A variable gain continuous reaching law sliding mode control method for electro-hydraulic servo system

Abstract

The present application relates to a kind of electro-hydraulic servo control method, the purpose is to provide a kind of variable gain continuous reaching law sliding mode control method of electro-hydraulic servo system, can effectively weaken the chattering phenomenon existing in sliding mode control while guaranteeing that system has robustness, fast convergence characteristics, improve the dynamic performance of system.The technical scheme is a kind of improved reaching law sliding mode control method of electro-hydraulic servo system, including the following steps: step 1: establish the mathematical model of electro-hydraulic servo system;Step 2: define the time-varying gain continuous reaching law sliding mode control method of electro-hydraulic servo system.

Description

TECHNICAL FIELD

[0001] The present application relates to an electro-hydraulic servo control method, in particular to a variable gain continuous reaching law sliding mode control method of an electro-hydraulic servo system. BACKGROUND

[0002] The electro-hydraulic servo system has the advantages of high power-to-weight ratio, high control precision and fast response speed, and is widely used in military, industrial and civil fields, such as underwater pipeline laying, material injection molding machine, aircraft landing gear, etc. The electro-hydraulic servo system is a typical strong coupling nonlinear system, and the inherent system uncertainty and external disturbances in the working process will significantly interfere with the realization of accurate control of the hydraulic servo system. With the continuous development of technology, the control accuracy of mechatronic systems is continuously improved, and the influence of the nonlinear characteristics of the electro-hydraulic servo system and external force disturbance on the control performance of the actuator is increasingly significant. How to suppress the inherent nonlinear characteristics of the system and the disturbance caused by external force has become an important factor to improve the control accuracy of the electro-hydraulic servo system. The traditional linear control method usually uses a local linearization method to simplify the nonlinear electro-hydraulic servo system, but the linearization error generated in the simplification process will affect the overall performance of the system and cannot meet the actual application requirements. Therefore, a nonlinear control method that can effectively improve the performance of the system must be designed according to the nonlinear characteristics existing in the electro-hydraulic servo system.

[0003] In order to suppress the nonlinear disturbance in the electro-hydraulic servo system, many nonlinear control methods have been proposed in recent years. When designing the controller of the electro-hydraulic servo system, the nonlinear characteristics should be considered first, which will seriously affect the stability of the system. In addition, the system should be less sensitive to parameter uncertainty and disturbance while meeting good robustness. The electro-hydraulic servo system is a large inertia system and is sensitive to high-frequency signals. Under the influence of high-frequency signals, the system will lose stability. The traditional sliding mode control method is not sensitive to parameter changes, and the control quantity often shuttles between the two sides of the sliding mode surface, which is prone to chattering phenomenon. These will seriously affect the performance of the control system and cause the electro-hydraulic servo system to lose stability and even damage the system during the working process, which greatly limits the control application of the electro-hydraulic servo system. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the above background art, and to provide a variable gain continuous reaching law sliding mode control method of an electro-hydraulic servo system, which can effectively weaken the chattering phenomenon existing in the sliding mode control while ensuring the robustness and fast convergence characteristics of the system, and improve the dynamic performance of the system.

[0005] The technical scheme adopted by the present application is: an improved reaching law sliding mode control method of an electro-hydraulic servo system, comprising the following steps:

[0006] Step 1: Establish the mathematical model of electro-hydraulic servo system;

[0007]

[0008]

[0009]

[0010] In the formula, x1, x2, x3 respectively represent the displacement, speed and acceleration of the end load of the electro-hydraulic servo system, respectively represent the speed, acceleration and jerk of the end load of the electro-hydraulic servo system, m represents the mass of the end load of the electro-hydraulic servo system, B represents the combined coefficient of the modelable damping and viscous friction of the end load of the electro-hydraulic servo system and the oil cylinder rod in the movement process, A f represents the amplitude of the Coulomb friction, u is the control input signal of the electromagnetic servo valve, A x , A0 respectively represent the gain coefficient of acceleration and the gain coefficient of system input signal in the electro-hydraulic servo system, and the specific forms are as follows:

[0011]

[0012]

[0013] In the formula, V 01 , V 02 respectively represent the initial volume of the oil supply chamber and the oil return chamber; βe represents the effective volume modulus of the oil; Q LI represents the total internal leakage of the hydraulic servo system, m represents the mass of the end load of the hydraulic cylinder, P1, P2 respectively represent the pressure of the oil supply chamber and the oil return chamber of the hydraulic cylinder; A1, A2 respectively represent the effective piston rod area of the oil supply chamber and the oil return chamber of the hydraulic cylinder; P s , P r respectively represent the oil supply and oil return pressure of the system; k1, k2 respectively represent the control input signal of the electromagnetic servo valve and the proportional coefficient of the oil flow of the oil supply chamber and the oil return chamber.

[0014] The establishment process of the mathematical model of the electro-hydraulic servo system is as follows:

[0015] (1) Establish the dynamic equation of the end load of the electro-hydraulic servo system:

[0016]

[0017] In the formula, y、 and respectively represent the displacement, speed and acceleration of the end load of the electro-hydraulic servo system; A f S frepresents the linearized approximation of the nonlinear Coulomb friction, where A f represents the coefficient of Coulomb friction, S f represents the linearized approximation equation of the nonlinear Coulomb friction;

[0018] The oil liquid has compressibility, and regardless of the external leakage of the hydraulic cylinder, the pressure dynamic equation of the oil liquid is:

[0019]

[0020]

[0021] Q LI =c1(P1-P2) 2 +c2(P1-P2)+c3

[0022] Q LI In the expression, c1, c2, and c3 represent the leakage coefficients of the quadratic term, the linear term, and the constant term of the pressure difference respectively; Q1 represents the supply flow of the supply cavity; Q2 represents the return flow of the return cavity; wherein the relationship between Q1, Q2 and the displacement of the electromagnetic servo valve spool is as follows:

[0023]

[0024]

[0025] wherein:

[0026]

[0027]

[0028] In the formula, x v represents the displacement of the electromagnetic servo valve spool; k q1 , k q2 respectively represent the proportional coefficients of the displacement of the electromagnetic servo valve spool and the oil flow in the supply cavity and the return cavity; C d represents the flow coefficient of the electromagnetic valve; ω1 and ω2 respectively represent the spool gradient of the supply cavity and the return cavity of the electromagnetic servo valve; and ρ represents the density of the hydraulic oil.

[0029] The bandwidth of the electromagnetic servo valve is much higher than the bandwidth of the system, and the valve spool displacement can be proportionally controlled by controlling the input, so the equation can be rewritten as:

[0030]

[0031]

[0032] wherein:

[0033] x v =λu

[0034]

[0035] where λ represents the proportional coefficient of the spool displacement of the electromagnetic valve to the control input signal; k1 and k2 represent the proportional coefficients of the oil flow in the oil supply chamber and the oil return chamber to the control input signal, respectively;

[0036] (2) The state variable of the system is defined as where x1, x2, and x3 represent the displacement, velocity, and acceleration of the end load of the electro-hydraulic servo system, respectively, represent the velocity, acceleration, and jerk of the end load of the electro-hydraulic servo system, respectively, and the state equation of the electro-hydraulic servo system is:

[0037]

[0038]

[0039]

[0040] where A x and A0 represent the gain coefficients of the acceleration and the system input signal in the electro-hydraulic servo system, respectively, and the specific form of the linearized approximation equation S f of the nonlinear Coulomb friction is as follows:

[0041]

[0042]

[0043]

[0044] Step 2: Define the time-varying gain continuous reaching law sliding mode control method of the electro-hydraulic servo system

[0045] (1) The time-varying gain continuous reaching law sliding mode control method of the electro-hydraulic servo system is defined as

[0046]

[0047] where m / n represents the exponential term coefficient of the velocity error, satisfying m / n ∈ (0, 1) and m and n are both odd numbers; γ represents the exponential term coefficient of the displacement absolute error, satisfying γ > 1; o / p and μ / v represent the exponential term coefficients in the sign function term and the arctangent function term, respectively, satisfying o, p, μ, v being odd numbers greater than zero, and o / p > 1, μ / v ∈ (0, 1); k s1 , k s2respectively represent the gain coefficient in the sign function term, the gain coefficient in the inverse tangent function term; l represents the gain coefficient of the inverse tangent function variable; a and b respectively represent the gain parameters of the constant term and the proportional term of the sliding mode surface, and are both odd numbers greater than zero; in addition, alpha represents the exponential term coefficient of the displacement absolute error, and satisfies alpha element of (1, 2); by adjusting a, b and alpha, the dynamic response characteristics of the system can be changed; x 1d 、 respectively represent the expected displacement and speed of the system; e = x1-x 1d represents the displacement tracking error of the system, represents the speed tracking error of the system.

[0048] Suppose that the expected displacement of the end load of the electro-hydraulic servo system is x 1d , and the expected speed The displacement error e = x1-x 1d , and the speed error

[0049] (1) a non-singular terminal sliding mode surface is designed:

[0050] s = ae + b|e| α sign(e);

[0051] The derivative operation is performed on the sliding mode surface:

[0052]

[0053] (2) in order to improve the transient characteristics of the system, accelerate the convergence speed of the system and weaken the chattering phenomenon existing in the sliding mode control, a time-varying gain continuous sliding mode reaching law is designed:

[0054]

[0055] (3) the sliding mode reaching law is combined with the derivative result of the sliding mode surface and the state equation of the electro-hydraulic servo system, so that the time-varying gain continuous reaching law sliding mode control method of the hydraulic servo system can be obtained as follows:

[0056]

[0057] Compared with the prior art, the beneficial effects of the present application are:

[0058] (1) the non-singular fast terminal sliding mode control method is introduced in the present application, and the traditional sliding mode reaching law is improved and designed, so that a time-varying gain continuous sliding mode controller is designed; by changing the gain parameters and introducing the continuous term function, it can be ensured that the system can quickly reach the sliding mode surface, and the chattering problem existing in the sliding mode controller can be effectively weakened;

[0059] (2) The application can effectively improve the nonlinear characteristics of the system, improve the control accuracy of the whole system, ensure the robustness of the system, and improve the dynamic response characteristics of the system. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 A schematic diagram of the principle of the electro-hydraulic servo system applied to the embodiment of the application.

[0061] Figure 2 A block diagram of the control method described in the embodiment of the application.

[0062] Figure 3 A flowchart of the control method described in the embodiment of the application.

[0063] Figure 4 A comparison chart of the results of tracking the desired step displacement using different algorithms provided by the application.

[0064] Figure 5 A comparison chart of the tracking errors generated by tracking the desired step displacement using different algorithms provided by the application. DETAILED DESCRIPTION

[0065] The application will be further described in detail below in combination with the embodiments shown in the drawings.

[0066] The variable gain continuous reaching law sliding mode control method of the electro-hydraulic servo system shown in the drawings includes the following steps:

[0067] 1. Establish a mathematical model of the electro-hydraulic servo system:

[0068] The schematic diagram of the principle of the electro-hydraulic servo system is shown in Figure 1 The end load is fixed to the end of the single-rod hydraulic cylinder, and the load can track any desired position trajectory as accurately as possible by controlling the position of the hydraulic cylinder piston rod. The dynamics equation of the end load is as follows:

[0069]

[0070] In the formula, m represents the mass of the end load of the hydraulic cylinder, y, and respectively represent the displacement, speed and acceleration of the end load of the electro-hydraulic servo system; P1 and P2 respectively represent the pressure of the oil supply chamber and the oil return chamber of the hydraulic cylinder; A1 and A2 respectively represent the effective piston rod area of the oil supply chamber and the oil return chamber of the hydraulic cylinder; B represents the combined coefficient of the modelable damping and viscous friction force of the load and the cylinder rod; A f S f represents the linear approximation of the nonlinear Coulomb friction, where A f represents the amplitude of the Coulomb friction, and S f represents the linear approximation equation of the nonlinear Coulomb friction.

[0071] The oil has compressibility, regardless of the external leakage of the hydraulic cylinder, the dynamic equation of the oil pressure is:

[0072]

[0073]

[0074] Q LI = c1(P1-P2) 2 + c2(P1-P2) + c3

[0075] In the formula, V 01 , V 02 respectively represent the initial volume of the oil supply chamber and the oil return chamber, wherein V1 = V 01 + A1y, V2 = V 02 - A2y; βe represents the effective bulk modulus of the oil; Q LI represents the total internal leakage of the hydraulic servo system, c1, c2, c3 respectively represent the leakage coefficients of the quadratic term, the linear term and the constant term of the pressure difference. Q1 represents the supply flow of the supply chamber; Q2 represents the oil return flow of the oil return chamber; wherein the relationship between Q1, Q2 and the spool displacement of the electromagnetic servo valve is as follows:

[0076]

[0077]

[0078] Wherein:

[0079]

[0080]

[0081]

[0082] In the formula, P s represents the supply oil pressure of the electro-hydraulic servo system; P r represents the oil return pressure of the electro-hydraulic servo system; x v represents the spool displacement of the electromagnetic servo valve; k q1 , k q2 respectively represent the proportional coefficient of the spool displacement of the electromagnetic servo valve and the oil flow in the supply chamber and the oil return chamber; C d represents the flow coefficient of the electromagnetic valve; ω1 and ω2 respectively represent the spool gradient of the supply chamber and the oil return chamber of the electromagnetic servo valve; ρ represents the density of the hydraulic oil;

[0083] The bandwidth of the electromagnetic servo valve is much higher than the bandwidth of the system, and the spool displacement can be controlled in proportion by controlling the input, so the equation can be rewritten as:

[0084]

[0085]

[0086] wherein:

[0087] x v = λu

[0088] k1 = λk q1

[0089] k2 = λk q2

[0090] In the formula, λ represents the proportional coefficient of the electromagnetic valve spool displacement and the control input signal; u represents the control input signal of the electromagnetic servo valve; k1 and k2 represent the proportional coefficients of the oil flow in the oil supply chamber and the oil return chamber and the control input signal, respectively;

[0091] Define the state variable of the system as wherein x1, x2, x3 represent the displacement, velocity, and acceleration of the end load of the electro-hydraulic servo system, respectively, represent the velocity, acceleration, and jerk of the end load of the electro-hydraulic servo system, respectively, and the state equation of the electro-hydraulic servo system is:

[0092]

[0093]

[0094]

[0095] wherein, A x and A0 represent the gain coefficients of the acceleration and the system input signal in the electro-hydraulic servo system, and the specific forms are as follows:

[0096]

[0097]

[0098]

[0099] The mathematical model of the electro-hydraulic servo system can be simplified as:

[0100]

[0101]

[0102]

[0103] Step 2: Define the time-varying gain continuous approach law sliding mode control method of the electro-hydraulic servo system

[0104] Assume that the desired displacement of the end load of the electro-hydraulic servo system is x 1d , the desired velocity The displacement tracking error e = x1-x 1d , the velocity tracking error

[0105] Design a nonsingular terminal sliding mode surface:

[0106] s = ae + b |e| α sign(e)

[0107] a and b represent the gain parameters of the constant term and the proportional term of the sliding mode surface respectively, and both are odd numbers greater than zero; in addition, a represents the exponential term coefficient of the displacement absolute error, and satisfies a e (1, 2); by adjusting a, b and a, the dynamic response characteristics of the system can be changed;

[0108] Derive the sliding mode surface:

[0109]

[0110] In order to improve the transient characteristics of the system, accelerate the convergence speed of the system, and effectively weaken the chattering phenomenon existing in the sliding mode control, a time-varying gain continuous reaching law is designed:

[0111]

[0112] In the formula: m / n represents the exponential term coefficient of the velocity error, and satisfies m / n e (0, 1) and m, n are odd numbers; g represents the exponential term coefficient of the displacement absolute error, and satisfies g > 1; o / p and m / v represent the exponential term coefficients in the sign function term and the arctangent function term respectively, and o, p, m, v are odd numbers greater than zero, and o / p > 1, m / v e (0, 1); k s1 and k s2 represent the gain coefficients in the sign function term and the arctangent function term respectively; l represents the gain coefficient of the arctangent function variable;

[0113] The two parts of the designed sliding mode reaching law are k s1 |e| γ |s| o / p sign(s), k s2 |e| 1 / γ |s| μ / vtanh(ls) can play a role in accelerating the convergence speed, and plays different roles in the convergence process. When the system state quantity is far from the sliding mode surface, the first part will make the system state move to the sliding mode surface at a faster speed; when the system approaches the sliding mode surface, the second part plays a major role, making the sliding mode variable gradually decrease to zero, so that the system remains stable. In the sliding mode reaching law, by introducing the state variable, the sliding mode reaching law can adjust the gain coefficient of the switching term according to the change of the state variable, which has stronger adaptability; by introducing the continuous arctangent function tanh(ls) instead of the common sign function sign(s), not only can the system reach the sliding mode surface at a faster speed, but also can make the system approach the sliding mode surface in a more smooth transition form, which can weaken the chattering of the system on the sliding mode surface.

[0114] The time-varying gain continuous reaching law sliding mode control method of the electro-hydraulic servo system can be obtained by combining the sliding mode reaching law with the derivative of the sliding mode surface and the state equation of the electro-hydraulic servo system.

[0115]

[0116] In order to prove the stability of the system, the Lyapunov function V and its derivative are taken as

[0117]

[0118]

[0119] The above formula is always less than zero at any time, so the state quantity of the electro-hydraulic servo system will gradually converge to the sliding mode surface, that is, the electro-hydraulic servo system will gradually stabilize.

[0120] The time-varying gain continuous reaching law sliding mode control method designed for the electro-hydraulic servo system can enhance the dynamic response characteristics of the system while improving the stability of the system and weakening the chattering phenomenon of the system. The block diagram of the time-varying gain continuous reaching law sliding mode control method of the electro-hydraulic servo system is as shown in Figure 2 , and the specific step flow of the implementation method is as shown in Figure 3 .

[0121] In order to verify the effectiveness and feasibility of the proposed theory, combined with Figure 2 , Figure 3 , the simulation model verification is carried out through the MATLAB / Simulink simulation platform, the simulation sampling time is 0.001s, and the specific model parameter setting is as shown in Table 1.

[0122] By giving the displacement of the end load of the electro-hydraulic servo system, the response speed and stability of the system are analyzed and compared to verify the effectiveness and superiority of the algorithm. The desired displacement of the end load is 75mm, and the results obtained by comparison with the PID control method, the model reference PID control method and the traditional non-continuous reaching law sliding mode control method are shown in Figure 4 、 Figure 5 As can be seen from Figure 4 , the time-varying gain continuous reaching law sliding mode control method converges at 1.3s, and the final convergence error is within 0.1mm; the PID control method still does not converge within 1.5s although the convergence error is maintained within 0.1mm; the model reference PID control method converges slowly, and the steady-state error is greater than 0.2mm; and the traditional non-continuous reaching law sliding mode control method accelerates the convergence speed of the system compared with the PID controller, so that the convergence speed of the system reaches 1.45s, but the steady-state error is only maintained within 0.2mm. As can be seen from Figure 5 , compared with the traditional non-continuous reaching law sliding mode control method, the electro-hydraulic servo system approaches the sliding mode surface at a faster speed, which can effectively enhance the robustness of the sliding mode control method and obtain better transient performance. By comparison, the time-varying gain continuous reaching law sliding mode control method proposed in the present application can further accelerate the convergence speed of the system while better resisting unknown disturbances of the system such as parameter uncertainty and disturbance unknownness, and has lower disturbance sensitivity compared with other algorithms.

[0123] Table 1 Electro-hydraulic servo system simulation model parameter table

[0124]

[0125] Table 2 Time-varying gain continuous reaching law sliding mode control method parameters

[0126]

[0127] As a kind of variable structure control, sliding mode control method pre-designs sliding surface by the state variable of system, so that system moves from starting position to sliding surface, and slides on sliding surface until reaching equilibrium point after reaching sliding surface. However, during the process of system sliding on sliding surface, since the robust term used by sliding mode control method is usually sign function, system will shuttle back and forth on both sides of sliding surface, which will cause chattering phenomenon of system and affect the running stability of system.

Claims

1. A time-varying gain continuous-type reaching law sliding mode control method for electro-hydraulic servo system, characterized in that, The method comprises the following steps: Step 1: establishing a mathematical model of an electro-hydraulic servo system The mathematical model of the electro-hydraulic servo system is as follows: Wherein: x1, x2, x3 represent displacement, velocity and acceleration of the end load of the electro-hydraulic servo system respectively, x1, x2, x3 represent velocity, acceleration and jerk of the end load of the electro-hydraulic servo system respectively, m represents the mass of the end load of the electro-hydraulic servo system, B represents the combined coefficient of the modelable damping and viscous friction of the end load of the electro-hydraulic servo system and the cylinder rod in the movement process, A f represents the amplitude of the Coulomb friction, u represents the control input signal of the electromagnetic servo valve, A x A0 represent the gain coefficients of acceleration and system input signal in the electro-hydraulic servo system respectively, and the specific forms are as follows: In the formula: V 01 , V 02 respectively represent the initial volume of the oil supply chamber and the oil return chamber; βe represents the effective volume modulus of the oil; Q LI represents the total internal leakage of the hydraulic servo system, m represents the mass of the load at the end of the hydraulic cylinder, P1 and P2 respectively represent the pressure of the oil supply chamber and the oil return chamber of the hydraulic cylinder; A1 and A2 respectively represent the effective piston rod pressure area of the oil supply chamber and the oil return chamber of the hydraulic cylinder; P s , P r respectively represent the system oil supply pressure and the oil return pressure, k1 and k2 respectively represent the proportional coefficient of the control input signal of the electromagnetic servo valve and the oil flow of the oil supply chamber and the oil return chamber; Step 2: defining a time-varying gain continuous reaching law sliding mode control method of the electro-hydraulic servo system The time-varying gain continuous reaching law sliding mode control method of the electro-hydraulic servo system is as follows: wherein: m / n represents the exponential term coefficient of the speed error, satisfying m / n ∈ (0, 1) and m, n are both odd numbers; γ represents the exponential term coefficient of the displacement absolute error, satisfying γ > 1; o / p and μ / v respectively represent the exponential term coefficients of the absolute value of the sliding mode surface in the sign function term and the arctangent function term, satisfying o, p, μ, v are odd numbers greater than zero, and o / p > 1, μ / v ∈ (0, 1); k s1 ,k s2 respectively represent the gain coefficients in the sign function term and the arctangent function term; l represents the gain coefficient of the arctangent function variable; a and b respectively represent the gain parameters of the constant term and the proportional term of the sliding mode surface, and are both odd numbers greater than zero; in addition, α represents the exponential term coefficient of the displacement absolute error, satisfying α ∈ (1, 2); by adjusting a, b and α, the dynamic response characteristics of the system can be changed; respectively represent the desired displacement and speed of the system; e = x1-x 1d represents the displacement tracking error of the system, represents the speed tracking error of the system; the designed non-singular terminal sliding mode surface: s = ae + b|e| α sign(e).

2. The method of claim 1, wherein the time-varying gain continuous reaching law of the electro-hydraulic servo system is characterized by: In step 1, the process of establishing the mathematical model of the electro-hydraulic servo system is as follows: (1) establishing a dynamic equation of an end load of the electro-hydraulic servo system: where y, and represent the displacement, velocity and acceleration of the end load of the electro-hydraulic servo system, respectively; A f S f represents the linearized approximation of the nonlinear Coulomb friction, where A f represents the coefficient of the Coulomb friction, S f represents the linearized approximation equation of the nonlinear Coulomb friction; The oil liquid is compressible, and the external leakage of the hydraulic cylinder is not considered, and a pressure dynamic equation of the oil liquid is as follows: Q LI = c1(P1-P2) 2 +c2(P1-P2)+c3 In the formula, Q LI In the formula, c1, c2, c3 respectively represent quadratic term, linear term and constant term of pressure difference leakage coefficient; Q1 represents supply flow of the supply cavity; Q2 represents oil return flow of the oil return cavity; wherein, the relationship between Q1, Q2 and the spool displacement of the electromagnetic servo valve is as follows: Wherein: where x v represents the displacement of the spool of the electromagnetic servo valve; k q1 , k q2 represent the proportional coefficients of the displacement of the spool of the electromagnetic servo valve and the flow of the oil in the oil supply chamber and the oil return chamber, respectively; C d represents the flow coefficient of the electromagnetic valve; ω1 and ω2 represent the spool gradients of the oil supply chamber and the oil return chamber of the electromagnetic servo valve, respectively; and ρ represents the density of the hydraulic oil. The frequency bandwidth of the electromagnetic servo valve is much higher than the frequency bandwidth of the system, and the valve core displacement can be proportionally controlled through control input, and the equation can be rewritten as: Wherein: x v = λu In the formula, λ represents a proportional coefficient of the electromagnetic valve core displacement and the control input signal; k1 and k2 respectively represent proportional coefficients of oil liquid flow in the oil supply cavity and the oil return cavity and the control input signal; (2) Define the state variables of the system as Where x1, x2, x3 represent the displacement, velocity, acceleration of the end load of the electro-hydraulic servo system respectively, Where x1, x2, x3 represent the displacement, velocity, acceleration of the end load of the electro-hydraulic servo system respectively, the velocity, acceleration and jerk of the end load of the electro-hydraulic servo system respectively, and the state equation of the system is: wherein the definition A x , A0 represent the gain coefficient of acceleration and system input signal in electro-hydraulic servo system, respectively, and the linear approximation equation of nonlinear Coulomb friction S f is specifically as follows:

3. The time-varying gain continuous sliding mode control method of electro-hydraulic servo system according to claim 1, characterized in that: In Step 2, assume the desired displacement of the end load of the electro-hydraulic servo system is x 1d , the desired velocity Displacement error e = x1 - x 1d , the velocity error (1) performing derivative operation on the sliding mode surface: (2) in order to improve the transient state characteristics of the system, accelerate the convergence speed of the system and weaken the chattering phenomenon existing in the sliding mode control, a time-varying gain continuous sliding mode reaching law is designed: (3) combining the sliding mode reaching law, the derivative result of the sliding mode surface and the state equation of the electro-hydraulic servo system, the time-varying gain continuous reaching law sliding mode control method of the hydraulic servo system is as follows:

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