CN109597403A - Mechatronic control system method for diagnosing faults based on iterative learning filter - Google Patents
Mechatronic control system method for diagnosing faults based on iterative learning filter Download PDFInfo
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- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
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- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
- G05B23/0254—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model based on a quantitative model, e.g. mathematical relationships between inputs and outputs; functions: observer, Kalman filter, residual calculation, Neural Networks
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Abstract
The invention discloses a kind of Mechatronic control system method for diagnosing faults based on iterative learning filter, it is related to iterative learning control field, this method is to contain actuator failures, the Mechatronic control system of uncertain disturbances and output transducer nonuniform sampling is research object, the novel fault diagnostic method based on iterative learning filter is provided in conjunction with the self-characteristic of nonuniform sampling system, by the state space equation for constructing actuator failures nonuniform sampling Mechatronic control system, equivalent transformation actuator failures signal, design iteration study Fault Detection Filter can solve the troubleshooting issue of nonuniform sampling Mechatronic control system, the efficiency and precision of fault diagnosis are high and are easy to Project Realization, with real-time detection and a plurality of types of actuator failures can be estimated, the diagnosis number of actuator failures can be effectively reduced simultaneously.
Description
Technical field
The present invention relates to iterative learning control field, especially a kind of Mechatronic control system based on iterative learning filter
Method for diagnosing faults.
Background technique
China manufactures process and automation is just being done step-by-step at present, digital computer and sensor skill in industrial system
Art is used widely, and more and more Mechatronic control systems are occurred in the form of sampled-data system in Practical Project, machine
Electrical integrated continuous depth integration, meanwhile, Mechatronic control system starts to develop to high complexity and large-scale direction, Electrical Control
The safety and stability of system processed are just particularly important.If the failure of large-scale Mechatronic control system cannot be found rapidly
And processing, it will lead to Mechatronic control system and be unable to operate normally, it could even be possible to hardware damage or product can be brought not to conform to
The serious consequence such as lattice, it is more serious or even can cause casualties and environmental pollution, therefore, for Mechatronic control system therefore
Barrier diagnostic techniques has become the important leverage of Mechatronic control system safe and highly efficient operation.
Fault diagnosis technology is rapidly developed in recent years, wherein the analysis method based on object model is always that failure is examined
The important component of disconnected technology obtains analytic modell analytical model and has great importance for this kind of method for diagnosing faults.Observer and
Algorithm filter is always to realize the main path based on analytic modell analytical model method for diagnosing faults, and investigative technique mainly includes being based on
The methods of adaptive kernel time-frequency distribution, Unknown Input Observer and fault diagnosis of Kalman filter.It is introduced in filter
Iterative Algorithm construction Fault Detection Filter is a kind of emerging fault diagnosis and Fault Estimation method, and this method is by iteration
The advantages that learning algorithm structure is simple, tracking accuracy is high applies in the fault diagnosis and Fault Estimation of system.But it passes at present
The method for diagnosing faults of system is all based on continuous system or discrete system, and the practical operation situations such as Mechatronic control system are then more
For complexity, tend not to simply be classified as continuous system or discrete system.This is because in Mechatronic control system, quilt
Object work is controlled in continuous-time domain, but its input and output is but presented with sample sequence, therefore the control in Mechatronic control system
Device processed design can only be realized by discrete signal, and need to carry out by technologies such as D/A and analog/digital conversions continuous signal and
The conversion of discrete signal, if system input and output are all uniform samplings, system can obtain its discrete differential by discretization
Descriptive equation is as Controlling model.But the main means of Mechatronic control system discretization are by sensor sample, usually vacation
If all the sensors synchronize and with identical polydispersity index, however all the sensors is wanted to realize that uniform sampling is suitable in engineering
Difficult, especially in complicated system, usually contain a variety of different types of sensors, system context temperature, pressure
The variations such as power can all have larger impact to sampling rate, unavoidably will appear nonuniform sampling phenomenon.Such that electromechanical
There is a part input in some cases in control system or output signal is discrete form and other parts are still continuous shape
The phenomenon that formula, therefore the system equation of the Mechatronic control system under actual conditions contains continuous and discrete two kinds of signal shapes simultaneously
Formula can not simply be classified as continuous system or discrete system, more precisely belong to a kind of nonuniform sampling system, therefore straight
It connects and is examined existing for discrete system or the method for diagnosing faults of continuous system applied to progress failure in Mechatronic control system
Disconnected is inaccurate.
Summary of the invention
The present inventor regarding to the issue above and technical need, proposes a kind of Electromechanical Control based on iterative learning filter
The fault diagnosis to nonuniform sampling system, the efficiency and essence of fault diagnosis may be implemented in diagnosis method for system fault, this method
It spends all higher.
Technical scheme is as follows:
A kind of Mechatronic control system method for diagnosing faults based on iterative learning filter, this method comprises:
Mechatronic control system is established in the system model that actuator failures occur and are disturbed when influencing, the system
It include system parameter, actuator failures signal, disturbing signal and the Electromechanical Control of the Mechatronic control system in model
The discrete sampling heterogeneous of system exports, and the actuator failures signal is nonlinear Time Continuous function；
Become according to the state that the system parameter of the Mechatronic control system and disturbing signal define the Mechatronic control system
Amount, input variable and disturbance variable, obtain the Mechatronic control system according to the system model of the Mechatronic control system and are based on
The state-space model of the actuator failures signal, the state-space model based on actuator failures signal include described
State equation of the Mechatronic control system based on the state variable, input variable, actuator failures signal and disturbance variable and
The output equation that the Mechatronic control system is exported based on the discrete sampling of the state variable, the output equation are to be based on adopting
The discrete form at sample moment；
Described hold is obtained according to the state-space model based on the actuator failures signal of the Mechatronic control system
The equivalent fault signal of row device fault-signal simultaneously obtains institute using actuator failures signal described in the equivalent fault signal substituting
The state-space model based on equivalent fault signal of Mechatronic control system is stated, the equivalent fault signal is Time Continuous function
And the equivalent fault signal is constant value in two neighboring sampling instant, the Mechatronic control system is in the equivalent fault
Sampling output under the action of signal is same with the sampling output phase under the action of actuator failures signal；
The Electromechanical Control is designed for the state-space model based on equivalent fault signal of the Mechatronic control system
The Fault Detection Filter based on Iterative Algorithm of system, the Fault Detection Filter include the Mechatronic control system
It is based on based on state estimation, the state equation of the input variable and virtual faults estimated value and the Mechatronic control system
The output equation of the discrete sampling output estimation value of state estimation, the output equation is conitnuous forms；
Determine the Mechatronic control system state-space model based on equivalent fault signal and the Electromechanical Control system
Discrete sampling between the Fault Detection Filter of system exports residual error, and whether the norm for detecting the discrete sampling output residual error reaches
To predetermined threshold；When discrete sampling output residual error is not up to the predetermined threshold, the Mechatronic control system fortune is determined
Row is normal；
When discrete sampling output residual error reaches the predetermined threshold, using discrete sampling output residual error to institute
The virtual faults estimated value stated in the Fault Detection Filter of Mechatronic control system is iterated update, until the discrete sampling
Output residual error is less than the predetermined threshold and the Fault Detection Filter of the Mechatronic control system is made to approach the Electromechanical Control
The state-space model based on equivalent fault signal of system；The electromechanics is exported according to finally obtained virtual faults estimated value
The fault diagnosis result of control system.
The method have the benefit that:
This application discloses a kind of Mechatronic control system method for diagnosing faults based on iterative learning filter, this method with
Mechatronic control system containing actuator failures, uncertain disturbances and output transducer nonuniform sampling is research object, knot
The self-characteristic for closing nonuniform sampling system provides the novel fault diagnostic method based on iterative learning filter, is held by building
The state space equation of row device failure nonuniform sampling Mechatronic control system, equivalent transformation actuator failures signal, design iteration
Study Fault Detection Filter can solve the troubleshooting issue of nonuniform sampling Mechatronic control system.
The application also analyzes fault diagnosis threshold values and output error signal characteristic, and selected fault diagnosis algorithm parameter simultaneously
Guarantee the convergence of virtual faults estimation procedure.The algorithm can be actuator continuous operation and output transducer is non-homogeneous adopts
The Mechatronic control system of sample process detects simultaneously and estimation is out of order, and can effectively reduce the diagnosis number of actuator failures, mention
The efficiency and precision of high fault diagnosis, fault diagnosis algorithm structure is simple, and algorithm parameter selection is convenient, is easy to Project Realization, can
With real-time detection and a plurality of types of actuator failures are estimated, while the diagnosis number of actuator failures can be effectively reduced,
Improve the efficiency and precision of fault diagnosis, the troubleshooting issue suitable for various types of nonuniform sampling industrial equipments.
Detailed description of the invention
Fig. 1 is that the failure of the Mechatronic control system method for diagnosing faults disclosed in the present application based on iterative learning filter is examined
Stop journey structure chart.
Fig. 2 is the jump signal fault diagnosis result in example provided by the present application.
Fig. 3 is the jump signal fault diagnosis residual error in example provided by the present application.
Fig. 4 is the gradual change signal fault diagnosis result in example provided by the present application.
Fig. 5 is the gradual change signal fault diagnosis residual error in example provided by the present application.
Fig. 6 is the periodic signal fault diagnosis result in example provided by the present application.
Fig. 7 is the periodic signal fault diagnosis residual error in example provided by the present application.
Specific embodiment
The following further describes the specific embodiments of the present invention with reference to the drawings.
This application discloses a kind of Mechatronic control system method for diagnosing faults based on iterative learning filter, please refer to figure
1 fault diagnosis flow scheme structure chart, the method for diagnosing faults include the following steps:
Step 1: establishing Mechatronic control system in the system model that actuator failures occur and are disturbed when influencing.
In view of Mechatronic control system also suffers from disturbing influence in actual application, therefore holding of establishing of the application
The system model of Mechatronic control system when row device unit breaks down describes are as follows:
The system model of the Mechatronic control system of the application includes system parameter, holds it can be seen from above system model
The discrete sampling heterogeneous of row device fault-signal, disturbing signal and Mechatronic control system exports.Wherein, system parameter includes
Armature resistance R in above-mentioned modela, armature supply ia, armature inductance La, back EMF coefficient Ce, motor speed ω, input
Voltage eV, rotor moment of inertia J, motor shaft mechanical damping CfWith torque coefficient CM.F (t) in above-mentioned model indicates Electromechanical Control
The actuator failures signal of system, actuator failures signal are nonlinear Time Continuous function.W in above-mentioned model1、w2And v
(ti) indicate Mechatronic control system disturbing signal.Y (t in above-mentioned modeli) indicate that the discrete output of Mechatronic control system is adopted
The nonuniform sampling of sample namely sensor exports, wherein tiIndicate each sampling instant heterogeneous, i is parameter, the Electrical Control
The system time domain of system processed is t ∈ [0, tN], then sampling instant meets 0 < t1< t2< ... < tN, the sampling configuration of output signal
For it is non-homogeneous can even is that it is random, maximum sampling interval value be customized value T, t0=0, ti-ti-1≤T。
Step 2: the state space equation of building actuator failures nonuniform sampling Mechatronic control system.Including walking as follows
It is rapid:
Step 1: defining the state variable, input variable and disturbance variable of Mechatronic control system.Due to Mechatronic control system
With repeating motion characteristic, thus according to the armature supply and motor speed definition status variable of the motor that persistently reruns
For xk(t)=[ia ω]T, it is u that the input voltage that the system parameter according to Mechatronic control system includes, which defines input variable,k(t)
=eV, the disturbance variable for defining Mechatronic control system is w (t)=[w1 w2]T.Wherein, subscript k indicates that Mechatronic control system is being
It is iteratively repeated operation batch in system time domain, within the scope of each operation batch, disturbing signal and fault-signal energy norm have
Boundary meets | | w (t) | | < dw, | | v (ti) | | < dv, dwAnd dvValue be not construed as limiting.The actuator in failure diagnostic process
Fault-signal f (t) be constant unknown function and be iteratively repeated operation batch k it is unrelated.
Step 2: being then based on state variable xk(t), input variable uk(t), actuator failures signal f (t) and disturbance variable w
(t) can rewrite system model shown in formula (1) indicates are as follows:
yk(ti)=[0 1] xk(ti)+v(ti)
Step 3: obvious formula (2) is continuous system and the system that discrete system mixes, and can further obtain Mechatronic control system
State-space model based on actuator failures signal are as follows:
Wherein, A, B, C, Bf, BwAnd DvFor the sytem matrix of corresponding dimension, matrix meets observability condition to (C, A),
The original state x of definition system operationk(0)=x0。
Step 3: determining the equivalent fault signal of actuator failures signal.
Since the output of formula (3) is a series of discrete point of nonuniform samplings, the information between the neighbouring sample moment can not
It obtains, therefore each discrete sampling output can only reflect actuator failures signal in previous sampling instant to this sampling instant
Influence in entire sampling time section to Mechatronic control system output introduces equivalent fault signal, including following several steps thus
It is rapid:
Step 1: being by the continuous state that formula (3) can obtain Mechatronic control system
Step 2: while the state that formula (3) can obtain the systematic sampling moment of Mechatronic control system again is represented by
Step 3: using sampling instant as boundary, segmentation indicates the integral expression of actuator failures signal are as follows:
Step 4: INTEGRAL THEOREM OF MEAN being applied to formula (6), is determined in two neighboring sampling instant ti-1And tiBetween meet it is following
The constant F (i) of expression formula:
Wherein min (f (t))≤F (i)≤max (f (t)), ti-1≤t≤ti。
Step 5: enabling ti-ti-1=li, then formula (7) can further indicate that are as follows:
The equivalent fault signal that a new failure function is actuator failures signal can be obtained according to formula (8):
According to formula (7), (8) and (9), the nonuniform sampling output of Mechatronic control system be may be expressed as:
By formula (10) it is found that Mechatronic control system system is in actuator failures signal f (t) and equivalent fault signal's
The lower sampled output value of effect is identical, i.e. fault-signal f (t) withGeneration system is exported influence it is of equal value, so claiming failureFor the equivalent fault of f (t).
Then utilize equivalent fault signalSubstitute actuator failures signal f (t) available Mechatronic control system based on
The state-space model of equivalent fault signal are as follows:
Step 4: the state-space model (11) based on equivalent fault signal for Mechatronic control system designs Electrical Control
The Fault Detection Filter based on Iterative Algorithm of system processed, and using Fault Detection Filter to Mechatronic control system into
Row fault diagnosis.
Since actuator failures signal f (t) is consecutive variations in two neighboring sampling instant, and sample output y
(ti) it is discrete signal, therefore y (t can not be exported by discrete samplingi) to actuator failures signal f (t) carry out accurate estimation and
Reconstruct, but the equivalent fault signal of actuator failures signal f (t)Although and Time Continuous function, adopted two neighboring
It is constant value in the sample moment, therefore the equivalent fault value F (i) in the every two neighbouring sample moment and discrete sampling export y (ti)
It is one-to-one relationship, therefore y (t can be exported with discrete samplingi) equivalent fault value F (i) is estimated.
By being analyzed above it is found that can be by sampled output signal to equivalent fault-signalEstimated, thus diagnostic machine
The troubleshooting issue of the actuator failures that electric control system actually occurs, nonuniform sampling Mechatronic control system (3) thus turns
Turn to equivalent fault signalTroubleshooting issue (11).
To carry out fault diagnosis to formula (11), it is necessary first to sampling holding is carried out to discrete sampling output, it is defeated according to lagging
Output equation can be expressed as again conitnuous forms by model out:
yk(t)=Cxk(t-θ(t))+Dvv(t-θ(t)) (12)
Wherein, θ (t)=t-ti,ti≤ t < ti+1.Convolution (11) and (12) design Mechatronic control system based on iteration
The Fault Detection Filter of learning algorithm are as follows:
Wherein,It is state space mould based on equivalent fault signal of the Fault Detection Filter to Mechatronic control system
The state estimation of the continuous state of type (11),Be Fault Detection Filter to Mechatronic control system based on equivalent fault
The estimated value of the discrete sampling output of the state-space model (11) of signal.Matrix L is the gain matrix being pre-designed, so that square
Left half-plane of the characteristic root of battle array (A-LC) in complex field.It is the virtual faults optimized in time domain after kth time iterative learning
Estimated value is defined as form:
In formulaIt is updated by the iterative learning control law of formula (15):
Wherein, Γ (i) is the corresponding iterative learning gain matrix of ith sample point, and γ is predetermined threshold, RkIt (i) is kth
A discrete sampling export residual error and:
Discrete sampling exports residual error Rk(i) indicate that the discrete sampling output determined based on formula (11) is determined with based on formula (13)
Discrete sampling output estimated value between difference namely Mechatronic control system the state space based on equivalent fault signal
Discrete sampling between model (11) and the Fault Detection Filter (13) of Mechatronic control system exports residual error.
The entry condition of iterative learning Fault Detection Filter are as follows:
That is, exporting residual error R in discrete samplingk(i) when being not up to predetermined threshold γ, Mechatronic control system operation is being determined just
Often.Residual error R is exported in discrete samplingk(i) fault diagnosis just is carried out to Mechatronic control system when reaching predetermined threshold γ.Formula (15)
It is the iterative learning Fault Estimation algorithm to virtual faults estimated value, exports residual error R using discrete samplingk(i) in optimization time domain
Inside repeatedly to virtual faults estimated valueValue within the ith sample timeIt is updated, until discrete sampling exports
Residual error Rk(i) being less than predetermined threshold γ makes the Fault Detection Filter (13) of Mechatronic control system approach Mechatronic control system
State-space model (11) based on equivalent fault signal obtains equivalence value F (i) of the failure within the ith sample time simultaneously,
Until reaching the required precision of setting, to achieve the purpose that fault detection and estimation namely finally obtained virtual faults are estimated
Evaluation obtains and outputs the fault diagnosis result of Mechatronic control system.
In method for diagnosing faults disclosed in the present application, Rational choice predetermined threshold γ can guarantee fault diagnosis algorithm both
Reach the required precision that time requirement meets Fault Estimation again, there is no interference, γ=0 can be taken.But as above
Described, there are probabilistic disturbing signals in Mechatronic control system actual moving process, even if output misses when no fault occurs
Difference is not also 0, therefore to reduce false alarm rate, threshold values restriction technology shown in formula (15) can be used and improve fault diagnosis algorithm
Reliability, this application provides the determination methods of predetermined threshold γ a kind of, namely system is defeated when providing a kind of determining fault-free
The method for the constraint condition that error need to meet out, includes the following steps:
Step 1: defining state error of the Mechatronic control system after kth time is iteratively repeated operation batch are as follows:
Define output error of the Mechatronic control system after kth time is iteratively repeated operation batch are as follows:
Define evaluated error of the Mechatronic control system after kth time is iteratively repeated operation batch are as follows:
Step 2: determine that the dynamical equation of error system can be described as:
Step 3: the output error r under the description of time lag output modelkIt (t) is actually the non-homogeneous output letter of discrete time
Number, it can be obtained after further rewriting the dynamical equation (21) of error system thus
Step 4: enabling ηk(t)=ek(t)-ek(t- θ (t))=ek(t)-ek(ti), then formula (22) can be further represented as
η in formula (23)k(t) it is considered as disturbing since sampling exports error caused by the serialization of Time-Delay model method,
Its value is represented by ek(t)-ek(ti), ti≤ t < ti+1, it is known that dk(t) value determines by kth time error, and in each sampling
Carving its value is zero.
The R of discrete formk(i) and the r of conitnuous formsk(t) signal is respectively present in formula (15) and formula (13), rk(t)
It is Rk(i) sampling of signal keeps form, residual error Rk(i) estimate for the iterative learning of failure；Due to the filter status being related to
It is continuous, so continuous feedback residual signals may only be added, by Rk(i) sampling keeps being allowed to being exactly continuously rk(t) shape
Formula.
Step 5: it can be obtained by formula (22):
Arbitrary intervals ti≤ t < ti+1Inside there is following relational expression:
Wherein, Φ () indicates the state-transition matrix of error equation, by ek(ti) move on to the left side and can obtain:
Step 6: by ηk(t) substituting into formula (26) can obtain:
Step 7: to can be obtained after formula (27) both sides derivation
Wherein ti≤ t < ti+1。
Step 8: it can be obtained after solving the differential equation to formula (28):
Wherein,
Due in closed interval [ti, ti+1] in, Φ (t, ti) continuous in time, Φ is known according to Sufficient condition uniform bound theorem
(t,ti) it in the time domain is norm-bounded, exist:
Norm is asked simultaneously to formula (29) both ends for this, and convolution (30) and (31) can obtain
||ηk(t)||≤(ti+1-ti)exep(a1+a2+a3)≤Texep(a1+a2+a3)=dη (32)
Wherein,
Therefore, for the state-space model (3) of actuator failures nonuniform sampling Mechatronic control system, in iterative learning
In the error equation (23) of Fault Detection Filter (13), error caused by the serialization of Time-Delay model method is exported as sampling and is disturbed
ηk(t) norm-bounded, i.e., | | ηk(t) | | < dη, ti≤ t < ti+1, since sampling interval is any choosing, so this conclusion pair
It is all to set up in entire time domain.
Step 9: in addition can further it be obtained by first equation in formula (23):
Take norm that can obtain (33) both members:
Step 10: it is obtained after taking norm by the both ends of the equation of second equation in formula (23):
It can further obtain:
||Rk(i)||≤ct(sldv+sbwdw+sdη)+d1dv=γ (36)
Wherein c=| | C | |,L=| | LDv||。
This makes it possible to obtain the estimated value expression formulas of predetermined threshold γ.When Mechatronic control system breaks down, in formula (35)
| | Φ (t, τ) BfΔfk(τ) | | ≠ 0, so | | Rk(i) | | > γ；It can thus be concluded that working as sampling instant residual norm | | Rk(i)|
| when > γ, the starting of iterative learning Fault Detection Filter is estimated virtual faults using iterative learning control law (15), is realized to equivalent
The diagnosis and estimation of failure.
In addition, the application is when using Fault Detection Filter, it is also necessary to which the parameter of reasonable selection fault diagnosis device guarantees
The convergence of virtual faults estimation procedure, present invention also provides a kind of methods of the parameter of determining fault diagnosis device, including such as
Lower step:
Step 1: can be obtained by formula (23)
Systematic sampling moment error equation can be obtained according to formula (37) simultaneously are as follows:
Wherein, i=1,2 ..., N.
Step 2: carrying out segmentation as the equation in bound pair formula (38) using each sampled point indicates:
Because of the Δ f in each sampling intervalkIt (t) is constant value Δ Fk(i), so formula (39) can be write as
Step 3: had according to INTEGRAL THEOREM OF MEAN:
Then formula (40) can be further represented as
It can similarly obtain
Wherein min (w (t))≤w(j)≤max(w(t)),ti-1≤t≤ti, and
Wherein min (ηk(t))≤η(i,k)≤max(ηk(t)),ti-1≤t≤tiAnd
Wherein v(j)=v (tj)。
Step 4: being obtained after formula (42) to formula (45) is substituted into formula (38)
Then output error can be expressed as:
Step 5: convolution (15) and formula (20) can obtain
ΔFk+1(i)=Δ Fk(i)-Γ(i)Rk(i) (48)
Formula (47) substitution (48) can be obtained
Wherein:
Step 6: it can be obtained by formula (49):
It is obtained after taking norm to formula (51) both sides:
Wherein,
Step 7: to formula (52) both ends simultaneously multiplied by0 < λ < 1, can obtain:
It can be obtained by λ norm property:
Step 8: thus such as state-space model (3) design of actuator failures nonuniform sampling Mechatronic control system
Fault Detection Filter shown in formula (13), using shown in formula (15) when virtual faults iterative learning algorithm for estimating, iteration
The parameter for practising fault diagnosis device should meet following condition:
||I-Γ(i)CliΦiBf| | < 1, i=1,2 ..., N (55)
Wherein, liFor i-th sampling step length, ΦiIt is Fault Detection Filter state-transition matrix in i-th sampling interval
Maximum value.As long as λ thus in modus ponens (54) is sufficiently small to make M < 1, according to λ norm property, as k → ∞
It can be obtained with reason formula (47)
Show as k → ∞, the output of Fault Detection Filter converges to reality output under λ norm meaning, estimates at this time
Failure convergence is counted to equivalent fault
Present invention also provides following example come the clearer process for showing method for diagnosing faults disclosed in the present application with
And obtained result:
A kind of sensor output containing actuator unit failure, uncertain interference for formula (1) form is non-homogeneous
The Mechatronic control system of sampling, as armature resistance Ra=2.1 Ω, rotor moment of inertia J=1kgm2, armature inductance La=800mH,
Back EMF coefficient Ce=0.18V/ (rad/s), motor shaft mechanical damping coefficient Cf=1.07 × 10-3Nm/ (rad/s), torque
Coefficient CMWhen=0.646Nm/A, constructed using the armature supply, motor speed and input voltage of motor such as formula (3) form
Actuator failures nonuniform sampling Mechatronic control system state space equation, wherein nonuniform sampling exports y (ti) in tiIt is non-
Uniform sampling moment, sampling period value change at random between 0.1~0.2s, T=0.1.Obvious system meets observability item
Part, as the state initial value x of system0=[0.1 0.2]T, when testing input voltage u (t)=48V, Mechatronic control system was being run
White noise acoustic disturbance w (t) and the v (t that armature supply and motor speed are respectively 0.02 by energy in journeyi) influence.According to
The method of the present invention designs the Fault Detection Filter based on iterative learning such as formula (13) form, and chooses gain matrix L=[1
1]T, further the virtual faults of design such as formula (15) form estimate more new algorithm, and iteration gain is selected as Γ (i)=3.Due to being
There are uncertain disturbances in system, therefore Fault Estimation residual error is not 0 in the process of running, but become in the range of threshold value limits
Change.Algorithm starting threshold value in method for diagnosing faults is 0.08.Fault diagnosis structure chart is as shown in Figure 1.Since Mechatronic Systems is transported
The jump signals failure f such as the mechanical axis that will appear during row is stuck or voltage source is abnormal1(t) and executing agency's fatigue and
The gradual change signal fault f that reduced performance caused by abrasion or the aging of brake long working and abrasion is shown2(t), with
And executing agency's unit damages caused periodic signal failure f3(t)。
Fig. 2-Fig. 7 is respectively to jump signal failure f1(t), gradual change signal fault f2(t) and periodic signal failure f3(t)
The result of virtual faults estimation and discrete sampling output residual error after real-time fault diagnosis is carried out by Fault Detection Filter.It can be seen that
Iterative learning method for diagnosing faults of the invention can detect the generation of failure and carry out accurate estimation to failure, and
There is certain adaptability to different types of failure, effectively reduce the number of iterations of fault detection and Fault Estimation process,
To improve the efficiency of fault diagnosis, and then improve the real-time of fault diagnosis result.
Above-described is only the preferred embodiment of the application, and present invention is not limited to the above embodiments.It is appreciated that this
The other improvements and change that field technical staff directly exports or associates without departing from the spirit and concept in the present invention
Change, is considered as being included within protection scope of the present invention.
Claims (7)
1. a kind of Mechatronic control system method for diagnosing faults based on iterative learning filter, which is characterized in that the method packet
It includes:
Mechatronic control system is established in the system model that actuator failures occur and are disturbed when influencing, the system model
In include the Mechatronic control system system parameter, actuator failures signal, disturbing signal and the Mechatronic control system
Discrete sampling heterogeneous output, the actuator failures signal be nonlinear Time Continuous function；
The state variable, defeated of the Mechatronic control system is defined according to the system parameter of the Mechatronic control system and disturbing signal
Enter variable and disturbance variable, the Mechatronic control system is obtained according to the system model of the Mechatronic control system and is based on described hold
The state-space model of row device fault-signal, the state-space model based on actuator failures signal include the Electrical Control
State equation and the machine of the system processed based on the state variable, input variable, actuator failures signal and disturbance variable
The output equation that electric control system is exported based on the discrete sampling of the state variable, the output equation are based on sampling instant
Discrete form；
The actuator is obtained according to the state-space model based on the actuator failures signal of the Mechatronic control system
The equivalent fault signal of fault-signal simultaneously obtains the machine using actuator failures signal described in the equivalent fault signal substituting
The state-space model based on equivalent fault signal of electric control system, the equivalent fault signal are Time Continuous function and institute
It is constant value that equivalent fault signal, which is stated, in two neighboring sampling instant, and the Mechatronic control system is in the equivalent fault signal
Under the action of sampling output it is same with the sampling output phase under the action of actuator failures signal；
The Mechatronic control system is designed for the state-space model based on equivalent fault signal of the Mechatronic control system
The Fault Detection Filter based on Iterative Algorithm, the Fault Detection Filter includes that the Mechatronic control system is based on
State estimation, the state equation of the input variable and virtual faults estimated value and the Mechatronic control system are based on state
The output equation of the discrete sampling output estimation value of estimated value, the output equation is conitnuous forms；
Determine the state-space model and the Mechatronic control system based on equivalent fault signal of the Mechatronic control system
Discrete sampling between Fault Detection Filter exports residual error, and whether the norm for detecting the discrete sampling output residual error reaches pre-
Determine threshold value；When discrete sampling output residual error is not up to the predetermined threshold, the Mechatronic control system operation is being determined just
Often；
When discrete sampling output residual error reaches the predetermined threshold, using discrete sampling output residual error to the machine
Virtual faults estimated value in the Fault Detection Filter of electric control system is iterated update, until the discrete sampling exports
Residual error is less than the predetermined threshold and the Fault Detection Filter of the Mechatronic control system is made to approach the Mechatronic control system
The state-space model based on equivalent fault signal；The Electromechanical Control is exported according to finally obtained virtual faults estimated value
The fault diagnosis result of system.
2. Mechatronic control system method for diagnosing faults according to claim 1, which is characterized in that described to establish Electromechanical Control
System is in the system model that actuator failures occur and are disturbed when influencing, including establishes such as drag:
The system parameter of the Mechatronic control system includes the armature resistance R in above-mentioned modela, armature supply ia, armature inductance
La, back EMF coefficient Ce, motor speed ω, input voltage eV, rotor moment of inertia J, motor shaft mechanical damping CfAnd torque
Coefficient CM, the actuator failures signal of f (t) the expression Mechatronic control system, y (ti) indicate the Mechatronic control system from
Dissipate output sampling, tiIndicate each sampling instant heterogeneous, i is parameter；w1、w2With v (ti) indicate the Mechatronic control system
Disturbing signal.
3. Mechatronic control system method for diagnosing faults according to claim 2, which is characterized in that described according to the electromechanics
The state variable, input variable and disturbance that the system parameter and disturbing signal of control system define the Mechatronic control system become
Amount, obtains the Mechatronic control system based on the actuator failures signal according to the system model of the Mechatronic control system
State-space model, comprising:
The armature supply and motor speed definition status variable that system parameter according to the Mechatronic control system includes are xk
(t)=[ia ω]T, it is u that the input voltage that the system parameter according to the Mechatronic control system includes, which defines input variable,k(t)
=eV, the disturbance variable for defining the Mechatronic control system is w (t)=[w1 w2]T, k indicates that the Mechatronic control system is being
Operation batch is iteratively repeated in system time domain；
Based on state variable, input variable, actuator failures signal and disturbance variable by the system mould of the Mechatronic control system
Type is rewritten:
yk(ti)=[01] xk(ti)+v(ti)
The Mechatronic control system, which is obtained, according to the system model of the revised Mechatronic control system is based on the actuator
The state-space model of fault-signal are as follows:
Wherein, A, B, C, Bf, BwAnd DvFor the sytem matrix of corresponding dimension, matrix meets observability condition to (C, A).
4. Mechatronic control system method for diagnosing faults according to claim 3, which is characterized in that described according to the electromechanics
The state-space model based on the actuator failures signal of control system obtains the equivalent event of the actuator failures signal
Barrier signal and using actuator failures signal described in the equivalent fault signal substituting obtain the Mechatronic control system based on
The state-space model of equivalent fault signal, includes the following steps:
Step 1: being obtained according to the state-space model based on the actuator failures signal of the Mechatronic control system described
The continuous state of Mechatronic control system are as follows:
Step 2: being obtained according to the state-space model based on the actuator failures signal of the Mechatronic control system described
The state of the sampling instant of Mechatronic control system are as follows:
Step 3: using sampling instant as boundary, determining the integral expression of the actuator failures signal are as follows:
Step 4: being determined according to the integral expression of the actuator failures signal based on INTEGRAL THEOREM OF MEAN and adopted two neighboring
Sample moment ti-1And tiBetween meet the constant F (i) of following expression formula:
Wherein min (f (t))≤F (i)≤max (f (t)), ti-1≤t≤ti；
Step 5: enabling ti-ti-1=li, the expression formula of step 4 is rewritten asAnd obtain described hold
The equivalent fault signal of row device fault-signal is
Step 6: determining the state-space model based on equivalent fault signal of the Mechatronic control system are as follows:
5. Mechatronic control system method for diagnosing faults according to claim 4, which is characterized in that described to be directed to the electromechanics
The state-space model based on equivalent fault signal of control system designs calculating based on iterative learning for the Mechatronic control system
The Fault Detection Filter of method, comprising:
It is adopted according to the output equation in state-space model of the Mechatronic control system based on the equivalent fault signal
The conitnuous forms that sample kept and obtained output equation are yk(t)=Cxk(t-θ(t))+DvV (t- θ (t)), wherein θ (t)=t-ti,
ti≤ t < ti+1；
Design the Fault Detection Filter based on Iterative Algorithm of the Mechatronic control system are as follows:
Wherein,It is that the Fault Detection Filter is empty to the state based on equivalent fault signal of the Mechatronic control system
Between model continuous state state estimation, L is the gain matrix being pre-designed, so that the characteristic root of matrix (A-LC) is multiple
The Left half-plane of number field,Be the Fault Detection Filter to the Mechatronic control system based on equivalent fault signal
The estimated value of the discrete sampling output of state-space model；It is the virtual faults estimated value after kth time iterative learning, definition
For following form:
AndIt is updated by following iterative learning control law:
Wherein, Γ (i) is the corresponding iterative learning gain matrix of ith sample point, Rk(i) residual error is exported for k-th of discrete sampling
Andγ is the predetermined threshold.
6. Mechatronic control system method for diagnosing faults according to claim 5, which is characterized in that the method also includes such as
Lower step:
Step 1: defining state error of the Mechatronic control system after kth time is iteratively repeated operation batch is
Output error isThe evaluated error of failure is
Step 2: determining the dynamical equation of error system are as follows:
Step 3: the dynamical equation of error system is rewritten are as follows:
Step 4: arbitrary intervals t is determined by the equation of step 3i≤ t < ti+1Inside there is following relational expression:
Wherein, Φ () indicates the state-transition matrix of error equation, by ek(ti) move on to the left side and can obtain:
Step 5: enabling ηk(t)=ek(t)-ek(t- θ (t))=ek(t)-ek(ti), then equation in step 4 is rewritten as:
Step 6: carrying out both sides derivation to the equation in step 5 can obtain:
Step 7: it can be obtained after further solving the differential equation to the equation in step 6:
Wherein,
Due in closed interval [ti, ti+1] in, Φ (t, ti) it is continuous in time, according to Sufficient condition uniform bound theorem know Φ (t,
ti) it in the time domain is norm-bounded, existAndSimultaneously to the solution differential equation
The both ends of the equation obtained afterwards while asking norm that can obtain:
||ηk(t)||≤(ti+1-ti)exep(a1+a2+a3)≤Texep(a1+a2+a3)=dη；
Wherein,
Step 8: enabling ηk(t)=ek(t)-ek(t- θ (t))=ek(t)-ek(ti), and the equation in step 3 is converted to
Following equation group:
Step 9: first equation in step 8 is further processed to obtain:
Both ends of the equation obtains following relational expression after taking norm:
Step 10: it is obtained after then taking norm to the both ends of the equation of second equation in step 8:
Further obtain | | Rk(i)||≤ct(sldv+sbwdw+sdη)+d1dv=γ and the value for determining the predetermined threshold,
Middle c=| | C | |,L=| | LDv||。
7. Mechatronic control system method for diagnosing faults according to claim 6, which is characterized in that the method also includes such as
Lower step:
Step 1: according to equationObtain the electromechanics
The error equation of control system sampling instant are as follows:
Wherein, i=1,2 ..., N；
Step 2: carrying out segmentation as the equation in bound pair step 1 using each sampled point indicates:
Because of the Δ f in each sampling intervalkIt (t) is constant value Δ Fk(i), so being further rewritten as:
Step 3: had according to INTEGRAL THEOREM OF MEAN:
Then the equation in step 2 is handled are as follows:
It can similarly obtain,
Wherein, min (w (t))≤w(j)≤max(w(t)),ti-1≤t≤ti, and
Wherein, min (ηk(t))≤η(i,k)≤max(ηk(t)),ti-1≤t≤tiAnd
Wherein, v(j)=v (tj)；
Step 4: the equation that step 3 substitutes into step 1 can be obtained:
Then output error indicates are as follows:
Step 5: Δ F is determined according to the evaluated error of failure and iterative learning control lawk+1(i)=Δ Fk(i)-Γ(i)Rk(i), and
The error originated from input that step 4 is obtained substitutes into:
Wherein,
Step 6: following relational expression is obtained by the equation of step 5:
Both sides obtain after taking normWherein,
Step 7: to the relational expression both ends in step 6 simultaneously multiplied byIt can obtain
It can be obtained by λ norm property:
Step 8: determine that the parameter of the Fault Detection Filter meets according to the relational expression that step 7 obtains:
||I-Γ(i)CliΦiBf| | < 1, i=1,2 ..., N；
Wherein, liFor i-th sampling step length, ΦiFor Fault Detection Filter state-transition matrix i-th sampling interval most
Big value.
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