A design method and control device of reduced-order active disturbance rejection controller

Abstract

The present invention discloses a reduced-order active disturbance rejection controller design method and control device, which relates to the technical field of active disturbance rejection controllers. The reduced-order active disturbance rejection controller design method includes: constructing a mathematical model of an electro-hydraulic position servo system; constructing a third-order model of the electro-hydraulic position servo system based on the mathematical model; selecting a state variable #imgabs0# to construct a system state equation and designing a reduced-order state observer; and obtaining the observed disturbance transfer function, observed noise transfer function, and input-end disturbance transfer function of the reduced-order state observer based on the reduced-order state observer. The feedback information of the displacement sensor in the electro-hydraulic position servo system is regarded as obtainable information, and there is no need to observe it again. This can reduce the phase lag caused by the observer, thereby improving the dynamic response speed of the system. Secondly, this solution can reduce the design difficulty of the state observer, reduce the parameters to be adjusted, and indirectly widen the system bandwidth and reduce system overshoot.

Description

Technical Field

[0001] The present invention relates to the field of active disturbance rejection controller technology, and more specifically, to a reduced-order active disturbance rejection controller design method. Furthermore, the present invention also relates to a control device based on the reduced-order active disturbance rejection controller design method. Background Art

[0002] The goal of a servo system is to improve its control performance so that the controlled variable can track a given input signal quickly, stably, without overshoot, and without error. In practical servo systems, active disturbance rejection control is generally used.

[0003] The electro-hydraulic position servo system model is generally third-order. Using traditional active disturbance rejection control (ADRC) control, the observer requires fourth-order observation variables, which has problems such as many observation variables, heavy burden, slow response speed and phase lag.

[0004] In summary, how to improve the response speed of the controller and avoid phase lag is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] In light of this, the present invention aims to provide a reduced-order active disturbance rejection controller design method. This method treats the displacement sensor feedback information in an electro-hydraulic position servo system as readily available information, eliminating the need for further observation. This reduces the phase lag caused by the observer and thus improves the system's dynamic response speed. Furthermore, this approach simplifies the design of the state observer, reducing the number of parameters to be tuned. It also indirectly broadens the system bandwidth and reduces overshoot.

[0006] Another object of the present invention is to provide a control device based on the above-mentioned reduced-order active disturbance rejection controller design method.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A reduced-order active disturbance rejection controller design method is applied to an electro-hydraulic position servo system, wherein the electro-hydraulic position servo system includes a hydraulic cylinder and a servo valve. The reduced-order active disturbance rejection controller design method includes:

[0009] Construct a mathematical model of the electro-hydraulic position servo system;

[0010] The third-order model of the electro-hydraulic position servo system is constructed according to the mathematical model; the third-order model is: x p is the piston rod displacement of the hydraulic cylinder, η1 and η2 are unknown parameters, ω is the external disturbance, b is the unknown gain, and μ is the control variable;

[0011] Select state variables Construct system state equations and design reduced-order state observers;

[0012] An observation disturbance transfer function, an observation noise transfer function and an input-end disturbance transfer function of the reduced-order state observer are obtained according to the reduced-order state observer.

[0013] Optionally, after obtaining the observed disturbance transfer function, the observed noise transfer function, and the input-end disturbance transfer function of the reduced-order state observer according to the reduced-order state observer, the method further includes:

[0014] The input and output variables of the fuzzy reasoning are obtained, and a fuzzy feedforward compensator is constructed according to the output variables and the feedforward compensation function F(v).

[0015] Optionally, constructing a mathematical model of the electro-hydraulic position servo system includes:

[0016] Construct the flow equation Q of the servo valve L , Q L =K Q x v -K C p L ;K Q is the flow gain of the servo valve; K c is the flow pressure amplification factor of the servo valve, x v is the spool displacement of the servo valve, P L is the load pressure difference;

[0017] The balance equation of the hydraulic cylinder is constructed, and the balance equation is: P1 is the rodless chamber pressure of the hydraulic cylinder; P2 is the rod chamber pressure of the hydraulic cylinder; A1 is the effective working area of the rodless chamber piston of the hydraulic cylinder; A2 is the effective working area of the rod chamber piston of the hydraulic cylinder; K is the load spring stiffness; m is the total mass of the hydraulic cylinder piston and the load converted to the piston rod; B c is the kinematic viscous damping coefficient; F is the sum of the external load force and the unknown disturbance force;

[0018] Construct the hydraulic cylinder flow continuity equation Q1 is the flow rate flowing into the rodless chamber of the hydraulic cylinder; Q2 is the flow rate flowing out of the rod chamber of the hydraulic cylinder; C i is the internal leakage coefficient; β is the effective bulk elastic modulus of the hydraulic oil in the hydraulic cylinder; V 10 V is the initial volume of the rodless chamber of the hydraulic cylinder; 20 is the initial volume of the rod chamber of the hydraulic cylinder;

[0019] The volume relationship between the rod chamber and the rodless chamber of the hydraulic cylinder is obtained, and the volume relationship is: V1 is the volume of the rodless chamber of the hydraulic cylinder, and V2 is the volume of the rod chamber of the hydraulic cylinder;

[0020] According to Q L =(Q1+Q2) / 2, P L =P1-P2, combined with the flow equation Q of the servo valve L The mathematical model of the electro-hydraulic position servo system is obtained by calculating the balance equation of the hydraulic cylinder. The mathematical model is: A me is the average piston area; V e =A eL , is the mean value of the equivalent volume of the hydraulic cylinder; A e is the equivalent area, L is the hydraulic cylinder stroke, K ce =K c +C i Indicates the total flow pressure coefficient.

[0021] Optionally, the Q L =(Q1+Q2) / 2, P L =P1-P2, combined with the flow equation Q of the servo valve L The mathematical model of the electro-hydraulic position servo system is obtained by calculating the balance equation of the hydraulic cylinder. The mathematical model is: Afterwards, include:

[0022] The mathematical model is simplified as follows: ξ h is the damping ratio of the hydraulic cylinder, and ω h is the natural frequency of the hydraulic cylinder, and

[0023] Optionally, select the state variable Constructing the system state equation and designing the reduced-order state observer includes:

[0024] according to The state equation of the electro-hydraulic position servo system is constructed, and the state equation is:

[0025] The reduced-order state observer is designed according to the state equation, and the reduced-order state observer is:

[0026]

[0027] Optionally, the step selects the state variable After constructing the system state equation and designing the reduced-order state observer, the step of obtaining the observed disturbance transfer function, the observed noise transfer function, and the input-end disturbance transfer function of the reduced-order state observer according to the reduced-order state observer includes:

[0028] The gain of the reduced-order state observer is set using pole placement, and the gain of the reduced-order state observer is:

[0029] Optionally, obtaining an observed disturbance transfer function, an observed noise transfer function, and an input-end disturbance transfer function of the reduced-order state observer according to the reduced-order state observer includes:

[0030] The transfer function of the reduced-order state observer is constructed according to the reduced-order state observer and the gain of the reduced-order state observer, and the transfer function of the reduced-order state observer is:

[0031]

[0032] The generalized disturbance f is obtained according to the state equation, and the generalized disturbance f is:

[0033]

[0034] The observation disturbance transfer function of the reduced-order state observer is calculated according to the transfer function of the reduced-order state observer and the generalized disturbance f, and the observation disturbance transfer function of the reduced-order state observer is:

[0035] According to the noise δ of the position information y n The influence of the control variable μ on the reduced-order state observer is combined with the transfer function of the reduced-order state observer to calculate the observation noise transfer function of the reduced-order state observer. The observation noise transfer function of the reduced-order state observer is:

[0036]

[0037] The input-end disturbance transfer function of the reduced-order state observer is calculated based on the transfer function of the reduced-order state observer. The input-end disturbance transfer function of the reduced-order state observer is:

[0038]

[0039] Optionally, the input of the fuzzy reasoning is: (e2, e3), e2=v2-z1, e3=v3-z2; v2 is velocity information, z1 is the velocity observed by the reduced-order state observer; v3 is acceleration information, z2 is the acceleration observed by the reduced-order state observer;

[0040] The output variables of the fuzzy reasoning are: (Δk2, Δk3),

[0041] According to the fuzzy rules, seven fuzzy language subsets are defined on their respective domains: {Negative Big (NB), Negative Middle (NM), Negative Small (NS), Zero (ZO), Positive Small (PS), Positive Middle (PM), Positive Big (PB)};

[0042] The domain of the input quantity (e2, e3) of the fuzzy reasoning is [-2, 2], [-6, 6];

[0043] The domain of the output variables (Δk2, Δk3) of the fuzzy reasoning is [-60, 60], [-5, 5];

[0044] The membership function selects Gaussian function, and the feedforward compensation function F (v) The coefficients of the velocity and acceleration terms contained in are: (k 20 , k 30 ) is the feedforward compensation function F (v) The initial value of the feedforward coefficient, (k2, k3) is the final value, and (Δk2, Δk3) is the output variable of the fuzzy inference.

[0045] A control device comprising:

[0046] Displacement sensor, used to obtain the displacement information of the piston rod of the hydraulic cylinder;

[0047] A tracking differentiator is configured to output a desired piston rod displacement v1, a desired velocity signal v2, and a desired acceleration signal v3 based on the input piston rod displacement signal; and output an error differential signal to the fuzzy feedforward compensator based on the velocity z1 and acceleration z2 output by the reduced-order state observer;

[0048] A fuzzy logic unit outputs variables (Δk2, Δk3) to an input terminal of a controlled object according to the input differential error signal;

[0049] The nonlinear state error feedback law unit outputs the state feedback controller output u0 according to the input error and error differential signal;

[0050] The reduced-order state observer outputs a velocity z1 and an acceleration z2 according to the input and output quantities of the controlled object, and obtains a final controller output according to the total disturbance z3 output by the reduced-order state observer and the state feedback controller output u0 output by the nonlinear state error feedback law unit to control the controlled object.

[0051] In the process of implementing the reduced-order active disturbance rejection controller design method provided by the present invention, it is first necessary to construct a mathematical model of the electro-hydraulic position servo system, and then construct a third-order model of the electro-hydraulic position servo system based on the mathematical model; select the state variable The system state equation is constructed and a reduced-order state observer is designed. The observed disturbance transfer function, observed noise transfer function and input disturbance transfer function of the reduced-order state observer are obtained according to the reduced-order state observer. The observed disturbance transfer function, observed noise transfer function and input disturbance transfer function are used as the output of the reduced-order state observer.

[0052] Compared to existing technologies, the proposed reduced-order active disturbance rejection controller design method treats the displacement sensor feedback information in an electro-hydraulic position servo system as readily available information, eliminating the need for further observation. This reduces the phase lag caused by the observer, thereby improving the system's dynamic response speed. Furthermore, this approach simplifies the design of the state observer, reducing the number of parameters to be tuned, and indirectly broadens the system bandwidth, reducing overshoot.

[0053] In addition, the present invention also provides a control device based on the above-mentioned reduced-order active disturbance rejection controller design method. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0055] Figure 1 Schematic diagram of the structure of the electro-hydraulic position servo system of the present invention;

[0056] Figure 2 This is a schematic diagram of the structure of the fuzzy feedforward reduced-order active disturbance rejection controller;

[0057] Figure 3 The amplitude-frequency characteristic curves of LESO and RLESO are drawn based on the observed disturbance transfer function under the same bandwidth conditions;

[0058] Figure 4 The amplitude-frequency characteristic curves of LESO and RLESO are drawn based on the observed noise-frequency transfer function under the same bandwidth conditions;

[0059] Figure 5 The LESO and RLESO input-end disturbance frequency domain characteristic curves are drawn based on the input disturbance transfer function;

[0060] Figure 6 for Figure 2 The system responds to the simulation results of a step signal with an input position signal amplitude of 0.15m.

[0061] Figure 7 for Figure 2The simulation results of the system position response when the sinusoidal signal r = 0.2 × sin (0.5πt) is input into the system;

[0062] Figure 8 for Figure 2 Simulation results of the system position tracking error response when a sinusoidal signal r = 0.2 × sin (0.5πt) is input into the system;

[0063] Figure 9 for Figure 2 When the system is given a sinusoidal signal r = 0.2 × sin (0.5πt), the simulation results of the hydraulic cylinder speed curve observed by the observer;

[0064] Figure 10 for Figure 2 When the system is given a sinusoidal signal r = 0.2 × sin (0.5πt), the observer observes the simulation results of the hydraulic cylinder operation acceleration curve of the system;

[0065] Figure 11 for Figure 2 When the system is given a sinusoidal signal r = 0.2 × sin (0.5πt), the observer observes the total disturbance of the system.

[0066] Figure 1-11 middle:

[0067] 1 is the displacement sensor, 2 is the tracking differentiator, 3 is the fuzzy logic unit, 4 is the nonlinear state error feedback law unit, and 5 is the reduced-order state observer. DETAILED DESCRIPTION

[0068] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0069] The core of this invention is a reduced-order active disturbance rejection controller design method. This method treats the displacement sensor feedback information in an electro-hydraulic position servo system as available information, eliminating the need for further observation. This reduces the phase lag caused by the observer, thereby improving the system's dynamic response speed. Furthermore, this approach simplifies the design of the state observer, reducing the number of parameters to be tuned, and indirectly broadens the system bandwidth, reducing overshoot.

[0070] Another core of the present invention is to provide a control device based on the above-mentioned reduced-order active disturbance rejection controller design method.

[0071] Please refer to Figure 1-11 .

[0072] This specific embodiment provides a reduced-order active disturbance rejection controller design method, which is applied to an electro-hydraulic position servo system. The electro-hydraulic position servo system includes a hydraulic cylinder and a servo valve. The reduced-order active disturbance rejection controller design method includes:

[0073] Step S1, constructing a mathematical model of the electro-hydraulic position servo system;

[0074] Step S2: construct a third-order model of the electro-hydraulic position servo system based on the mathematical model; the third-order model is: x p is the piston rod displacement of the hydraulic cylinder, η1 and η2 are unknown parameters, ω is the external disturbance, b is the unknown gain, and μ is the control variable;

[0075] Step S3, select state variables Construct the system state equation and design the reduced-order state observer5;

[0076] Step S4 : obtaining the observed disturbance transfer function, the observed noise transfer function, and the input-end disturbance transfer function of the reduced-order state observer 5 according to the reduced-order state observer 5 .

[0077] In the process of implementing the reduced-order active disturbance rejection controller design method provided in this specific embodiment, it is necessary to first construct a mathematical model of the electro-hydraulic position servo system, and then construct a third-order model of the electro-hydraulic position servo system based on the mathematical model; select the state variable Construct the system state equation and design the reduced-order state observer 5, obtain the observed disturbance transfer function, observed noise transfer function and input-end disturbance transfer function of the reduced-order state observer 5 according to the reduced-order state observer 5; and use the observed disturbance transfer function, observed noise transfer function and input-end disturbance transfer function as the output of the reduced-order state observer 5.

[0078] Compared to existing technologies, the reduced-order active disturbance rejection controller design method of this specific embodiment treats the displacement sensor feedback information in the electro-hydraulic position servo system as available information, eliminating the need for further observation. This reduces the phase lag caused by the observer, thereby improving the system's dynamic response speed. Furthermore, this solution simplifies the design difficulty of the state observer and reduces the number of parameters to be tuned. It also indirectly broadens the system bandwidth and reduces system overshoot.

[0079] The above step S1 includes:

[0080] Step S11, construct the flow equation Q of the servo valve L , Q L =K Q x v -K C p L ;K Q is the flow gain of the servo valve; Kc is the flow pressure amplification factor of the servo valve, x v is the spool displacement of the servo valve, P L is the load pressure difference;

[0081] In step S11, the servo valve acts as the system hub, and the load flow Q of the servo valve L , load pressure P L and valve core displacement x v , the functional relationship between the three is: Q L =f(x v , p L ); Ideally, the steady-state characteristic equation of the servo valve can be obtained as:

[0082]

[0083] Among them, Q L is the load flow, in m3 / s; w is the servo valve area gradient, in m; Cd is the flow coefficient of the valve port; P L is the load pressure difference, in MPa; P S is the system oil supply pressure, in MPa; ρ is the oil density, in kg / m3; x v is the displacement of the servo valve, in m. Simplifying, we can get the formula Q L =K Q x v -K C p L .

[0084] Step S12: construct the balance equation of the hydraulic cylinder. The balance equation is:

[0085]

[0086] P1 is the pressure of the rodless cavity of the hydraulic cylinder; P2 is the pressure of the rod cavity of the hydraulic cylinder; A1 is the effective working area of the rodless cavity piston of the hydraulic cylinder; A2 is the effective working area of the rod cavity piston of the hydraulic cylinder; K is the stiffness of the load spring; m is the total mass of the hydraulic cylinder piston and the load converted to the piston rod; B c is the kinematic viscous damping coefficient; F is the sum of the external load force and the unknown disturbance force;

[0087] Step S13, construct the hydraulic cylinder flow continuity equation as follows:

[0088]

[0089] Q1 is the flow rate flowing into the rodless chamber of the hydraulic cylinder; Q2 is the flow rate flowing out of the rod chamber of the hydraulic cylinder; C iis the internal leakage coefficient; β is the effective bulk elastic modulus of the hydraulic oil in the hydraulic cylinder; V 10 V is the initial volume of the rodless chamber of the hydraulic cylinder; 20 is the initial volume of the rod chamber of the hydraulic cylinder;

[0090] Step S14: Obtain the volume relationship between the rod chamber and the rodless chamber of the hydraulic cylinder. The volume relationship is:

[0091]

[0092] V1 is the volume of the hydraulic cylinder without rod cavity, and V2 is the volume of the hydraulic cylinder with rod cavity;

[0093] Step S15, according to Q L =(Q1+Q2) / 2, P L =P1-P2, combined with the servo valve flow equation Q L And the balance equation of the hydraulic cylinder is used to calculate the mathematical model of the electro-hydraulic position servo system, which is:

[0094]

[0095] A me is the average piston area; V e =A eL , is the mean value of the equivalent volume of the hydraulic cylinder; A e is the equivalent area, L is the hydraulic cylinder stroke, K ce =K c +C i Indicates the total flow pressure coefficient.

[0096] In the above step S15, according to Q L =(Q1+Q2) / 2, P L =P1-P2, ignoring the external leakage factor, we can get:

[0097] Q L =A me x p +C i p L +4β -1 V e p L ;

[0098] Combined with formula Q L =K Q x v -K C p L And the equilibrium equation of the hydraulic cylinder can be obtained:

[0099]

[0100] After step S15, the following steps are included:

[0101] Step S16, simplify the mathematical model to:

[0102]

[0103] ξ h is the damping ratio of the hydraulic cylinder, and ω h is the natural frequency of the hydraulic cylinder, and

[0104] In the above step S16, there are many time-varying parameters in the mathematical model of the electro-hydraulic position servo system, and it is difficult to obtain its accurate mathematical model. The load and external force interference, the motion viscous damping coefficient B c The system model can be simplified as

[0105] In a specific embodiment, the above step S3 includes:

[0106] Step S31, according to Construct the state equation of the electro-hydraulic position servo system, and the state equation is:

[0107] Step S32: design a reduced-order state observer 5 according to the state equation. The reduced-order state observer 5 is:

[0108]

[0109] After step S3 and before step S4, the following steps are included:

[0110] In step S301, the gain of the reduced-order state observer 5 is set by using pole placement, and the gain of the reduced-order state observer 5 is:

[0111] The above step S4 includes:

[0112] In step S41, a transfer function of the reduced-order state observer 5 is constructed according to the reduced-order state observer 5 and the gain of the reduced-order state observer 5. The transfer function of the reduced-order state observer 5 is:

[0113]

[0114] In step S42, a generalized disturbance f is obtained according to the state equation, and the generalized disturbance f is:

[0115]

[0116] In step S43, the observed disturbance transfer function of the reduced-order state observer 5 is calculated according to the transfer function of the reduced-order state observer 5 and the generalized disturbance f, and the observed disturbance transfer function of the reduced-order state observer 5 is:

[0117] Step S44: according to the noise δ of the position information y n The influence of the control variable μ on the reduced-order state observer 5 is combined with the transfer function of the reduced-order state observer 5 to calculate the observation noise transfer function of the reduced-order state observer 5. The observation noise transfer function of the reduced-order state observer 5 is:

[0118]

[0119] In step S45, the input disturbance transfer function of the reduced-order state observer 5 is calculated based on the transfer function of the reduced-order state observer 5. The input disturbance transfer function of the reduced-order state observer 5 is:

[0120]

[0121] After step S4, the following steps are included:

[0122] Step S5: Obtain the input and output variables of the fuzzy reasoning, and construct a fuzzy feedforward compensator according to the output variables and the feedforward compensation function F(v).

[0123] In step S5, the input of fuzzy reasoning is: (e2, e3), e2 = v2 - z1, e3 = v3 - z2; v2 is velocity information, z1 is the velocity observed by the reduced-order state observer 5; v3 is acceleration information, z2 is the acceleration observed by the reduced-order state observer 5;

[0124] The output variables of fuzzy reasoning are: (Δk2, Δk3),

[0125] According to the fuzzy rules, seven fuzzy language subsets are defined on their respective domains: {Negative Big (NB), Negative Middle (NM), Negative Small (NS), Zero (ZO), Positive Small (PS), Positive Middle (PM), Positive Big (PB)};

[0126] The domain of the fuzzy inference input (e2, e3) is [-2, 2], [-6, 6];

[0127] The domain of the output variables (Δk2, Δk3) of fuzzy reasoning is [-60, 60], [-5, 5];

[0128] The membership function selects Gaussian function, and the feedforward compensation function F (v) The coefficients of the velocity and acceleration terms contained in are: (k 20 , k30 ) is the feedforward compensation function F (v) The initial value of the feedforward coefficient, (k2, k3) is the final value, and (Δk2, Δk3) is the output variable of fuzzy inference.

[0129] Specifically, the real-time operating status information of the electro-hydraulic position servo system is obtained to constitute fuzzy feedforward compensation. The real-time operating status information here includes: the given signal is the system displacement, the speed of the given signal is obtained through the differential tracker, and then the displacement and speed signals of the system real-time feedback obtained by the displacement sensor 1 and the observer constitute the fuzzy feedforward; based on the previous debugging experience, the fuzzy feedforward compensation control law is obtained, and according to the current system operating status information, the hydraulic cylinder operating speed error rate and acceleration information are obtained, the fuzzy feedforward coefficient is inferred, and the system operating status is compensated in real time.

[0130] Figure 3 The amplitude-frequency characteristic curves of LESO (Linear Extended State Observer) and RLESO (Reduced Order State Observer) are drawn based on the observed disturbance transfer function under the same bandwidth conditions; Figure 3 It can be seen that compared with the original state reduction, the system bandwidth of RLESO has been improved, and the low-frequency phase lag has been improved to a certain extent.

[0131] Figure 4 The LESO and RLESO amplitude-frequency characteristic curves are drawn based on the same physical quantity of the observed noise transfer function under the same bandwidth conditions; Figure 4 It can be seen that for the low frequency band, the LESO observation noise has a certain overshoot and serious phase lag, while the RLESO has a better noise suppression effect.

[0132] Figure 5 The LESO and RLESO input disturbance frequency domain characteristic curves are drawn based on the input disturbance transfer function; Figure 5 It can be seen that the phase lag of LESO to the system tracking input is more obvious. The use of RLESO can effectively reduce the lag of the position tracking signal and still has good suppression capability for the low-frequency tracking position system.

[0133] In addition to the above-mentioned reduced-order active disturbance rejection controller design method, the present invention also provides a control device based on the reduced-order active disturbance rejection controller design method disclosed in the above-mentioned embodiment, the control device comprising: a displacement sensor 1 for acquiring piston rod displacement information of a hydraulic cylinder; a tracking differentiator 2 for outputting a desired piston rod displacement v1, a desired velocity signal v2, and a desired acceleration signal v3 based on the input piston rod displacement signal; and outputting an error differential signal to a fuzzy feedforward compensator based on the velocity z1 and acceleration z2 output by a reduced-order state observer 5; a fuzzy logic unit 3 for outputting variables (Δk2, Δk3) to the input end of a controlled object based on the input error differential signal; a nonlinear state error feedback law unit 4 for outputting a state feedback controller output u0 based on the input error and the error differential signal; and a reduced-order state observer 5 for outputting a velocity z1 and an acceleration z2 based on the input and output of the controlled object, and obtaining a final controller output based on the total disturbance z3 output by the reduced-order state observer 5 and the state feedback controller output u0 output by the nonlinear state error feedback law unit 4 to control the controlled object. For the structures of other parts of the control device, please refer to the prior art and will not be described in detail in this article.

[0134] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other. Any combination of all the embodiments provided by the present invention is within the scope of protection of this invention and will not be described in detail here.

[0135] The above describes in detail the design method and control device of the reduced-order active disturbance rejection controller provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only intended to help understand the method and core concept of the present invention. It should be noted that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A reduced-order active disturbance rejection controller design method, applied to an electro-hydraulic position servo system, the electro-hydraulic position servo system comprising a hydraulic cylinder and a servo valve; characterized in that: The reduced-order active disturbance rejection controller design method includes: Construct a mathematical model of the electro-hydraulic position servo system; The third-order model of the electro-hydraulic position servo system is constructed according to the mathematical model; the third-order model is: ; is the piston rod displacement of the hydraulic cylinder, is an unknown parameter, ω is an external disturbance, b is an unknown gain, To control the amount; Select state variables 、 , construct the system state equation and design the reduced-order state observer (5); Obtaining an observation disturbance transfer function, an observation noise transfer function, and an input-end disturbance transfer function of the reduced-order state observer (5) according to the reduced-order state observer (5); The input and output variables of the fuzzy reasoning are obtained, and a fuzzy feedforward compensator is constructed according to the output variables and the feedforward compensation function F(v).

2. The reduced-order active disturbance rejection controller design method according to claim 1, characterized in that: The mathematical model for constructing the electro-hydraulic position servo system includes: Constructing the flow equation for the servo valve , ; is the flow gain of the servo valve; is the flow pressure amplification factor of the servo valve, is the spool displacement of the servo valve, is the load pressure difference; The balance equation of the hydraulic cylinder is constructed, and the balance equation is: ; is the rodless chamber pressure of the hydraulic cylinder; is the rod chamber pressure of the hydraulic cylinder; is the effective working area of the rodless piston of the hydraulic cylinder; is the effective working area of the piston in the rod cavity of the hydraulic cylinder; K is the stiffness of the load spring; m is the total mass of the hydraulic cylinder piston and the load converted to the piston rod; is the kinematic viscous damping coefficient; F is the sum of the external load force and the unknown disturbance force; Construct the hydraulic cylinder flow continuity equation ; is the flow rate flowing into the rodless chamber of the hydraulic cylinder; is the flow rate out of the rod chamber of the hydraulic cylinder; is the internal leakage coefficient; β is the effective bulk elastic modulus of the hydraulic oil in the hydraulic cylinder; V 10 V is the initial volume of the rodless chamber of the hydraulic cylinder; 20 is the initial volume of the rod chamber of the hydraulic cylinder; The volume relationship between the rod chamber and the rodless chamber of the hydraulic cylinder is obtained, and the volume relationship is: ; V1 is the volume of the rodless chamber of the hydraulic cylinder, and V2 is the volume of the rod chamber of the hydraulic cylinder; according to 、 , combined with the servo valve flow equation The mathematical model of the electro-hydraulic position servo system is obtained by calculating the balance equation of the hydraulic cylinder. The mathematical model is: ; is the average piston area; , is the mean value of the equivalent volume of the hydraulic cylinder; is the equivalent area, L is the stroke of the hydraulic cylinder, Indicates the total flow pressure coefficient.

3. The reduced-order active disturbance rejection controller design method according to claim 2, characterized in that: The basis 、 , combined with the servo valve flow equation The mathematical model of the electro-hydraulic position servo system is obtained by calculating the balance equation of the hydraulic cylinder. The mathematical model is: Afterwards, include: The mathematical model is simplified as follows: , is the damping ratio of the hydraulic cylinder, and , is the natural frequency of the hydraulic cylinder, and .

4. The reduced-order active disturbance rejection controller design method according to claim 1, characterized in that: Select state variables 、 , constructing the system state equation and designing the reduced-order state observer (5) includes: according to 、 The state equation of the electro-hydraulic position servo system is constructed, and the state equation is: ; The reduced-order state observer (5) is designed according to the state equation. The reduced-order state observer (5) is: .

5. The reduced-order active disturbance rejection controller design method according to claim 4, characterized in that: Step selection state variables 、 After constructing the system state equation and designing the reduced-order state observer (5), the steps of obtaining the observed disturbance transfer function, the observed noise transfer function and the input-end disturbance transfer function of the reduced-order state observer (5) according to the reduced-order state observer (5) include: The gain of the reduced-order state observer (5) is set by adopting pole configuration, and the gain of the reduced-order state observer (5) is: .

6. The reduced-order active disturbance rejection controller design method according to claim 5, characterized in that: The step of obtaining the observed disturbance transfer function, the observed noise transfer function, and the input-end disturbance transfer function of the reduced-order state observer (5) according to the reduced-order state observer (5) includes: The transfer function of the reduced-order state observer (5) is constructed according to the reduced-order state observer (5) and the gain of the reduced-order state observer (5), and the transfer function of the reduced-order state observer (5) is: ； The generalized disturbance f is obtained according to the state equation, and the generalized disturbance f is: ; The observed disturbance transfer function of the reduced-order state observer (5) is calculated based on the transfer function of the reduced-order state observer (5) and the generalized disturbance f, and the observed disturbance transfer function of the reduced-order state observer (5) is: ； According to the noise of position information y and control volume The influence on the reduced-order state observer (5) is combined with the transfer function of the reduced-order state observer (5) to calculate the observation noise transfer function of the reduced-order state observer (5), and the observation noise transfer function of the reduced-order state observer (5) is: ； The input-end disturbance transfer function of the reduced-order state observer (5) is calculated based on the transfer function of the reduced-order state observer (5). The input-end disturbance transfer function of the reduced-order state observer (5) is: 。 7. The reduced-order active disturbance rejection controller design method according to claim 1, characterized in that: The input of the fuzzy reasoning is: (e2, e3), , ; is the speed information, is the speed observed by the reduced-order state observer (5); is the acceleration information, is the acceleration observed by the reduced-order state observer (5); The output variables of the fuzzy reasoning are: , According to the fuzzy rules, seven fuzzy language subsets are defined on their respective domains: {Negative Big (NB), Negative Middle (NM), Negative Small (NS), Zero (ZO), Positive Small (PS), Positive Middle (PM), Positive Big (PB)}; The domain of the input quantity (e2, e3) of the fuzzy reasoning is [-2, 2], [-6, 6]; The output variable of the fuzzy inference The domain of is [-60, 60], [-5, 5]; The membership function selects Gaussian function, the feedforward compensation function The coefficients of the velocity and acceleration terms contained in are: ; is the feedforward compensation function The initial value of the feedforward coefficient is is the final value, is the output variable of the fuzzy inference.

8. A control device, characterized in that: include: A displacement sensor (1) for obtaining displacement information of a piston rod of a hydraulic cylinder; Tracking differentiator (2), used to output the desired piston rod displacement according to the input piston rod displacement signal , expected speed signal And the expected acceleration signal ; And according to the speed output by the reduced-order state observer (5) , acceleration Outputting the error differential signal to the fuzzy feedforward compensator; The fuzzy logic unit (3) outputs the variable according to the input error differential signal To the input end of the controlled object; The nonlinear state error feedback law unit (4) outputs the state feedback controller output according to the input error and error differential signal ; The reduced-order state observer (5) outputs the speed according to the input and output of the controlled object. and acceleration , and according to the total disturbance of its output And the state feedback controller output of the nonlinear state error feedback law unit (4) is The final controller output is obtained to control the controlled object.

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