FTDO-based hydraulic multi-way valve control system preset performance control method

Abstract

The application discloses a hydraulic multi-way valve control system preset performance control method based on FTDO, the control method is based on the specified time preset performance function constructed, the idea of backstepping control is fused, a nonlinear position controller combining instruction filtering, parameter self-adaption, disturbance observation and suppression is designed. For the position control problem of the hydraulic multi-way valve control system, the preset time convergence of the tracking error is realized through the design of the preset performance function, the transient and steady state performances of the system are ensured, and the robust self-adaptive controller based on the FTDO is constructed to effectively handle various model uncertainties existing in the system, and the high-precision asymptotic tracking performance of the system is realized.

Description

Technical Field

[0001] This invention relates to the field of electro-hydraulic servo control technology, specifically to a preset performance control method for a hydraulic multi-way valve control system based on a finite-time disturbance observer (FTDO). Background Technology

[0002] Hydraulic multi-way valves, with their fast response, high integration, and high reliability, are widely used in various hydraulic systems of engineering machinery. A hydraulic multi-way valve control system can be simply described as an electromechanical-hydraulic system composed of a control system, power source, multi-way valve, actuator, and supporting hydraulic circuits; it is a typical strongly nonlinear system. The system suffers from uncertainties in parameters such as system dynamics, friction, and fluid elastic modulus, as well as modeling errors that are difficult to characterize precisely, complex leakage characteristics of hydraulic components, unmodeled external disturbances, and nonlinear friction, all of which severely restrict the system's control performance. With increasing industrialization, hydraulic multi-way valve control systems are being used more and more extensively in electro-hydraulic servo systems. To meet the complex and diverse tasks and high-performance requirements, higher demands are being placed on performance indicators such as transient and steady-state tracking accuracy. Traditional model-free linear control, such as PID control, while widely used, struggles to meet the high-precision tracking performance requirements. Therefore, researching advanced nonlinear control based on system dynamic models is of great significance.

[0003] Numerous research achievements have been made on the nonlinear control problems of electro-hydraulic valve control systems, such as hydraulic multi-way valve control systems. Among them, model-based control methods, such as feedback linearization control, exhibit good robustness and can provide effective solutions for high-precision trajectory tracking control. However, due to the large amount of uncertainty in the model, their control performance is greatly limited. Adaptive control can effectively handle most uncertainties, but its ability to handle unmodeled disturbances is poor. Traditional adaptive robust control can effectively address the high nonlinearity in the system and handle most model uncertainties and uncertain nonlinearities, but uncertain disturbances in the system may lead to potentially high-gain feedback designs, and increasing the system order can easily cause the differential explosion problem in controllers designed based on the backstepping method. Adaptive control based on error sign integral robustness can reduce the feedback burden of the controller and achieve asymptotic tracking performance; however, this controller cannot handle mismatched disturbances and cannot completely solve the control problems in hydraulic systems. Active disturbance rejection control can achieve model compensation for matched and mismatched disturbances in high-order systems and improve the robustness of the system, but it is difficult to achieve asymptotic tracking performance within a finite time. Furthermore, most of the above nonlinear controllers pay little attention to the convergence speed performance of tracking errors, making it difficult to obtain the preset transient and steady-state performance, and still have significant limitations in practical applications. Summary of the Invention

[0004] The purpose of this invention is to provide a position control method for a hydraulic multi-way valve control system that has the ability to observe and suppress interference, preset transient and steady-state performance of error, and asymptotic tracking performance. It can not only ensure the transient and steady-state performance of tracking error by designing preset performance functions, but also effectively handle various model uncertainties in the system by constructing a robust adaptive controller based on FTDO, thus realizing high-precision asymptotic tracking control of the system.

[0005] The technical solution to achieve the objective of this invention is: a preset performance control method for a hydraulic multi-way valve control system based on FTDO, comprising the following steps:

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

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

[0008] Step 3: Apply Lyapunov stability theory to perform stability analysis on the robust adaptive preset performance controller based on FTDO, and obtain the result that the system tracking error is asymptotically stable.

[0009] Compared with the prior art, the significant advantages of this invention are: (1) By combining model feedforward based on FTDO and parameter adaptive law with nonlinear robust control, the steady-state asymptotic tracking performance of the system is guaranteed while avoiding high-gain feedback; (2) By designing a preset performance function for the error at a specified time, the transient performance of the system is further precisely controlled within a specified time; (3) The introduction of the instruction filter function avoids the differentiation of the virtual control input, solves the differential explosion problem in traditional backstepping control, improves the practicality of the controller, and the simulation results verify its effectiveness. Attached Figure Description

[0010] Figure 1 This is a schematic diagram illustrating the principle of the preset performance control method for a hydraulic multi-way valve control system based on FTDO according to the present invention.

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

[0012] Figure 3 This is a graph showing the expected and actual trajectories of the system tracked by the robust adaptive preset performance controller (RAPPC-FTDO) based on FTDO designed in this invention.

[0013] Figure 4 This is a comparison curve of the tracking error under the action of the RAPPC-FTDO controller designed in this invention and the VFPID controller commonly used in engineering.

[0014] Figure 5 This is an adaptive parameter estimation curve under the action of the RAPPC-FTDO controller designed in this invention.

[0015] Figure 6 This is a curve showing the upper bound estimation of the disturbance under the action of the RAPPC-FTDO controller designed in this invention.

[0016] Figure 7 This is a graph showing the system state and disturbance observation curves under the action of the RAPPC-FTDO controller designed in this invention.

[0017] Figure 8 This is a system control input curve diagram under the action of the RAPPC-FTDO controller designed in this invention. Detailed Implementation

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Combination Figure 1 and Figure 2 The preset performance control method for a hydraulic multi-way valve control system based on FTDO described in this invention includes the following steps:

[0020] Step 1: Establish a mathematical model of the hydraulic multi-way valve control system.

[0021] Step 1-1: The hydraulic multi-way valve control system is applied to the linear motion of large equipment driven by the hydraulic system. The load is fixedly connected to the head of the hydraulic cylinder piston rod. The hydraulic multi-way valve controls the hydraulic cylinder piston rod to make linear motion, thereby driving the load to move. Based on the dynamic characteristics of the load, hydraulic cylinder and hydraulic multi-way valve, a mathematical model of the hydraulic multi-way valve control system is established.

[0022] According to Newton's equations of motion, the force balance equations for a hydraulic multi-way valve control system are as follows:

[0023]

[0024] In equation (1), m is the total weight of the hydraulic cylinder piston rod and the fixed load at the head of the system. Let F be the acceleration of the hydraulic cylinder piston rod, A1 be the effective working area of ​​the hydraulic cylinder inlet chamber, A2 be the effective working area of ​​the hydraulic cylinder outlet chamber, P1 be the pressure of the hydraulic cylinder inlet chamber, P2 be the pressure of the hydraulic cylinder outlet chamber, and F be the acceleration of the hydraulic cylinder piston rod. f The frictional force acting on the system is specifically defined as follows: Among them, f v f represents the coefficient of viscous friction. c Let α represent the modelable Coulomb friction amplitude. c Represents the coefficients of the tanh curve. f is the speed of the hydraulic cylinder piston rod. b Here, d1(t) represents the friction bias constant, d1(t) represents the unmodeled mechanical dynamic disturbance of the system, and t represents time.

[0025] In a hydraulic multi-way valve control system, neglecting external leakage, the dynamic equation for the two-chamber pressure is written as follows:

[0026]

[0027] In equation (2), The derivative of P1, β is the derivative of P2. e The equivalent elastic modulus of the hydraulic fluid in the two chambers of the hydraulic cylinder is given by V1 = V. 01 +A1y,V 01 The initial volume of the inlet chamber is V2, and the volume of the outlet chamber of the hydraulic cylinder is V2 = V 02 +A2y,V 02 Let y be the initial volume of the oil outlet chamber, y be the displacement of the hydraulic cylinder, and C be the displacement of the hydraulic cylinder. t The internal leakage coefficient of the hydraulic rod is given by the load pressure P. L =P1-P2, Q1 represents the supply flow rate of the hydraulic cylinder inlet chamber, Q2 represents the return flow rate of the hydraulic cylinder outlet chamber, Q e1 (t) represents the modeling error caused by the complex internal leakage and pressure dynamics of the hydraulic cylinder's inlet chamber, Q. e2 (t) represents the modeling error caused by the complex internal leakage and pressure dynamics of the hydraulic cylinder's oil outlet chamber.

[0028] A hydraulic multi-way valve includes a pilot valve and a main valve. Ignoring the spool dynamics of the pilot and main valves, and defining the system control input u as the voltage acting on the pilot valve spool, then u and the force F exerted by the hydraulic pressure through the pilot valve on the main valve spool are... xd Proportional relationship, F xd With the displacement x of the main valve core v A proportional relationship, that is, satisfying:

[0029]

[0030] In equation (3), k xd k is the gain coefficient of the output force corresponding to the pilot valve spool voltage. f The gain coefficient corresponding to the main valve spool displacement for the output force, neglecting pipeline flow loss, is used to write the main valve flow equation as follows:

[0031]

[0032] In equation (4), k q The main valve flow gain, relative to the total gain k of u t =k q k xdk f The intermediate variables R1 and R2 are written as follows:

[0033]

[0034] In equation (5), P s P is the system oil supply pressure. r Let be the system return oil pressure, and s(·) be a function of ·, written as:

[0035]

[0036] Steps 1-2: Define the state variables required for controller design and reconstruct the mathematical model of the hydraulic multi-way valve control system into state-space equation form.

[0037] Define state variables Where, state variable x1 = y, state variable State variable x3 = A1P1 - A2P2, with the superscript T indicating the transpose operation.

[0038] Combining equations (1) to (6), the system state-space equations are rewritten in the following form:

[0039]

[0040] In equation (7), d2(t) represents the lumped disturbance caused by the complex internal leakage and pressure dynamics of the two chambers of the hydraulic cylinder, specifically d2(t) = β e [A1Q e1 (t)V1 -1 +A2Q e2 (t)V2 -1 ], The derivative of x1, The derivative of x² The derivative of x3, the intermediate variable f1 = A1R1 / V1 + A2R2 / V2, the intermediate variable The intermediate variable f3 = A1 / V1 + A2 / V2.

[0041] To improve the accuracy of the system model compensation terms, the uncertainty of hydraulic parameters is taken into account, and the uncertain parameter vector θ is defined as:

[0042] θ = [θ2, θ3] T =[β e ,β e C t ] T (8)

[0043] In equation (8), the uncertain parameter θ2 = β e Uncertain parameter θ3=β e Ct According to equation (7), the parameter vector corresponding to θ is defined. as follows:

[0044]

[0045] In equation (9), the parameter parameter

[0046] By combining equations (7) and (9), the function N3 is defined as follows:

[0047]

[0048] Equation (7) can then be rewritten as follows:

[0049]

[0050] The following assumptions are made regarding the hydraulic system:

[0051] Assumption 1: The system supply oil pressure can remain stable, the return oil pressure is approximately 0, the system operates under normal conditions, and the pressure in both chambers is determined by the supply oil pressure P. s and return oil pressure P r The constraint is that 0 < P. r <P1<P s and 0 < P r <P2<P s , where P s and P r It is a constant; in addition, the elastic modulus of the hydraulic oil in both chambers of the hydraulic cylinder is the same.

[0052] Assumption 2: The system expects the motion tracking trajectory x 1d It has a third-order bounded derivative.

[0053] Assumption 3: All elements in the system's unknown parameter vector θ have definite and known upper and lower bounds, that is:

[0054]

[0055] In equation (12), Ω θ The upper bound vector θ represents the range of values ​​for an uncertain parameter. max Defined as θ max =[θ 2max ,θ 3max ] T , where θ kmax The upper bound value of the corresponding element and the lower bound value vector θ are the parameters. min Defined as θ min =[θ 2min ,θ 3min ] T, where θ kmin The lower bound of the corresponding element is given by index k = 2, 3.

[0056] Assumption 4: Distractor term d i (t) is sufficiently smooth and bounded, and is differentiable of order 4-i, with all its derivatives being bounded. Furthermore... Having Lipschitz constant l i , where i = 1, 2.

[0057] Assumption 5: There exist positive integrable functions ω2(t) and ω3(t) that satisfy the following conditions:

[0058]

[0059] In equation (13), and It is a positive number.

[0060] Proceed to step 2.

[0061] Step 2: Based on the mathematical model of the hydraulic multi-way valve control system, design a robust adaptive preset performance controller based on FTDO.

[0062] Step 2-1: To solve the problem of uncertainty in hydraulic parameters in the system, a parameter adaptive law is constructed to achieve accurate estimation of uncertain parameters θ2 and θ3. To effectively suppress the lumped disturbance d2(t) in hydraulic dynamics, an FTDO is designed to achieve accurate estimation of d2(t).

[0063] Define the estimated value of θ estimation error of θ To ensure that the estimated parameter ya value determined by the parameter adaptive law is within the design range, the following discontinuous mapping function is defined.

[0064]

[0065] The adaptive law is designed in the following form:

[0066]

[0067] In equation (15), for The first derivative of Γ is the adaptive gain positive definite diagonal matrix, τ is the parameter adaptive function, and the parameter adaptive law has the following properties:

[0068]

[0069] In equation (16), This represents the range of values ​​for the estimated uncertain parameter.

[0070] definition The estimate of N3 is as follows:

[0071]

[0072] To reduce the burden on the robust controller, an FTDO is designed to effectively and quickly estimate and compensate for the lumped disturbance d2(t) in hydraulic dynamics. z3 is defined as the estimated value of x3, and z4 is the estimated value of d2(t).

[0073] The FTDO design is as follows:

[0074]

[0075] In equation (18), The first derivative of the estimated value of the state variable x3 is given by . sgn(·) denotes a sign function with respect to the variable ·. Let represent the first derivative of the estimate of the lumped perturbation d2(t). λ3 and λ4 are the desired FTDO parameters, λ3 > 0, λ4 > 0, ω 3f and ω 4f It is an intermediate variable.

[0076] The FTDO estimation error is defined as follows:

[0077] σ3=z3-x3,σ4=z4-d2(t) (19)

[0078] Combining equations (18) and (19), the derivative of the estimation error σ3 is obtained. The derivative of σ₄ Specifically, it is expressed as follows:

[0079]

[0080] In equation (20), l2 is The corresponding Lipschitz constant.

[0081] The designed FTDO estimation error has the characteristic of being stable in finite time, that is, it has a finite time constant t. f The system satisfies: when t > t f , σ3=0, σ4=0.

[0082] Step 2-2: To ensure both steady-state and transient performance of the tracking, and to ensure that the tracking error converges rapidly to a specified range within a specified time, a preset performance function F is designed. φ (t), construct the error preset boundary, construct the transformation error μ1 to replace the position tracking error e1, and ensure the convergence performance of e1 by ensuring the convergence performance of μ1.

[0083] Design the following preset performance function F φ (t):

[0084]

[0085] In equation (21), f0 and f ∞ T1 and a are both positive adjustable parameters, and satisfy 0 < f ∞ <|e1(0)|<f0, 0<T1<∞ and 1<a, e1(0) is the position tracking error e1=x1-x 1d The initial value, 'a' represents the preset convergence rate, and 'T1' represents F. φ (t) converges from f0 to f ∞ The preset maximum allowable convergence time, f0 represents the preset initial value of the performance function, f ∞ F represents the maximum allowable steady-state error, e is the natural constant, and F φ The derivative of (t) Represented as:

[0086]

[0087] The preset boundary of the position tracking error e1 is guaranteed by the following constraints:

[0088]

[0089] In equation (23), the parameter and They are represented as follows:

[0090]

[0091] To achieve preset performance control of tracking error, the error transformation variable μ1(t) and its derivative are defined.

[0092]

[0093] Steps 2-3: Integrating the concept of backstepping control, define errors e2 and e3. Based on the designed parameter adaptive law and FTDO, construct the model feedforward term. Based on the designed preset performance function, ensure the preset convergence characteristics of the position tracking error e1. Further ensure the convergence performance of each level of error by introducing linear robust feedback terms and nonlinear robust terms. Based on this, design virtual control laws α1 and α2 step by step, and design the filtered signal α of the virtual control input through command filtering. 1f and α 2f Finally, the control input u was designed to control the system.

[0094] According to the state-space equation, the position tracking error e1 = x1 - x 1d derivative for:

[0095]

[0096] To avoid the differential explosion problem in the system, the following instruction filtering function is designed for the virtual control inputs α1 and α2 required by the controller:

[0097]

[0098] In equation (27), τ i α is the adjustable filter time constant. if Indicates virtual control input α i The filtered signal, ε is the derivative of the filtered signal. i This indicates the filtering error.

[0099] The error variable e2 is defined as follows:

[0100] e2=x2-α 1f (28)

[0101] Substituting equations (26) and (28) into equation (25), the derivative of the error transformation variable is obtained. Write in the following format:

[0102]

[0103] Based on the properties of the preset performance function, if the conversion error μ1(t) converges under the action of the designed robust adaptive preset performance controller based on FTDO, then the system position tracking error e1 will also converge to the specified steady-state value. Based on this, the virtual control input α1 is designed as follows:

[0104]

[0105] In equation (30), α 1a For the model feedforward compensation term, α 1s For linear robust feedback terms, s1 is a positive adjustable parameter and k1 is a positive feedback gain.

[0106] Solving equations (11) and (28) simultaneously, the derivative of e² as follows:

[0107]

[0108] Define the error variable e3 as follows:

[0109] e3=x3-α 2f=x³ - α² - ε² (32)

[0110] In equation (32), α 2f Let α2 be the command filter signal and ε2 be the filter error. Then, equation (31) can be rewritten as follows:

[0111]

[0112] Based on this, the virtual control input α2 is designed as follows:

[0113]

[0114] In equation (34), α 2a For the model feedforward compensation term, α 2s1 The linear robust feedback term is used to stabilize the nominal model of the hydraulic system, where k2 is the positive feedback gain and α is the linear robust feedback term. 2s2 For nonlinear robust terms, k 2s Positive feedback gain For the bounded perturbation d1(t), the critical value δ1 is estimated, and |d1(t)| < δ1, and ω2(t) is a positive integrable function.

[0115] Equation (33) is written in the following form:

[0116]

[0117] In the above formula, if e3 = 0, then the disturbance d1(t) can be controlled by α. 2s2 Under the premise of effective suppression, the expected output tracking can be obtained through stability analysis. Therefore, it is necessary to design the control input u to make e3 approach 0.

[0118] According to the system state-space equation and equation (32), the derivative of error e3 It can be expressed in the following form:

[0119]

[0120] In equation (36), The estimated value of the designed adaptive function N3, and the estimation error.

[0121] The control input u is designed as follows:

[0122]

[0123] In equation (37), u a For the model feedforward compensation term, u s1 For linear robust feedback terms, k3 is the positive feedback gain, and u s2 For nonlinear robust terms, k 3sPositive feedback gain This is an estimate of the upper bound δ2 of the observation error σ4 of the bounded perturbation d2(t). δ2 satisfies |σ4|<δ2, and ω3(t) is a positive integrable function.

[0124] Combine equations (36) and (37). The derivative is reconstructed as:

[0125]

[0126] The designed nonlinear robust term achieves the estimation of δ1 and δ2 through parameter adaptation, and the smooth continuity of the nonlinear robust term is achieved by designing a continuous tanh function and a positive integrable function, which improves the practicality of the designed controller in engineering practice. When FTDO can achieve disturbance estimation accurately enough, the upper bound of the observation error is suppressed, and it has the characteristic of finite-time stability.

[0127] Based on the above assumptions, the specific adaptive law is designed as follows:

[0128]

[0129] In equation (39), Let Γ be the adaptive parameter derivative vector. θ It is a positive definite diagonal adaptive gain matrix. for The derivative, for The derivatives of γ1 and γ2 are the adaptive law gains. Define matrix Λ1 and select gains s1,k1,k2,k3,k that satisfy the conditions. 2s ,k 3s To keep it positive definite, Λ1 has the following specific form:

[0130]

[0131] Proceed to step 3.

[0132] Step 3: Apply Lyapunov stability theory to perform stability analysis on the robust adaptive preset performance controller based on FTDO, and obtain the asymptotic stability result of the system tracking error, as follows:

[0133] The Lyapunov functions V1 and V2 are constructed as follows:

[0134]

[0135] In equation (42), This represents the estimation error of the corresponding adaptive parameters. and This represents the estimation error corresponding to the upper bound of the perturbation.

[0136] Solving equations (25), (29), (30), and (41) simultaneously, the derivative of V1 is... writing:

[0137]

[0138] Time derivative of V2 Represented as:

[0139]

[0140] Substituting the error derivatives and the nonlinear robustness term, equation (44) is reconstructed as follows:

[0141]

[0142] The following inequalities are used to handle the disturbance and nonlinear robustness terms:

[0143]

[0144] In equation (46), κ, p, q, and r are all constants;

[0145] Combining equations (45) and (46), we obtain the following about The following inequalities apply:

[0146]

[0147] Further results were obtained:

[0148]

[0149] Substituting equations (39) and (40), equation (48) can be further written as:

[0150]

[0151] In equation (49), the error vector Z = [μ1, e2, e3] T W1 is a positive function, λ min (Λ1) is the smallest eigenvalue of matrix Λ1. Integrating both sides of equation (49) with respect to time, according to assumption 5, we get:

[0152]

[0153] From equation (50), we know that V2(t)∈L ∞ And W1∈L2, that is, μ1, e2, e3, and Since all are bounded, the position tracking error e1 is bounded according to the properties of the preset performance function. According to assumptions 1 and 2, the system state x is bounded. According to assumption 5, the control input u is bounded. Therefore, all closed-loop signals are bounded.

[0154] At the same time, based on the dynamics of errors μ1, e2, and e3, we can obtain Since W1 is bounded, we can conclude that W1 is uniformly continuous. Based on Barbarat's lemma, we know that W1→0 as t→∞, leading to the following conclusion:

[0155] The proposed control law can achieve asymptotic output tracking, i.e., when t→∞, e1→0, and guarantees the boundedness of all closed-loop system signals. A schematic diagram of the principle of the preset performance control method for a hydraulic multi-way valve control system based on FTDO is shown below. Figure 1 As shown.

[0156] Example

[0157] 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:

[0158] Table 1 System Physical Parameters

[0159] physical parameters numerical values physical parameters numerical values <![CDATA[A1(m 2 )]]> <![CDATA[2×10 -4 ]]> <![CDATA[P s (MPa)]]> 7 <![CDATA[A2(m 2 )]]> <![CDATA[2×10 -4 ]]> <![CDATA[P r (MPa)]]> 0 <![CDATA[V 01 (m 3 )]]> <![CDATA[1×10 -3 ]]> m(kg) 40 <![CDATA[V 02 (m 3 )]]> <![CDATA[1×10 -3 ]]> <![CDATA[f v (Pa / s)]]> 80 <![CDATA[β e (MPa)]]> <![CDATA[7×10 2 ]]> <![CDATA[f c (N)]]> 10 <![CDATA[C t (m 5 / (N·s))]]> <![CDATA[1.4×10 -13 ]]> <![CDATA[α c ]]> 900 <![CDATA[k t (m / V)]]> <![CDATA[2.39×10 -8 ]]> <![CDATA[f o (N)]]> 10

[0160] Given the desired instruction of the system as x 1d =0.4sin(0.4πt)(1-e -t )m.

[0161] The following controller is used for comparison in the simulation:

[0162] Robust Adaptive Preset Performance Controller Based on FTDO (RAPPC-FTDO): Controller gain s1 = 1, k1 = 100, k2 = 50, k3 = 25, k... 2s =1,k 3s =1; Take the adaptive gain Γ θ =diag{5×10 9 1×10 -10}, γ1=9×10 2 γ2=1×10 2 ; Determine the upper and lower bounds of the adaptive parameters θ max = [7.5×10 8 1×10 -4 ] T θ min = [6.5×10 8 ,0] T ;Take FTDO parameter λ3 = 1 × 10 3 λ4=5×10 4Take the command filter parameter τ1 = 1 × 10 -3 τ2=1×10 -3 Take a positive integrable function ω2(t) = 5000 / (1+0.01t). 2 ), ω3(t)=5000 / (1+0.01t) 2 ).

[0163] VFPID Controller: First, ignoring the nonlinear dynamics of the hydraulic multi-way valve control system, a set of controller parameters is obtained by adjusting the VFPID parameters to achieve optimal tracking performance. The final selected controller parameter is k. P =40,k I =400,k D =3,k v =3.16.

[0164] The curves showing the desired and actual system trajectory tracked by the RAPPC-FTDO controller, the comparison curves of tracking errors under the action of the RAPPC-FTDO and VFPID controllers, the adaptive parameter estimation curve under the action of the RAPPC-FTDO controller, the disturbance upper bound estimation curve under the action of the RAPPC-FTDO controller, the system state and disturbance observation curves under the action of the RAPPC-FTDO controller, and the system control input curves under the action of the RAPPC-FTDO controller are respectively as follows: Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 As shown. By Figure 4 It can be seen that the hydraulic multi-way valve control system achieved good tracking performance under the action of the RAPPC-FTDO controller, with the amplitude of its steady-state tracking error absolute value being approximately 9.98 × 10⁻⁶. -6 m, with a mean of approximately 3.88 × 10 -6 m, and can be quickly and effectively constrained by preset performance boundaries, achieving rapid convergence. Its tracking performance is far superior to VFPID control, and VFPID control cannot guarantee that the tracking error will always converge to within the preset boundaries. Figure 5 and Figure 6 It can be seen that the estimates of the uncertain parameters and disturbances gradually converge under the action of the adaptive law. Figure 7 It can be seen that FTDO's observation accuracy is relatively high. Figure 8 It can be seen that the designed controller has a smoother and more continuous control input, which is more conducive to the controller's execution in practical applications.

Claims

1. A preset performance control method for a hydraulic multi-way valve control system based on FTDO, characterized in that, Includes the following steps: Step 1: Establish the mathematical model of the hydraulic multi-way valve control system, then proceed to Step 2; Step 2: Based on the mathematical model of the hydraulic multi-way valve control system, design a robust adaptive preset performance controller based on FTDO, as follows: Step 2-1: To solve the problem of uncertainty in hydraulic parameters in the system, a parameter adaptive law is constructed to achieve accurate estimation of uncertain parameters θ2 and θ3. To effectively suppress the lumped disturbance d2(t) in hydraulic dynamics, an FTDO is designed to achieve accurate estimation of d2(t). Step 2-2: To ensure both steady-state and transient performance of the tracking, and to ensure that the tracking error converges rapidly to a specified range within a specified time, a preset performance function F is designed. φ (t), construct the error preset boundary, construct the transformation error μ1 to replace the position tracking error e1, and ensure the convergence performance of e1 by ensuring the convergence performance of μ1; Steps 2-3: Integrating the concept of backstepping control, define errors e2 and e3. Based on the designed parameter adaptive law and FTDO, construct the model feedforward term. Based on the designed preset performance function, ensure the preset convergence characteristics of the position tracking error e1. Further ensure the convergence performance of each level of error by introducing linear robust feedback terms and nonlinear robust terms. Based on this, design virtual control laws α1 and α2 step by step, and design the filtered signal α of the virtual control input through command filtering. 1f and α 2f Finally, the control input u was designed to achieve system control; Wherein, the control input u is: In equation (37), P L For load pressure, β e k is the equivalent elastic modulus of the hydraulic fluid in the two chambers of the hydraulic cylinder. t For the total gain relative to u, u a For the model feedforward compensation term, u s For robust feedback, u s1 For linear robust feedback terms, k3 is the positive feedback gain, and u s2 For nonlinear robust terms, k 3s The feedback gain is positive, f1, f2, and f3 are all intermediate variables, and x2 is a state variable. This is an estimate of the upper bound δ2 of the observation error σ4 of the bounded perturbation d2(t). δ2 satisfies |σ4|<δ2, and ω3(t) is a positive integrable function. This is an estimate of the uncertain parameter θ2. This is an estimate of the uncertain parameter θ3. For the estimated value of the disturbance d2(t), To design a filtered signal α for the virtual control input through instruction filtering. 2f The first derivative of ω3, where e3 is the error variable and ω3(t) is a positive integrable function; Proceed to step 3; Step 3: Apply Lyapunov stability theory to perform stability analysis on the robust adaptive preset performance controller based on FTDO, and obtain the result that the system tracking error is asymptotically stable.

2. The preset performance control method for a hydraulic multi-way valve control system based on FTDO according to claim 1, 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 the linear motion of large equipment driven by the hydraulic system. The load is fixedly connected to the head of the hydraulic cylinder piston rod. The hydraulic multi-way valve controls the hydraulic cylinder piston rod to make linear motion, thereby driving the load to move. Based on the dynamic characteristics of the load, hydraulic cylinder and hydraulic multi-way valve, a mathematical model of the hydraulic multi-way valve control system is established. Steps 1-2: Define the state variables required for controller design and reconstruct the mathematical model of the hydraulic multi-way valve control system into state-space equation form.

3. The preset performance control method for a hydraulic multi-way valve control system based on FTDO according to claim 2, characterized in that, In step 1-1, the hydraulic multi-way valve control system is applied to the linear motion of large equipment driven by a hydraulic system. The load is fixedly connected to the head of the hydraulic cylinder piston rod. The hydraulic multi-way valve controls the linear motion of the hydraulic cylinder piston rod, thereby driving the load motion. Based on the dynamic characteristics of the load, the hydraulic cylinder, and the hydraulic multi-way valve, a mathematical model of the hydraulic multi-way valve control system is established, as follows: According to Newton's equations of motion, the force balance equations for a hydraulic multi-way valve control system are as follows: In equation (1), m is the total weight of the hydraulic cylinder piston rod and the fixed load at the head of the system. Let F be the acceleration of the hydraulic cylinder piston rod, A1 be the effective working area of ​​the hydraulic cylinder inlet chamber, A2 be the effective working area of ​​the hydraulic cylinder outlet chamber, P1 be the pressure of the hydraulic cylinder inlet chamber, P2 be the pressure of the hydraulic cylinder outlet chamber, and F be the acceleration of the hydraulic cylinder piston rod. f The frictional force acting on the system is specifically defined as follows: Among them, f v f represents the coefficient of viscous friction. c Let α represent the modelable Coulomb friction amplitude. c Represents the coefficients of the tanh curve. f is the speed of the hydraulic cylinder piston rod. b Here, d1(t) represents the friction bias constant, d1(t) represents the unmodeled mechanical dynamic disturbance of the system, and t represents time. In a hydraulic multi-way valve control system, neglecting external leakage, the dynamic equation for the two-chamber pressure is written as follows: In equation (2), The derivative of P1, β is the derivative of P2. e The equivalent elastic modulus of the hydraulic fluid in the two chambers of the hydraulic cylinder is given by V1 = V. 01 +A1y,V 01 The initial volume of the inlet chamber is V2, and the volume of the outlet chamber of the hydraulic cylinder is V2 = V 02 +A2y,V 02 Let y be the initial volume of the oil outlet chamber, y be the displacement of the hydraulic cylinder, and C be the displacement of the hydraulic cylinder. t The internal leakage coefficient of the hydraulic rod is given by the load pressure P. L =P1-P2, Q1 represents the supply flow rate of the hydraulic cylinder inlet chamber, Q2 represents the return flow rate of the hydraulic cylinder outlet chamber, Q e1 (t) represents the modeling error caused by the complex internal leakage and pressure dynamics of the hydraulic cylinder's inlet chamber, Q. e2 (t) represents the modeling error caused by the complex internal leakage and pressure dynamics of the hydraulic cylinder's oil outlet chamber; A hydraulic multi-way valve includes a pilot valve and a main valve. Ignoring the spool dynamics of the pilot and main valves, and defining the system control input u as the voltage acting on the pilot valve spool, then u and the force F exerted by the hydraulic pressure through the pilot valve on the main valve spool are... xd Proportional relationship, F xd With the displacement x of the main valve core v A proportional relationship, that is, satisfying: In equation (3), k xd k is the gain coefficient of the output force corresponding to the pilot valve spool voltage. f The gain coefficient corresponding to the main valve spool displacement for the output force, neglecting pipeline flow loss, is used to write the main valve flow equation as follows: In equation (4), k q The main valve flow gain, relative to the total gain k of u t =k q k xd k f The intermediate variables R1 and R2 are written as follows: In equation (5), P s P is the system oil supply pressure. r Let be the system return oil pressure, and s(·) be a function of ·, written as:

4. The preset performance control method for a hydraulic multi-way valve control system based on FTDO according to claim 3, characterized in that, In steps 1-2, the state variables required for controller design are defined, and the mathematical model of the hydraulic multi-way valve control system is reconstructed into a state-space equation form, as follows: Define state variables Where, state variable x1 = y, state variable State variable x3 = A1P1 - A2P2, the superscript T indicates the transpose operation; Combining equations (1) to (6), the system state-space equations are rewritten in the following form: In equation (7), d2(t) represents the lumped disturbance caused by the complex internal leakage and pressure dynamics of the two chambers of the hydraulic cylinder, d2(t) = β e [A1Q e1 (t)V1 -1 +A2Q e2 (t)V2 -1 ], The derivative of x1, The derivative of x² The derivative of x3, the intermediate variable f1 = A1R1 / V1 + A2R2 / V2, the intermediate variable Intermediate variable f3 = A1 / V1 + A2 / V2; To improve the accuracy of the system model compensation terms, the uncertainty of hydraulic parameters is taken into account, and the uncertain parameter vector θ is defined as: θ=[θ2,θ3] T =[β e ,b e C t ] T (8) In equation (8), the uncertain parameter θ2 = β e Uncertain parameter θ3=β e C t ; According to equation (7), the parameter vector corresponding to θ is defined. as follows: In equation (9), the parameter parameter By combining equations (7) and (9), the function N3 is defined as follows: Equation (7) can then be rewritten as follows:

5. The preset performance control method for a hydraulic multi-way valve control system based on FTDO according to claim 4, characterized in that, In step 1, the following assumptions are made for the hydraulic multi-way valve control system: Assumption 1: The system supply oil pressure can remain stable, the return oil pressure is approximately 0, the system operates under normal conditions, and the pressure in both chambers is determined by the supply oil pressure P. s and return oil pressure P r The constraint is that 0 < P. r <P1<P s and 0 < P r <P2<P s , where P s and P r It is a constant; in addition, the elastic modulus of the hydraulic oil in both chambers of the hydraulic cylinder is the same. Assumption 2: The system expects the motion tracking trajectory x 1d It has a third-order bounded derivative; Assumption 3: All elements in the system's unknown parameter vector θ have definite and known upper and lower bounds, that is: In equation (12), Ω θ The upper bound vector θ represents the range of values ​​for an uncertain parameter. max Defined as θ max =[θ 2max ,θ 3max ] T , where θ kmax The upper bound value of the corresponding element and the lower bound value vector θ are the parameters. min Defined as θ min =[θ 2min ,θ 3min ] T , where θ kmin The lower bound of the corresponding element is given by index k = 2, 3; Assumption 4: Distractor term d i (t) is sufficiently smooth and bounded, and is differentiable of order 4-i, with all its derivatives being bounded. Furthermore... Having Lipschitz constant l i where i = 1, 2; Assumption 5: There exist positive integrable functions ω2(t) and ω3(t) that satisfy the following conditions: In equation (13), and It is a positive number; Proceed to step 2.

6. The preset performance control method for a hydraulic multi-way valve control system based on FTDO according to claim 5, characterized in that, In step 2-1, to address the uncertainty of hydraulic parameters in the system, a parameter adaptive law is constructed to achieve accurate estimation of the uncertain parameters θ2 and θ3. To effectively suppress the lumped disturbance d2(t) in hydraulic dynamics, an FTDO is designed to achieve accurate estimation of d2(t), as detailed below: Define the estimated value of θ estimation error of θ To ensure that the parameter estimates determined by the adaptive parameter law are within the design range, the following discontinuous mapping function is defined. The adaptive law is designed in the following form: In equation (15), for The first derivative of Γ is the adaptive gain positive definite diagonal matrix, τ is the parameter adaptive function, and the parameter adaptive law has the following properties: In equation (16), The range of values ​​to which the estimated value of the uncertain parameter belongs; definition The estimate of N3 is as follows: To reduce the burden on the robust controller, an FTDO is designed to effectively and quickly estimate and compensate for the lumped disturbance d2(t) in hydraulic dynamics. z3 is defined as the estimated value of x3, and z4 is the estimated value of d2(t). The FTDO design is as follows: In equation (18), The first derivative of the estimated value of the state variable x3 is given by . sgn(·) denotes a sign function with respect to the variable ·. Let represent the first derivative of the estimate of the lumped perturbation d2(t). λ3 and λ4 are the desired FTDO parameters, λ3 > 0, λ4 > 0, ω 3f and ω 4f As an intermediate variable; The FTDO estimation error is defined as follows: σ3=z3-x3,σ4=z4-d2(t) (19) Combining equations (18) and (19), the derivative of the estimation error σ3 is obtained. The derivative of σ₄ Specifically, it is expressed as follows: In equation (20), l2 is The corresponding Lipschitz constant; The designed FTDO estimation error has the characteristic of being stable in finite time, that is, it has a finite time constant t. f The system satisfies: when t > t f , σ3=0, σ4=0.

7. The preset performance control method for a hydraulic multi-way valve control system based on FTDO according to claim 6, characterized in that, In step 2-2, to ensure both steady-state and transient tracking performance and to achieve rapid convergence of the tracking error to a specified range within a given time, a preset performance function F is designed. φ (t), construct the error preset boundary, construct the transformation error μ1 to replace the position tracking error e1, and ensure the convergence performance of e1 by ensuring the convergence performance of μ1, as follows: Design the following preset performance function F φ (t): In equation (21), f0 and f ∞ T1 and a are both positive adjustable parameters, and satisfy 0 < f ∞ <|e1(0)|<f0, 0<T1<∞ and 1<a, e1(0) is the position tracking error e1=x1-x 1d The initial value, 'a' represents the preset convergence rate, and 'T1' represents F. φ (t) converges from f0 to f ∞ The preset maximum allowable convergence time, f0 represents the preset initial value of the performance function, f ∞ Represents the maximum allowable steady-state error, e is the natural constant, and x 1d The desired motion tracking trajectory for the system; F φ The derivative of (t) Represented as: The preset boundary of the position tracking error e1 is guaranteed by the following constraints: In equation (23), the parameter and They are represented as follows: To achieve preset performance control of tracking error, the error transformation variable μ1(t) and its derivative are defined.

8. The preset performance control method for a hydraulic multi-way valve control system based on FTDO according to claim 7, characterized in that, In steps 2-3, the concept of backstepping control is integrated, and errors e2 and e3 are defined. Based on the designed parameter adaptive law and FTDO, the model feedforward term is constructed. Based on the designed preset performance function, the preset convergence characteristics of the position tracking error e1 are guaranteed. Furthermore, the convergence performance of each level of error is further guaranteed by introducing linear robust feedback terms and nonlinear robust terms. Based on this, virtual control laws α1 and α2 are designed step by step, and the filtered signal α of the virtual control input is designed through command filtering. 1f and α 2f Finally, the control input u is designed to control the system, as follows: According to the state-space equation, the position tracking error e1 = x1 - x 1d derivative for: To avoid the differential explosion problem in the system, the following instruction filtering function is designed for the virtual control inputs α1 and α2 required by the controller: In equation (27), τ i α is the adjustable filter time constant. if Indicates virtual control input α i The filtered signal, ε is the derivative of the filtered signal. i Indicates the filtering error; The error variable e2 is defined as follows: e2=x2-a 1f (28) Substituting equations (26) and (28) into equation (25), the derivative of the error transformation variable is obtained. Write in the following format: Based on the properties of the preset performance function, if the conversion error μ1(t) converges under the action of the designed robust adaptive preset performance controller based on FTDO, then the system position tracking error e1 will also converge to the specified steady-state value. Based on this, the virtual control input α1 is designed as follows: In equation (30), α 1a For the model feedforward compensation term, α 1s For linear robust feedback terms, s1 is a positive adjustable parameter and k1 is a positive feedback gain; Solving equations (11) and (28) simultaneously, the derivative of e² as follows: Define the error variable e3 as follows: e3=x3-a 2f =x3-α2-ε2 (32) In equation (32), α 2f Let α2 be the command filter signal and ε2 be the filter error. Then, equation (31) can be rewritten as follows: Based on this, the virtual control input α2 is designed as follows: In equation (34), α 2a For the model feedforward compensation term, α 2s1 The linear robust feedback term is used to stabilize the nominal model of the hydraulic system, where k2 is the positive feedback gain and α is the linear robust feedback term. 2s2 For nonlinear robust terms, k 2s Positive feedback gain To estimate the critical value δ1 of the bounded perturbation d1(t), we have |d1(t)|<δ1, and ω2(t) is a positive integrable function. Then equation (33) can be written in the following form: In the above formula, if e3 = 0, then the disturbance d1(t) can be controlled by α. 2s2 Under the premise of effective suppression, the expected output tracking can be obtained through stability analysis. Therefore, it is necessary to design the control input u to make e3 approach 0. According to the system state-space equation and equation (32), the derivative of error e3 It can be expressed in the following form: In equation (36), The estimated value of the designed adaptive function N3, and the estimation error. The control input u is designed as follows: In equation (37), u a For the model feedforward compensation term, u s1 For linear robust feedback terms, k3 is the positive feedback gain, and u s2 For nonlinear robust terms, k 3s Positive feedback gain This is an estimate of the upper bound δ2 of the observation error σ4 of the bounded perturbation d2(t). δ2 satisfies |σ4|<δ2, ω3(t) is a positive integrable function, combining equations (36) and (37), The derivative is reconstructed as: Based on the above assumptions, the specific adaptive law is designed as follows: In equation (39), Let Γ be the adaptive parameter derivative vector. θ It is a positive definite diagonal adaptive gain matrix. for The derivative, for The derivatives of γ1 and γ2 are the adaptive law gains. Define matrix Λ1 and select gains s1, k1, k2, k3, k that satisfy the conditions. 2s k 3s To keep it positive definite, Λ1 has the following specific form: Proceed to step 3.

9. The preset performance control method for a hydraulic multi-way valve control system based on FTDO according to claim 8, characterized in that, In step 3, the stability analysis of the robust adaptive preset performance controller based on FTDO is performed using Lyapunov stability theory, and the asymptotic stability of the system tracking error is obtained, as follows: The Lyapunov functions V1 and V2 are constructed as follows: V1=1 / 2ln[1 / (1-μ1 2 )] (41) in, Let the estimation error of θ be denoted as . The stability of a robust adaptive preset performance controller based on FTDO is analyzed using Lyapunov stability theory, and the asymptotic stability of the system tracking error is obtained.

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