Self-adaptive asymptotic preset performance tracking control method for hydraulic multi-way valve control system

Abstract

The invention discloses a self-adaptive asymptotic preset performance tracking control method for a hydraulic multi-way valve control system, which is characterized in that a self-adaptive hydraulic multi-way valve control system controller is designed on the basis of a constructed asymptotic preset performance function by fusing an error symbol integral robust method. Aiming at the hydraulic multi-way valve control problem, the adaptive recursive error symbol integral robust control law is adopted, compensation of parameter uncertainty is achieved, error symbol integral robust control and preset performance control are fused, system matching and mismatching interference can be processed, the transient performance and the steady-state performance of the system are guaranteed, and the system reliability is improved. The specified tracking performance can be achieved, and the asymptotic stability of the system is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of electromechanical servo control, and in particular to an adaptive asymptotic preset performance tracking control method for a hydraulic multi-way valve control system. Background Art

[0002] The hydraulic multi-way valve control system occupies a vital position in the hydraulic transmission system of modern engineering machinery, especially in equipment that needs to perform complex operations, playing a core role. When cranes, rotary excavators, bulldozers and other engineering machinery are performing tasks, they often need to coordinate multiple working mechanisms to operate simultaneously to complete various operating requirements, such as lifting, rotating, bulldozing, excavation and other compound actions. The hydraulic multi-way valve control system has just this function. Through the coordinated control of multiple hydraulic valves, it can efficiently control the compound actions of multiple actuators. In this system, the hydraulic multi-way valve is the core component, which is usually composed of two or more reversing valves, one-way valves, brake valves and other hydraulic components with the required functions. However, the hydraulic multi-way valve control system has a high degree of nonlinear characteristics. These nonlinear factors lead to certain limitations in the system's dynamic response and steady-state accuracy. In addition, external load disturbances, parameter uncertainties and system coupling effects also increase the complexity of system control. In order to ensure that the hydraulic multi-way valve control system can achieve good control effects and minimize the impact of nonlinear systems, the control strategy of the hydraulic multi-way valve control system must have the characteristics of high precision, high response speed and strong robustness. The traditional linear control method has been difficult to meet the requirements of high-precision control.

[0003] In response to the above problems, domestic and foreign scholars have conducted extensive research on the nonlinear control strategy of hydraulic multi-way valve control systems. The classical sliding mode control method has good robustness and anti-interference ability, and can effectively deal with system parameter uncertainty and external disturbances. However, since the input contains a sign function, it is easy to cause chattering, which causes mechanical wear on the system actuators and affects the smooth operation of the system; the adaptive robust control method effectively handles the problems of system matching and mismatching interference, and by adaptively adjusting the control parameters, the system obtains a certain steady-state performance, but this method can only guarantee convergence within a sufficiently small range when matching interference and mismatching interference exist at the same time; the error sign integral robustness (RISE) method has strong robustness and continuity. The control method formed by combining with the adaptive control based on the backstepping method is compared with the adaptive robust control. The biggest feature is that the tracking error of the system can converge to zero asymptotically, but when facing matching and mismatching disturbances, its smoothness and boundedness need to be determined. The above control methods mainly focus on improving the steady-state tracking performance, but pay little attention to transient performance. Summary of the invention

[0004] The object of the present invention is to provide an adaptive asymptotic preset performance tracking control method for a hydraulic multi-way valve control system, which adopts an adaptive recursive error sign integral robust control law. This control law combines an adaptive law based on the desired trajectory to achieve compensation for parameter uncertainties, and also integrates error sign integral robust control and preset performance control, capable of handling system matching and mismatching disturbances, ensuring the transient and steady-state performance of the system, achieving the specified tracking performance, and realizing the asymptotic stability of the system.

[0005] The technical solution for achieving the object of the present invention is as follows: An adaptive asymptotic preset performance tracking control method for a hydraulic multi-way valve control system, comprising the following steps:

[0006] Step 1: Establish the mathematical model of the hydraulic multi-way valve control system, and proceed to Step 2.

[0007] Step 2: Based on the mathematical model of the hydraulic multi-way valve control system, design a tracking controller with adaptive asymptotic preset performance, and proceed to Step 3.

[0008] Step 3: Use Lyapunov stability theory to prove the stability of the adaptive asymptotic preset performance tracking controller, and obtain the result that the system tracking error is limited within the specified constraint conditions and is asymptotically stable.

[0009] Compared with the prior art, the present invention has the following remarkable advantages: (1) It adopts an adaptive recursive error sign integral robust control law, which combines an adaptive law based on the desired trajectory to achieve compensation for parameter uncertainties; (2) It integrates error sign integral robust control and preset performance control, capable of handling system matching and mismatching disturbances, ensuring the transient and steady-state performance of the system, achieving the specified tracking performance, and realizing the asymptotic stability of the system. The simulation results verify its effectiveness. Description of the Drawings

[0010] Figure 1 It is a schematic diagram of the principle of the adaptive asymptotic preset performance tracking control method for the hydraulic multi-way valve control system of the present invention.

[0011] Figure 2 It is a schematic diagram of the principle of the hydraulic multi-way valve control system of the present invention.

[0012] Figure 3 It is a curve graph of the desired command that the system output needs to track under the action of the adaptive asymptotic preset performance tracking controller designed by the present invention.

[0013] Figure 4 It is a curve graph of the tracking error of the system changing with time under the action of the adaptive asymptotic preset performance tracking controller designed by the present invention.

[0014] Figure 5It is a comparison curve graph of the tracking error of the system and the preset performance boundary under the action of the adaptive asymptotic preset performance tracking controller designed by the present invention and the traditional PID controller.

[0015] Figure 6 under the action of the adaptive asymptotic preset performance tracking controller designed by the present invention is a curve graph that changes with time.

[0016] Figure 7 under the action of the adaptive asymptotic preset performance tracking controller designed by the present invention is a curve graph that changes with time. Specific embodiments

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] Combined with Figure 1 and Figure 2 , the adaptive asymptotic preset performance tracking control method for the hydraulic multi-way valve control system of the present invention includes the following steps:

[0019] Step 1, establish a mathematical model of the hydraulic multi-way valve control system.

[0020] In step 1-1, the hydraulic multi-way valve control system is applied to large heavy-duty construction machinery, mining, and metallurgical industry equipment, where an electric signal controls an electro-hydraulic proportional pressure reducing valve, and its output pressure is changed by adjusting the voltage, thereby changing the pressure in the main valve control chamber, moving the spool, controlling the movement of the piston rod on the hydraulic cylinder, and driving the load fixedly connected to the piston rod of the hydraulic cylinder.

[0021] According to Newton's second law, the force balance equation of the hydraulic multi-way valve control system is:

[0022]

[0023] In formula (1), m represents the mass of the load, y represents the displacement of the piston rod of the hydraulic cylinder, represents the velocity of the piston rod of the hydraulic cylinder, represents the acceleration of the piston rod of the hydraulic cylinder, A represents the effective action area of the piston of the hydraulic cylinder, P 1 represents the oil pressure in the oil inlet chamber of the hydraulic cylinder, P 2 represents the oil pressure in the oil outlet chamber of the hydraulic cylinder, B represents the total viscous damping coefficient of the hydraulic cylinder and the load, K represents the elastic load coefficient, d(t) represents the mechanical unmodeled disturbance of the system, and t represents time.

[0024] Then formula (1) is rewritten as:

[0025]

[0026] In the hydraulic multi-way valve control system, ignoring the external leakage of the oil in the cylinder, the pressure dynamic equation is as follows:

[0027]

[0028] In Equation (3), β e represents the effective elastic modulus of the oil, V t represents the equivalent volume of the hydraulic cylinder, C t represents the internal leakage coefficient of the hydraulic cylinder, and the pressure difference P L = P 1 - P 2 , Q L represents the overcurrent flow rate of the load, q represents the unmodeled disturbance of P L , represents the first derivative of P L .

[0029] The mathematical model of the spool movement of the main valve in the hydraulic multi-way valve control system is as follows:

[0030]

[0031] In Equation (4), m v represents the mass of the spool, x v represents the displacement of the spool, represents the velocity of the spool,

[0032] represents the acceleration of the spool, A v represents the effective acting area of the main valve control chamber, P i represents the output pressure of the pressure reducing valve, B v represents the viscous damping coefficient of the spool, K v represents the elastic coefficient of the spool, d 1 (t) represents the unmodeled disturbance of the main valve mechanical system, and t represents time. Assume that the output pressure P i of the pressure reducing valve is proportional to the control input signal U in the steady state, that is, P i = k t U, k t represents the gain coefficient of the output pressure of the pressure reducing valve relative to the input voltage.

[0033] The overcurrent flow rate Q L of the load has the following relationship with the spool displacement x v of the main valve in the hydraulic multi-way valve control system:

[0034]

[0035] In Equation (5), C d represents the flow coefficient of the main valve, w represents the spool area gradient of the main valve, ρ represents the oil density, Ps Denote the fuel supply pressure as $P$, and the function $sgn(·)$ of the intermediate variable $·$ is defined as:

[0036]

[0037] After linearization, Equation (5) is rewritten as:

[0038] $Q$ L $ = k$ d1 $x$ v $-k$ d2 $P$ L (7)

[0039] In Equation (7), $k$ d1 denotes the main valve flow gain coefficient, and $k$ d2 denotes the main valve flow - pressure gain coefficient.

[0040] Step 1 - 2: Define the state variables: Among them, the intermediate variable $x$ 1 $ = y$, and the intermediate variable The intermediate variable $x$ 3 $ = AP$ L $ / m$, and the intermediate variable $x$ 4 $ = x$ v , and the intermediate variable Then, Equations (2), (3), (4), and (7) are transformed into state equations:

[0041]

[0042] In Equation (8), denotes the first - order derivative of $x$ 1 , denotes the first - order derivative of $x$ 2 , denotes the first - order derivative of $x$ 3 , denotes the first - order derivative of $x$ 4 , denotes the first - order derivative of $x$ 5 .

[0043] Neglect the viscous damping acting on the main valve, select the state variable The control variable $u$ is the displacement of the main valve spool, and Equation (8) is simplified to obtain a new system state - space equation:

[0044]

[0045] In Equation (9), the intermediate variable The intermediate variable The unknown dynamics of the system The intermediate variable Intermediate variable Intermediate variable System unknown dynamics

[0046] For the convenience of designing the controller, the following assumptions are made:

[0047] Assumption 1: The desired tracking position command x of the system 1d is three - order continuously differentiable, and the desired position command, velocity command, and acceleration command of the system are all bounded.

[0048] Assumption 2: The system unknown dynamics Δ 1 (t) and Δ 2 (t) are smooth enough, and their first - order and second - order derivatives exist and are bounded, that is:

[0049]

[0050] In Equation (10), ζ 1 , ζ 2 , ζ 3 and ζ 4 are all unknown positive constants.

[0051] Proceed to Step 2.

[0052] Step 2: Based on the mathematical model of the hydraulic multi - valve control system, design a tracking controller with adaptive asymptotic preset performance. The specific steps are as follows:

[0053] Step 2 - 1: Design the preset performance function and transform the tracking error, as follows:

[0054] Define the tracking error e of the system 1 = x 1 - x 1d , where x 1d is the desired tracking position command of the system. To constrain the tracking error, introduce the preset performance function μ(t)=(μ 0 - μ ∞ )e -κt + μ ∞ , where μ 0 , μ ∞

[0055] are all parameters to be designed, μ 0 > μ ∞ > 0, and the convergence rate κ > 0, so as to constrain the tracking error and keep it within the performance boundary range all the time, that is:

[0056]

[0057] In Equation (11), δ and Denote a positive adjustable parameter, then - δ μ 0 and denote the lower limit of overshoot and the upper limit of undershoot of the tracking error, - δ μ ∞ and denote the preset steady-state error interval.

[0058] Introduce a strictly increasing function ψ(z 1 ) that satisfies the following properties:

[0059]

[0060] In Equation (12), z 1 denotes the conversion error signal corresponding to the tracking error e 1 . Then, based on the above properties, introduce the following non-linear mapping:

[0061] e 1 (t) = μ(t)ψ(z 1 ) (13)

[0062] The strictly increasing function ψ(z 1 ) is defined as:

[0063]

[0064] In Equation (14), λ represents an intermediate variable. Obtain the inverse function of Equation (14) to get:

[0065]

[0066] As long as the conversion error z 1 is bounded under the action of the controller, according to the properties of ψ(z 1 ), Equation (11) can be guaranteed to hold, which indicates that if z 1 asymptotically converges to 0, then the tracking error e 1 will also asymptotically converge to 0.

[0067] Differentiate Equation (15) with respect to time to get:

[0068]

[0069] In Equation (16), denotes the first derivative of z 1 , denotes the first derivative of e 1 , denotes the first derivative of μ. The intermediate variable It is obtained that the intermediate variable ρ is bounded and satisfies:

[0070]

[0071] Step 2-2: Design an adaptive asymptotic preset performance tracking controller according to the mathematical model and conversion error z of the hydraulic multi-way valve control system as follows: 1

[0072] Differentiate Equation (16) with respect to time and substitute Equation (9) to obtain:

[0073]

[0074] In Equation (18), represents the first derivative of ρ, represents the second derivative of z 1 , represents the second derivative of μ, represents the second derivative of x 1d .

[0075] Define a set of error signals as follows:

[0076]

[0077] In Equation (19), z 2 , z 3 , r 1 and r 2 represent error signals, k 1 , k 2 and k 3 represent positive gains, represents the first derivative of z 2 , represents the first derivative of z 3 , and α 2 represents the virtual control law.

[0078] Substitute Equation (18) into the error signal r 1 in Equation (19) to obtain:

[0079]

[0080] In Equation (20), the actual value θ = [θ 1 , θ 2 T , the intermediate variable φ(x) = [-x 1 , -x 2 T , and the intermediate variable

[0081] Design the virtual control law α 2 as:

[0082]

[0083] ​​​In Equation (21), k s , k r1 and β 1 represent positive gains, α 2a represents a model-based compensation term, α 2s1 represents a linear robust term, α 2s2 represents a RISE feedback control term, the real-time estimated value of θ z 2 (0) represents the initial value of z 2 , and dτ represents the differentiation with respect to time.

[0084] Define the adaptation law of the real-time estimated value as:

[0085]

[0086] In Equation (22), represents 's first derivative, Γ represents an adjustable positive definite diagonal adaptation gain matrix, represents 's first derivative, and the intermediate variable

[0087] By integrating Equation (22) by parts, we get:

[0088]

[0089] In Equation (23), represents 's initial value, represents 's second derivative.

[0090] Substitute Equation (21) into Equation (20) to get:

[0091]

[0092] In Equation (24), the intermediate variable The intermediate variable χ = ρθ T (φ(x) - φ d (x)), and the parameter estimation error value of θ

[0093] Differentiate Equation (24) with respect to time to get:

[0094]

[0095] In Equation (25), represents the first derivative of r 1 , and the intermediate variable The intermediate variable Denotes the first derivative of E, Denotes Δ 1 (t) of the first derivative.

[0096] For Applying the mean value theorem gives:

[0097]

[0098] In Equation (26), the error signal vector z = [z 1 , z 2 , r 1 , z 3 , r 2 T , η(·) represents a positive globally invertible non-decreasing function. According to Equation (10) and Equation (17), N d Satisfies the following properties:

[0099]

[0100] In Equation (27), ζ 5 And ζ 6 Are both unknown positive constants.

[0101] Substitute Equation (9) into Equation (19) for the error signal r 2 To get:

[0102]

[0103] In Equation (28), Denotes the first derivative of α 2 .

[0104] According to Equation (28), design the controller input u as:

[0105]

[0106] In Equation (29), k r2 And β 2 Represent positive gains, u a Represents the model-based compensation term, u s1 Represents the linear robust term, u s2 Represents the RISE feedback control term, z 3 (0) represents the initial value of z 3 .

[0107] Substitute Equation (29) into Equation (28) to get:

[0108]

[0109] Differentiate Equation (30) with respect to time to get:

[0110] ​

[0111] In Equation (31), represents the first derivative of r 2 , represents the first derivative of Δ 2 (t).

[0112] Proceed to Step 3.

[0113] Step 3: Use Lyapunov stability theory to prove the stability of the adaptive asymptotic preset performance tracking controller, and obtain the result that the system tracking error is limited within the specified constraint conditions and is asymptotically stable, as follows:

[0114] Before proving the stability, the following lemma is given for subsequent analysis:

[0115] Lemma 1: The system satisfies ε = f(ε, t), where ε represents the intermediate variable. The function has a solution, where represents the n-dimensional real number set, represents the set of real numbers greater than or equal to 0. Define the following domain where υ represents a positive constant. Define a continuously differentiable function that satisfies the following conditions That is, for it satisfies:

[0116]

[0117] In Equation (32), U 1 (ε) and U 2 (ε) represent continuously positive definite functions, and U(ε) represents a uniformly continuous semi-positive definite function, represents the first derivative of V(ε, t). If Equation (32) is satisfied and ε(0) ∈ S, the following conclusion holds:

[0118] When t → ∞, U(ε(t)) → 0 (33)

[0119] where the domain S is defined as:

[0120]

[0121] In Equation (34), represents a positive constant.

[0122] Proof:

[0123] Define the auxiliary function as follows:

[0124]

[0125] In Equation (35), L1 (t), L 2 (t), P 1 (t) and P 2 (t) represents an auxiliary function, N d (0) and respectively represent the initial values of N d and The initial value of

[0126] Define the Lyapunov function as follows:

[0127]

[0128] In Equation (36), the intermediate variable ε is an expression with respect to time t and can be written as ε(t). Assuming a domain D contains ε(t) = 0, the intermediate variable ε(t) is expressed as:

[0129]

[0130] For V(ε, t) satisfies:

[0131] U 1 (ε) ≤ V(ε, t) ≤ U 2 (ε) (38)

[0132] In Equation (38), the intermediate variable function U 1 (ε) = σ 1 ||ε|| 2 and U 2 (ε) = σ 2 ||ε|| 2 are continuous positive definite functions, and the intermediate variables and λ min (·) and λ max (·) respectively represent the minimum eigenvalue and the maximum eigenvalue of the matrix.

[0133] Differentiate Equation (36) with respect to time and substitute Equations (19), (22), (25), (31), and (35) to obtain:

[0134]

[0135] In Equation (39), represents the first derivative of V(ε, t).

[0136] Define the intermediate variable Λ as:

[0137]

[0138] By adjusting the gains k 1 、k2 , k 3 , k r1 and k r2 , such that the symmetric matrix Λ is a positive definite matrix, then Equation (39)

[0139] gives:

[0140]

[0141] Substituting Equation (26) into Equation (41) gives:

[0142]

[0143] In Equation (42), the intermediate variable is positive when the following conditions are satisfied:

[0144]

[0145] In Equation (43), η -1 (·) represents the inverse function of η(·).

[0146] In Equation (42), U(ε) is a semi - positive definite function defined in the domain D, and the domain D satisfies the following conditions:

[0147]

[0148] According to Equation (38), we have V ∈ L ∞ and U ∈ L 2 . According to Equation (36), the error signals z 1 , z 2 , z 3 , r 1 , r 2 and the parameter estimation error value are all bounded. According to Assumption 1, the intermediate variables x 1 , x 2 and x 3 are also all bounded. According to Equations (19), (25) and (31), the derivatives of the error signals z 1 , z 2 , z 3 , r 1 and r 2 with respect to time are all bounded, indicating that is bounded. Therefore, U(ε) is a uniformly continuous function in the domain D. Define a domain S ∈ D, which is expressed as:

[0149]

[0150] According to Lemma 1, we have:

[0151] When t → ∞,

[0152] Based on Equation (15), it can be obtained that the tracking error of the system will be restricted under the specified constraints of Equation (11), and when time approaches infinity, the tracking error e 1 tends to 0, that is:

[0153] When t→∞, e 1 (t)→0(47)

[0154] Therefore, the conclusion is: by adjusting the gains k 1 、k 2 、k 3 、k r1 and k r2 , only by choosing a sufficiently large gain coefficient to make the symmetric matrix Λ a positive definite matrix, so that the system can obtain the result that the tracking error asymptotically converges to 0 according to the specified constraints. The schematic diagram of the adaptive asymptotic preset performance tracking controller for the hydraulic multi-way valve control system is as Figure 1 shown.

[0155] Embodiment

[0156] To evaluate the performance of the designed controller, the physical parameters of the hydraulic multi-way valve control system in the simulation are shown in Table 1:

[0157] Table 1 System physical parameters

[0158] Physical parameter Value Physical parameter Value <![CDATA[A(m 2 )]]> <![CDATA[2×10 -4 > <![CDATA[β e (Pa)]]> <![CDATA[2×10 8 > m (kg) 5 B (N·s / m) 40 K (N / m) 20 <![CDATA[V t (m 3 )]]> 0.04 <![CDATA[K d1 (m 2 / s)]]> 1.608 <![CDATA[K d2 (m 5 / (N·s))]]> <![CDATA[3.717×10 -12 > <![CDATA[C t (m 5 / (N·s))]]> <![CDATA[7×10 -12 >

[0159] The desired command of the given system is

[0160] In the simulation, the following controllers are taken for comparison:

[0161] Adaptive asymptotic preset performance tracking controller for the hydraulic multi-way valve control system: take the gains k 1 =5, k 2 =10, k 3 =15, β 1 =1.2, β 2 =0.8, k s =400, k r1 =100, k r2 =150, take the adjustable parameter δ = 0.04, μ 0 =0.01, μ ∞ =0.0015, κ = 2,

[0162]

[0163] PID Controller: The steps for selecting the PID controller parameters are as follows: First, a set of controller parameters are obtained through the PID parameter self-tuning function in Matlab while ignoring the nonlinear dynamics of the hydraulic multi-way valve control system. Then, after adding the nonlinear dynamics of the system, the obtained self-tuning parameters are finely tuned to enable the system to achieve the best tracking performance.

[0164] The comparison between the desired command of the system, the tracking error of the adaptive asymptotic preset performance tracking controller, and the tracking errors of the adaptive asymptotic preset performance tracking controller and the PID controller with the preset performance boundary are respectively as Figure 3 , Figure 4 and Figure 5 shown. From Figure 4 it can be seen that under the action of the adaptive asymptotic preset performance tracking controller, the position output of the hydraulic multi-way valve control system has a very high tracking accuracy for the command, and the amplitude of the steady-state tracking error is approximately 2×10 -7 m. From the comparison of the tracking errors of the two controllers in Figure 5 , it can be seen that the tracking error of the adaptive asymptotic preset performance tracking controller proposed in the present invention is much smaller than that of the PID controller, and the adaptive asymptotic preset performance tracking controller can ensure that the error is within the preset performance boundary, and the tracking performance is more excellent. Figure 6 and Figure 7 are respectively the real-time estimated values of θ 1 and θ 2 , that is, and . According to the given physical parameters of the system, it can be seen that the adaptive method proposed in the present invention can accurately estimate the parameters of the system in real time.

Claims

1. A method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the hydraulic multi-way valve control system, and then proceed to step 2; Step 2: Based on the mathematical model of the hydraulic multi-way valve control system, design a tracking controller with adaptive asymptotic preset performance, and then proceed to step 3; Step 3: Use Lyapunov stability theory to prove the stability of the adaptive asymptotic preset performance tracking controller, and obtain the result that the system tracking error is limited to the specified constraints and is asymptotically stable.

2. The method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system according to claim 1 is characterized in that: In step 1, a mathematical model of the hydraulic multi-way valve control system is established, as follows: Step 1-1, the hydraulic multi-way valve control system is applied to large-scale heavy-load engineering machinery, mining, and metallurgical industry equipment, wherein the electric signal controls the electric proportional pressure reducing valve, and changes its output pressure by adjusting the voltage, thereby changing the pressure of the main valve control chamber, so that the valve core moves, controls the movement of the piston rod on the hydraulic cylinder, and drives the load connected to the hydraulic cylinder piston rod to move. According to the dynamic characteristics of the load, the hydraulic cylinder, and the main valve core of the multi-way valve, the mathematical model of the hydraulic multi-way valve control system is derived; Step 1-2: To facilitate controller design, define state variables and convert the derived hydraulic multi-way valve control system mathematical model into state space equations.

3. The method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system according to claim 2 is characterized in that: In step 1-1, the mathematical model of the hydraulic multi-way valve control system is derived according to the dynamic characteristics of the load, the hydraulic cylinder and the main valve core of the multi-way valve, as follows: According to Newton's second law, the force balance equation of the hydraulic multi-way valve control system is: In formula (1), m represents the mass of the load, y represents the displacement of the hydraulic cylinder piston rod, Indicates the speed of the hydraulic cylinder piston rod, represents the acceleration of the hydraulic cylinder piston rod, A represents the effective action area of ​​the hydraulic cylinder piston, P1 represents the oil pressure of the hydraulic cylinder oil inlet chamber, P2 represents the oil pressure of the hydraulic cylinder oil outlet chamber, B represents the total viscous damping coefficient of the hydraulic cylinder and the load, K represents the elastic load coefficient, d(t) represents the unmodeled mechanical disturbance of the system, and t represents time; Then formula (1) can be rewritten as: In the hydraulic multi-way valve control system, ignoring the leakage of the cylinder oil, the pressure dynamic equation is: In formula (3), β e Represents the effective elastic modulus of the oil, V t Indicates the equivalent volume of the hydraulic cylinder, C t Indicates the leakage coefficient of the hydraulic cylinder, the oil pressure difference P on both sides of the cylinder in and out of the oil chamber L =P1-P2,Q L represents the load overcurrent flow, q represents P L The unmodeled disturbance Indicates P L The first derivative of ; The mathematical model of the valve core movement of the main valve in the hydraulic multi-way valve control system is: In formula (4), m v Indicates the mass of the valve core, x v Indicates the displacement of the valve core, Indicates the speed of the valve core, Indicates the acceleration of the valve core, A v Indicates the effective area of ​​the main valve control chamber, P i Indicates the output pressure of the pressure reducing valve, B v Indicates the viscous damping coefficient of the valve core, K v represents the valve core elastic coefficient, d1(t) represents the unmodeled interference of the main valve mechanical system, and t represents time; assuming that the output pressure of the pressure reducing valve is P i In the stable state, it is proportional to the control input signal U, that is, P i =k t U,k t It indicates the gain coefficient of the pressure reducing valve output pressure relative to the input voltage; Load overcurrent flow Q L The valve core displacement x of the main valve of the hydraulic multi-way valve control system v There are the following relationships: In formula (5), C d represents the flow coefficient of the main valve, w represents the valve core area gradient of the main valve, ρ represents the oil density, P s represents the oil supply pressure, sgn(·) represents the function of the intermediate variable ·, and is defined as: After linearization, equation (5) is rewritten as: Q L =k d1 x v -k d2 P L (7) In formula (7), k d1 Indicates the main valve flow gain coefficient, k d2 Indicates the main valve flow-pressure gain coefficient.

4. The method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system according to claim 3 is characterized in that: In step 1-2, the state variables are defined and the derived mathematical model of the hydraulic multi-way valve control system is converted into a state space equation, as follows: Define the state variables: Among them, the intermediate variable x1 = y, the intermediate variable Intermediate variable x3 = AP L / m, intermediate variable x4=x v , intermediate variable Then transform equations (2), (3), (4) and (7) into state equations: In formula (8), represents the first-order derivative of x1, represents the first-order derivative of x2, represents the first-order derivative of x3, represents the first-order derivative of x4, represents the first-order derivative of x5; Ignore the viscous damping of the main valve and select the state variable The control variable u is the displacement of the main valve core. Simplifying equation (8) yields a new system state space equation: In formula (9), the intermediate variable Intermediate variables System unknown dynamics Intermediate variables Intermediate variables Intermediate variables System unknown dynamics 5. The method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system according to claim 4, characterized in that: In step 1, the following assumptions are made to facilitate controller design: Assumption 1: The system is expected to track the position command x 1d It is third-order continuously differentiable, and the system expects that the position command, velocity command and acceleration command are all bounded; Assumption 2: The unknown dynamics Δ1(t) and Δ2(t) of the system are sufficiently smooth, and their first-order and second-order derivatives exist and are bounded, that is: In formula (10), ζ1, ζ2, ζ3 and ζ4 are all unknown positive constants; Go to step 2.

6. The method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system according to claim 5, characterized in that: In step 2, based on the mathematical model of the hydraulic multi-way valve control system, a tracking controller with adaptive asymptotic preset performance is designed as follows: Step 2-1: To facilitate the design of the controller, a preset performance function is designed and the tracking error is converted; Step 2-2: Design an adaptive asymptotic preset performance tracking controller based on the mathematical model of the hydraulic multi-way valve control system and the conversion error z1.

7. The method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system according to claim 6, characterized in that: In step 2-1, a preset performance function is designed and the tracking error is converted as follows: Define the tracking error of the system as e1 = x1-x 1d , x 1d is the position command that the system expects to track. In order to constrain the tracking error, a preset performance function μ(t)=(μ0-μ ∞ ) -κt +μ ∞ , where μ0, μ ∞ Both represent parameters to be designed, μ0>μ ∞ >0, the convergence speed κ>0, thus constraining the tracking error so that it always remains within the performance boundary, that is: In formula (11), δ and represents a positive adjustable parameter, then - δ μ0 and Indicates the lower limit of undershoot and upper limit of overshoot of tracking error, - δ μ ∞ and Indicates the preset steady-state error interval; The strictly increasing function ψ(z1) is introduced to satisfy the following properties: In formula (12), z1 represents the conversion error signal corresponding to the tracking error e1. Based on the above properties, the following nonlinear mapping is introduced: e1(t)=μ(t)ψ(z1) (13) The strictly increasing function ψ(z1) is defined as: In formula (14), λ represents the intermediate variable. The inverse function of formula (14) is obtained as follows: As long as the conversion error z1 is bounded under the action of the controller, the property of ψ(z1) can ensure that Equation (11) This means that if z1 converges to 0 asymptotically, the tracking error e1 will also converge to 0 asymptotically. Differentiating formula (15) with respect to time yields: In formula (16), represents the first-order derivative of z1, represents the first-order derivative of e1, represents the first derivative of μ, an intermediate variable It turns out that the intermediate variable ρ is bounded and satisfies:

8. The method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system according to claim 7, characterized in that: In step 2-2, according to the mathematical model of the hydraulic multi-way valve control system and the conversion error z1, an adaptive asymptotic preset performance tracking controller is designed, as follows: Differentiate equation (16) with respect to time and substitute equation (9) into it to obtain: In formula (18), represents the first-order derivative of ρ, represents the second-order derivative of z1, represents the second-order derivative of μ, Represents x 1d The second derivative of A set of error signals are defined as follows: In formula (19), z2, z3, r1 and r2 represent error signals, k1, k2 and k3 represent positive gains, represents the first-order derivative of z2, represents the first-order derivative of z3, α2 represents the virtual control law; Substituting equation (18) into equation (19), the error signal r1 is obtained as follows: In formula (20), the actual value θ = [θ1, θ2] T , intermediate variable φ(x)=[-x1,-x2] T , intermediate variable Design the virtual control law α2 as: In formula (21), k s , k r1 and β1 represent positive gain, α 2a represents the model-based compensation term, α 2s1 represents the linear robust term, α 2s2 represents the RISE feedback control term, the real-time estimate of θ z2(0) represents the initial value of z2, dτ represents the differential with respect to time; Defining real-time estimates The adaptive law is: In formula (22), express The first-order derivative of , Γ represents the adjustable positive constant diagonal adaptive gain matrix, express The first derivative of, intermediate variable Formula (22) can be obtained by partial integration: In formula (23), express The initial value of express The second derivative of Substituting formula (21) into formula (20), we get: In formula (24), the intermediate variable Intermediate variable χ=ρθ T (φ(x)-φ d (x)), the parameter estimation error value of θ Differentiating formula (24) with respect to time yields: In formula (25), Represents the first-order derivative of r1, an intermediate variable Intermediate variables represents the first-order derivative of E, represents the first-order derivative of Δ1(t), Applying the mean value theorem, we get: In formula (26), the error signal vector z = [z1, z2, r1, z3, r2] T , η(·) represents a positive, globally reversible, non-decreasing function; According to formula (10) and formula (17), we can get N d Satisfy the following properties: In formula (27), ζ5 and ζ6 are both unknown positive constants; Substituting equation (9) into equation (19), the error signal r2 is obtained as follows: In formula (28), represents the first-order derivative of α2; According to formula (28), the controller input u is designed as: In formula (29), k r2 and β2 represent positive gain, u a represents the model-based compensation term, u s1 represents the linear robust term, u s2 represents the RISE feedback control term, z3(0) represents the initial value of z3; Substituting formula (29) into formula (28), we get: Differentiating formula (30) with respect to time yields: In formula (31), represents the first-order derivative of r2, represents the first derivative of Δ2(t); Go to step 3.

9. The method for adaptive asymptotic preset performance tracking control of a hydraulic multi-way valve control system according to claim 8, characterized in that: In step 3, the stability of the adaptive asymptotic preset performance tracking controller is proved by using Lyapunov stability theory, and the result that the system tracking error is limited to the specified constraints and is asymptotically stable is obtained, as follows: Define the helper function as follows: In formula (35), L1(t), L2(t), P1(t) and P2(t) represent auxiliary functions, N d (0) and Respectively represent N d and The initial value of The Lyapunov function is defined as follows: In formula (36), the intermediate variable ε is an expression about time t, which can be written as ε(t), specifically expressed as: The stability is proved by using Lyapunov stability theory, and the result is that the system tracking error is limited within the specified constraints and is asymptotically stable.

Images