Pilot-operated type multi-way valve control system position control method considering output state constraint

Abstract

The invention discloses a pilot-operated type multi-way valve control system position control method considering output state constraint, and the position control method is based on a constructed output state constraint function, is fused with a backstepping method control thought, and designs a nonlinear position control controller with instruction filtering and state and interference observation. Aiming at the position control problem of the pilot-operated type multi-way valve system, the method can only depend on system output state signal feedback, construct an extended state observer and a state constraint nonlinear conversion function to obtain an unmeasurable state of the system and realize output state constraint and interference compensation of the system; and the differential explosion problem in a traditional nonlinear control method can be avoided through an instruction filter, the influence of closed-loop control overshoot on the system is reduced, and the high-precision position tracking performance is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of electro-hydraulic control, and in particular to a pilot-operated multi-way valve control system position control method (SCRC) taking output state constraints into consideration. Background Art

[0002] Pilot-operated multi-way valves play an important role in engineering machinery, agricultural machinery, industrial hydraulics and other fields due to their strong environmental adaptability, few pipeline connections and high reliability. The pilot-operated multi-way valve control system can be simply described as an electro-hydraulic valve control system composed of a power source, a multi-way valve, a hydraulic actuator and related accessories. The system contains various characteristic links such as flow nonlinearity, friction nonlinearity, hysteresis of the pilot valve and the main valve, input nonlinearity, hydraulic force, and system parameter and nonlinear uncertainty. Among them, parameter uncertainty includes the uncertainty of the load mass equivalent to the end of the actuator, the leakage coefficient of the system, the related gain coefficient of the valve, the effective elastic modulus of the hydraulic oil, etc. Nonlinear uncertainty includes the unmodeled high-order valve core dynamics, external interference, etc. With the development of industrial modernization, higher safety, accuracy and response requirements are put forward for the control performance of the pilot-operated multi-way valve control system, resulting in the gradual emergence of the potential nonlinear characteristics of the system. At the same time, in order to control costs, it is often impossible to equip the product with multiple sensors, resulting in the problem that some states of the system cannot be measured. Therefore, the linear control method designed based on the traditional control theory framework can no longer meet the growing system performance requirements. It is necessary to study better nonlinear control methods based on the characteristics and uncertainties of the pilot-operated multi-way valve control system.

[0003] A large number of research results have been published for the nonlinear control problems of electro-hydraulic valve control systems such as pilot multi-way valve control systems. Among them, adaptive control can obtain the real parameters of the system and solve the parameter uncertainty problem within the system by reasonably designing the system adaptive law. However, this method still mainly relies on high-gain feedback strategies for nonlinear problems such as external interference, and has slow convergence speed and is prone to instability, which makes it difficult to promote and apply adaptive control in actual industrial situations; although traditional sliding mode control can effectively deal with the inherent parameters and nonlinear uncertainties of the system, the calculated system control input has discontinuity problems, which can easily lead to flutter problems of the motion system; robust control designed based on the traditional backstepping framework can attribute the inherent uncertainty of the system to system interference, and deal with interference and instability by designing linear and nonlinear robust feedback terms. The system uncertainty increases the difficulty of designing the virtual controller in the backstepping method, and the strong nonlinearity and high-order system are prone to differential explosion problems. The anti-disturbance control can estimate and compensate for the matching and mismatching interference of the high-order system by estimating the system modeling error and external disturbance, thereby improving the robustness of the system. However, the anti-disturbance control technology does not constrain the system state. When the motion command is close to the stroke of the controlled actuator, it is still easy to cause internal impact of the actuator due to slight overshoot, affecting the service life of the system. Although the traditional state constraint control can constrain the position state, speed state, etc. of the system, its control effect depends on the feedback of the full state information of the system, which puts forward higher requirements on the sensor. Summary of the invention

[0004] The purpose of the present invention is to provide a position control method for a pilot-operated multi-way valve control system with state constraint capability, system state observation capability and strong robustness, which can not only realize the constraint of the output state and unknown interference compensation based on relying solely on the output state feedback, but also avoid the differential explosion problem in the traditional backstepping control through the instruction filter, and realize high-precision tracking performance.

[0005] The technical solution to achieve the purpose of the present invention is: a pilot-operated multi-way valve control system position control method considering output state constraints, comprising the following steps:

[0006] Step 1: Establish a mathematical model of the pilot-operated multi-way valve control system and proceed to step 2.

[0007] Step 2: Based on the mathematical model of the pilot-operated multi-way valve control system, design a nonlinear position controller that takes output state constraints into consideration, and then proceed to step 3.

[0008] Step 3: Use Lyapunov stability theory to prove the stability of the nonlinear position controller considering the output state constraint, and obtain the result that the system tracking error is stable.

[0009] Compared with the prior art, the present invention has the following significant advantages: (1) It only depends on the system state x 1 The system state x is realized based on the feedback 1 The constraints of the unmeasured system state x are estimated and obtained. 2 、x 3 and the unknown dynamics of the system, reducing the system's dependence on sensors; (2) through the command filter, the derivation process of the virtual controller is simplified, avoiding the differential explosion problem in traditional backstepping control and achieving high-precision tracking performance. The simulation results verify its effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a schematic diagram of the principle of the position control method of the pilot-operated multi-way valve control system considering the output state constraint of the present invention.

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

[0012] Figure 3 It is a tracking process curve diagram of the actual motion position of the system to the expected tracking position instruction of the system under the action of the SCRC 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 SCRC controller designed by the present invention.

[0014] Figure 5 It is a comparison curve of the tracking errors of the system under the action of the SCRC controller designed by the present invention and the VFPID controller commonly used in industry.

[0015] Figure 6 It is a system state observation curve diagram of the SCRC controller designed by the present invention.

[0016] Figure 7 It is the interference observation curve diagram of the SCRC controller designed by the present invention.

[0017] Figure 8 It is a comparison diagram of the system output state constraints under the action of the SCRC controller designed by the present invention and the VFPID controller commonly used in industry.

[0018] Fig. 9 It is a curve diagram of the input voltage signal of the pilot-operated multi-way valve of the system under the action of the SCRC controller designed by the present invention. DETAILED DESCRIPTION

[0019] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Combination Figure 1and Figure 2 The present invention provides a method for controlling a position of a pilot-operated multi-way valve control system taking into account output state constraints, comprising the following steps:

[0021] Step 1: Establish a mathematical model of the pilot-operated multi-way valve control system.

[0022] In step 1-1, the pilot multi-way valve control system is applied to the linear motion of large equipment driven by the hydraulic system, wherein the load is fixedly connected to the piston rod on the hydraulic cylinder, and the pilot multi-way valve controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move. According to the dynamic characteristics of the load, hydraulic cylinder and pilot multi-way valve, the mathematical model of the pilot multi-way valve control system is obtained.

[0023] According to Newton's second law, the force balance equation of the pilot-operated multi-way valve control system is:

[0024]

[0025] In formula (1), m represents the weight of the load connected to the piston rod of the hydraulic cylinder, y represents the displacement of the piston rod of the hydraulic cylinder, Indicates the speed of the hydraulic cylinder piston rod. It represents the acceleration of the piston rod of the hydraulic cylinder, A represents the effective action area of ​​the piston of the hydraulic cylinder, and the pressure difference P between the oil pressure in and out of the oil chamber on both sides of the cylinder L =P 1 -P 2 , P 1 Indicates the oil pressure in the hydraulic cylinder oil inlet chamber, P 2 represents the oil pressure in the oil outlet chamber of the hydraulic cylinder, B represents the viscous damping coefficient of the hydraulic cylinder, f(t) represents the external unknown disturbance and internal unmodeled disturbance of the system, and t represents time.

[0026] Then formula (1) can be rewritten as:

[0027]

[0028] In the pilot-operated multi-way valve control system, considering the oil characteristics of the system and ignoring the leakage of the system oil, the pressure dynamic equation is:

[0029]

[0030] In formula (3), β e Indicates the effective elastic modulus of the hydraulic oil used in the system, V t represents the control volume of the hydraulic cylinder, Indicates P L The first derivative of t Indicates the leakage coefficient of the hydraulic cylinder, Q L represents the load flow of the hydraulic cylinder and q(t) represents the unmodeled disturbance.

[0031] The pilot-operated multi-way valve includes a pilot valve and a main valve. Ignoring the high-order spool dynamics of the pilot valve and the main valve, it is assumed that the input voltage signal u acting on the pilot-operated multi-way valve and the output oil pressure of the pilot valve act on the output force F of the main valve spool RF is in a proportional relationship, and the output force F RF is in a proportional relationship with the displacement x of the main valve spool v , that is, it satisfies:

[0032]

[0033] In equation (4), k f represents the gain coefficient of the input voltage signal relative to the output force of the pilot valve, and k y represents the gain coefficient of the displacement of the main valve spool relative to the output force of the pilot valve. Then, the main valve flow rate Q of the pilot-operated multi-way valve L has the following relationship with the input voltage signal u of the pilot-operated multi-way valve:

[0034]

[0035] In equation (5), the flow coefficient k of the main valve of the pilot-operated multi-way valve q = k f k y , u represents the input voltage signal of the pilot-operated multi-way valve, P s represents the oil supply pressure of the system, and sign(·) represents the function of the intermediate variable ·, which is defined as:

[0036]

[0037] In step 1-2, to facilitate the design of the controller, state variables are defined: where the system state x 1 = y, the system state system state Then, equation (2) is converted into a state-space equation:

[0038]

[0039] In equation (7), represents the first derivative of x 1 , represents the first derivative of x 2 , represents the first derivative of x 3 , the unknown dynamics of the system represents the first derivative of f(t), and the intermediate variable intermediate variable intermediate variable

[0040] In steps 1-3, reasonable assumptions are made about the system to facilitate controller design, as follows:

[0041] Assumption 1: The system is expected to track the position command x d It is second-order continuous, and the system expects the tracking position command, velocity command and acceleration command to be bounded.

[0042] Assumption 2: The unknown dynamics D(t) of the system satisfies:

[0043]

[0044] In formula (8), δ 1 ,δ 2 ,δ 3 are all unknown positive constants, represents the first-order derivative of D(t), H(t) is an unknown continuous function, f(t) represents the external unknown disturbance and internal unmodeled disturbance of the system, and t represents time.

[0045] Assumption 3: Based on the force balance equation represented by equation (1) and the restrictions imposed by Assumption 1 on the system's desired tracking position command, we can derive P L is about the system state x 2 and x 3 Lipschitz function, then according to the intermediate variable f 1 、f 2 、f 3 The definition of f 1 In practical terms, it is about the system state x 2 and x 3 The Lipschitz function, f 2 In the global scope, it is about the system state x 2 The Lipschitz function, f 3 In the global scope, it is about the system state x 3 The Lipschitz function of .

[0046] Assumption 4: System state x 1 =y is completely measurable.

[0047] Go to step 2.

[0048] Step 2: Based on the mathematical model of the pilot-operated multi-way valve control system, a nonlinear position controller considering the output state constraints is designed, as follows:

[0049] In step 2-1, to obtain the unmeasured system state x 2 、x 3As well as the unknown dynamics of the system D(t), an extended state observer is constructed to estimate the system state and unknown dynamics, as follows:

[0050] Take the expanded state variable x e =D(t), then based on Assumption 2, in, represents the first-order derivative of D(t), and H(t) represents the unknown continuous function.

[0051] Combined with formula (7), the following extended state observer is designed:

[0052]

[0053] In formula (9), the extended state observer variable Represents the system state x i The observed estimate of the extended state observer variable Represents the expanded state variable x e The observed estimate of express The first derivative of express The first-order derivative of , ω represents the gain of the extended state observer, and the intermediate variable Represents the intermediate variable f i Observational estimator of , subscript i=1,2,3;.

[0054] Combining equation (7) and equation (9), the dynamic error of the extended state observer is:

[0055]

[0056] In formula (10), and Both represent the observation estimation error of the extended state observer on the system state. Intermediate variables Represents the intermediate variable f i The observation estimation error is Subscript i=1,2,3.

[0057] Define intermediate variables: Among them, the intermediate variable Intermediate variables Intermediate variables Intermediate variables Then the dynamic error of the extended state observer represented by equation (10) is further rewritten as:

[0058]

[0059] In formula (11), represents the first-order derivative of the intermediate variable ε, the intermediate variable A ESO , B ESO With C ESO are matrices that characterize the dynamic error of the extended state observer and are defined as:

[0060]

[0061]

[0062] In step 2-2, define the error z 1 =ζ 1 -α 0 , where the intermediate variable ζ 1 is the system state x 1 The state variable obtained by the nonlinear conversion function, α 0 Indicates 1 The virtual controllers are as follows:

[0063] In order to simplify the design process of the controller, the following command filter is designed:

[0064]

[0065] In formula (14), α 1f Represents α 1 The filter value, α 1 Represents x 2 Virtual controller, Represents α 1f The first-order derivative of, filter gain τ 1 >0,α 1 The filtering error e 1 =α 1f -α 1 , η 1 (t) represents a function that is always positive and satisfies Among them, ν represents the integral variable, c c1 represents an arbitrary constant, η 1max represents a positive constant, The upper bound of 1 >0, Indicates l 1 The estimated value of .

[0066] The update law for:

[0067]

[0068] In formula (15), σ 1 Indicates positive gain.

[0069] Design the following nonlinear transfer function:

[0070]

[0071] In formula (16), ρ 1 Represents the system state x 1 Design boundary, ρ 1 is a positive constant and satisfies:

[0072]

[0073] In formula (17), Indicates that the system expects to track the position instruction x d The upper bound of Indicates that the system expects to track the position instruction x d The lower bound of .

[0074] Designing a virtual controller α 0 for:

[0075]

[0076] Right 1 The derivative is:

[0077]

[0078] In formula (19), Indicates 1 The first derivative of Represents α 0 The first derivative of Represents x d The first derivative of, intermediate variable error Intermediate variables

[0079] Designing a virtual controller α 1 for:

[0080]

[0081] In formula (20), the gain k 1 >0.

[0082] Substituting formula (20) into formula (19), we get:

[0083]

[0084] In step 2-3, define the error error in, Represents the system state x 2 The observed estimate of α1f Represents α 1 The filter value, α 1 Represents x 2 Virtual controller, Represents the system state x 3 The observed estimate of α 2f Represents α 2 The filter value, α 2 Represents x 3 To simplify the design process of the virtual controller, the following command filter is designed:

[0085]

[0086] In formula (22), the filter gain τ 2 >0, Represents α 2f The first derivative of 2 The filtering error e 2 =α 2f -α 2 , η 2 (t) represents a function that is always positive and satisfies Among them, ν represents the integral variable, c c2 represents an arbitrary constant, η 2max represents a positive constant, The upper bound of 2 >0, Indicates l 2 The estimated value of .

[0087] The update law for:

[0088]

[0089] In formula (23), σ 2 indicates positive gain;

[0090] Right 2 The derivative is:

[0091]

[0092] Designing a virtual controller α 2 for:

[0093]

[0094] In formula (25), the gain k 2 >0,α 2a Represents the virtual controller α 2 The model compensation term, α 2s1 Represents the virtual controller α2 The linear robust term, α 2s2 Virtual Controller α 2 The nonlinear robust term.

[0095] Substituting formula (25) into formula (24), we get:

[0096]

[0097] Right 3 The derivative is:

[0098]

[0099] The input voltage signal u of the pilot-operated multi-way valve is designed to be:

[0100]

[0101] In formula (28), the gain k 3 >0.

[0102] Substituting equation (28) into equation (27), we get:

[0103]

[0104] Go to step 3.

[0105] Step 3, using Lyapunov stability theory to prove the stability of the nonlinear position controller considering the output state constraint, the result of the system tracking error stability is obtained, as follows:

[0106] The Lyapunov function is defined as follows:

[0107]

[0108] In formula (30), the error z 1 =ζ 1 -α 0 ,error error Intermediate variables Intermediate variables σ 1 With σ 2 Indicates a positive gain, the intermediate variable ε=[ε 1 ,ε 2 ,ε 3 ,ε 4 ] T , intermediate variable Intermediate variables Intermediate variables Intermediate variables Intermediate variable ε Trepresents the transposed vector of the intermediate variable ε, P represents a positive definite matrix, and the filtering error e 1 =α 1f -α 1 , filtering error e 2 =α 2f -α 2 .

[0109] Deriving equation (30) and substituting it into equations (11), (15), (21), (23), (26) and (29), we obtain:

[0110]

[0111] In formula (31), |·| represents the absolute value of the intermediate variable ·.

[0112] According to formula (12), we can get A ESO is a Hurwitz matrix, and we can find a positive definite matrix P that satisfies:

[0113] PA ESO +A ESO T P=-I 4×4 (32)

[0114] In formula (32), the intermediate variable A ESO T Represents the matrix A ESO The transposed matrix of the intermediate variable I 4×4 represents a fourth-order identity matrix.

[0115] According to Assumptions 2 and 3, we can get:

[0116]

[0117] In formula (33), the intermediate variable Represents the intermediate variable f i The observation estimation error, constant L 1 ,L 2 ,L 3 ,L 4 ,L 5 Represents the Lipschitz constant, subscript i=1,2,3.

[0118] In addition, note that:

[0119]

[0120] Then we have:

[0121]

[0122] Substituting equations (32), (33) and (35) into equation (31), equation (31) is further rewritten as:

[0123]

[0124] In formula (36), the intermediate variable |μ 1 | max Represents μ 1 The upper bound of the absolute value of the intermediate variable Constant λ max (P) represents the maximum eigenvalue of the matrix P, |u| max represents the upper bound of the absolute value of u,

[0125] Intermediate variable C N =max{L 1 |u| max / ω 2 ,L 2 |u| max / ω 2 ,L 3 |u| max / ω 2 ,L 4 / ω 2 ,L 5 / ω 2};

[0126] Define the intermediate variables χ and Λ as:

[0127] χ=[z 1 ,z 2 ,z 3 ,ε 1 ,ε 2 ,ε 3 ,ε 4 ,e 1 ,e 2 ] (37)

[0128]

[0129] In formula (38), the intermediate variable Λ 1 and Λ 2 They are:

[0130]

[0131] The gain k can be adjusted 1 , k 2 , k 3 , τ 1 , τ 2 , which can make the matrix Λ positive definite, then:

[0132]

[0133] In formula (40), the intermediate variable χ T Represents the transposed vector of the intermediate variable χ, the intermediate variable M = χ T Λχ, intermediate variable ν 1 (t) = η 1 (t)+0.5c 1 , the intermediate variable ν 2 (t) = η 2 (t)+0.5c 1 .

[0134] Integrating both sides of equation (40), we have:

[0135]

[0136] In formula (41), V(0) is a constant and ν represents the integral variable.

[0137] Considering c 1 is a constant, then formula (41) can be further written as:

[0138]

[0139] In formula (42), η 1max and η 2max Represents a positive constant.

[0140] From (42), we can conclude that V is bounded and the integral of M is bounded, and hence all states of the system are bounded.

[0141] Therefore, it is concluded that by adjusting the gain k 1 , k 2 , k 3 , ω and filter gain τ 1 , τ 2 The nonlinear position controller designed for the pilot-operated multi-way valve control system, which takes into account the output state constraint for the first time, can enable the system to innovatively obtain the result that the system output state error is bounded and the input state is constrained. The principle diagram of the position controller of the pilot-operated multi-way valve control system considering the output state constraint is shown in Figure 1 shown.

[0142] Example

[0143] In order to evaluate the performance of the designed controller, the physical parameters of the pilot multi-way valve control system in the simulation are shown in Table 1:

[0144] Table 1 System physical parameters

[0145] parameter Numeric Physical parameters Numeric <![CDATA[(m 2 )]]> <![CDATA[2×10 -4 ]]> <![CDATA[β e (Pa)]]> 2×10 (kg) 40 B(N·s / m) 80 (N·s) <![CDATA[7×10 -12 ]]> <![CDATA[K q (m / V)]]> 9.25×1 <![CDATA[(m 3 )]]> <![CDATA[1×10 -3 ]]> <![CDATA[P s (MPa)]]> 7

[0146] Given the system's desired tracking position command is

[0147] The following controllers are used for comparison in the simulation:

[0148] Pilot-operated multi-way valve control system position controller (SCRC) considering output state constraints: Take gain k 1 =250, k 2 =100, k 3 =50,σ 1 =1,σ 2 =1,τ 1 =3000, τ 2 =3000,ρ 1 =0.52.

[0149] VFPID controller: The steps for selecting the parameters of the VFPID controller are: first, ignoring the nonlinear dynamics of the pilot-operated multi-way valve control system, a set of controller parameters is obtained by adjusting the VFPID parameters to enable the system to achieve the best tracking performance. The selected controller parameters are k P =700, k I =400, k D =100, k velocity =0.85.

[0150] The tracking process curve of the actual motion position of the system under the action of the SCRC controller to the system's expected tracking position instruction, the tracking error of the system under the action of the SCRC controller, the tracking error comparison between the SCRC controller and the VFPID controller, the system state observation of the SCRC controller, the interference observation of the SCRC controller, and the state constraint of the SCRC controller are shown as follows, respectively. Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 and Figure 8 As shown. Figure 3 and Figure 4 It can be seen that under the action of the SCRC controller, the position output of the pilot-operated multi-way valve system has a high tracking accuracy for the command, and the mean value of the tracking error is about 2.74×10 -6 m. From Figure 5 It can be seen that the SCRC controller proposed in the present invention has better tracking performance than the VFPID controller commonly used in industry. Figure 6 It shows the observation of the unknown state of the system by the SCRC controller. Figure 6 It can be seen that the observed values ​​are relatively accurate. Figure 7 The observation of the SCRC controller for unknown disturbances in the system is demonstrated. Figure 8The state constraint capability of the SCRC controller is demonstrated compared with the VFPID controller commonly used in industry. Fig. 9 It is the input voltage signal of the pilot operated multi-way valve obtained by the SCRC controller. It can be seen from the figure that the obtained input voltage signal is a low-frequency continuous signal, which is more conducive to execution in practical applications.

Claims

1. A method for position control of a pilot-operated multi-way valve control system considering output state constraints, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the pilot-operated multi-way valve control system, and then proceed to step 2; Step 2: Based on the mathematical model of the pilot-operated multi-way valve control system, a nonlinear position controller considering output state constraints is designed, and then the process goes to step 3; Step 3: Use Lyapunov stability theory to prove the stability of the nonlinear position controller considering the output state constraint, and obtain the result that the system tracking error is stable.

2. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 1, characterized in that: In step 1, a mathematical model of the pilot-operated multi-way valve control system is established, as follows: Step 1-1, the pilot multi-way valve control system is applied to the linear motion of large equipment driven by the hydraulic system, wherein the load is fixedly connected to the piston rod on the hydraulic cylinder, and the pilot multi-way valve controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move. According to the dynamic characteristics of the load, the hydraulic cylinder and the pilot multi-way valve, the mathematical model of the pilot multi-way valve control system is obtained; Step 1-2: To facilitate controller design, define state variables and convert the mathematical model of the pilot-operated multi-way valve control system into a state space equation; Steps 1-3: To facilitate controller design, make reasonable assumptions about the system.

3. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 2, characterized in that: In step 1-1, the pilot multi-way valve control system is applied to the linear motion of large equipment driven by the hydraulic system, wherein the load is fixedly connected to the piston rod on the hydraulic cylinder, and the pilot multi-way valve controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move. According to the dynamic characteristics of the load, the hydraulic cylinder and the pilot multi-way valve, the mathematical model of the pilot multi-way valve control system is obtained, as follows: According to Newton's second law, the force balance equation of the pilot-operated multi-way valve control system is: In formula (1), m represents the weight of the load connected to the piston rod of the hydraulic cylinder, y represents the displacement of the piston rod of the hydraulic cylinder, Indicates the speed of the hydraulic cylinder piston rod. It represents the acceleration of the piston rod of the hydraulic cylinder, A represents the effective action area of ​​the piston of the hydraulic cylinder, and the pressure difference P between the oil pressure in and out of the oil chamber on both sides of the cylinder L =P1-P2, P1 represents the oil pressure of the hydraulic cylinder inlet chamber, P2 represents the oil pressure of the hydraulic cylinder outlet chamber, B represents the viscous damping coefficient of the hydraulic cylinder, f(t) represents the external unknown disturbance and internal unmodeled disturbance of the system, and t represents time; Then formula (1) can be rewritten as: In the pilot-operated multi-way valve control system, considering the oil characteristics of the system and ignoring the leakage of the system oil, the pressure dynamic equation is: In formula (3), β e Indicates the effective elastic modulus of the hydraulic oil used in the system, V t represents the control volume of the hydraulic cylinder, Indicates P L The first derivative of t Indicates the leakage coefficient of the hydraulic cylinder, Q L represents the load flow of the hydraulic cylinder, q(t) represents the unmodeled disturbance; The pilot-operated multi-way valve includes a pilot valve and a main valve. The high-order valve core dynamics of the pilot valve and the main valve are ignored. Assume that the input voltage signal u acting on the pilot-operated multi-way valve and the output oil pressure of the pilot valve act on the output force F of the main valve core. RF Proportional relationship, output force F RF With the main valve core displacement x v Proportional relationship, that is, satisfying: In formula (4), k f Indicates the input voltage signal relative to the pilot valve output force gain coefficient, k y Indicates the main valve spool displacement relative to the pilot valve output force gain coefficient, then the main valve flow rate Q of the pilot multi-way valve L The relationship with the input voltage signal u of the pilot-operated multi-way valve is as follows: In formula (5), the flow coefficient k of the main valve of the pilot-operated multi-way valve is q =k f k y , u represents the input voltage signal of the pilot operated multi-way valve, P s represents the oil supply pressure of the system, sign(·) represents the function of the intermediate variable ·, and is defined as:

4. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 3, characterized in that: In step 1-2, in order to facilitate the design of the controller, the state variables are defined and the mathematical model of the pilot-operated multi-way valve control system is converted into a state space equation, as follows: Define the state variables: Among them, the system state x1 = y, the system state System Status Then transform equation (2) into the state space equation: In formula (7), represents the first-order derivative of x1, represents the first-order derivative of x2, represents the first-order derivative of x3, the unknown dynamics of the system Represents the first-order derivative of f(t), an intermediate variable Intermediate variables Intermediate variables 5. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 4, characterized in that: In steps 1-3, reasonable assumptions are made about the system to facilitate controller design, as follows: Assumption 1: The system is expected to track the position command x d It is second-order continuous, and the system expects the tracking position command, velocity command and acceleration command to be bounded; Assumption 2: The unknown dynamics D(t) of the system satisfies: In formula (8), δ1, δ2, and δ3 are all unknown positive constants. represents the first-order derivative of D(t), H(t) is an unknown continuous function, f(t) represents the external unknown disturbance and internal unmodeled disturbance of the system, and t represents time; Assumption 3: Based on the force balance equation represented by equation (1) and Assumption 1, the system expects to track the position command x d The restrictions made give P L is the Lipschitz function of the system states x2 and x3. According to the definition of the intermediate variables f1, f2, and f3, it can be further concluded that f1 is the Lipschitz function of the system states x2 and x3 in the actual scope, f2 is the Lipschitz function of the system state x2 in the global scope, and f3 is the Lipschitz function of the system state x3 in the global scope. Assumption 4: The system state x1=y is completely measurable; Go to step 2.

6. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 5, characterized in that: In step 2, based on the mathematical model of the pilot-operated multi-way valve control system, a nonlinear position controller considering the output state constraint is designed, as follows: Step 2-1: In order to obtain the unmeasured system states x2, x3 and the unknown system dynamics D(t), an extended state observer is constructed to estimate the system state and unknown dynamics; Step 2-2, define error z1 = ζ1-α0, where the intermediate variable ζ1 is the state variable obtained by converting the system state x1 through the nonlinear conversion function, and α0 represents the virtual controller of ζ1. To ensure that the system state x1 can accurately track the system's expected tracking position instruction x d And to realize the state constraint of x1, it is necessary to ensure that the error z1 is bounded; Step 2-3: Define the error error in, represents the observed estimated value of the system state x2, α 1f represents the filtered value of α1, α1 represents the virtual controller of x2, represents the observed estimated value of the system state x3, α 2f Represents the filtered value of α2, α2 represents the virtual controller of x3. To ensure that the tracking error z1 is bounded, the error z2 must be bounded. To ensure that the error z2 is bounded, the error z3 must be bounded.

7. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 6, characterized in that: In step 2-1, in order to obtain the unmeasured system states x2, x3 and the unknown system dynamics D(t), an extended state observer is constructed to estimate the system state and unknown dynamics, as follows: Take the expanded state variable x e =D(t), then based on Assumption 2, in, represents the first-order derivative of D(t), and H(t) represents the unknown continuous function; Combined with formula (7), the following extended state observer is designed: In formula (9), the extended state observer variable Represents the system state x i The observed estimate of the extended state observer variable Represents the expanded state variable x e The observed estimate of express The first derivative of express The first-order derivative of , ω represents the gain of the extended state observer, and the intermediate variable Represents the intermediate variable f i Observational estimator of , subscript i=1,2,3; Combining equation (7) and equation (9), the dynamic error of the extended state observer is: In formula (10), and Both represent the observation estimation error of the extended state observer on the system state. Intermediate variables Represents the intermediate variable f i The observation estimation error is Subscript i=1,2,3; Define intermediate variables: Among them, the intermediate variable Intermediate variables Intermediate variables Intermediate variables Then the dynamic error of the extended state observer represented by equation (10) is further rewritten as: In formula (11), represents the first-order derivative of the intermediate variable ε, the intermediate variable A ESO , B ESO With C ESO are matrices that characterize the dynamic error of the extended state observer and are defined as:

8. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 7, characterized in that: In step 2-2, the error z1 is defined as ζ1-α0, where the intermediate variable ζ1 is the state variable obtained by converting the system state x1 through the nonlinear conversion function, and α0 represents the virtual controller of ζ1. To ensure that the system state x1 can accurately track the system's expected tracking position instruction x d And to realize the state constraint of x1, it is necessary to ensure that the error z1 is bounded, as follows: In order to simplify the design process of the controller, the following command filter is designed: In formula (14), α 1f represents the filtered value of α1, α1 represents the virtual controller of x2, Represents α 1f The first-order derivative of , filter gain τ1>0, filter error e1=α 1f -α1,η1(t) represents a function that is always positive and satisfies Among them, ν represents the integral variable, c c1 represents an arbitrary constant, η 1max represents a positive constant, The upper bound of l1>0, represents the estimated value of l1; The update law for: In formula (15), σ1 represents a positive gain; Design the following nonlinear transfer function: In formula (16), ρ1 represents the boundary designed for the system state x1, ρ1 is a positive constant and satisfies: In formula (17), Indicates that the system expects to track the position instruction x d The upper bound of x d Indicates that the system expects to track the position instruction x d The lower bound of Design the virtual controller α0 as: Taking the derivative of z1 we get: In formula (19), represents the first-order derivative of ζ1, represents the first-order derivative of α0, Represents x d The first derivative of, intermediate variable error Intermediate variables Design the virtual controller α1 as: In formula (20), gain k1>0; Substituting formula (20) into formula (19), we get:

9. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 8, characterized in that: In step 2-3, define the error error in, represents the observed estimated value of the system state x2, α 1f represents the filtered value of α1, α1 represents the virtual controller of x2, represents the observed estimated value of the system state x3, α 2f Represents the filtered value of α2, α2 represents the virtual controller of x3. To ensure that the tracking error z1 is bounded, the error z2 must be bounded. To ensure that the error z2 is bounded, the error z3 must be bounded, as follows: In order to simplify the design process of the controller, the following command filter is designed: In formula (22), the filter gain τ2>0, Represents α 2f The first-order derivative of α2, the filtering error e2 = α 2f -α2,η2(t) represents a function that is always positive and satisfies Among them, ν represents the integral variable, c c2 represents an arbitrary constant, η 2max represents a positive constant, The upper bound of l2>0, represents the estimated value of l2; The update law for: In formula (23), σ2 represents the positive gain; Taking the derivative of z2 we get: Design the virtual controller α2 as: In formula (25), gain k2>0, α 2a represents the model compensation term of the virtual controller α2, α 2s1 represents the linear robust term of the virtual controller α2, α 2s2 The nonlinear robust term of the virtual controller α2; Substituting formula (25) into formula (24), we get: Taking the derivative of z3 we get: The input voltage signal u of the designed pilot-operated multi-way valve is: In formula (28), gain k3>0; Substituting equation (28) into equation (27), we get: Go to step 3.

10. The position control method of a pilot-operated multi-way valve control system considering output state constraints according to claim 9, characterized in that: In step 3, the stability of the nonlinear position controller considering the output state constraint is proved by using Lyapunov stability theory, and the result of system tracking error stability is obtained, as follows: The Lyapunov function V is defined as follows: In formula (30), error z1 = ζ1-α0, error error Intermediate variables Intermediate variables σ1 and σ2 represent positive gains, and the intermediate variable ε=[ε1,ε2,ε3,ε4] T , intermediate variable Intermediate variables Intermediate variables Intermediate variables Intermediate variable ε T represents the transposed vector of the intermediate variable ε, P represents a positive definite matrix, and the filtering error e1 = α 1f -α1, filtering error e2 = α 2f -α2; The stability is proved by using Lyapunov stability theory, and the result is that the system tracking error is stable.

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