CN113359438A - Two-axis engraving machine fault estimation method based on two-dimensional gain adjustment mechanism - Google Patents
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Abstract
A two-axis engraving machine fault estimation method based on a two-dimensional gain adjustment mechanism comprises the following steps: step 1), carrying out model identification on the two-axis servo motion control system, and determining a mathematical model of the two-axis servo motion control system; step 2), designing an intermediate observer based on a two-dimensional gain adjustment mechanism; and 3), initializing observer parameters, and calculating observer gains L (k, t) and F (k, t). According to the invention, some key parameters are adjusted on line through a two-dimensional gain adjustment mechanism, so that the on-line fault estimation performance is improved, the reliability of the estimation effect is improved, and the precision of fault estimation is improved.
Description
Technical Field
The invention belongs to the field of fault detection and estimation, and particularly provides an IE-based online fault estimation method for simultaneously estimating process faults and sensor faults. A dynamic two-dimensional gain adjustment mechanism is provided, and the mechanism improves the online fault estimation performance by adjusting some key parameters online.
Background
In some complex industrial scenarios requiring real-time supervision, due to possible system component aging or improper operation, a working machine body process failure or a numerical control system sensor failure is inevitably caused, so that a predetermined control performance cannot be timely realized in an emergency. To solve this problem, it is necessary to first identify and estimate the fault and to use online real-time identification, which will be more accurate than looking at the operation of the device through historical data. Fault estimation techniques are powerful tools for ensuring efficient operation of a system because, in addition to being able to capture the time at which a fault occurred, the equipment operator can also know the waveform, magnitude, and extent of damage to the system.
The fault estimation method based on the analytical model at the present stage comprises the following steps: sliding mode observers, adaptive observers, unknown input observers, robust observers, and the like. Among them, robust Extended State Observers (ESOs) based on the worst case performance index are the most common methods in the field of fault diagnosis. However, most of the fault estimation observers are designed off-line, and it is difficult to flexibly improve the fault estimation effect when dealing with some complex and variable systems. In particular, a sliding mode observer and an adaptive observer Intermediate observer (IE) may obtain an upper bound of the fault estimation error, but the upper bound is usually a very large number, which may hardly reflect the effective estimation performance. Since the design of robust ESOs is based on an optimization strategy where the performance indicators are worst-case, the same problem occurs in this type of observer. On the other hand, it should be emphasized that the existing fault estimation methods are still strict in conservatism, for example, robust ESOs usually use convex hull theory to solve some linear matrix inequalities, but the actual system parameters only use a small part of vertices formed by convex set. In addition, the adaptive observer needs to set several equality constraints, which are difficult to satisfy when system parameters change. Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a two-axis engraving machine fault estimation method based on a two-dimensional gain adjustment mechanism, and the provided dynamic two-dimensional gain adjustment mechanism can adjust some key parameters on line and improve the on-line fault estimation performance.
The invention provides the following technical scheme for solving the technical problems:
a two-axis engraving machine fault estimation method based on a two-dimensional gain adjustment mechanism comprises the following steps:
step 1), carrying out model identification on the two-axis servo motion control system, determining a mathematical model of the two-axis servo motion control system, and obtaining the mathematical model of the motion control platform after system identification as follows
x(k+1)=Ax(k)+Bu(k)+Eufu(k) (1)
y(k)=Cx(k)+Eyfy(k) (2)
WhereinRespectively representing system status, control inputs, measurement outputs, process faults and sensor faults,each representing a matrix of system parameters of appropriate dimensions,a parameter distribution matrix representing the corresponding fault, wherein Eu is assumed to be a column full rank matrix, if EuB, then the process fault f at this timeu(k) Can be considered as an actuator failure, willRates of change, denoted as process fault and sensor fault, respectively, are assumed to be bounded, i.e., both are bounded
Wherein eta is more than 0 and gamma is more than 0;
step 2), designing an intermediate observer based on a two-dimensional gain adjustment mechanism, wherein the process is as follows:
first, the following intermediate variables are defined
Where ω is a manipulated variable to be determined, from which the value of the intermediate variable τ (k) is ultimately determined, the following system model is derived from (2) and (4)
The dynamic equation of the system is only related to the time axis parameter k, and in the novel IE to be mentioned later, besides the updating of the parameter along the time axis and the operation of the system, the improvement of the fault estimation result in another dimension is considered, namely, a set of T-step updating processes are additionally added in the interval of each sampling period; before the form of the observer is given, it is necessary to first explain the estimation update strategy of the two dimensions as follows: in order to ensure the estimation performance of the fault, an online estimation performance index with a threshold value is introduced, IE usually carries out parameter updating along a time axis, when the performance index falls into a range which does not meet the threshold value condition, a longitudinal gain adjustment process in a sampling period interval is activated, IE operates under the two-dimensional gain adjustment mechanism until the performance index meets the threshold value condition again, and then IE continues to operate along the time axis, namely returns to a common one-dimensional updating mode;
step 3), initializing observer parameters, and calculating observer gains L (k, t) and F (k, t), wherein the process is as follows:
initializing observer parametersNumber: k: -0, kn:=0,t=0,ω(k,t):=ω(kn,tn),ts:=0,tmaxAnd a threshold δ; starting iteration IE, calculating observer gains L (k, t), F (k, t) through (6);
given a positive scalar α ∈ (0,1) and a parameter ω > 0, if a matrix exists And a scalar ε > 0, satisfy
Then the estimated error of the IE is guaranteed to be consistent with the system state and eventually bounded, and satisfiedWherein the content of the first and second substances,
Π′11=Π11-αP1(k,t),Π′22=Π22-αP2(k,t)
the iteration IE is started and the following estimates are obtained:
further, the method comprises the following steps:
step 4), defining an estimation performance evaluation function and judging whether to perform longitudinal updating according to the evaluation function, wherein the process is as follows:
If the value of the performance evaluation function J ≧ δ, a longitudinal update, ω (k), will be maden,tn):=ω(k,t)+ξ1When the maximum vertical update step t is exceededmaxWhen the estimated performance evaluation function is still larger than the threshold value, then ω (k)n,tn):=ω(k,t)+ξ2,ξ1And xi2Respectively representing the step size of ω (k, t) updating in two dimensions;
step 5), judging whether to perform transverse updating according to the evaluation function, wherein the process is as follows:
if the value J of the performance evaluation function is less than or equal to delta, then the performance evaluation function is transversely updated, and the estimation value obtained by IE is used as the final estimation value at the current moment, namely Output of
In the above step, the observer gains L (k, t) and F (k, t) are obtained by solving the stability condition, respectively representing the estimated values obtained after the t-th iteration at the sampling time k. Is the final estimate at time k, and, in addition,the moving average value indicating the output estimation error is a performance index for evaluating the estimation effect of the design. q. q.sdThe window time representing the sliding average, δ is a threshold value pre-selected according to the particular system.
The invention considers the application of the two-axis servo motion control platform. The platform adopts a small two-axis engraving machine, the movement of an actuator on an x axis and a y axis is controlled by an alternating current servo motor reaching the ECMA-C10604SS model, the rated power of the platform is 400w, the CANopen protocol is integrated in the interior of the platform with the highest rotating speed of 1500(r/min), and the bus communication speed is about 1 Mb/s; meanwhile, in order to realize high-precision positioning, a Taida ASDA-A2 series servo driver is adopted to realize communication conversion; the control panel selects an STM32F407 development board, and carries an STM32F407ZGT6 chip and a CAN/485 communication interface; the upper computer runs the algorithm and sends corresponding processing results and control instructions to the servo system through the single chip microcomputer. The invention has the beneficial effects that: some key parameters are adjusted on line through a two-dimensional gain adjustment mechanism, so that the on-line fault estimation performance is improved, the reliability of the estimation effect is improved, and the fault estimation precision is improved.
Drawings
FIG. 1 is a flow chart of a two-dimensional gain adjustment mechanism algorithm;
FIG. 2 is a fault estimation performance indicator response curve;
FIG. 3 is a process fault and estimate;
FIG. 4 is a sensor fault and estimate.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention are further described below with reference to the accompanying drawings and simulation experiments.
Referring to fig. 1 to 4, a two-axis engraver fault estimation method based on a two-dimensional gain adjustment mechanism includes the steps of firstly, performing model identification on a two-axis servo motion control system to determine a mathematical model of the two-axis servo motion control system; and then designing an intermediate observer based on a two-dimensional gain adjustment mechanism, and finally judging to perform longitudinal updating or transverse updating according to a performance cost function.
The invention discloses a two-axis engraving machine fault estimation method based on a two-dimensional gain adjustment mechanism, which comprises the following steps of:
1) carrying out model identification on the two-axis servo motion control system, and determining a mathematical model of the two-axis servo motion control system;
2) designing an intermediate observer based on a two-dimensional gain adjustment mechanism;
3) initializing observer parameters and calculating observer gain;
4) performing longitudinal updating according to the performance evaluation function;
5) and performing horizontal updating according to the performance evaluation function.
Further, in the step 1), model identification is performed on the two-axis servo motion control system, a mathematical model of the two-axis servo motion control system is determined, and the mathematical model of the motion control platform obtained after system identification is as follows
x(k+1)=Ax(k)+Bu(k)+Eufu(k) (1)
y(k)=Cx(k)+Eyfy(k) (2)
WhereinRespectively representing system status, control inputs, measurement outputs, process faults and sensor faults,B=[0 3.4414]T,C=[0 1]respectively representing a system parameter matrix, Eu=[0.1 0]T,Ey=[0 1]TDenotes a parameter distribution matrix corresponding to the fault, where E is assumeduIs a column full rank matrix if EuB, then the process fault f at this timeu(k) Can be considered as an actuator failure with process failure set to fu(k)=0.3sin(0.4k),In addition to that, willRates of change, denoted as process fault and sensor fault, respectively, are assumed to be bounded, i.e., both are bounded
Wherein eta is more than 0 and gamma is more than 0.
In the step 2), an intermediate observer is designed based on a two-dimensional gain adjustment mechanism, and the process is as follows:
first, the following intermediate variables are defined
Where ω is a manipulated variable to be determined, from which the value of the intermediate variable τ (k) is ultimately determined, the following system model is derived from (2) and (4)
The dynamic equation of the system is only related to a time axis parameter k, and in a novel IE to be mentioned later, besides updating the parameter along the time axis and running the system, the improvement of the fault estimation result in the other dimension is considered, namely, a group of T-step updating processes are additionally added in the interval of each sampling period, before the form of an observer is given, the estimation updating strategies of the two dimensions are necessarily explained as follows, in order to ensure the estimation performance of the fault, an online estimation performance index with a threshold value is introduced, the IE usually updates the parameter along the time axis, when the performance index falls into the range which does not meet the threshold value condition, a longitudinal gain adjusting process in the interval of the sampling period is activated, the IE runs under the gain adjusting mechanism of the two dimensions until the performance index meets the threshold value condition again, the IE will then continue to run along the time axis, i.e. return to the normal one-dimensional update mode.
In the step 3), observer parameters are initialized, and observer gains L (k, t), F (k, t) are calculated, wherein the process is as follows:
initializing observer parameters: k: -0, kn:=0,t=0,ω(k,t):=ω(kn,tn),ts:=0,tmax5 and a threshold δ; the start-up of the iteration IE,and (6) calculating observer gains L (k, t), F (k, t).
Given a positive scalar α ∈ (0,1) and a parameter ω > 0, if a matrix exists And a scalar ε > 0, satisfy
Then the estimated error of the IE is guaranteed to be consistent with the system state and eventually bounded, and satisfiedSetting the threshold delta to 0.22, wherein,
Π′11=Π11-αP1(k,t),Π′22=П22-αP2(k,t)
the iteration IE is started and the following estimates are obtained:
in the step 4), an estimation performance evaluation function is defined and whether longitudinal updating is performed is judged according to the evaluation function, and the process is as follows:
If the value of the performance evaluation function J ≧ δ, a longitudinal update, ω (k), will be maden,tn):=ω(k,t)+ξ1When the maximum vertical update step t is exceededmaxWhen the estimated performance evaluation function is still larger than the threshold value, then ω (k)n,tn):=ω(k,t)+ξ2,ξ1And xi2Representing the step size of ω (k, t) updates in two dimensions, respectively.
In the step 5), whether to perform transverse updating is judged according to the evaluation function, and the process is as follows:
if the value J of the performance evaluation function is less than or equal to delta, then the performance evaluation function is transversely updated, and the estimation value obtained by IE is used as the final estimation value at the current moment, namely Output of
In the above step, the observer gains L (k, t) and F (k, t) are obtained by solving the stability condition, respectively representing the estimated values obtained after the t-th iteration at the sampling time k, is the final estimate at time k, and, in addition,a sliding average value representing an output estimation error is a performance index for evaluating the estimation effect of the design, qdRepresents the window time of the sliding average. δ is a threshold value pre-selected according to the particular system.
The invention provides a novel IE-based fault estimation method, which can limit fault estimation errors in a smaller energy range by introducing a TDGRM algorithm to update observer gains and various estimation values in real time on line. Compared with a common robust control method, the fault estimation method has higher reliability.
The embodiments of the present invention have been described and illustrated in detail above with reference to the accompanying drawings, but are not limited thereto. Many variations and modifications are possible which remain within the knowledge of a person skilled in the art, given the concept underlying the invention.
Claims (2)
1. A two-axis engraving machine fault estimation method based on a two-dimensional gain adjustment mechanism is characterized by comprising the following steps:
step 1), carrying out model identification on the two-axis servo motion control system, determining a mathematical model of the two-axis servo motion control system, and obtaining the mathematical model of the motion control platform after system identification as follows
x(k+1)=Ax(k)+Bu(k)+Eufu(k) (1)
y(k)=Cx(k)+Eyfy(k) (2)
WhereinRespectively representing system status, control inputs, measurement outputs, process faults and sensor faults,each representing a matrix of system parameters of appropriate dimensions,a parameter distribution matrix representing the corresponding fault, wherein Eu is assumed to be a column full rank matrix, if EuB, then the process fault f at this timeu(k) Can be considered as an actuator failure, willRates of change, denoted as process fault and sensor fault, respectively, are assumed to be bounded, i.e., both are bounded
Wherein eta is more than 0 and gamma is more than 0;
step 2), designing an intermediate observer based on a two-dimensional gain adjustment mechanism, wherein the process is as follows:
first, the following intermediate variables are defined
Where ω is a manipulated variable to be determined, from which the value of the intermediate variable τ (k) is ultimately determined, the following system model is derived from (2) and (4)
The dynamic equation of the system is only related to the time axis parameter k, and in the novel IE to be mentioned later, besides the updating of the parameter along the time axis and the operation of the system, the improvement of the fault estimation result in another dimension is considered, namely, a set of T-step updating processes are additionally added in the interval of each sampling period; before the form of the observer is given, it is necessary to first explain the estimation update strategy of the two dimensions as follows: in order to ensure the estimation performance of the fault, an online estimation performance index with a threshold value is introduced, IE usually carries out parameter updating along a time axis, when the performance index falls into a range which does not meet the threshold value condition, a longitudinal gain adjustment process in a sampling period interval is activated, IE operates under the two-dimensional gain adjustment mechanism until the performance index meets the threshold value condition again, and then IE continues to operate along the time axis, namely returns to a common one-dimensional updating mode;
step 3), initializing observer parameters, and calculating observer gains L (k, t) and F (k, t), wherein the process is as follows:
initializing observer parameters: k: -0, kn:=0,t=0,ω(k,t):=ω(kn,tn),ts:=0,tmaxAnd a threshold δ; starting iteration IE, calculating observer gains L (k, t), F (k, t) through (6);
given a positive scalar α ∈ (0,1) and a parameter ω > 0, if a matrix exists And a scalar ε > 0, satisfy
Then the estimated error of the IE is guaranteed to be consistent with the system state and eventually bounded, and satisfiedWherein the content of the first and second substances,
Π′11=Π11-αP1(k,t),Π′22=Π22-αP2(k,t)
the iteration IE is started and the following estimates are obtained:
2. the method of claim 1 for estimating a fault in a two-axis engraver based on a two-dimensional gain adjustment mechanism, the method further comprising the steps of:
step 4), defining an estimation performance evaluation function and judging whether to perform longitudinal updating according to the evaluation function, wherein the process is as follows:
If the value of the performance evaluation function J ≧ δ, a longitudinal update, ω (k), will be maden,tn):=ω(k,t)+ξ1When the maximum vertical update step t is exceededmaxWhen the estimated performance evaluation function is still larger than the threshold value, then ω (k)n,tn):=ω(k,t)+ξ2,ξ1And xi2Respectively representing the step size of ω (k, t) updating in two dimensions;
step 5), judging whether to perform transverse updating according to the evaluation function, wherein the process is as follows:
if the value J of the performance evaluation function is less than or equal to delta, then the performance evaluation function is transversely updated, and the estimation value obtained by IE is used as the final estimation value at the current moment, namely Output of
In the above step, the observer gains L (k, t) and F (k, t) are obtained by solving the stability condition, respectively representing the estimated values obtained after the t-th iteration at the sampling time k,is the final estimate at time k, and, in addition,a sliding average value representing an output estimation error is a performance index for evaluating the estimation effect of the design, qdThe window time representing the sliding average, δ is a threshold value pre-selected according to the particular system.
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