Asymmetric full-state constraint robust control method for electro-hydraulic direct-drive proportional servo valve

Abstract

The invention discloses an asymmetric full-state constraint robust control method for an electro-hydraulic direct drive type proportional servo valve. According to the method, a full-state constraint strategy based on a nonlinear conversion function is designed, a nonlinear robust item with gain self-learning is designed, and a nonlinear filter is introduced to solve the problem of differential explosion of virtual control input. Aiming at the problems of asymmetric time-varying full-state constraint, time-varying uncertain parameters and unmodeled time-varying disturbance existing in the electro-hydraulic direct-driven proportional servo valve, the invention ensures that the position and speed state strictly meet the asymmetric time-varying constraint requirement through a novel full-state constraint strategy; and limitation on feasibility conditions of a virtual controller in a traditional obstacle Lyapunov function method is avoided, and effective suppression on parameter perturbation, time-varying disturbance and differential explosion is realized by a nonlinear robust item and a filtering mechanism, so that full-state constraint and high-precision tracking performance of the system are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of electromechanical servo control, and in particular to an asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve. Background Art

[0002] Electro-hydraulic servo systems, with their advantages of high power density, fast dynamic response, and strong load capacity, have become a core drive solution for high-precision motion control in aerospace, defense, and other industries. As the core control element of such systems, the electro-hydraulic direct-drive proportional servo valve, its control performance directly impacts the tracking accuracy and robustness of the overall system. However, direct-drive proportional servo valves face challenges from multiple sources of complex uncertainty in practical applications. As electro-hydraulic direct-drive proportional servo valves strive for high-performance indicators such as high precision and high-frequency response, various nonlinear factors in the system become increasingly prominent, primarily including uncertain nonlinearities and parameter uncertainties. Uncertain nonlinearities include the effects of fluid dynamics, unmodeled friction dynamics, and external time-varying disturbances on the valve core during motion. Parameter uncertainties include the viscous friction coefficient, the mass of moving parts, and the stiffness of springs. Furthermore, given that electro-hydraulic direct-drive proportional servo valves, when equipped with different actuators, have varying position and velocity requirements during operation, and these state constraints are asymmetric and time-varying, a method that ensures both high-precision tracking and full state constraints is particularly important.

[0003] First, to address the modeling uncertainty in the system, sliding mode control (SMC) employs discontinuous switching terms (such as sign functions) to force the system state to move along the sliding surface. This approach offers strong robustness to modeling errors and external disturbances. However, its core flaw lies in chattering. Hard switching of the sign function excites the system's high-frequency unmodeled dynamics, leading to control input oscillations that severely impact actuator life and tracking accuracy. Even with improved SMC, chattering remains difficult to completely eliminate, and its adaptability to time-varying disturbances is limited. To address parameter uncertainty, adaptive robust control (ARC) integrates parameter adaptation with robust feedback within a backstepping framework. This approach effectively compensates for constant disturbances and parameter drift, but it cannot effectively handle time-varying disturbances in the system. To address the full-state constraint problem, the state constraint method based on the barrier Lyapunov function (BLF) embeds the state constraint into the controller design by designing an inverse or logarithmic barrier Lyapunov function to ensure that the state constraint is within the corresponding range. During the backstepping recursive design, it is necessary to ensure that the virtual control input at each level does not violate the constraint boundary, resulting in the feasibility condition problem of the virtual controller and the need for offline optimization. As the system order increases, the recursive design leads to a sharp increase in computational complexity. Summary of the Invention

[0004] The purpose of the present invention is to provide an asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve with full-state constraints, gain self-learning, strong anti-interference ability and high tracking performance, which can not only ensure the strict boundedness of position and velocity states within the asymmetric time-varying constraint range, but also does not require the feasibility condition constraints of a virtual controller; autonomous learning and active compensation of system gain and time-varying disturbances, reducing the burden of manual parameter setting; fundamentally circumventing the differential explosion problem in traditional backstepping control, and suppressing the adverse effects of measurement noise on control accuracy; high-precision and strong robust position tracking performance under parameter uncertainty and time-varying disturbances.

[0005] The technical solution for achieving the purpose of the present invention is: a method for asymmetric full-state constrained robust control of an electro-hydraulic direct-drive proportional servo valve, comprising the following steps:

[0006] Step 1: Establish a mathematical model of the electro-hydraulic direct-drive proportional servo valve and proceed to step 2.

[0007] Step 2: Based on the mathematical model of the electro-hydraulic direct-drive proportional servo valve, the Lyapunov function is combined with the backstepping method to design an asymmetric full-state constrained robust controller for the electro-hydraulic direct-drive proportional servo valve, and then proceed to step 3.

[0008] Step 3: Use Lyapunov stability theory to prove the stability of the asymmetric full-state constrained robust controller of the electro-hydraulic direct-drive proportional servo valve.

[0009] Compared with the prior art, the present invention has the following significant advantages: (1) while realizing the full state constraint of the system, it avoids the feasibility condition constraint of the virtual controller; (2) it realizes the adaptive learning of the system gain, reducing the complexity of parameter setting; (3) it effectively avoids the differential explosion problem of the electro-hydraulic direct-drive proportional servo valve system in the traditional backstepping control, and reduces the influence of measurement noise on the control accuracy, thereby achieving high-precision tracking performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a schematic diagram of the principle of the asymmetric full-state constrained robust control method of the electro-hydraulic direct-drive proportional servo valve of the present invention.

[0011] Figure 2 It is a schematic diagram of the principle of the electro-hydraulic direct-drive proportional servo valve of the present invention.

[0012] Figure 3 It is the expected instruction curve diagram that the system output needs to track under the action of the FSCRC controller designed by the present invention.

[0013] Figure 4 It is a curve diagram showing the tracking error of the system changing with time under the action of the FSCRC controller designed by the present invention.

[0014] Figure 5 This is a comparison curve of the tracking error of the system under the action of the FSCRC controller designed by the present invention and the traditional PID controller.

[0015] Figure 6 This is a control input curve diagram of the system under the action of the FSCRC controller designed by the present invention.

[0016] Figure 7 It is a graph of the actual position of the system under the constraint of asymmetric time-varying position state under the action of the FSCRC controller designed by the present invention.

[0017] Figure 8 It is a graph of the actual speed of the system under the constraints of asymmetric time-varying speed state under the action of the FSCRC controller designed by the present invention.

[0018] Figure 9 It is a graph of the actual position of the system under the constraint of an asymmetric time-varying position state under the action of the PID controller designed by the present invention.

[0019] Figure 10 It is a graph of the actual speed of the system under the constraint of asymmetric time-varying speed state under the action of the PID controller designed by the present invention. DETAILED DESCRIPTION

[0020] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] Combine Figure 1 and Figure 2 The present invention provides an asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve, comprising the following steps:

[0022] Step 1: Establish a mathematical model of the electro-hydraulic direct-drive proportional servo valve.

[0023] Step 1-1: Build a mathematical model of a typical electro-hydraulic direct-drive proportional servo valve.

[0024] According to Newton's second law, the force balance equation of the electro-hydraulic direct-drive proportional servo valve is:

[0025]

[0026] In formula (1), F M Indicates the output force of the proportional solenoid, m v Indicates the mass of the valve core and other moving components, x ν Indicates the displacement of the valve core, Indicates the speed of the valve core, Indicates the acceleration of the valve core, B f represents the viscous friction coefficient, Fh Indicates the servo valve hydraulic power, K s represents the spring stiffness coefficient, represents the system lumped unmodeled time-varying disturbance, and t represents time.

[0027] Among them, the output force of the proportional solenoid can be expressed as:

[0028] F M =K u u(2),

[0029] In formula (2), K u is the torque amplification factor of the proportional electromagnet, and u is the control input.

[0030] The hydraulic force affects the motion performance of the servo valve. The relationship between the hydraulic force and the valve core displacement can be expressed by the following polynomial:

[0031]

[0032] In formula (3), a, b, and c represent coefficients of the polynomial.

[0033] Combining equations (1), (2) and (3), the mathematical model of the electro-hydraulic direct-drive proportional servo valve is:

[0034]

[0035] Step 1-2: To facilitate controller design, define state variables and convert the obtained mathematical model of the electro-hydraulic direct-drive proportional servo valve into a state space equation.

[0036] Define state variables: Convert Equation (4) into the first state space equation:

[0037]

[0038] In formula (5), x1 represents the displacement of the valve core, represents the first derivative of x1, x2 represents the speed of the valve core, represents the first derivative of x2, and T represents the transpose.

[0039] Define the unknown parameter vector Intermediate variable θ1(t)=(B f +b) / m ν ,θ2(t)=(K s +c) / m ν ,θ3(t)=a / m ν , intermediate error variable is unknown, subscript i=1,2,3, represents θ i(t) is a nominal constant value; the control input gain K = K u / m v , so the first state space equation (5) is transformed into the second state space equation:

[0040]

[0041] In formula (6), the lumped disturbance f of the electro-hydraulic direct-drive proportional servo valve is t (x1,x2,t)=-F t (x1,x2,t) / m ν , including unmodeled system dynamics, unmodeled friction, interference caused by the difference between the real system parameters and the modeled parameters, etc.; and The expression is as follows:

[0042]

[0043] In order to simplify the development and implementation of the controller, it is assumed that the physical parameter K in the system u and m v The nominal value of is known, but due to the wear caused by long-term use of the electro-hydraulic direct-drive proportional servo valve, the parameters θ1, θ2, and θ3 are time-varying and unknown, but their nominal constant values ​​are is known.

[0044] The goal of designing an asymmetric full-state constrained robust controller for an electro-hydraulic direct-drive proportional servo valve is: given the system desired command signal x 1d (t), design a continuously bounded control input u to ensure that all closed-loop signals are bounded, the valve core displacement x v Track the system's desired command signal x as accurately as possible 1d (t), and the valve core displacement x1=x v and spool speed None of the states violate the following state constraints:

[0045]

[0046] State constraint boundary function F 11 、F 12 、F 21 and F 22 They are all positive time-varying functions, D1 represents the position constraint set, D2 represents the velocity constraint set, and R represents the real number set.

[0047] To facilitate controller design, the following assumptions are made:

[0048] Assumption 1: The system expects instruction x 1d(t) and its second-order derivative are continuous and bounded. Among them, there are intermediate variables and intermediate variables Make And there exists a positive constant r0 such that the following holds:

[0049]

[0050] In formula (9) Represents x 1d The first derivative of Represents x 1d The second derivative of .

[0051] Assumption 2: The lumped disturbance f of the electro-hydraulic direct-drive proportional servo valve t (x1,x2,t) satisfies:

[0052] f t (x1,x2,t)≤δ t (10),

[0053] In formula (9), δ t is an unknown positive constant.

[0054] Go to step 2.

[0055] Step 2: Based on the mathematical model of the electro-hydraulic direct-drive proportional servo valve, an asymmetric full-state constrained robust controller for the electro-hydraulic direct-drive proportional servo valve is designed. The specific steps are as follows:

[0056] Step 2-1. In order to facilitate the design of the controller, the tracking error, coordinate transformation error and filtering error of the system are defined. In order to deal with the full-state constraint problem, a nonlinear state transition function is designed for direct state constraint, and based on the constructed first Lyapunov function V1, a virtual control input α1 is designed.

[0057] Define the tracking error of the system as z1=x1-x 1d , the present invention proposes the following nonlinear state transition function for the first time:

[0058]

[0059] The expressions of the intermediate variables β1(t) and β2(t) in formula (11) are as follows:

[0060]

[0061] By deriving the nonlinear state transition functions ζ1(x1) and ζ2(x2) in Equation (12), we can obtain:

[0062]

[0063] In formula (13), represents the first-order derivative of ζ1, represents the first-order derivative of ζ2, the intermediate variable μ 11 , μ 12 , μ 21 and μ 22 The expression is as follows:

[0064]

[0065] First, define the following coordinate transformation:

[0066]

[0067] The intermediate variable α0 in formula (15) = x 1d / [(F 11 +x 1d )(F 12 -x 1d )], α1 represents the virtual control input, which will be designed in the future, 1f represents the virtual control input after nonlinear filtering, ε1 represents the filtering error, e1 represents the coordinate transformation error, and the relationship between the tracking error z1 and the coordinate transformation error e1 is z1=ρe1, the intermediate variable ρ=[(F 11 +x1)(F 12 -x1)(F 11 +x 1d )(F 12 -x 1d )] / (F 11 F 12 +x1x 1d ).

[0068] In order to facilitate the design of the controller, the following nonlinear filter with gain self-learning is innovatively proposed:

[0069]

[0070] In formula (16), η1 represents the filter gain, which is a constant positive constant; ψ(t) represents a function that is always positive and satisfies ν represents the integration variable, represents a constant that is always positive, Represents α 1f The first-order derivative of , κ1 is a constant parameter, representing the gain self-learning parameter, represents the estimated value of κ1, and its update law for:

[0071]

[0072] In formula (17), λ1 is a positive constant.

[0073] According to the coordinate transformation of formula (15), the derivative of e1 with respect to time t is:

[0074]

[0075] In formula (18), represents the first-order derivative of e1, represents the first-order derivative of α0, Represents x 1d The first derivative of , the intermediate variable μ 01 and μ 02 The expression is as follows:

[0076]

[0077] Construct the first Lyapunov function V1 as follows:

[0078]

[0079] Derivative of formula (20) yields:

[0080]

[0081] In formula (21) represents the first-order derivative of V1, and using Young’s inequality we get:

[0082]

[0083] Substituting formula (22) into formula (21) yields:

[0084]

[0085] Design the virtual control input α1 as:

[0086]

[0087] In formula (24), the control gain k1>0. Substituting formula (24) into formula (23) yields:

[0088]

[0089] Derivative e2 in formula (15) yields:

[0090]

[0091] Step 2-2: Design an asymmetric full-state constrained robust controller for the electro-hydraulic direct-drive proportional servo valve based on the constructed second Lyapunov function V2.

[0092] Define the self-learning gain variable Ξ(t)=supt≥0 ||Φ(t)||,Ξ(t) is unknown, where the intermediate variable Φ(t)=[μ 21 θ(t),μ 21 f t (x1,x2,t),μ 11 ] T , define the second Lyapunov function V2 as:

[0093]

[0094] In formula (25), γ is a positive constant, and the intermediate variable Represents the estimate of Ξ, and the derivative of formula (27) is:

[0095]

[0096] In formula (28), Represents the first-order derivative of V2, intermediate variable Represents α 1f The first derivative of Representatives The first-order derivative of , according to formula (28), the control input u is designed as:

[0097]

[0098] u s1 =-k2e2

[0099]

[0100]

[0101] In formula (29), the control gain k2>0, u s1 represents the linear robust term, u s2 is a nonlinear robust term, u a is a compensation term based on the model, an intermediate variable

[0102] This is represented by the following update rates:

[0103]

[0104] Substituting equations (29) and (30) into equation (28), we obtain:

[0105]

[0106] Notice that

[0107]

[0108] Substituting formula (32) into formula (31) yields:

[0109]

[0110] Go to step 3.

[0111] Step 3: Use Lyapunov stability theory to prove the stability of the asymmetric full-state constrained robust controller for the electro-hydraulic direct-drive proportional servo valve, as follows:

[0112] Define the third Lyapunov function V3 as follows:

[0113]

[0114] Where λ1 represents a positive constant. Taking the derivative of equation (34) and substituting equations (17) and (33) into equation (34) yields:

[0115]

[0116] Combining equations (15) and (16), the first-order derivative of the filtering error ε1 can be obtained: The expression is as follows:

[0117]

[0118] Multiply both sides of equation (34) by ε1 and use Young's inequality to obtain:

[0119]

[0120] Substituting formula (35) into formula (33) yields:

[0121]

[0122] Choose a suitable constant η1 to satisfy Then formula (36) can be expressed as:

[0123]

[0124] The filter gain coefficient η in formula (37) * It is a normal number.

[0125] Taking into account

[0126]

[0127] Available

[0128]

[0129] Substituting equation (39) into equation (37) yields

[0130]

[0131] In formula (40), the intermediate variable H = Ξ + 2, the intermediate variable M = e T Λe, intermediate variable e=[e1,e2,ε1] T , the matrix Λ is defined as

[0132]

[0133] Select appropriate control gains k1, k2 and filter gain coefficients The matrix Λ must be positive definite, so integrating both sides of equation (40) yields:

[0134]

[0135] From Equation (42), we can see that V3 is bounded and M is integrally bounded. It can be concluded that all signals in the system are bounded, so M is uniformly continuous. According to Barbalat's lemma, when time tends to positive infinity, the coordinate transformation error e1 tends to 0. Because x1 and x 1d They all operate in a closed interval of a proper subset of the open interval D1, so there is a positive constant ρ and Make Since the coordinate transformation error e1 is bounded, the tracking error z1 is also bounded.

[0136] Therefore, it is concluded that by adjusting the control gains k1, k2 and filter gain The innovatively designed electro-hydraulic direct-drive proportional servo valve asymmetric full-state constrained robust controller can not only make the displacement and velocity states of the system meet the asymmetric state constraint requirements, but also eliminate the feasibility constraints of the virtual controller. The principle diagram of the electro-hydraulic direct-drive proportional servo valve asymmetric full-state constrained robust controller is shown in the figure. Figure 1 shown.

[0137] Example

[0138] In order to evaluate the performance of the designed controller, the physical parameters of the electro-hydraulic direct-drive proportional servo valve in the simulation are shown in Table 1:

[0139] Table 1 System physical parameters

[0140] Physical parameters Numerical Physical parameters Numerical <![CDATA[K s (N / m)]]> 5 <![CDATA[a(N / mm 2 )]]> 0.01 <![CDATA[K u (N / mA)]]> 2.5 b(Ns / mm) -0.005 <![CDATA[m v (kg)]]> 0.15 c(N / mm) -0.05 <![CDATA[F u (N)]]> 0.5cos(0.8t) <![CDATA[B f (N·s / m)]]> 5

[0141] Given a system with the expected instruction x 1d =0.8sin(0.8t)mm.

[0142] The following controllers are used for comparison in the simulation:

[0143] Asymmetric full-state constrained robust controller (FSCRC) for electro-hydraulic direct-drive proportional servo valve: take gains k1 = 65, k2 = 40, γ = 500, λ1 = 1, ψ(t) = 1000 / (1+t 2 ), η1=200, define the initial value of the virtual control input α1(0)=α 1f (0)=0, defines the nominal constant value and They are 18, 20 and 0.04 respectively.

[0144] PID controller: The steps for selecting PID controller parameters are: first, ignoring the nonlinear dynamics of the electro-hydraulic direct-drive proportional servo valve, obtain a set of controller parameters through the PID parameter self-tuning function in Matlab, and then fine-tune the obtained self-tuning parameters after adding the nonlinear dynamics of the system to achieve the best tracking performance. The selected controller parameters are k P =70,k I =40,k D =0.1.

[0145] The expected instruction of the system, the tracking error of the FSCRC controller, and the tracking error comparison between the FSCRC controller and the PID controller are as follows: Figure 3 、 Figure 4 and Figure 5 As shown. Figure 4 It can be seen that under the action of the FSCRC controller, the position output of the electro-hydraulic direct-drive proportional servo valve has a high tracking accuracy for the command, and the amplitude of the steady-state tracking error is about 5×10 -4 mm. From Figure 5 The comparison of the tracking errors of the two controllers shows that the tracking error of the FSCRC controller proposed in the present invention is much smaller than that of the PID controller, and the tracking performance is more superior.

[0146] Figure 6 This is a graph showing the change in control input of the electro-hydraulic direct-drive proportional servo valve over time under the action of the FSCRC controller. It can be seen from the figure that the obtained control input is a low-frequency continuous signal, which is more conducive to execution in practical applications.

[0147] Figure 7 、 Figure 8 、 Figure 9 and Figure 10 They are the actual position of FSCRC controller, the actual speed of FSCRC controller, the actual position of PID controller and the actual speed of PID controller. Figure 6 and Figure 7 It can be seen from the figure that in the FSCRC controller, the actual position and actual speed of the electro-hydraulic direct-drive proportional servo valve are well limited within the constraint range; however, Figure 9 and Figure 10 It can be seen that although the actual position of the electro-hydraulic direct-drive proportional servo valve is limited to the corresponding constraint range in the PID controller, the actual speed of the electro-hydraulic direct-drive proportional servo valve exceeds the upper and lower limits of the constraint in the initial stage, which seriously affects the normal operation of the electro-hydraulic direct-drive proportional servo valve and easily causes problems such as speed imbalance.

Claims

1. A method for asymmetric full-state constrained robust control of an electro-hydraulic direct-drive proportional servo valve, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the electro-hydraulic direct-drive proportional servo valve, and proceed to step 2; Step 2: Based on the mathematical model of the electro-hydraulic direct-drive proportional servo valve, the Lyapunov function is combined with the backstepping method to design an asymmetric full-state constrained robust controller for the electro-hydraulic direct-drive proportional servo valve, and then proceed to step 3. Step 3: Use Lyapunov stability theory to prove the stability of the asymmetric full-state constrained robust controller of the electro-hydraulic direct-drive proportional servo valve.

2. The asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve according to claim 1, characterized in that: In step 1, a mathematical model of the electro-hydraulic direct-drive proportional servo valve is established as follows: Step 1-1: Build a mathematical model of a typical electro-hydraulic direct-drive proportional servo valve; Step 1-2: To facilitate controller design, define state variables and convert the obtained mathematical model of the electro-hydraulic direct-drive proportional servo valve into a state space equation.

3. The asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve according to claim 2, characterized in that: In step 1-1, a mathematical model of a typical electro-hydraulic direct-drive proportional servo valve system is constructed as follows: According to Newton's second law, the force balance equation of the electro-hydraulic direct-drive proportional servo valve is: In formula (1), F M Indicates the output force of the proportional solenoid, m v Indicates the mass of the valve core and other moving components, x ν Indicates the displacement of the valve core, Indicates the speed of the valve core, Indicates the acceleration of the valve core, B f represents the viscous friction coefficient, F h Indicates the servo valve hydraulic power, K s represents the spring stiffness coefficient, represents the system lumped unmodeled time-varying interference, t represents time; Among them, the output force of the proportional solenoid is expressed as: F M =K u u (2), In formula (2), K u is the torque amplification factor of the proportional electromagnet, and u is the control input; The hydraulic force affects the motion performance of the servo valve. The relationship between the hydraulic force and the valve core displacement is expressed by the following polynomial: In formula (3), a, b, and c represent the coefficients of the polynomial; Combining equations (1), (2) and (3), the mathematical model of the electro-hydraulic direct-drive proportional servo valve is:

4. The asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve according to claim 3, characterized in that: In steps 1-2, to facilitate controller design, state variables are defined and the obtained mathematical model of the electro-hydraulic direct-drive proportional servo valve is converted into a state-space equation, as follows: Define state variables: The mathematical model of the electro-hydraulic direct-drive proportional servo valve in equation (4) is transformed into the first state space equation: In formula (5), x1 represents the displacement of the valve core, represents the first derivative of x1, x2 represents the speed of the valve core, represents the first-order derivative of x2, and T represents transpose; Define the unknown parameter vector Intermediate variable θ1(t)=(B f +b) / m ν ,θ2(t)=(K s +c) / m ν ,θ3(t)=a / m ν , intermediate error variable is unknown, subscript i=1,2,3, represents θ i (t) is a nominal constant value; the control input gain K = K u / m v , so the first state space equation (5) is transformed into the second state space equation: In formula (6), the lumped disturbance f of the electro-hydraulic direct-drive proportional servo valve is t (x1,x2,t)=-F t (x1,x2,t) / m ν , including unmodeled system dynamics, unmodeled friction, and disturbances caused by the difference between the true system parameters and the modeled parameters; Intermediate variables and The expression is as follows: In order to simplify the development and implementation of the controller, it is assumed that the physical parameter K in the system u and m v The nominal value of is known, but due to the wear caused by long-term use of the electro-hydraulic direct-drive proportional servo valve, the intermediate variables θ1, θ2, and θ3 are time-varying and unknown, but their nominal constant values ​​are is known; The goal of designing an asymmetric full-state constrained robust controller for an electro-hydraulic direct-drive proportional servo valve is: given the system desired command signal x 1d (t), design a continuously bounded control input u to ensure that all closed-loop signals are bounded, the valve core displacement x v Track the system's desired command signal x as accurately as possible 1d (t), and the valve core displacement x1=x v and spool speed None of the states violate the following state constraints: State constraint boundary function F 11 、F 12 、F 21 and F 22 They are all positive time-varying functions, D1 represents the position constraint set, D2 represents the velocity constraint set, and R represents the real number set.

5. The asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve according to claim 4, characterized in that: In step 1, to facilitate controller design, the following assumptions are made: Assumption 1: The system expects instruction x 1d (t) and its second-order derivative are continuous and bounded; among them, there are intermediate variables and intermediate variables Make And there exists a positive constant r0 such that the following holds: In formula (9) Represents x 1d The first derivative of Represents x 1d The second derivative of Assumption 2: The lumped disturbance f of the electro-hydraulic direct-drive proportional servo valve t (x1,x2,t) satisfies: f t (x1,x2,t)≤δ t (10), In formula (9), δ t is an unknown positive constant; Go to step 2.

6. The asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve according to claim 5, characterized in that: In step 2, based on the mathematical model of the electro-hydraulic direct-drive proportional servo valve, an asymmetric full-state constrained robust controller for the electro-hydraulic direct-drive proportional servo valve is designed. The specific steps are as follows: Step 2-1: To facilitate controller design, the tracking error, coordinate transformation error, and filtering error of the system are defined. To handle the full-state constraint problem, a nonlinear state transition function is designed for direct state constraint. Based on the constructed first Lyapunov function V1, a virtual control input α1 is designed. Step 2-2: Design an asymmetric full-state constrained robust controller for the electro-hydraulic direct-drive proportional servo valve based on the constructed second Lyapunov function V2.

7. The asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve according to claim 6, characterized in that: In step 2-1, in order to facilitate the design of the controller, the tracking error, coordinate transformation error, and filtering error of the system are defined. In order to deal with the full state constraint problem, a nonlinear state transition function is designed for direct state constraint. Based on the constructed first Lyapunov function V1, the virtual control input α1 is designed. Define the tracking error of the system as z1=x1-x 1d , the nonlinear state transition function is as follows: The expressions of the intermediate variables β1(t) and β2(t) in formula (11) are as follows: By deriving the nonlinear state transition functions ζ1(x1) and ζ2(x2) in Equation (12), we can obtain: In formula (13), represents the first-order derivative of ζ1, represents the first-order derivative of ζ2, the intermediate variable μ 11 、μ 12 、μ 21 and μ 22 The expression is as follows: First, define the following coordinate transformation: The intermediate variable α0 in formula (15) = x 1d / [(F 11 +x 1d )(F 12 -x 1d )], α1 represents the virtual control input, which will be designed in the future, 1f represents the virtual control input after nonlinear filtering, ε1 represents the filtering error, e1 represents the coordinate transformation error, and the relationship between the tracking error z1 and the coordinate transformation error e1 is z1=ρe1, the intermediate variable ρ=[(F 11 +x1)(F 12 -x1)(F 11 +x 1d )(F 12 -x 1d )] / (F 11 F 12 +x1x 1d ); In order to facilitate the design of the controller, the following nonlinear filter with gain self-learning is designed: In formula (16), η1 represents the filter gain, which is a constant positive constant; ψ(t) represents a function that is always positive and satisfies ν represents the integration variable, represents a constant that is always positive, Represents α 1f The first-order derivative of , κ1 is a constant parameter, representing the gain self-learning parameter, represents the estimated value of κ1, and its update law for: In formula (17), λ1 is a positive constant; According to the coordinate transformation of formula (15), the derivative of e1 with respect to time t is: In formula (18), represents the first-order derivative of e1, represents the first-order derivative of α0, Represents x 1d The first derivative of , the intermediate variable μ 01 and μ 02 The expression is as follows: Construct the first Lyapunov function V1 as follows: Derivative of formula (20) yields: In formula (21) represents the first-order derivative of V1, and using Young's inequality we get: Substituting formula (22) into formula (21) yields: Design the virtual control input α1 as: In formula (24), the control gain k1>0. Substituting formula (24) into formula (23) yields:

8. The asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve according to claim 7, characterized in that: In step 2-2, an asymmetric full-state constrained robust controller for an electro-hydraulic direct-drive proportional servo valve is designed based on the constructed second Lyapunov function V2, as follows; Define the self-learning gain variable Ξ(t)=sup t≥0 ||Φ(t)||,Ξ(t) is unknown, where the intermediate variable Φ(t)=[μ 21 θ(t),μ 21 f t (x1,x2,t),μ 11 ] T , define the second Lyapunov function V2 as: In formula (25), γ is a positive constant, and the intermediate variable Represents the estimate of Ξ, and the derivative of formula (27) is: In formula (28), Represents the first-order derivative of V2, intermediate variable Represents α 1f The first derivative of Representatives The first-order derivative of , according to formula (28), the control input u is designed as: In formula (29), the control gain k2>0, u s1 represents the linear robust term, u s2 is a nonlinear robust term, u a is a compensation term based on the model, an intermediate variable This is represented by the following update rates: Substituting equations (29) and (30) into equation (28), we obtain: Notice that Substituting formula (32) into formula (31) yields: Go to step 3.

9. The asymmetric full-state constrained robust control method for an electro-hydraulic direct-drive proportional servo valve according to claim 8, characterized in that: In step 3, the stability of the asymmetric full-state constrained robust controller for the electro-hydraulic direct-drive proportional servo valve is proved using Lyapunov stability theory, as follows: Define the third Lyapunov function V3 as follows: Where λ1 represents a positive constant. Taking the derivative of equation (34) and substituting equations (17) and (33) into equation (34) yields: Combining equations (15) and (16), the first-order derivative of the filtering error ε1 can be obtained: The expression is as follows: Multiply both sides of equation (34) by ε1 and use Young's inequality to obtain: Substituting formula (35) into formula (33) yields: Choose a suitable constant η1 to satisfy Then formula (36) can be expressed as: The filter gain coefficient η in formula (37) * is a positive number, considering that: We can get: Substituting formula (39) into formula (37) yields: In formula (40), the intermediate variable H = Ξ + 2, the intermediate variable M = e T Λe, intermediate variable e=[e1,e2,ε1] T , the matrix Λ is defined as: Select appropriate control gains k1, k2 and filter gain coefficients The matrix Λ must be positive definite, so integrating both sides of equation (40) yields: From Equation (42), we can see that V3 is bounded and M is integrally bounded. It can be concluded that all signals in the system are bounded. Therefore, M is uniformly continuous. According to Barbalat’s lemma, when time tends to positive infinity, the coordinate transformation error e1 tends to 0, because x1 and x 1d They all operate in a closed interval of a proper subset of the open interval D1, so there is a positive constant ρ and Make Since the coordinate transformation error e1 is bounded, the tracking error z1 is also bounded.

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