Hydraulic multi-way valve control system preset performance control method based on FTDO

Abstract

The invention discloses an FTDO-based preset performance control method for a hydraulic multi-way valve control system, which is characterized in that a nonlinear position controller combining instruction filtering, parameter self-adaption and interference observation and suppression is designed on the basis of a built specified time preset performance function and by fusing the thought of backstepping control. Aiming at the position control problem of the hydraulic multi-way valve control system, preset time convergence of tracking errors is realized by designing a preset performance function, transient and steady-state performance of the system is ensured, and a robust adaptive controller is constructed based on FTDO to effectively process uncertainty of various models in the system, so that the accuracy of the position control of the hydraulic multi-way valve control system is improved. And the high-precision asymptotic tracking performance of the system is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of electro-hydraulic servo control, and in particular to a method for controlling a preset performance of a hydraulic multi-way valve control system based on a finite time disturbance observer (FTDO). Background Art

[0002] Hydraulic multi-way valves are widely used in a variety of engineering machinery hydraulic systems due to their fast response speed, high integration and high reliability. The hydraulic multi-way valve control system can be simply described as an electromechanical hydraulic system consisting of a control system, a power source, a multi-way valve, an actuator and a supporting hydraulic circuit. It is a typical strong nonlinear system. The system contains uncertainties in parameters such as system dynamics, friction and liquid elastic modulus, as well as modeling errors that are difficult to accurately characterize, complex leakage characteristics of hydraulic components, unmodeled external interference and nonlinear friction, which seriously restrict the control performance of the system. With the increasing degree of industrialization, the application of hydraulic multi-way valve control systems in electro-hydraulic servo systems is becoming more and more extensive. In order to meet the complex and diverse tasks and high-performance index requirements, higher requirements are put forward for its performance indicators such as position transient and steady-state tracking accuracy. Although traditional model-free linear control such as PID control has a wide range of applications, it is difficult to meet the requirements of high-precision tracking performance. Therefore, it is very meaningful to study advanced nonlinear control based on system dynamic models.

[0003] There have been many research results 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 show good robustness and can provide effective solutions for high-precision trajectory tracking control. However, due to the large number of uncertainties in the model, its 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 target the high nonlinearity in the system and handle most model uncertainties and uncertain nonlinearities at the same time. However, the uncertain disturbances in the system may lead to potential high-gain feedback design, and the increase in system order can easily cause the controller designed based on the backstepping method to produce differential explosion problems. Adaptive control based on error sign integral robustness can reduce the feedback burden of the controller and obtain asymptotic tracking performance. However, this controller cannot handle unmatched disturbances and cannot completely solve the control problems in hydraulic systems. Active disturbance rejection control can realize model compensation of matched and unmatched disturbances of high-order systems and improve the robustness of the system, but it is difficult to achieve asymptotic tracking performance in a limited time. In addition, most of the above nonlinear controllers pay little attention to the tracking error convergence speed performance, making it difficult to obtain the preset transient and steady-state performance, and still have great limitations in practical applications. Summary of the invention

[0004] The purpose of the present invention is to provide a hydraulic multi-way valve control system position control method with interference observation and suppression capabilities, error transient and steady-state performance preset capabilities, and asymptotic tracking performance. The method can not only ensure the transient and steady-state performance of the tracking error by designing a preset performance function, but also construct a robust adaptive controller based on FTDO to effectively handle various model uncertainties in the system, thereby realizing high-precision asymptotic tracking control of the system.

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

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

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

[0008] Step 3: Use Lyapunov stability theory to analyze the stability of the FTDO-based robust adaptive preset performance controller and obtain the result that the system tracking error is asymptotically stable.

[0009] Compared with the prior art, the present invention has the following significant advantages: (1) by combining the model feedforward constructed 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, precise control of the transient performance of the system is further achieved within the specified time; (3) by introducing the command filter function to avoid the derivation of the virtual control input, the differential explosion problem existing in the traditional backstepping control is solved, and the practicality of the controller is improved. The simulation results verify its effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0012] Figure 3 It is a curve diagram of the expected trajectory and actual trajectory of the system to be tracked by the robust adaptive preset performance controller based on FTDO (RAPPC-FTDO) designed by the present invention.

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

[0014] Figure 5 It is a graph of adaptive parameter estimation under the action of the RAPPC-FTDO controller designed by the present invention.

[0015] Figure 6 It is a curve diagram of the upper limit estimation of disturbance under the action of the RAPPC-FTDO controller designed by the present invention.

[0016] Figure 7 It is a system state and interference observation curve diagram under the action of the RAPPC-FTDO controller designed by the present invention.

[0017] Figure 8 It is a system control input curve diagram under the action of the RAPPC-FTDO controller designed by the present invention. DETAILED DESCRIPTION

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

[0019] Combination Figure 1 and Figure 2 The method for controlling the preset performance of the hydraulic multi-way valve control system based on FTDO of the present invention comprises 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, wherein the load is fixedly connected to the head of the hydraulic cylinder piston rod, and the hydraulic multi-way valve controls the hydraulic cylinder piston rod to make linear motion, thereby driving the load to move, and a mathematical model of the hydraulic multi-way valve control system is established according to the dynamic characteristics of the load, the hydraulic cylinder and the hydraulic multi-way valve;

[0022] According to Newton's dynamic equation, the force balance equation of the hydraulic multi-way valve control system is:

[0023]

[0024] In formula (1), m is the total weight of the system hydraulic cylinder piston rod and the head fixed load, is the hydraulic cylinder piston rod acceleration, A 1 A is the effective area of ​​the hydraulic cylinder oil inlet cavity, 2 P is the effective area of ​​the hydraulic cylinder oil outlet cavity, 1 is the oil inlet pressure of the hydraulic cylinder, P 2 is the oil outlet pressure of the hydraulic cylinder, F f is the friction force on the system, which is defined as Among them, f v represents the viscous friction coefficient, f crepresents the modelable Coulomb friction amplitude, α c represents the tanh curve coefficient, is the speed of the hydraulic cylinder piston rod, f b is the friction bias constant, d 1 (t) is the unmodeled disturbance of the system mechanical dynamics, and t represents time.

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

[0026]

[0027] In formula (2), P 1 The derivative of P 2 The derivative of e is the equivalent elastic modulus of the oil in the two chambers of the hydraulic cylinder, and the volume of the oil inlet chamber of the hydraulic cylinder V 1 =V 01 +A 1 y,V 01 is the initial volume of the oil inlet chamber, and the volume of the oil outlet chamber of the hydraulic cylinder is V 2 =V 02 +A 2 y,V 02 is the initial volume of the oil outlet chamber, y is the displacement of the hydraulic cylinder, C t is the internal leakage coefficient of the hydraulic rod, the load pressure P L =P 1 -P 2 , Q 1 Indicates the flow rate of the hydraulic cylinder oil inlet chamber, Q 2 Indicates the return flow of the hydraulic cylinder oil chamber, Q e1 (t) represents the modeling error caused by the complex internal leakage and pressure dynamics of the hydraulic cylinder oil inlet chamber, Q e2 (t) represents the modeling error caused by the complex internal leakage and pressure dynamics of the hydraulic cylinder oil outlet chamber.

[0028] The hydraulic multi-way valve includes a pilot valve and a main valve. Ignoring the valve core dynamics of the pilot valve and the main valve, the system control input u is defined as the voltage acting on the pilot valve core. Then u and the force F applied to the main valve core by the oil pressure of the pilot valve are xd Proportional relationship, F xd Displacement of main valve core x v Proportional relationship, that is, satisfying:

[0029]

[0030] In formula (3), k xd k is the gain coefficient of the pilot valve core voltage corresponding to the output force,f is the gain coefficient of the output force corresponding to the displacement of the main valve core, ignoring the pipeline flow loss, the main valve flow equation is written as:

[0031]

[0032] In formula (4), k q is the main valve flow gain, the total gain k relative to u t =k q k xd k f , the intermediate variable R 1 and R 2 Write separately:

[0033]

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

[0035]

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

[0037] Defining state variables Among them, the state variable x 1 =y, state variable State variable x 3 =A 1 P 1 -A 2 P, superscript T indicates transpose operation.

[0038] By combining equations (1) to (6), the system state space equation can be rewritten as follows:

[0039]

[0040] In formula (7), d 2 (t) represents the lumped disturbance caused by the complex internal leakage and pressure dynamics of the two chambers of the hydraulic cylinder, specifically: For x 1 The derivative of For x 2 The derivative of For x 3 The derivative of the intermediate variable f 1 =A 1 R 1 / V 1 +A 2R 2 / V 2 , intermediate variable Intermediate variable f 3 =A 1 / V 1 +A 2 / V 2 .

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

[0042] θ=[θ 2 ,θ 3 ] T =[β e ,β e C t ] T (8)

[0043] In formula (8), the uncertain parameter θ 2 =β e , the uncertain parameter θ 3 =β e C t , according to formula (7), define the parameter vector corresponding to θ as follows:

[0044]

[0045] In formula (9), the parameters parameter

[0046] Combining equations (7) and (9), we define function N 3 , specifically:

[0047]

[0048] Then formula (7) can be rewritten as follows:

[0049]

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

[0051] Assumption 1: The system oil supply pressure can be kept stable, the return oil pressure is approximately 0, the system works under normal working conditions, and the pressure between the two chambers is determined by the oil supply pressure P s and return oil pressure P r Limit, that is, satisfy 0<P r <P 1 <P s and 0<P r <P 2 <P s, where P s and P r is a constant. In addition, the elastic modulus of the hydraulic oil in the two chambers of the hydraulic cylinder is the same.

[0052] Assumption 2: The system expects the motion tracking trajectory x 1d There are third-order bounded derivatives.

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

[0054]

[0055] In formula (12), Ω θ Indicates the range of values ​​of uncertain parameters, and the upper limit vector θ of the parameters max Defined as θ max =[θ 2max ,θ 3max ] T , where θ kmax is the upper bound of the corresponding element, and the parameter lower bound vector θ min Defined as θ min =[θ 2min ,θ 3min ] T , where θ kmin is the lower bound of the corresponding element, subscript k=2,3.

[0056] Assumption 4: Disturbance d i (t) is sufficiently smooth and bounded, and is 4-i order differentiable, and its derivatives are bounded. In addition, With Lipschitz constant l i , where i=1,2.

[0057] Assumption 5: There exists a positive integrable function ω 2 (t) and ω 3 (t) The following conditions are met:

[0058]

[0059] In formula (13), and Is a normal number.

[0060] Go 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 hydraulic parameter uncertainty in the system, a parameter adaptive law is constructed to achieve the uncertainty of the parameter θ 2 and θ3 The accurate estimation of d is necessary to effectively suppress the lumped disturbance d in hydraulic dynamics. 2 (t), design FTDO to achieve d 2 (t) accurate estimate;

[0063] Define an estimate of θ The estimated error of θ In order to ensure that the parameter estimation 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 as follows:

[0066]

[0067] In formula (15), for The first-order 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 formula (16), is the range of values ​​to which the uncertain parameter estimate belongs.

[0070] definition N 3 The estimates are as follows:

[0071]

[0072] In order to reduce the burden of the robust controller, the lumped disturbance d in the hydraulic dynamics is 2 (t) Design FTDO to effectively and quickly estimate interference and compensate for it. Define z 3 For x 3 The estimated value of z 4 is d 2 (t) is an estimated value;

[0073] The FTDO design is as follows:

[0074]

[0075] In formula (18), Represents the state variable x 3 The first derivative of the estimate of , represents a symbolic function with respect to the variable , represents the lumped disturbance d 2The first derivative of the estimate of (t), λ 3 and λ 4 is the FTDO parameter to be designed, λ 3 >0,λ 4 >0,ω 3f and ω 4f is an intermediate variable.

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

[0077] σ 3 =z 3 -x 3 , σ 4 =z 4 -d 2 (t) (19)

[0078] Combining equations (18) and (19), we can get the estimated error σ 3 The derivative of and σ 4 The derivative of Specifically expressed as:

[0079]

[0080] In formula (20), l 2 for The corresponding Lipschitz constant.

[0081] The designed FTDO estimation error has the characteristic of finite time stability, that is, there is a finite time constant t f So that the system satisfies: when t>t f , σ 3 =0,σ 4 =0.

[0082] Step 2-2: To ensure the steady-state performance and transient performance of the tracking, and to achieve rapid convergence of the tracking error to the specified range within the specified time, design a preset performance function F φ (t), construct the error preset boundary, and construct the transformation error μ 1 To replace the position tracking error e 1 , by ensuring μ 1 The convergence performance of e 1 Convergence performance.

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

[0084]

[0085] In formula (21), f 0 、f∞ , T 1 and a are both positive adjustable parameters and satisfy 0<f ∞ <|e 1 (0)|<f 0 , 0<T 1 <∞ and 1<a,e 1 (0) is the position tracking error e 1 =x 1 -x 1d The initial value of a represents the preset convergence speed, T 1 Represents F φ (t) from f 0 Converges to f ∞ The preset maximum allowed convergence time, f 0 Represents the initial value of the preset performance function, f ∞ represents the maximum allowable steady-state error, e is a natural constant, F φ The derivative of (t) It is expressed as:

[0086]

[0087] Position tracking error e 1 The preset boundaries of are guaranteed by the following constraints:

[0088]

[0089] In formula (23), the parameters and Respectively expressed as:

[0090]

[0091] In order to achieve the preset performance control of the tracking error, the error conversion variable μ is defined 1 (t) and its derivative

[0092]

[0093] Step 2-3: Integrate the idea of ​​backstepping control and define the error e 2 and e 3 Based on the designed parameter adaptation law and FTDO model feedforward term, the position tracking error e is guaranteed based on the designed preset performance function. 1 The preset convergence characteristics of the control law α are designed step by step based on the linear robust feedback term and the nonlinear robust term. 1 and α 2 , and design the virtual control input filter signal α through command filtering 1f and α2f , and finally design the control input u to achieve control of the system.

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

[0095]

[0096] In order to avoid the differential explosion problem in the system, the virtual control input α required by the controller is designed. 1 and α 2 , design the following instruction filtering function:

[0097]

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

[0099] Define the error variable e 2 as follows:

[0100] e 2 =x 2 -α 1f (28)

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

[0102]

[0103] According to the properties of the preset performance function, if the conversion error μ 1 (t) converges under the action of the designed FTDO-based robust adaptive preset performance controller, then the system position tracking error e 1 It will also converge to the specified steady-state value. Based on this, the virtual control input α is designed. 1 for:

[0104]

[0105] In formula (30), α 1a is the model feedforward compensation term, α 1s is the linear robust feedback term, s 1 is a positive adjustable parameter, k 1is the positive feedback gain.

[0106] Combining equation (11) and equation (28), e 2 The derivative of as follows:

[0107]

[0108] Define the error variable e 3 , specifically:

[0109] e 3 =x 3 -α 2f =x 3 -α 2 -ε 2 (32)

[0110] In formula (32), α 2f is α 2 The command filter signal, ε 2 is the filtering error, then equation (31) can be rewritten as follows:

[0111]

[0112] Based on this, the virtual control input α is designed 2 for:

[0113]

[0114] In formula (34), α 2a is the model feedforward compensation term, α 2s1 is the linear robust feedback term used to stabilize the nominal model of the hydraulic system, k 2 is the positive feedback gain, α 2s2 is the nonlinear robust term, k 2s is the positive feedback gain, is a bounded perturbation d 1 The threshold value δ of (t) 1 The estimate is |d 1 (t)|<δ 1 ,ω 2 (t) is a positive integrable function.

[0115] Then formula (33) can be written as follows:

[0116]

[0117] In the above formula, if e 3 = 0, then in the disturbance d 1 (t) can be 2s2Under 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 so that e 3 Approaching 0.

[0118] According to the system state space equation and equation (32), the error e 3 The derivative of It is expressed as follows:

[0119]

[0120] In formula (36), The designed adaptive function N 3 The estimated value, estimated error

[0121] The design control input u is:

[0122]

[0123] In formula (37), u a is the model feedforward compensation term, u s1 is the linear robust feedback term, k 3 is the positive feedback gain, u s2 is the nonlinear robust term, k 3s is the positive feedback gain, is a bounded perturbation d 2 The observation error σ of (t) 4 The upper bound of δ 2 The estimate, δ 2 Satisfy |σ 4 |<δ 2 ,ω 3 (t) is a positive integrable function.

[0124] Combining equation (36) and equation (37), The derivative of is reconstructed as:

[0125]

[0126] The designed nonlinear robust term realizes the control of δ by parameter adaptation. 1 With δ 2 The estimation of the disturbance is carried out accurately, and the smooth continuity of the nonlinear robust term is achieved through the design of continuous tanh function and positive integrable function, which improves the practicability of the designed controller in engineering practice. When the FTDO can realize the 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 formula (39), is the adaptive parameter derivative vector, Γ θ is a positive definite diagonal adaptive gain matrix, for The derivative of for The derivative of γ 1 and γ 2 is the adaptive law gain, and the matrix Λ is defined 1 , and select the gain s that satisfies the condition 1 ,k 1 ,k 2 ,k 3 ,k 2s ,k 3s To keep it positive, 1 The specific form is as follows:

[0130]

[0131] Go to step 3.

[0132] Step 3: Use Lyapunov stability theory to analyze the stability of the FTDO-based robust adaptive preset performance controller and obtain the result that the system tracking error is asymptotically stable, as follows:

[0133] Construct Lyapunov function V 1 and V 2 They are as follows:

[0134]

[0135]

[0136] In formula (42), is the estimation error of the corresponding adaptive parameters, and is the estimation error of the corresponding perturbation upper bound.

[0137] Combining equations (25), (29), (30) and (41), V 1 The derivative of writing:

[0138]

[0139] V 2 The time derivative of It is expressed as:

[0140]

[0141] Substituting the error derivatives and nonlinear robust terms, equation (44) is reconstructed as:

[0142]

[0143] The disturbance and nonlinear robust terms are handled using the following inequalities:

[0144]

[0145] In formula (46), κ, p, q, and r are all constants;

[0146] Combining equation (45) and equation (46), we can get The following inequality:

[0147]

[0148] Further we get:

[0149]

[0150] Substituting into equation (39) and equation (40), equation (48) can be further written as:

[0151]

[0152] In formula (49), the error vector Z = [μ 1 ,e 2 ,e 3 ] T , W 1 is a positive function, λ min (Λ 1 ) is the matrix Λ 1 The minimum eigenvalue of , integrating both sides of equation (49) with respect to time, according to assumption 5, we get:

[0153]

[0154] From formula (50), we know that V 2 (t)∈L ∞ And W 1 ∈L 2 , that is, μ 1 、e 2 、e 3 , and are all bounded, then the position tracking error e can be obtained from the properties of the preset performance function: 1 Bounded. According to Assumptions 1 and 2, we know that the system state x is bounded. According to Assumption 5, we know that the control input u is bounded. Therefore, all closed-loop signals are bounded.

[0155] At the same time, according to the error μ 1 、e 2 、e 3 Dynamically available , so we know that W 1 Based on Barbarat's lemma, we know that when t→∞, W 1 →0, we can get the following conclusion:

[0156] The proposed control law can achieve asymptotic output tracking, that is, when t→∞, e 1 →0, and ensures the boundedness of all closed-loop system signals. The schematic diagram of the preset performance control method of the hydraulic multi-way valve control system based on FTDO is shown in Figure 1 shown.

[0157] Example

[0158] In order 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:

[0159] Table 1 System physical parameters

[0160] Physical parameters Numeric Physical parameters Numeric <![CDATA[A 1 (m 2 )]]> <![CDATA[2×10 -4 ]]> <![CDATA[P s (MPa)]]> 7 <![CDATA[A 2 (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

[0161] Given a system with the expected instruction x 1d =0.4sin(0.4πt)(1-e -t )m.

[0162] The following controllers are used for comparison in the simulation:

[0163] Robust Adaptive Preset Performance Controller Based on FTDO (RAPPC-FTDO): Take the controller gain s 1 =1, k 1 =100, k 2 =50, k 3 =25, k 2s =1, k 3s =1; take adaptive gain Γ θ =diag{5×10 9 ,1×10 -10}, γ 1 =9×10 2 , γ 2 =1×10 2 ; Take 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 ,λ 4 =5×10 4 , fetch the instruction filter parameter τ 1 =1×10 -3 , τ 2 =1×10 -3 ; Take the positive integrable function ω 2 (t) = 5000 / (1 + 0.01t 2 ),ω 3 (t) = 5000 / (1 + 0.01t 2 ).

[0164] 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 enable the system to achieve the best tracking performance. The final selected controller parameters are k P =40, k I =400, k D =3, k v =3.16.

[0165] The expected trajectory and actual trajectory curve of the system to be tracked by the RAPPC-FTDO controller, the tracking error comparison curve under the action of the RAPPC-FTDO controller and the VFPID controller, 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 curve under the action of the RAPPC-FTDO controller, and the system control input curve under the action of the RAPPC-FTDO controller are shown as follows: Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 As shown. Figure 4 It can be seen that the hydraulic multi-way valve control system has achieved good tracking performance under the action of the RAPPC-FTDO controller, and the amplitude of the absolute value of its steady-state tracking error is about 9.98×10 -6 m, with an average value of approximately 3.88×10 -6 m, and can be quickly and effectively constrained by the preset performance boundary to achieve rapid convergence. Its tracking performance is much better than that of VFPID control, and VFPID control cannot guarantee that the tracking error will always converge to within the preset boundary. Figure 5 and Figure 6 It can be seen that the estimated values ​​of uncertain parameters and disturbances gradually converge under the action of the adaptive law. Figure 7 It can be seen that the observation accuracy of FTDO is relatively high. Figure 8It can be seen that the control input of the designed controller is relatively smooth and continuous, which is more conducive to the execution of the controller in practical applications.

Claims

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

2. The method for controlling the preset performance of 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, wherein the load is fixedly connected to the head of the hydraulic cylinder piston rod, and the hydraulic multi-way valve controls the hydraulic cylinder piston rod to make linear motion, thereby driving the load to move, and a mathematical model of the hydraulic multi-way valve control system is established according to the dynamic characteristics of the load, the hydraulic cylinder and the hydraulic multi-way valve; Step 1-2: define the state variables required for controller design and reconstruct the mathematical model of the hydraulic multi-way valve control system into the form of state space equations.

3. The method for controlling the preset performance of 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 the hydraulic system, wherein the load is fixedly connected to the head of the hydraulic cylinder piston rod, and the hydraulic multi-way valve controls the hydraulic cylinder piston rod to perform linear motion, thereby driving the load to move. According to 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 dynamic equation, the force balance equation of the hydraulic multi-way valve control system is: In formula (1), m is the total weight of the system hydraulic cylinder piston rod and the head fixed load, is the acceleration of the hydraulic cylinder piston rod, A1 is the effective area of ​​the hydraulic cylinder oil inlet chamber, A2 is the effective area of ​​the hydraulic cylinder oil outlet chamber, P1 is the hydraulic cylinder oil inlet chamber pressure, P2 is the hydraulic cylinder oil outlet chamber pressure, F f is the friction force on the system, which is defined as Among them, f v represents the viscous friction coefficient, f c represents the modelable Coulomb friction amplitude, α c represents the tanh curve coefficient, is the speed of the hydraulic cylinder piston rod, f b is the friction bias constant, d1(t) is the unmodeled disturbance of the system mechanical dynamics, and t represents time; In the hydraulic multi-way valve control system, ignoring external leakage, the dynamic equation of the two-chamber pressure is written as: In formula (2), is the derivative of P1, is the derivative of P2, β e is the equivalent elastic modulus of the oil in the two chambers of the hydraulic cylinder, and the volume of the hydraulic cylinder oil inlet chamber V1=V 01 +A1y,V 01 is the initial volume of the oil inlet chamber, and the volume of the oil outlet chamber of the hydraulic cylinder V2 = V 02 +A2y,V 02 is the initial volume of the oil outlet chamber, y is the displacement of the hydraulic cylinder, C t is the internal leakage coefficient of the hydraulic rod, the load pressure P L =P1-P2, Q1 represents the supply flow of the hydraulic cylinder oil inlet chamber, Q2 represents the return flow of the hydraulic cylinder oil outlet chamber, Q e1 (t) represents the modeling error caused by the complex internal leakage and pressure dynamics of the hydraulic cylinder oil inlet chamber, Q e2 (t) represents the modeling error caused by the complex internal leakage and pressure dynamics of the hydraulic cylinder oil outlet cavity; The hydraulic multi-way valve includes a pilot valve and a main valve. Ignoring the valve core dynamics of the pilot valve and the main valve, the system control input u is defined as the voltage acting on the pilot valve core. Then u and the force F applied to the main valve core by the oil pressure of the pilot valve are xd Proportional relationship, F xd With the main valve core displacement x v Proportional relationship, that is, satisfying: In formula (3), k xd k is the gain coefficient of the pilot valve core voltage corresponding to the output force, f is the gain coefficient of the output force corresponding to the displacement of the main valve core, ignoring the pipeline flow loss, the main valve flow equation is written as: In formula (4), k q is the main valve flow gain, the total gain k relative to u t =k q k xd k f , the intermediate variables R1 and R2 are written as: In formula (5), P s is the system oil supply pressure, P r is the system return oil pressure, s(·) is a function of ·, written as:

4. The method for controlling the preset performance of a hydraulic multi-way valve control system based on FTDO according to claim 3, characterized in that: In step 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 the form of state space equations, as follows: Defining state variables Among them, the state variable x1 = y, the state variable State variable x3 = A1P1-A2P, superscript T indicates transposition operation; By combining equations (1) to (6), the system state space equation can be rewritten as follows: In formula (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 ], is the derivative of x1, is the derivative of x2, is the derivative of x3, the intermediate variable f1=A1R1 / V1+A2R2 / V2, the intermediate variable Intermediate variable f3 = A1 / V1 + A2 / V2; In order to improve the accuracy of the compensation term of the system model, the uncertainty of the 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 formula (8), the uncertainty parameter θ2 = β e , the uncertain parameter θ3 = β e C t ; According to formula (7), the parameter vector corresponding to θ is defined as as follows: In formula (9), the parameters parameter By combining equations (7) and (9), we define function N3, which is: Then formula (7) can be rewritten as follows:

5. The method for controlling the preset performance of 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 oil supply pressure can be kept stable, the return oil pressure is approximately 0, the system works under normal working conditions, and the pressure between the two chambers is determined by the oil supply pressure P s and return oil pressure P r Limit, that is, satisfy 0<P r <P1<P s and 0<P r <P2<P s , where P s and P r is a constant. In addition, the elastic modulus of the hydraulic oil in the two chambers of the hydraulic cylinder is the same; Assumption 2: The system expects the motion tracking trajectory x 1d There are third-order bounded derivatives; Assumption 3: All elements in the unknown parameter vector θ of the system have clear and known upper and lower bounds, that is: In formula (12), Ω θ Indicates the range of values ​​of uncertain parameters, and the upper limit vector θ of the parameters max Defined as θ max =[θ 2max ,θ 3max ] T , where θ kmax is the upper bound of the corresponding element, and the parameter lower bound vector θ min Defined as θ min =[θ 2min ,θ 3min ] T , where θ kmin is the lower bound of the corresponding element, subscript k = 2, 3; Assumption 4: Disturbance d i (t) is sufficiently smooth and bounded, and is 4-i order differentiable, and its derivatives are bounded. In addition, With Lipschitz constant l i , where i = 1, 2; Assumption 5: There exist positive integrable functions ω2(t) and ω3(t) satisfying the following conditions: In formula (13), and is a positive constant; Go to step 2.

6. The method for controlling the preset performance of a hydraulic multi-way valve control system based on FTDO according to claim 5, characterized in that: In step 2, based on the mathematical model of the hydraulic multi-way valve control system, a robust adaptive preset performance controller based on FTDO is designed as follows: Step 2-1: To solve the uncertainty problem of 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, FTDO is designed to achieve accurate estimation of d2(t). Step 2-2: To ensure the steady-state performance and transient performance of the tracking, and to achieve rapid convergence of the tracking error to the specified range within the specified time, design a preset performance function F 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; Step 2-3, integrate the idea of ​​backstepping control, define errors e2 and e3, build model feedforward items based on the designed parameter adaptive law and FTDO, ensure the preset convergence characteristics of position tracking error e1 based on the designed preset performance function, and further ensure the convergence performance of errors at all levels by introducing linear robust feedback items and nonlinear robust items. Based on this, virtual control laws α1 and α2 are designed step by step, and the filter signal α of virtual control input is designed through command filtering. 1f and α 2f , and finally design the control input u to achieve control of the system.

7. The method for controlling the preset performance of a hydraulic multi-way valve control system based on FTDO according to claim 6, characterized in that: In step 2-1, in order to solve the uncertainty problem of hydraulic parameters in the system, a parameter adaptive law is constructed to achieve accurate estimation of uncertain parameters θ2 and θ3. In order to effectively suppress the lumped disturbance d2(t) in hydraulic dynamics, FTDO is designed to achieve accurate estimation of d2(t), as follows: Define an estimate of θ The estimated error of θ In order to ensure that the estimated values ​​of the parameters determined by the parameter adaptation law are within the design range, the following discontinuous mapping function is defined: The adaptive law is designed as follows: In formula (15), for The first-order 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 formula (16), is the range of values ​​to which the uncertain parameter estimate belongs; definition It represents the estimate of N3, specifically: In order to reduce the burden of the robust controller, the FTDO is designed to effectively and quickly estimate the disturbance and compensate for the lumped disturbance d2(t) in the hydraulic dynamics. z3 is defined as the estimated value of x3, and z4 is defined as the estimated value of d2(t). The FTDO design is as follows: In formula (18), represents the first-order derivative of the estimated value of the state variable x3, sgn(·) represents the symbolic function of the variable ·, represents the first-order derivative of the estimate of the lumped disturbance d2(t), λ3 and λ4 are the FTDO parameters required for design, λ3>0, λ4>0, ω 3f and ω 4f is an intermediate variable; The FTDO estimation error is defined as follows: σ3=z3-x3, σ4=z4-d2(t) (19) Combining equations (18) and (19), we can estimate the derivative of the error σ3 and the derivative of σ4 Specifically expressed as: In formula (20), l2 is The corresponding Lipschitz constant; The designed FTDO estimation error has the characteristic of finite time stability, that is, there is a finite time constant t f So that the system satisfies: when t>t f ,σ3=0,σ4=0.

8. The method for controlling the preset performance of a hydraulic multi-way valve control system based on FTDO according to claim 7, characterized in that: In step 2-2, in order to ensure the steady-state performance and transient performance of the tracking, and to achieve rapid convergence of the tracking error to the specified range within the specified time, a preset performance function F is designed. φ (t), construct the error preset boundary, construct the conversion 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 formula (21), f0, f ∞ , T1 and a are all positive adjustable parameters and satisfy 0<f ∞ <|e1(0)|<f0,0<T1<∞and1<a,e1(0) is the position tracking error e1=x1-x 1d The initial value of a represents the preset convergence speed, 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, and e is a natural constant; F φ The derivative of (t) It is expressed as: The preset limit of the position tracking error e1 is guaranteed by the following constraints: In formula (23), the parameters and Respectively expressed as: In order to achieve the preset performance control of the tracking error, the error conversion variable μ1(t) and its derivative are defined as 9. The method for controlling the preset performance of a hydraulic multi-way valve control system based on FTDO according to claim 8, characterized in that: In step 2-3, the idea of ​​backstepping control is integrated to define errors e2 and e3. Based on the designed parameter adaptation 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. 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 filter signal α of the virtual control input is designed through command filtering. 1f and α 2f , and finally design the control input u to realize the control of the system, as follows: According to the state space equation, the position tracking error e1 = x1-x 1d The derivative of for: In order to avoid the differential explosion problem in the system, the following instruction filter function is designed for the virtual control inputs α1 and α2 required by the controller: In formula (27), τ i is the adjustable filter time constant, α if represents the virtual control input α i The filtered signal, is the derivative of the filtered signal, ε i represents the filtering error; Define the error variable e2 as follows: e2=x2-a 1f (28) Substituting equations (26) and (28) into equation (25), the error conversion variable derivative is Write in the following format: According to the properties of the preset performance function, if the conversion error μ1(t) converges under the action of the designed FTDO-based robust adaptive preset performance controller, 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: In formula (30), α 1a is the model feedforward compensation term, α 1s is the linear robust feedback term, s1 is a positive adjustable parameter, and k1 is a positive feedback gain; Combining equations (11) and (28), the derivative of e2 is as follows: Define the error variable e3 as follows: e3=x3-a 2f =x3-α2-ε2 (32) In formula (32), α 2f is the command filtering signal of α2, ε2 is the filtering error, then equation (31) can be rewritten as follows: Based on this, the virtual control input α2 is designed as: In formula (34), α 2a is the model feedforward compensation term, α 2s1 is the linear robust feedback term used to stabilize the nominal model of the hydraulic system, k2 is the positive feedback gain, α 2s2 is the nonlinear robust term, k 2s is the positive feedback gain, is an estimate of the bounded disturbance d1(t)'s bounded value δ1, with |d1(t)| < δ1, ω2(t) is a positive integrable function, then equation (33) can be written as follows: In the above formula, if e3 = 0, then the disturbance d1(t) can be 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 so that e3 approaches 0; According to the system state space equation and equation (32), the derivative of the error e3 is It is expressed as follows: In formula (36), is the estimated value of the designed adaptive function N3, and the estimated error The design control input u is: In formula (37), u a is the model feedforward compensation term, u s1 is the linear robust feedback term, k3 is the positive feedback gain, u s2 is the nonlinear robust term, k 3s is the positive feedback gain, is an estimate of the upper bound δ2 of the observation error σ4 of the bounded disturbance d2(t), δ2 satisfies |σ4|<δ2, ω3(t) is a positive integrable function, and by combining equations (36) and (37), The derivative of is reconstructed as: Based on the above assumptions, the specific adaptive law is designed as follows: In formula (39), is the adaptive parameter derivative vector, Γ θ is a positive definite diagonal adaptive gain matrix, for The derivative of for The derivative of γ1 and γ2 are adaptive law gains, define the matrix Λ1, and select the gains s1, k1, k2, k3, k 2s , k 3s In order to keep it positive, the specific form of Λ1 is as follows: Go to step 3.

10. The method for controlling the preset performance of a hydraulic multi-way valve control system based on FTDO according to claim 9, characterized in that: In step 3, the stability analysis of the FTDO-based robust adaptive preset performance controller is performed using the Lyapunov stability theory, and the result that the system tracking error is asymptotically stable is obtained, as follows: The Lyapunov functions V1 and V2 are constructed as follows: The Lyapunov stability theory is used to analyze the stability of the FTDO-based robust adaptive preset performance controller, and the result that the system tracking error is asymptotically stable is obtained.

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