control system.

[0063] Furthermore, the specific process of step 3.1 is as follows:

[0064] The expression for the gap inverse model is:

[0065]

[0066] set up For the ideal output displacement, This is the actual output displacement after compensation. Ignoring gap nonlinearity, the piston rod and load device are considered rigidly connected. In this case, the output displacement of the piston rod and the output displacement of the load device satisfy a linear relationship:

[0067]

[0068] at this time:

[0069]

[0070] make Then we have:

[0071]

[0072] Let the objective function be:

[0073]

[0074] Assuming the left and right clearances are equal during the reciprocating motion of the hydraulic cylinder, the gradient of the objective function is:

[0075]

[0076] Projecting the gradient onto a certain direction, the adaptive law is:

[0077]

[0078] In the formula: For adaptive gain, The parameter projection terms of the controlled object satisfy the following formula:

[0079]

[0080] In the formula, These are estimated values ​​for the parameters; and Upper and lower constraints for parameter estimation, satisfying .

[0081] Furthermore, the specific process of step 3.2 is as follows:

[0082] The structure of the linear active disturbance rejection control system is determined based on the system structure. In order to make the parameters easier to select, all poles are placed in the same position from the perspective of pole placement of the LESO and LSEF characteristic equations.

[0083] The mathematical expression for the error state feedback control law is:

[0084]

[0085] In the formula, For error feedback environment parameters, For feedback control rate, This is a compensation factor.

[0086] Based on the system configuration, we can conclude that:

[0087]

[0088] The characteristic equation of the system can be obtained as follows:

[0089]

[0090] In the formula, For equivalent control gain, .

[0091] The mathematical expression for the tracking differentiator is:

[0092]

[0093] In the formula, Given an input signal and its derivatives, This is the equivalent observation gain.

[0094] The mathematical expression for the extended state observer is:

[0095]

[0096] In the formula, For the actual output, To control the input coefficients, This is the gain coefficient.

[0097] The observer gain can be obtained based on the characteristic polynomial Hurwitz stability:

[0098]

[0099] In the formula: For the observer bandwidth, ;

[0100] Therefore, after parametric design, the parameters that LADRC needs to adjust are simplified to: , , , .

[0101] like Figure 2 The valve-controlled cylinder system shown uses the following parameters:

[0102] The electro-hydraulic servo valve is type FF102-30, with a rated oil supply pressure of 21MPa, a rated current of 40 mA, and a flow gain coefficient K. sv =0.006 m 3 / (s∙A), damping ratio ξ sv =0.5, no-load flow rate is 2.315×10 -4 (m 3 / s), the actual oil supply pressure is P s =4.5 MPa, inertial load mass is m=150 kg, ±10 V is the saturation value of the servo amplifier control voltage, piston rod diameter d=35 mm, effective piston rod area A p =0.001 m 2 The piston rod stroke is ±100 mm, and the effective bulk modulus β e =7×10 8 Pa, the position sensor gain coefficient is 50 V / m, the range is ±100 mm, and the viscous damping coefficient is negligible.

[0103] The controller parameters are: =1000, =1000, =160, =500000, sampling time is 1 ms. A simulation study of a high-order valve-controlled cylinder system is conducted under these parameters. The input signal is a sinusoidal signal. The experimental simulation comparison graph of the gap model response curve is shown below. Figure 4 As shown in the figure, the gap-based model effectively reproduces the load device displacement curve, fully verifying the accuracy of the overall system model and laying the foundation for subsequent controller design and simulation verification. To verify the effectiveness of the gap-elimination method, a sinusoidal input signal is given, and the load device response curve is shown in the figure. Figure 5As shown in the figure, the backlash elimination method has a better control effect on the operation of the high-order valve-controlled cylinder system, which is far superior to the traditional active disturbance rejection control method. It effectively compensates for the position lag phenomenon that still exists in the initial stage and the reversing stage, and the position and speed tracking effect is significantly improved.

Claims

1. A backlash elimination control method for a high-order valve-controlled cylinder system, characterized in that, Includes the following steps: Step 1: Perform mechanism modeling of the high-order valve-controlled cylinder system; Step 2: Identify the gap model parameters based on the established mathematical model and relevant data from the servo system operation; Step 3: Based on the obtained backlash value of the transmission mechanism, design a backlash elimination control method based on model adaptive compensation and high-order active disturbance rejection. The specific process of step 1 includes: Step 1.1: Model the mechanism of the high-order valve-controlled cylinder system in two steps. First, ignore the relevant nonlinearities and construct the transfer function of the high-order valve-controlled cylinder system. Step 1.2: Design a nonlinear mathematical model for the clearance of the valve-controlled cylinder system; The specific process of step 1.1 is as follows: Based on the valve core position with the lowest natural frequency of the system, the servo valve flow equation, the hydraulic cylinder load flow continuity equation, and the valve control cylinder system torque balance equation are established. Irrelevant intermediate variables are eliminated, and the transfer function of the higher-order valve control cylinder system is derived. The specific process of step 1.2 is as follows: The load device and the hydraulic power mechanism are connected by a kinematic pair. The clearance nonlinearity is transmitted to the system in the form of position disturbance, which has a coupled effect on the control performance, affecting the actual output displacement of the load device. Described as: In the formula, and These represent the clearance values ​​on the left and right sides of the hinge joint between the piston rod and the load device, respectively. This represents the actual output displacement of the piston rod. and These are the maximum input values ​​for the gap amplitude on both sides. and The transmission ratio between the piston rod and the load device; To simplify the description, we will first introduce an indicator function to quasi-linearize the piecewise function: The indicator function of the gap hysteresis nonlinear model is extended as follows: Clearly, the indicator function satisfies the following expression: The actual output displacement of the load device can be described as follows: The specific process of step 2 is as follows: Data is acquired based on the high-order valve-controlled cylinder system. The sampled data undergoes preprocessing to eliminate trend terms, achieve zero mean, and remove DC components and interference signals. The resulting data is then stored. The whale optimization algorithm parameters are initialized, and the individual whale dimension for the gap model to be identified is: In the formula, This refers to the size of the whale population; The gap identification value is given by the following formula: The identification value of the gap model is then obtained, and the identification error is: The optimal whale location is determined based on the identification error value. The distance between the individual whale and the optimal whale location is: In the formula, The location of the whale with the lowest identification error in the t-th iteration. It is the swing factor; Then, a position update operation is performed based on the updated optimal position, and its expression is: In the formula, This represents the location of a random whale in the current population. The convergence factor is A random number in (-1, 1). It is a constant. As a determinant of search strategy, , , The maximum number of iterations, A random number in (0,1); Based on the experimental data obtained from the piston rod displacement and load device displacement, repeat the above operation until the optimal identification value is obtained. Step 3 includes the following specific steps: Step 3.1: In order to offset the effects of gap nonlinearity, a model adaptive compensation structure design is carried out to eliminate the adverse effects of gap on system function before the controller gives the drive command, so as to ensure accurate tracking of the given signal. Step 3.2: Introduce a high-order linear active disturbance rejection controller on the basis of the main control loop to improve the overall robustness of the control system; The specific process of step 3.1 is as follows: The inverse model expression for the clearance of a high-order valve-controlled cylinder system is: set up For the ideal output displacement, The actual output displacement after compensation; neglecting the nonlinearity of the gap, the piston rod and the load device are considered to be rigidly connected. In this case, the output displacement of the piston rod and the output displacement of the load device satisfy a linear relationship: at this time: make Then we have: Let the objective function be: Assuming the left and right clearances are equal during the reciprocating motion of the hydraulic cylinder, the gradient of the objective function is: Projecting the gradient onto a certain direction, the adaptive law is: In the formula: For adaptive gain, The parameter projection terms of the controlled object satisfy the following formula: In the formula, These are estimated values ​​for the parameters; and Upper and lower constraints for parameter estimation, satisfying , The specific process of step 3.2 is as follows: Based on the structure of the high-order valve-controlled cylinder system, the structure of the linear active disturbance rejection control system is determined. In order to make the parameters easy to select, from the perspective of pole placement of the characteristic equation of the extended state observer and the error state feedback control law, all poles are placed in the same position. The mathematical expression for the error state feedback control law is: In the formula, For error feedback environment parameters, For feedback control rate, As a compensation factor; Based on the system configuration, we can conclude that: The characteristic equation of the system can be obtained as follows: In the formula, For equivalent control gain, ; The mathematical expression for the tracking differentiator is: In the formula, Given an input signal and its derivatives, Equivalent observation gain; The mathematical expression for the extended state observer is: In the formula, For the actual output, To control the input coefficients, This is the gain coefficient; The observer gain is calculated based on the characteristic polynomial Hurwitz stability: In the formula: For the observer bandwidth, ; Therefore, after parametric design, the parameters of the active disturbance rejection controller are adjusted. , , , This continues until the desired gap control effect is achieved.

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