CN110500339B - Additive fault detection method for electro-hydraulic servo system - Google Patents

Additive fault detection method for electro-hydraulic servo system Download PDF

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CN110500339B
CN110500339B CN201810478572.9A CN201810478572A CN110500339B CN 110500339 B CN110500339 B CN 110500339B CN 201810478572 A CN201810478572 A CN 201810478572A CN 110500339 B CN110500339 B CN 110500339B
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杨贵超
姚建勇
乐贵高
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Nanjing University of Science and Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F15—FLUID-PRESSURE ACTUATORS; HYDRAULICS OR PNEUMATICS IN GENERAL
    • F15B—SYSTEMS ACTING BY MEANS OF FLUIDS IN GENERAL; FLUID-PRESSURE ACTUATORS, e.g. SERVOMOTORS; DETAILS OF FLUID-PRESSURE SYSTEMS, NOT OTHERWISE PROVIDED FOR
    • F15B19/00—Testing; Calibrating; Fault detection or monitoring; Simulation or modelling of fluid-pressure systems or apparatus not otherwise provided for
    • F15B19/005—Fault detection or monitoring
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F15—FLUID-PRESSURE ACTUATORS; HYDRAULICS OR PNEUMATICS IN GENERAL
    • F15B—SYSTEMS ACTING BY MEANS OF FLUIDS IN GENERAL; FLUID-PRESSURE ACTUATORS, e.g. SERVOMOTORS; DETAILS OF FLUID-PRESSURE SYSTEMS, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention discloses an additive fault detection method for an electro-hydraulic servo system. The method comprises the following steps: selecting a double-rod hydraulic cylinder electro-hydraulic position servo system as a research object, and establishing a nonlinear model of the system; designing and analyzing an observer for non-matching additive faults and model uncertainty; designing and analyzing an observer for matching additive faults and model uncertainty; adjusting parameters to perform additive fault estimation on the electro-hydraulic servo system; the matched additive faults can be effectively estimated by designing the extended state observer; by designing the disturbance observer, the estimation can be effectively carried out on the non-matched additive faults. The additive fault detection control strategy in the method is simple in parameter adjustment, can actively miss detection for slight additive faults, can warn serious faults in time, can warn early warning for early small-amplitude additive faults in time, and is more beneficial to application in engineering practice.

Description

Additive fault detection method for electro-hydraulic servo system
Technical Field
The invention relates to the technical field of electromechanical-hydraulic servo control, in particular to an additive fault detection method for an electro-hydraulic servo system.
Background
The electro-hydraulic servo system has the outstanding advantages of high power density and quick dynamic response, and is widely applied to various fields of aviation, aerospace, industrial engineering and the like. In recent years, with the rapid development of basic subjects such as a signal processing technology, an artificial intelligence technology, a control theory and the like, the fault detection of a hydraulic system is widely regarded and made important progress at home and abroad.
According to the performance of the faults in the mathematical model of the electro-hydraulic servo system, the fault types can be divided into additive faults (actuator faults, sensor faults and the like) and multiplicative faults (parameter faults). The method for detecting the fault can be divided into signal-based fault detection and model-based fault detection, wherein the signal-based fault detection depends on signal measurement and data processing technology, and fault characteristics are extracted to evaluate whether the system is abnormal or not; and the fault detection based on the model utilizes the redundant system analysis model output and the system real output to generate residual errors so as to judge whether the system has faults or not. Generally, signal-based fault detection is more accurate, the false alarm rate is lower, but the data processing amount is larger; the fault detection based on the model depends on a more accurate system model and is easy to realize on line, but the robustness and the sensitivity of the fault detection are difficult to balance.
At present, the following problems exist in the fault detection of the electro-hydraulic servo system: one, lack the effective trouble on-line measuring method: at present, most researchers detect or identify possible faults by adopting a method of extracting fault signal characteristics or estimating system parameters and/or states based on a model through data processing based on known single faults or a few fault combinations, and the designed fault detection means is too extensive and difficult to use practically when the system is faced with unknown faults. Although the data processing technology based on fault feature extraction can better identify the known faults of the system, the algorithm with good fault detection rate is very complex, huge and clumsy, and the complex fault detection method is not beneficial to the realization of the targets of on-line early detection and timely maintenance and prevention and is also not beneficial to the subsequent potential fault-tolerant design. Although online learning methods such as parameter identification and/or state estimation based on models are easy to implement in engineering, potential risks of fault learning exist, and the problem of selecting a detection threshold, namely the optimal balance problem of robustness and sensitivity of fault detection, is not solved. Secondly, a fault detection method with simple parameter adjustment is lacked: in the existing fault detection method, the adjustment is complicated due to more parameters.
Disclosure of Invention
The invention aims to provide an additive fault detection method of an electro-hydraulic servo system based on a disturbance observer and an extended state observer, which has ideal effect and simple parameters.
The technical solution for realizing the purpose of the invention is as follows: an additive fault detection method of an electro-hydraulic servo system is based on a disturbance observer and an extended state observer and comprises the following specific steps:
step 1, establishing a mathematical model of a position servo system of a double-rod hydraulic cylinder;
step 2, designing and analyzing a non-matching additive fault and model uncertainty observer;
step 3, designing and analyzing a matching additive fault and model uncertainty observer;
and 4, adjusting parameters to perform additive fault estimation on the electro-hydraulic servo system.
Further, step 1, establishing a mathematical model of the position servo system of the double-out-rod hydraulic cylinder specifically comprises the following steps:
according to Newton's second law and considering model uncertainty and non-matching additive faults in the system, the kinematic equation of the system is obtained as follows:
Figure BDA0001665148750000021
in the formula (1), m and y respectively represent the mass and the motion displacement of the inertial load of the system; pL＝P1-P2The pressure difference of the oil inlet cavity and the oil outlet cavity of the double-rod hydraulic cylinder is shown, wherein P1To the pressure of the oil-feeding chamber, P2The pressure of the oil outlet cavity; a represents the effective piston area of the left and right cavities of the double-rod hydraulic cylinder; b is a viscous friction coefficient;
Figure BDA0001665148750000022
is the total uncertainty nonlinear term caused by system external disturbances, unmodeled friction, and difficult-to-model factors; eta1(t) and
Figure BDA0001665148750000023
time description and mathematical model, eta, respectively, of potential non-matching additive faults1The expression of (t) is as follows:
Figure BDA0001665148750000024
in the formula (2), T1Time of occurrence of the failure,. mu.1The rate of progression of the fault is characterized by a μ less than the set value, as shown by equation (2)1Mu greater than set value for representing graded fault1Characterizing the catastrophic failure;
the load pressure of the double-out-rod hydraulic cylinder actuator is dynamically expressed as:
Figure BDA0001665148750000025
v in formula (3)t、βe、Ct、QLRespectively the total volume of a control cavity of the double-rod hydraulic cylinder, the elastic modulus of hydraulic oil, the leakage coefficient of the double-rod hydraulic cylinder and the load flow of a servo valve, wherein QL＝(Q1+Q2)/2，Q1For the hydraulic flow entering the oil inlet chamber of the double-outlet-rod hydraulic cylinder from the servo valve, Q2The hydraulic flow which flows out of the oil return cavity of the double-rod hydraulic cylinder through the servo valve is provided; j is a function of2(t) is the modeling error, η2(t) and g2(t) time description and mathematical model, η, respectively, of potential matching additive faults2(t) is the same as the expression (2);
if the response speed of the servo valve is faster than the set value, that is, the bandwidth of the servo valve is far higher than the bandwidth of the system, that is, the servo dynamics is simplified as a proportional link, so the load flow equation of the servo valve is written as follows:
Figure BDA0001665148750000031
in the formula (4), ktRepresenting the total flow gain, P, associated with the control input voltage usFor the hydraulic source supply pressure, s (u) is expressed as:
Figure BDA0001665148750000032
for a double-rod hydraulic cylinder servo system, a nonlinear model represented by formulas (1), (3) and (4) defines a system state variable as
Figure BDA0001665148750000033
The state space form of the nonlinear model of the system is then:
Figure BDA0001665148750000034
phi in the formula (6)1(x2)＝-Bx2/m，
Figure BDA0001665148750000035
For non-matching additive faults and model uncertainty terms,
Figure BDA0001665148750000036
xq＝4βeA[j2(t)+η2(t)g2(t)]/Vtthe/J is a matching additive fault and model uncertainty item; where the parameters are nominal and known, the uncertainty effect of the variation in parameter B, m is attributed to xfAnd xqPerforming the following steps;
the following assumptions were made before designing an additive fault detection strategy:
assume that 1: function r (u, x)3) With respect to x3In practical terms Lipschitz is bounded and r (u, x)3) Away from 0;
assume 2: non-matching additive faults and model uncertainty xfAnd non-matching additive faults and model uncertainty xqAre bounded and satisfy:
|xf|≤M1,|xq|≤M2 (7)
m in formula (7)1、M2Are all known normal numbers, and xf、xqThe first derivative of (a) exists and is bounded.
Further, the step 2 of designing and analyzing the non-matching additive fault and model uncertainty observer is specifically as follows:
definition of
Figure BDA0001665148750000041
For non-matching additive faults and model uncertainty term xfBased on equation (6), the disturbance observer is designed as follows:
Figure BDA0001665148750000042
in the formula (8), l is an adjustable normal number;
the disturbance observer designed by the formula (8) adjusts l to make the observation error
Figure BDA0001665148750000043
Is less than the set threshold.
Further, the step 3 of designing and analyzing the observer for matching additive faults and model uncertainty is as follows:
matching additive faults and model uncertainty term x in equation (6)qExpand to redundant state and define
Figure BDA0001665148750000044
Based on the third equation in equation (6), the extended state observer is designed as:
Figure BDA0001665148750000045
in the formula (9)
Figure BDA0001665148750000046
Are respectively a state x3And redundant state xqEstimate of, ωoIs the bandwidth of the extended state observer and omegao＞0。
Further, the adjusting parameters in step 4 are used for additive fault estimation of the electro-hydraulic servo system, and the method specifically comprises the following steps:
adjusting gain l to enable the disturbance observer to estimate the non-matching additive faults and model uncertainty of the system, wherein l is larger than 0; adjusting the gain omegaoMatching additive faults and model uncertainty, ω, for an extended state observer estimation systemo＞0。
Compared with the prior art, the invention has the following remarkable advantages: (1) the method comprises the following steps that a double-out-rod hydraulic cylinder electro-hydraulic position servo system is selected as a research object, a nonlinear model of the system is established, matched and unmatched additive faults and model uncertainty of the system are considered, a matched additive fault can be effectively estimated by designing an extended state observer, and a unmatched additive fault can be effectively estimated by designing a disturbance observer; (2) the designed additive fault detection control strategy parameters are simple to adjust, slight additive faults can be actively missed, serious faults can be timely warned, early warning can be timely carried out on early small-amplitude additive faults, and the method is more beneficial to application in engineering practice.
Drawings
FIG. 1 is a schematic diagram of a dual-out-rod hydraulic cylinder electro-hydraulic servo position system of the present invention.
FIG. 2 is a schematic diagram of an additive fault detection principle of the electro-hydraulic servo system.
Fig. 3 is a schematic diagram of online monitoring performance of non-matching additive faults.
Fig. 4 is a schematic diagram of non-matching additive fault identification.
FIG. 5 is a schematic diagram of non-matching additive fault observation errors.
Fig. 6 is a schematic diagram of online monitoring performance of matched additive faults.
Fig. 7 is a schematic diagram of matching additive fault signatures.
FIG. 8 is a schematic diagram of matching additive fault observation errors.
FIG. 9 is a schematic diagram of the tracking performance of the system under the action of a PID controller.
FIG. 10 is a schematic diagram of the tracking error of the system under the action of a PID controller.
Detailed Description
With reference to fig. 1 to 2, the method for detecting additive faults of an electro-hydraulic servo system based on a disturbance observer and an extended state observer includes the following steps:
step one, establishing a mathematical model of a position servo system of a double-rod hydraulic cylinder:
the method comprises the following steps of taking a double-rod hydraulic cylinder shown in figure 1 as a research object, establishing a mathematical model of an electro-hydraulic position servo system, and obtaining a kinematic equation of the system according to Newton's second law and by considering model uncertainty and non-matching additive faults in the system, wherein the mathematical model comprises the following steps:
Figure BDA0001665148750000051
formulas (1) m and y respectively represent the mass and the motion displacement of the inertial load of the system; pL＝P1-P2The pressure difference of the oil inlet cavity and the oil outlet cavity of the double-rod hydraulic cylinder is shown, wherein P1To the pressure of the oil-feeding chamber, P2The pressure of the oil outlet cavity; a represents the effective piston area of the left and right cavities of the double-rod hydraulic cylinder; b is a viscous friction coefficient;
Figure BDA0001665148750000052
is the total uncertainty nonlinear term caused by system external disturbances, unmodeled friction, and difficult-to-model factors; eta1(t) and
Figure BDA0001665148750000053
time description and mathematical model eta of potential non-matching additive faults respectively1The expression of (t) is as follows:
Figure BDA0001665148750000054
t in formula (2)1Time of occurrence of the failure,. mu.1The rate of progression of the fault is characterized by a smaller μ as can be seen from equation (2)1Gradual (early) failure can be characterized, in contrast to a larger μ1Catastrophic failure can be characterized.
The load pressure dynamics of a double-out-rod hydraulic cylinder actuator can be expressed as:
Figure BDA0001665148750000061
v in formula (3)t、βe、Ct、QLRespectively the total volume of a control cavity of the double-rod hydraulic cylinder, the elastic modulus of hydraulic oil, the leakage coefficient of the double-rod hydraulic cylinder and the load flow of a servo valve, wherein QL＝(Q1+Q2) /2 (wherein Q)1For the hydraulic flow entering the oil inlet chamber of the double-outlet-rod hydraulic cylinder from the servo valve, Q2Hydraulic flow out of the return chamber of the dual-rod hydraulic cylinder via the servo valve), j)2(t) is the modeling error, η2(t) and g2(t) are respectively potential matches plusTime description and mathematical model of sexual faults, eta2The expression of (t) is similar to equation (2).
If the response speed of the servo valve is very high, that is, the bandwidth of the servo valve is far higher than the bandwidth of the system, the servo dynamics can be simplified as a proportional link, so the load flow equation of the servo valve can be written as follows:
Figure BDA0001665148750000062
k in formula (4)tRepresenting the total flow gain, P, associated with the control input voltage usFor the hydraulic source supply pressure, s (u) is expressed as:
Figure BDA0001665148750000063
in order to make the design of the observer more extensive, aiming at the double-output-rod hydraulic cylinder servo system, the nonlinear model represented by the formulas (1), (3) and (4) defines the system state variable as
Figure BDA0001665148750000064
The state space form of the nonlinear model of the system is then:
Figure BDA0001665148750000065
phi in the formula (6)1(x2)＝-Bx2/m，
Figure BDA0001665148750000066
For non-matching additive faults and model uncertainty terms,
Figure BDA0001665148750000067
xq＝4βeA[j2(t)+η2(t)g2(t)]/Vtand/J is a matching additive fault and model uncertainty term. Where the parameters are nominal and known, the effect of uncertainty due to variations in parameters B, m, etcThe sound can be attributed to xfAnd xqIn (1).
The following assumptions were made before designing an additive fault detection strategy:
assume that 1: function r (u, x)3) With respect to x3In practical terms Lipschitz is bounded and r (u, x)3) Away from 0.
Assume 2: non-matching additive faults and model uncertainty xfAnd non-matching additive faults and model uncertainty xqAre bounded and satisfy:
|xf|≤M1,|xq|≤M2 (7)
m in formula (7)1、M2Are all known normal numbers, and xf、xqThe first derivative of (a) exists and is bounded.
Designing and analyzing a non-matching additive fault and model uncertainty observer:
is defined as
Figure BDA0001665148750000071
For non-matching additive faults and model uncertainty term xfBased on equation (6), the disturbance observer is designed as follows:
Figure BDA0001665148750000072
in equation (8), l is an adjustable normal number.
Is defined as
Figure BDA0001665148750000073
For non-matching additive faults and model uncertainty term xfThe estimated value of (c) can be obtained from equations (6) and (8):
Figure BDA0001665148750000074
from equation (9), it is further obtained:
Figure BDA0001665148750000075
in the formula (10)
Figure BDA0001665148750000076
Is that
Figure BDA0001665148750000077
Is a positive function and satisfies
Figure BDA0001665148750000078
It can be seen from equation (10) that the observation error can be made by reducing l
Figure BDA0001665148750000079
To a very small value.
Thirdly, designing and analyzing an observer for matching additive faults and model uncertainty:
firstly, matching additive fault and model uncertainty term x in formula (6)qExpand to redundant state and define
Figure BDA00016651487500000710
Based on the third equation in equation (6), the extended state observer is designed as:
Figure BDA0001665148750000081
in formula (11)
Figure BDA0001665148750000082
Are respectively a state x3And redundant state xqEstimate of, ωoIs the bandwidth of the extended state observer and omegao＞0。
Defining states
Figure BDA0001665148750000083
Respectively extended state observer(11) The dynamic equation of the estimation error obtained from equations (6) and (11) is:
Figure BDA0001665148750000084
define status vector ζ ═ ζ1,ζ2]T(wherein
Figure BDA0001665148750000085
) Then, the dynamic equation of the scaled estimation error can be obtained as follows:
Figure BDA0001665148750000086
matrix A in equation (13)1And F1The expressions of (a) are respectively as follows:
Figure BDA0001665148750000087
from matrix A1The definition of (A) is such that it satisfies the Hurwitz criterion, and thus there is a positive and symmetric matrix N1So that
Figure BDA0001665148750000088
(I is an identity matrix) holds.
According to the theory of the extended state observer, the following steps are carried out: if h (t) is bounded, the state of the system (11) and the estimation error of the matching additive fault and model uncertainty are always bounded and present a constant1,2> 0 and a finite time T1> 0 so that:
Figure BDA0001665148750000089
wherein
Figure BDA00016651487500000810
Is an infinitesimal number and gamma is a positive integer. From the above(15) It can be seen that by increasing the bandwidth ω of the extended state observer (11)oThe estimation error can be made to tend to a small value in a finite time.
The principle of the additive fault detection method of the electro-hydraulic servo system is shown in FIG. 2.
Step four, adjusting parameters to perform additive fault estimation on the electro-hydraulic servo system:
adjusting gain l (l > 0) to ensure that the disturbance observer accurately estimates the non-matching additive faults and model uncertainty of the system, adjusting gain ωo(ωo> 0) to ensure that the extended state observer accurately estimates the matching additive faults and model uncertainty of the system.
The present invention will be described in further detail with reference to FIGS. 1 to 10 and embodiments.
Example 1
And (3) verifying an additive fault detection method of the electro-hydraulic servo system by adopting Matlab/Simulink, wherein the parameters of the electro-hydraulic position servo system are as follows: the load mass m is 30 kg; area a of piston rod 9.0478 × 10-4m2(ii) a Total leakage coefficient Ct＝3×10- 12m3(ii)/s/Pa; pressure P of fuel supplys＝1×107Pa; the viscous friction coefficient B is 90 N.s/m; elastic modulus beta of hydraulic oile＝7×108Pa; total flow gain k of servo valvet＝2×10-8m3/s/V/Pa-1/2(ii) a Total volume V of control chambert＝7.962×10-5m3(ii) a The position command that the system expects to track is a curve x1d(t)＝sin(t)[1-exp(-0.01t3)]. In general, there are four situations, namely, no fault situation, sudden fault situation, early small-amplitude fault situation, and tolerable minor fault situation, in an actual system. In order to comprehensively reflect the influence of the non-matching additive faults and the matching additive faults on the fault detection and tracking performance, the situation that sudden faults exist in the system is assumed in the example. During the simulation, it is assumed that there is no model uncertainty, i.e.
Figure BDA0001665148750000091
And j is2(t) is 0, minAnd respectively adding a mismatch additive fault and a match additive fault. When adding sudden non-matching additive fault at 10s (i.e. non-matching additive fault occurrence time is T110s), the system mismatch additive fault is described as:
Figure BDA0001665148750000092
the fault tolerance level is 2000N. When adding sudden matching additive fault at 20s (i.e. matching additive fault occurrence time is T220s), the system matching additive fault is described as:
Figure BDA0001665148750000093
fault tolerance of 1 x 10-4m3/s。
The system selects a PID controller, and the parameters of the PID controller are as follows: proportional gain k P1000, integral gain kI300, differential gain k D0. The parameter selection of the fault detection control method designed by the invention is omega0＝120，l＝0.001。
As can be seen from the system tracking performance graph 9 and the position tracking error map 10, the tracking performance of the system deteriorates rapidly after two times, i.e., time t is 10s and time t is 20s, which indicates that a large system failure occurs before and after the two times. Fig. 4 and fig. 7 also verify that an additive fault occurs in the system when t is 10s and t is 20 s. Meanwhile, as can be seen from fig. 3 and 6, the curves of the additive fault level observed on line and the additive fault level actually existing in the system are basically coincident, which shows that the fault detection method provided by the invention can completely observe the fault level occurring in the system in real time under the condition of sudden fault, and detect the fault condition of the system in real time.
As can be seen from fig. 3, 4, 6 and 7, for the sudden large-amplitude fault, the detection strategy detects the fault almost at the same time as the fault occurs, and when t is 10s and t is 20s, the non-matching additive fault flag and the matching additive fault flag of the detection strategy are set to 1, which indicates that an intolerable additive fault occurs at these two times, and fault tolerance control is required.
As can be seen from fig. 5 and 8, the observer is designed to have a relatively small observation error, so that the non-matching additive fault and the change of the matching additive fault of the system are well identified, and further, the active fault-tolerant control strategy can be triggered, and the observer can provide information for the active fault-tolerant control of the system. The method provides guarantee for the purpose that the active fault-tolerant control strategy achieves emergency control on the fault of the electro-hydraulic servo system in a service state and ensures the safety of the system.

Claims (1)

1. The additive fault detection method of the electro-hydraulic servo system is characterized by being based on a disturbance observer and an extended state observer and comprising the following specific steps of:
step 1, establishing a mathematical model of a position servo system of a double-rod hydraulic cylinder;
step 2, designing and analyzing a non-matching additive fault and model uncertainty observer;
step 3, designing and analyzing a matching additive fault and model uncertainty observer;
step 4, adjusting parameters to perform additive fault estimation on the electro-hydraulic servo system;
step 1, establishing a mathematical model of a double-rod hydraulic cylinder position servo system, which comprises the following specific steps:
according to Newton's second law and considering model uncertainty and non-matching additive faults in the system, the kinematic equation of the system is obtained as follows:
Figure FDA0002707385200000011
in the formula (1), m and y respectively represent the mass and the motion displacement of the inertial load of the system; pL＝P1-P2The pressure difference of the oil inlet cavity and the oil outlet cavity of the double-rod hydraulic cylinder is shown, wherein P1To the pressure of the oil-feeding chamber, P2For the oil outlet chamberPressure; a represents the effective piston area of the left and right cavities of the double-rod hydraulic cylinder; b is a viscous friction coefficient;
Figure FDA0002707385200000012
is the total uncertainty nonlinear term caused by system external disturbances, unmodeled friction, and difficult-to-model factors; eta1(t) and
Figure FDA0002707385200000013
time description and mathematical model, eta, respectively, of potential non-matching additive faults1The expression of (t) is as follows:
Figure FDA0002707385200000014
in the formula (2), T1Time of occurrence of the failure,. mu.1The rate of progression of the fault is characterized by a μ less than the set value, as shown by equation (2)1Mu greater than set value for representing graded fault1Characterizing the catastrophic failure;
the load pressure of the double-out-rod hydraulic cylinder actuator is dynamically expressed as:
Figure FDA0002707385200000015
v in formula (3)t、βe、Ct、QLRespectively the total volume of a control cavity of the double-rod hydraulic cylinder, the elastic modulus of hydraulic oil, the leakage coefficient of the double-rod hydraulic cylinder and the load flow of a servo valve, wherein QL＝(Q1+Q2)/2，Q1For the hydraulic flow entering the oil inlet chamber of the double-outlet-rod hydraulic cylinder from the servo valve, Q2The hydraulic flow which flows out of the oil return cavity of the double-rod hydraulic cylinder through the servo valve is provided; j is a function of2(t) is the modeling error, η2(t) and g2(t) time description and mathematical model, η, respectively, of potential matching additive faults2(t) is the same as the expression (2);
if the response speed of the servo valve is faster than the set value, that is, the bandwidth of the servo valve is far higher than the bandwidth of the system, that is, the servo dynamics is simplified as a proportional link, so the load flow equation of the servo valve is written as follows:
Figure FDA0002707385200000021
in the formula (4), ktRepresenting the total flow gain, P, associated with the control input voltage usFor the hydraulic source supply pressure, s (u) is expressed as:
Figure FDA0002707385200000022
for a double-rod hydraulic cylinder servo system, a nonlinear model represented by formulas (1), (3) and (4) defines a system state variable as
Figure DA00027073852034602
The state space form of the nonlinear model of the system is then:
Figure FDA0002707385200000024
phi in the formula (6)1(x2)＝-Bx2/m，
Figure FDA0002707385200000025
For non-matching additive faults and model uncertainty terms,
Figure FDA0002707385200000026
xq＝4βeA[j2(t)+η2(t)g2(t)]/Vtthe/J is a matching additive fault and model uncertainty item; where the parameters are nominal and known, the uncertainty effect of the variation in parameter B, m is attributed to xfAnd xqPerforming the following steps;
the following assumptions were made before designing an additive fault detection strategy:
assume that 1: function r (u, x)3) With respect to x3In practical terms Lipschitz is bounded and r (u, x)3) Away from 0;
assume 2: non-matching additive faults and model uncertainty xfAnd non-matching additive faults and model uncertainty xqAre bounded and satisfy:
|xf|≤M1,|xq|≤M2 (7)
m in formula (7)1、M2Are all known normal numbers, and xf、xqThe first derivative of (a) is present and bounded;
step 2, designing and analyzing the non-matching additive fault and model uncertainty observer, which is specifically as follows:
definition of
Figure FDA0002707385200000031
For non-matching additive faults and model uncertainty term xfBased on equation (6), the disturbance observer is designed as follows:
Figure FDA0002707385200000032
in the formula (8), l is an adjustable normal number;
the disturbance observer designed by the formula (8) adjusts l to make the observation error
Figure FDA0002707385200000033
Is less than a set threshold;
and 3, designing and analyzing the observer for matching additive faults and model uncertainty, specifically as follows:
matching additive faults and model uncertainty term x in equation (6)qExpand to redundant state and define
Figure FDA0002707385200000034
Based on the third equation in equation (6), the extended state observer is designed as:
Figure FDA0002707385200000035
in the formula (9)
Figure FDA0002707385200000036
Are respectively a state x3And redundant state xqEstimate of, ωoIs the bandwidth of the extended state observer and omegao＞0；
And 4, performing additive fault estimation on the electro-hydraulic servo system by the adjusting parameters, which specifically comprises the following steps:
adjusting gain l to enable the disturbance observer to estimate the non-matching additive faults and model uncertainty of the system, wherein l is larger than 0; adjusting the gain omegaoMatching additive faults and model uncertainty, ω, for an extended state observer estimation systemo＞0。
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