Multi-parameter identification method for electro-hydraulic servo system of valve control cylinder

Abstract

The invention discloses a multi-parameter identification method for a valve-controlled cylinder electro-hydraulic servo system, and belongs to the field of servo technology control. The method comprises the following steps: firstly, carrying out mathematical modeling according to components and a working principle of the valve-controlled cylinder electro-hydraulic servo system to obtain a system model and to-be-identified parameters; secondly, an improved multi-strategy firefly algorithm is provided, the randomness and uniformity of an initial solution are enhanced through an improved Chebyshev polynomial, the global search capability of the algorithm is improved, an updating algorithm is introduced to modify a step length factor of the firefly algorithm, and balance between local search and global exploration is achieved; finally, parameters of the established model are identified through an improved algorithm, simulation and experimental analysis are conducted, and according to the result, the accuracy of the model can be effectively improved, the robustness of the model can be improved, and reliable theoretical and practical support is provided for actual engineering application of the high-precision electro-hydraulic servo system.

Description

Technical Field

[0001] The present invention belongs to the field of servo technology control, and in particular relates to a multi-parameter identification method for a valve-controlled cylinder electro-hydraulic servo system. Background Art

[0002] Valve-controlled cylinder electro-hydraulic servo systems offer advantages such as high power density, fast response, and high output force, making them suitable for heavy-load applications requiring rapid response. However, during operation, they can be affected by factors such as sudden changes in load mass and internal and external environmental interference, resulting in reduced control accuracy and stability. Furthermore, existing research on electro-hydraulic servo system models often overlooks certain structural characteristics, leading to a gap between theoretical models and practical engineering applications, impacting system control performance.

[0003] The firefly algorithm (FA) is a heuristic optimization algorithm based on swarm intelligence. It abstracts and simulates the natural behavior of fireflies, which glow to attract mates and prey, to achieve optimization for practical problems. Compared with other metaheuristic algorithms, FA has a simple concept, a clear process, and requires fewer parameters to adjust, resulting in good operability and adaptability. However, the optimization mechanisms of FA attraction models and stochastic models have not been fully analyzed and studied. In addition, the standard FA algorithm is prone to falling into local optimal solutions and has low solution accuracy during optimization. How to select appropriate control parameters and how to optimize and improve the algorithm to better balance the relationship between exploration and exploitation remain important challenges in the development of the firefly algorithm. Summary of the Invention

[0004] In light of this, the present invention provides a multi-parameter identification method for a valve-controlled cylinder electro-hydraulic servo system. This method addresses the inaccurate modeling of conventional electro-hydraulic servo systems, the tendency of conventional firefly algorithms to fall into local optimal solutions, and the low accuracy of their solutions. This method enables rapid and accurate identification of parameters in valve-controlled cylinder electro-hydraulic servo systems.

[0005] In order to solve the above problems, the technical solution adopted by the present invention is:

[0006] A multi-parameter identification method for a valve-controlled cylinder electro-hydraulic servo system, characterized by comprising the following steps:

[0007] Step 1: Develop a mathematical model based on the components and working principle of the valve-controlled cylinder electro-hydraulic servo system, introduce inertia compensation to improve the stability of the system, and ultimately determine the structural characteristics of the model and the parameters that need to be identified;

[0008] Step 1-1: Build a valve-controlled cylinder electro-hydraulic servo system model

[0009] The constructed system model is shown below:

[0010]

[0011] Where: K0 is the open-loop gain of the system; G sv (s) is the transfer function of the servo valve when the servo valve gain is 1; ω m ,ω0,ω r are the natural frequency of the load, the natural frequency formed by the stiffness of the hydraulic spring coupled in parallel with the load and the load, and the stiffness-damping coefficient ratio of the hydraulic spring coupled in series with the load spring; ζ0 is the system damping ratio;

[0012] Step 1-2: Inertia compensation strategy

[0013] In the electro-hydraulic servo system, since the hydraulic components have high inertia when working, the hydraulic oil is compressible, and the mechanical structure has a natural frequency, phase lag and resonance are prone to occur. Therefore, it is necessary to compensate for the high inertia of the system. By adding two second-order inertia links to reduce the oscillation of the system and adjust the natural frequency of the system, the stability of the system is enhanced. The improved system model is shown below:

[0014]

[0015] Where: K in is the compensation gain; ω1, ω2 are the natural frequencies of the two inertia links; ζ1, ζ2 are the damping ratios of the two inertia links;

[0016] Steps 1-3: Parameter vector to be identified

[0017] The state space expression is constructed based on the obtained model. The state space expression of the established closed-loop system is as follows:

[0018]

[0019] Where:

[0020]

[0021] B=[001000000] T ,

[0022] C=[000000010],

[0023] D = 0;

[0024] The parameter vector to be identified is: θ = [a1a2a3a4a5a6a7] T , where a1=ω0,a2=ω r , a3=ζ0, a4=ω1, a5=ζ1, a6=ω2, a7=ζ2;

[0025] Step 2: Propose an improved multi-strategy firefly algorithm, which uses the improved Chebyshev polynomial to enhance the randomness and uniformity of the initial solution and improve the global search capability of the algorithm; introduce an update algorithm to modify the step size factor of the firefly algorithm to achieve a balance between local search and global exploration;

[0026] Step 2-1, Firefly algorithm initialization

[0027] The equal oscillation property of Chebyshev polynomials is used to reduce the local aggregation phenomenon of the population generated by random sampling in the firefly algorithm, and the randomness and exploration ability of the algorithm are enhanced by improving the polynomials. Specifically:

[0028] In the d-dimensional search space, the individual is X i =(x1,x2,…,x d ), select the initial value X0∈[0,1] as the starting value of the Chebyshev polynomial, and the mathematical expression is:

[0029] T n (x i )=(2x i T n-1 (x i )-T n-2 (x i ))%N

[0030] Where: T0(x) = 1, T1(x) = x0; n is the degree of the polynomial, satisfying n ≥ 2; N is a large prime number;

[0031] The obtained result is in the range of [0,1]. Through linear transformation, the position is mapped to the boundary range of the target [lb,ub],,obtaining a uniform and random initialization population;

[0032] Step 2-2: Dynamic update of step factor

[0033] The fixed step size of the Firefly Algorithm makes it difficult to achieve a balance between local search and global exploration. By improving the step size factor of the Firefly Algorithm, the step size factor can be dynamically updated. Specifically:

[0034] Improve the fixed step size α of the firefly algorithm to a variable step size α v The hyperbolic sine function grows linearly when it approaches 0 in the positive interval, and transitions to exponential growth as x increases. This feature enables the firefly algorithm to obtain a larger step size in the early stage of the operation, which is convenient for global search, and a smaller step size in the later stage of the operation, which is convenient for local search. The adjustment of the step size factor is as follows:

[0035]

[0036] Where: α max , αmin is the maximum and minimum value of α; β i is the current iteration number; β max is the maximum number of iterations;

[0037] Step 3: Based on the expected input function, the improved multi-strategy firefly algorithm is used to perform parameter identification on the mathematical model of the valve-controlled cylinder electro-hydraulic servo system. The error evaluation function is introduced to identify the identification results, and an accurate valve-controlled cylinder electro-hydraulic servo system model is obtained. The effectiveness of the established model is verified through simulation and experiments.

[0038] Step 3-1: Parameter identification and error evaluation

[0039] The system's expected input and output functions are calculated using a sine function, namely:

[0040] y(kT s )=sin(2πkT s ),k=1,2,…,M

[0041] Where: T s is the sampling period, M is the number of sampling points;

[0042] Considering that there are still unidentified nonlinear factors in reality, the model identified in the actual process is:

[0043] y(kT s )=sin(2πkT s )+e(kT s ),k=1,2,…,M

[0044] Where: e(T s ) is the residual value caused by the identification factor;

[0045] The error evaluation function is defined as:

[0046]

[0047] Step 3-2: Simulation and experimental verification

[0048] The obtained valve-controlled cylinder electro-hydraulic servo system model is simulated and experimentally verified, specifically:

[0049] First, the algorithm's fitness curves are compared and analyzed to analyze the convergence ability and convergence speed of the improved algorithm. Second, the Bode plots before and after identification are simulated and compared to analyze the stability of the improved system. Finally, the obtained model is experimentally analyzed on a constructed electro-hydraulic force servo system test bench to prove its accuracy.

[0050] Due to the adoption of the above technical solution, the technical advancements achieved by the present invention are:

[0051] (1) The present invention designs a multi-parameter identification method for a valve-controlled cylinder electro-hydraulic servo system. First, a mathematical model is constructed based on the components and working principle of the valve-controlled cylinder electro-hydraulic servo system. The parameters to be identified are determined by the constructed model. Compared with directly identifying the system, this identification method has higher accuracy, stronger robustness, and higher efficiency.

[0052] (2) The present invention designs a multi-parameter identification method for the valve-controlled cylinder electro-hydraulic servo system, introduces an improved Chebyshev polynomial and an update algorithm to improve the traditional firefly algorithm, and constructs a multi-strategy firefly algorithm. Compared with the original algorithm, the improved algorithm has a faster convergence speed and higher convergence accuracy, can effectively improve the algorithm's optimization ability, and has certain engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 , Valve-controlled cylinder electro-hydraulic servo system force control system block diagram

[0054] Figure 2 Parameter identification method flow chart

[0055] Figure 3 Fitness value curves of different algorithms

[0056] Figure 4 Comparison of Bode diagrams before and after identification

[0057] Figure 5 Actual picture of the electro-hydraulic servo system test bench

[0058] Figure 6 MFA parameter identification experimental results DETAILED DESCRIPTION

[0059] In order to enable those skilled in the art to better understand the technical solution of the present invention and to be able to implement it, the present invention is 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 solution of the present invention and are not intended to limit the scope of protection of the present invention.

[0060] Example

[0061] In the specific implementation process, the specific implementation steps of the present invention are as follows:

[0062] Step 1: Establish a mathematical model of the valve-controlled cylinder electro-hydraulic servo system. The model mainly consists of a servo amplifier, an electro-hydraulic servo valve transfer function, a flow quantization linear equation, a hydraulic cylinder, and a load force balance equation.

[0063] (1) Servo amplifier model

[0064] When mathematically modeling the electro-hydraulic servo system, the dynamic characteristics of the system are ignored and the deviation voltage signal Ue for:

[0065] U e =U r -U f

[0066] Where: U e is the deviation voltage signal, V; U r is the command voltage signal, V; U f is the feedback voltage signal, V.

[0067] The force sensor equation is:

[0068] U f =K fF F g

[0069] Where: K fF is the force sensor gain, V / m; F g is the output force of the hydraulic cylinder, N.

[0070] The servo amplifier dynamics can be ignored and its output current is:

[0071] ΔI=K a U e

[0072] Where: ΔI is the output current of the servo amplifier, A; K a is the servo amplifier gain.

[0073] (2) Transfer function of electro-hydraulic servo valve

[0074] The servo valve transfer function can be expressed as:

[0075]

[0076] Where: X v is the displacement of the servo valve core, m; K xv is the servo valve gain, m / A; G sv (s) is K xv =1 when the transfer function of the servo valve.

[0077] (3) Flow quantization linear equation of electro-hydraulic servo valve

[0078] Assuming that the load is mass, elasticity and damping, for the convenience of processing and calculation, the load flow of the servo valve meets its inlet and outlet flow Q L =(Q L1 +Q L2 ) / 2, and after linearizing the flow valve equation of the servo valve, we get:

[0079] Q L =K qX v -K c p L

[0080] Where: K q is the flow gain coefficient of the slide valve, K c Slide valve flow pressure coefficient, m 5 / N·s, P L is the system output pressure, Pa; Q L is the load flow rate, L / min.

[0081] (4) Hydraulic cylinder flow continuity equation

[0082] The continuity equation for inlet and outlet flow is:

[0083]

[0084] Where: A p is the effective area of ​​the actuator, m 2 ;X p is the stroke of the cylinder, m; C tp is the total leakage coefficient, m 3 / (s·MPa);V t is the total volume of the actuator; β e is the effective bulk elastic modulus, Pa.

[0085] (5) Hydraulic cylinder and load force balance equation

[0086] The electro-hydraulic servo system includes load mass, elasticity and damping, so the balance equation of the valve-controlled hydraulic cylinder and load force is:

[0087] F g =A p p L =m t s 2 X p +B p sX p +KX P

[0088] Where: B p is the equivalent viscous damping coefficient of the hydraulic cylinder, N·s / m; m t is the load mass, kg; K is the equivalent spring stiffness of the hydraulic cylinder, N / m.

[0089] By combining, simplifying and simplifying the above formulas, we can draw a block diagram of the force control system, as shown in Figure 1 As shown in the figure, K ce =K c +C tp, the transfer function of the system can be obtained from the figure:

[0090]

[0091] Where: K0 is the open-loop gain of the system:

[0092]

[0093] Step 2: To solve the phase lag and resonance that are prone to occur in the system, it is necessary to compensate for the high inertia of the system. By adding two second-order inertia links to reduce the system's oscillation and adjust the system's natural frequency, the stability of the system is enhanced. The added links are:

[0094]

[0095] Where: K in is the gain of the dual inertia compensator, N / m; ω1, ω2 are the natural frequencies of the two inertia links, rad / s; ζ1, ζ2 are the damping ratios of the two inertia links.

[0096] The improved system model is:

[0097]

[0098] Step 3: Establish the state space expression of the closed-loop system of the electro-hydraulic servo system:

[0099]

[0100] Where:

[0101]

[0102] B=[001000000] T ,

[0103] C=[000000010],

[0104] D = 0;

[0105] The parameter vector to be identified is: θ = [a1a2a3a4a5a6a7] T , where a1=ω0,a2=ω r , a3=ζ0, a4=ω1, a5=ζ1, a6=ω2, a7=ζ2;

[0106] Step 4: Introduce the improved Chebyshev polynomials and sine and cosine operators, and update the algorithm to improve the firefly algorithm:

[0107] (1) Firefly algorithm initialization:

[0108] The equal oscillation property of Chebyshev polynomials is used to reduce the local aggregation phenomenon of the population generated by random sampling in the firefly algorithm, and the randomness and exploration ability of the algorithm are enhanced by improving the polynomial. The improved Chebyshev polynomials are as follows:

[0109] T n (x i )=(2x i T n-1 (x i )-T n-2 (x i ))%N

[0110] Where: T0(x) = 1, T1(x) = x0; n is the degree of the polynomial, satisfying n ≥ 2; N is a large prime number;

[0111] We can get:

[0112] T r·s (x) = T r (T s (x))=T s (T r (x))

[0113] We show that the semigroup property still holds and that the augmented Chebyshev polynomials are still commutative in composite functions.

[0114] The obtained result is in the range of [0,1]. Through linear transformation, the position is mapped to the boundary range of the target [lb,ub],,obtaining a uniform and random initialization population;

[0115] (2) Sine and Cosine Operators

[0116] The periodic fluctuation of sine and cosine functions is used to realize the two thread functions of global search and local development. The mathematical expression is as follows:

[0117]

[0118] Where: t represents the current number of iterations, is the component of the position of individual i at the tth iteration in the jth dimension, is the optimal solution in the jth dimension in t iterations, r1, r2, r3 and r4 are random parameters;

[0119] There are four main parameters in the sine-cosine algorithm: r1, r2, r3 and r4. Parameter r1∈[0,2] is used to realize the transformation of the control algorithm from global search to local development; parameter r2∈[0,2π] is used to describe the direction of movement and the extreme value of the iteration step when updating to the current optimal solution; parameter r3∈[0,2] is used to randomly emphasize (r3>1) or weaken (r3<1) right The parameter r4∈[0,1] is used to determine the switch between sine and cosine. In order to balance exploration and development, r1 is defined as the following adaptive value:

[0120]

[0121] Where: T is the maximum number of iterations, a is a constant, usually 2;

[0122] (3) Dynamic update of step size factor

[0123] Improve the fixed step size α of the firefly algorithm to a variable step size α v The hyperbolic sine function grows linearly when it approaches 0 in the positive interval, and transitions to exponential growth as x increases. This feature enables the firefly algorithm to obtain a larger step size in the early stage of the operation, which is convenient for global search, and a smaller step size in the later stage of the operation, which is convenient for local search. The adjustment of the step size factor is as follows:

[0124]

[0125] Where: α max , α min is the maximum and minimum value of α; β i is the current iteration number; β max is the maximum number of iterations;

[0126] Step 5: Use the improved multi-strategy firefly algorithm to adjust the parameters of the model built in step 1. The flow chart is as follows: Figure 2 shown.

[0127] (1) Initialize the firefly swarm

[0128] During the initialization phase, a modified Chebyshev polynomial was used to generate the initial firefly positions, resulting in a 7-dimensional swarm. The population size was 100, and the resulting mapping was within the range [0, 1]. A linear transformation was used to map the positions to the target boundary range [0, 20]. The light intensity attenuation coefficient γ was set to 0.5, and the maximum attractiveness β was set to 0.1. This initialization method improved the uniformity of the distribution of individual fireflies in the search space.

[0129] (2) Operation system model

[0130] Run the MFA algorithm constructed in step 2, set the maximum number of iterations T of the sine and cosine operators to 100, a to 2, r2, r3, and r4 to be randomly selected; set the maximum number of iterations of the adjustment algorithm for the step size factor β max is 100, a max is 0.6, a min is 0.3; the expected input function is y(kTs )=sin(2πkT s ), run the model, and generate model output.

[0131] (3) Calculating fitness

[0132] The difference between the model output and the target data is measured by the error evaluation function. The lower the fitness value of the firefly, the better the corresponding parameter vector. The error evaluation function is:

[0133]

[0134] (4) Update the global optimal solution

[0135] In each iteration, the global optimal solution is updated. After each fitness calculation, the algorithm compares the fitness of the current firefly with the fitness of the global optimal solution and updates the optimal solution based on the smaller fitness.

[0136] (5) Termination conditions and output

[0137] The algorithm terminates by reaching a maximum number of iterations, which is 100. When the termination condition is met, the algorithm stops iterating and outputs the current global optimal solution. The optimal solution is the optimal parameter solution found for a given problem.

[0138] The optimal parameter combination identified by MFA was obtained through ten experiments. The optimal fitness function value in the ten groups of experiments was 0.0115. The fitness curve is shown in the figure below. Figure 3 As shown in the figure, the FA algorithm converges more slowly than the MFA algorithm, reaching 0.0189 only at the 64th iteration. The MFA algorithm converges faster, reaching the optimal solution of 0.0115 at the 15th iteration. This demonstrates that the MFA algorithm is superior to the FA algorithm in both convergence speed and convergence accuracy.

[0139] Substitute the identified parameters into the system transfer function for simulation, obtain the Bode diagram of the system after identification, and compare it with the Bode diagram of the system before identification, as shown in Figure 4 As shown in the figure, the blue line represents the pre-identification result. The system exhibits significant fluctuations in gain and phase response, particularly in the mid- and high-frequency bands, where gain peaks and phase mismatches occur. This poses a risk of system instability in these frequency bands. The red line represents the post-identification result. The system's gain curve becomes more stable, and the phase response remains within a safe range, avoiding gain fluctuations and phase lag, significantly improving system stability. Therefore, the post-identification system is significantly more stable than the pre-identification system.

[0140] Finally, under the premise of determining the controlled object, an experimental platform is built for verification. Figure 5The figure is a physical picture of the electro-hydraulic force servo system test bench. Through the experiment, the measured curve of the model output is obtained. The input curve, measured curve, FA simulation curve and MFA simulation curve are compared, as shown in the figure. Figure 6 As shown in the figure, the most accurate result is obtained by the MFA method. The waveform closely matches the input signal, with an error of only 0.09%, demonstrating a high degree of match. The FA method is second, with a value of 1.12%. The experimental method, on the other hand, has a value of 2.69%, demonstrating that the parameters identified by simulation are superior to those obtained by the experimental method.

[0141] In summary, the proposed identification method can effectively improve the accuracy of the model and enhance the robustness of the model, providing reliable theoretical and practical support for the practical engineering application of high-precision electro-hydraulic force servo systems.

Claims

1. A multi-parameter identification method for a valve-controlled cylinder electro-hydraulic servo system, characterized in that: The following steps are involved: Step 1: Develop a mathematical model based on the components and working principle of the valve-controlled cylinder electro-hydraulic servo system, introduce inertia compensation to improve the stability of the system, and ultimately determine the structural characteristics of the model and the parameters that need to be identified; Step 1-1: Build a valve-controlled cylinder electro-hydraulic servo system model The constructed system model is shown below: Where: K0 is the open-loop gain of the system; G sv (s) is the transfer function of the servo valve when the servo valve gain is 1; ω m ,ω0,ω r are the natural frequency of the load, the natural frequency formed by the stiffness of the hydraulic spring coupled in parallel with the load and the load, and the stiffness-damping coefficient ratio of the hydraulic spring coupled in series with the load spring; ζ0 is the system damping ratio; Step 1-2: Inertia compensation strategy In the electro-hydraulic servo system, since the hydraulic components have high inertia when working, the hydraulic oil is compressible, and the mechanical structure has a natural frequency, phase lag and resonance are prone to occur. Therefore, it is necessary to compensate for the high inertia of the system. By adding two second-order inertia links to reduce the oscillation of the system and adjust the natural frequency of the system, the stability of the system is enhanced. The improved system model is shown below: Where: K in is the compensation gain; ω1, ω2 are the natural frequencies of the two inertia links; ζ1, ζ2 are the damping ratios of the two inertia links; Steps 1-3: Parameter vector to be identified The state space expression is constructed based on the obtained model. The state space expression of the established closed-loop system is as follows: Where: B＝[001000000] T , C＝[000000010], D＝0； The parameter vector to be identified is: θ = [a1a2a3a4a5a6a7] T , where a1=ω0,a2=ω r , a3=ζ0, a4=ω1, a5=ζ1, a6=ω2, a7=ζ2; Step 2: Propose an improved multi-strategy firefly algorithm, which uses the improved Chebyshev polynomial to enhance the randomness and uniformity of the initial solution and improve the global search capability of the algorithm; introduce an update algorithm to modify the step size factor of the firefly algorithm to achieve a balance between local search and global exploration; Step 2-1, Firefly algorithm initialization The equal oscillation property of Chebyshev polynomials is used to reduce the local aggregation phenomenon of the population generated by random sampling in the firefly algorithm, and the randomness and exploration ability of the algorithm are enhanced by improving the polynomials. Specifically: In the d-dimensional search space, the individual is X i =(x1,x2,…,x d ), select the initial value X0∈[0,1] as the starting value of the Chebyshev polynomial, and the mathematical expression is: T n (x i )=(2x i T n-1 (x i )-T n-2 (x i ))%N (4) Where: T0(x) = 1, T1(x) = x0; n is the degree of the polynomial, satisfying n ≥ 2; N is a large prime number; The obtained result is in the range of [0,1]. Through linear transformation, the position is mapped to the boundary range of the target [lb,ub],,obtaining a uniform and random initialization population; Step 2-2: Dynamic update of step factor The fixed step size of the Firefly Algorithm makes it difficult to achieve a balance between local search and global exploration. By improving the step size factor of the Firefly Algorithm, the step size factor can be dynamically updated. Specifically: Improve the fixed step size α of the firefly algorithm to a variable step size α v The hyperbolic sine function grows linearly when it approaches 0 in the positive interval, and transitions to exponential growth as x increases. This feature enables the firefly algorithm to obtain a larger step size in the early stage of the operation, which is convenient for global search, and a smaller step size in the later stage of the operation, which is convenient for local search. The adjustment of the step size factor is as follows: Where: α max , α min are the maximum and minimum values ​​of α; β i is the current iteration number; β max is the maximum number of iterations; Step 3: Based on the expected input function, the improved multi-strategy firefly algorithm is used to perform parameter identification on the mathematical model of the valve-controlled cylinder electro-hydraulic servo system. The error evaluation function is introduced to identify the identification results, and an accurate valve-controlled cylinder electro-hydraulic servo system model is obtained. The effectiveness of the established model is verified through simulation and experiments. Step 3-1: Parameter identification and error evaluation The system's expected input and output functions are calculated using a sine function, namely: y(kT s )=sin(2πkT s ),k=1,2,…,M (6) Where: T s is the sampling period, M is the number of sampling points; Considering that there are still unidentified nonlinear factors in reality, the model identified in the actual process is: y(kT s )=sin(2πkT s )+e(kT s ),k=1,2,…,M (7) Where: e(T s ) is the residual value caused by the identification factor; The error evaluation function is defined as: Step 3-2: Simulation and experimental verification The obtained valve-controlled cylinder electro-hydraulic servo system model is simulated and experimentally verified, specifically: First, the fitness value curves of the algorithm are compared and analyzed to analyze the convergence ability and convergence speed of the improved algorithm; secondly, the Bode diagrams before and after identification are simulated and compared to analyze the stability of the improved system; finally, the obtained model is experimentally analyzed through the constructed electro-hydraulic force servo system test bench to prove the accuracy of the obtained model.

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