CN114142782A - Fault estimation and compensation method for asynchronous motor actuator - Google Patents
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Abstract
The invention provides an estimation and compensation method for faults of an actuator of an asynchronous motor, which comprises the following steps: building a five-order nonlinear mathematical model of the asynchronous induction motor based on the assumption of a linear magnetic circuit, improving the built mathematical model of the asynchronous induction motor according to the switching characteristic of the asynchronous motor to obtain an improved nonlinear mathematical model of the asynchronous induction motor, and discretizing the improved nonlinear mathematical model of the asynchronous induction motor; establishing a fault detection filter, generating a residual signal through the fault detection filter, and judging whether the motor has an actuator fault according to the value of the residual signal; designing a fault estimator for estimating the fault size of the actuator; compensating the actuator fault through fault reconstruction; the fault estimation and compensation scheme of the asynchronous motor actuator provided by the invention can well estimate the fault when the fault of the actuator occurs, and offset the negative effect caused by the fault, thereby realizing the compensation of the fault.
Description
Technical Field
The invention relates to the field of asynchronous motor actuators, in particular to a fault estimation and compensation method for an asynchronous motor actuator.
Background
Asynchronous motors have a very important position for the industrial production and daily life of the current society, and have been applied to various fields of national economy, so that the reliability of realizing the operation of the asynchronous motors in severe working environments is a basic and main requirement of the asynchronous motors in many applications. Essentially, an asynchronous machine is a complex system that is nonlinear, time-varying in parameters, and strongly coupled. In order to achieve better control of the asynchronous motor, the three-phase inverter is widely applied to control of the asynchronous motor due to good control performance of the three-phase inverter.
In addition, the efficient, stable and safe operation of the motor is a very much concerned problem, the motor can be out of order in frequent starting, braking and artificial illegal operation of the motor, if the fault can be found in time before the fault occurs, the loss can be greatly reduced and the safety of operators can be ensured by compensating the fault and stopping the machine for maintenance in time, and the inverter in the asynchronous motor system is one of the parts with higher fault rate, and because the inverter is very important to control the asynchronous motor, an effective strategy for estimating and compensating the fault of the three-phase inverter of the asynchronous motor is urgently needed, so that the estimation and effective compensation of the fault of the inverter of the asynchronous motor can be carried out highly corrected, thereby the influence of the fault on the asynchronous motor is counteracted and the loss is reduced.
Since the inverter corresponds to an actuator in a control system of an asynchronous motor, we refer to the three-phase inverter as the actuator. Currently, many studies have been made on fault estimation and compensation methods for asynchronous motor actuators, such as fault estimation based on signal processing, fault estimation based on statistical analysis, fault estimation based on experts, fault estimation based on mathematical models, and so on. However, certain disadvantages and drawbacks exist, and most do not provide an effective means for fault compensation. On the other hand, both the existing fault estimation and compensation methods are obtained without considering the handover method. At present, based on a switching system method, the problem of comprehensive design aiming at an actuator of fault detection, estimation and compensation of a linear parameter change system with residence time constraint is adopted, and an effective solution is not provided.
Disclosure of Invention
The invention mainly aims to overcome the defects in the prior art, and provides a fault estimation and compensation method for an asynchronous motor actuator, which can accurately estimate and compensate the fault of the asynchronous motor actuator.
The invention adopts the following technical scheme:
a method for estimating and compensating for faults of an asynchronous motor actuator is characterized by comprising the following steps:
building a five-order nonlinear mathematical model of the asynchronous induction motor based on the assumption of a linear magnetic circuit, improving the built mathematical model of the asynchronous induction motor according to the switching characteristics of the asynchronous motor to obtain the improved nonlinear mathematical model of the asynchronous induction motor, and discretizing the improved nonlinear mathematical model of the asynchronous induction motor;
establishing a fault detection filter, generating a residual signal through the fault detection filter, and judging whether the motor has an actuator fault according to the value of the residual signal;
designing a fault estimator for estimating the fault size of the actuator;
and compensating the actuator fault through fault reconstruction.
Specifically, a five-order nonlinear mathematical model of the asynchronous induction motor is built on the assumption of a linear magnetic circuit, and the built mathematical model of the asynchronous induction motor is improved according to the switching characteristic of the asynchronous motor, so that the improved nonlinear mathematical model of the asynchronous induction motor is obtained; the method specifically comprises the following steps:
a five-order nonlinear mathematical model of the asynchronous induction motor is constructed on the assumption of a linear magnetic circuit, and the mathematical model comprises the following steps:
the nonlinear mathematical model of the improved asynchronous induction motor is as follows:
where ω is the rotor speed, the letters are marked ". cndot." andrespectively representing the differential of the corresponding letter physical quantity and defining the left side as the right side; tau isLRepresenting a load moment disturbance;the state vector is represented by a vector of states,which represents the magnetic flux of the rotor,which is representative of the stator current,representing the stator voltage and as a control system input vector;
and the rotor speed range is omega epsilon [ omega ]min,ωmax]=[-110,110]rad/s;a1=npLsr/(DmLr),a2=-Rm/Dm, a3=-1/Dm,a4,i=-1/Tr,i,a5,i=Lsr/Tr,i,a6,i=Lsr/(Tr,iσLsLr),a7=npLsr/(σLsLr), a8=1/(σLs), wherein LsIs a stator inductance, LrIs the rotor inductance, LsrIs mutual inductance, σ is leakage factor, Rs,iIs stator resistance, Rr,iIs rotor resistance, DmIs the moment of inertia, RmIs a viscous damping constant, npIs the number of magnetic pole pairs;
specifically, discretizing the improved nonlinear mathematical model of the asynchronous induction motor specifically comprises:
where x (k) represents system state, y (k) represents system output, u (k) represents control input, d (k) represents unknown input, f (k) represents fault input, and matrix Aσk(ρk),Bσk(ρk),Cσk(ρk) Is a known function of p of a measurable parameter variable, BdIs a given constant matrix of appropriate dimensions, BfIs a matrix representing the impact of each fault on the system; switching signal sigmakThe residence time constraint is satisfied,n represents the number of subsystems in the system; let σ for conveniencekI.e. i
Specifically, a fault detection filter is established, and a residual signal is generated by the fault detection filter, specifically:
is an estimate of x (k) and,is a residual estimate signal, AF,i(ρk),BF,i(ρk),CF,i(ρk),DF,i(ρk) Is the parameter matrix of the fault detection filter.
Specifically, whether the motor has an actuator fault is judged according to the magnitude of the residual signal value, specifically:
the residual estimation equation and its critical values are:
sL is the time window of the residual estimate, k0Representing an initial estimate; f and d represent fault and external disturbance, respectively; l2Represents the euclidean 2 norm with values of 0, ∞; sup denotes the supremum, i.e. the minimum upper bound.
Specifically, a fault estimator is designed to estimate the fault size of the actuator, specifically:
wherein ,in order to be able to estimate the state,in order to be able to estimate the fault,andis the observer gain matrix.
Specifically, the actuator fault is compensated through fault reconstruction, specifically:
ur(k) is a reference input, Ki(ρk) Is the LPV feedback gain matrix to be determined,is used to compensate for the effect of the fault on the system.
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
(1) the fault estimation and compensation scheme of the asynchronous motor actuator provided by the invention can well estimate the fault when the fault of the actuator occurs, and offset the negative effect caused by the fault, thereby realizing the compensation of the fault.
Drawings
FIG. 1 is a diagram of steps implemented in a method for estimating and compensating for faults in an asynchronous motor actuator;
FIG. 2 is a schematic diagram of estimation and compensation of asynchronous motor actuator faults;
FIG. 3 is a schematic diagram of a fault detection structure of an asynchronous motor actuator;
FIG. 4 is a schematic diagram of a fault estimation structure of an asynchronous motor actuator;
fig. 5 is a schematic diagram of a fault reconstruction structure of an asynchronous motor actuator.
Detailed Description
The invention is further described below by means of specific embodiments.
Referring to fig. 1, the method for estimating and compensating the fault of the actuator of the asynchronous motor is implemented by the invention, firstly, a dynamic model of the asynchronous motor is built, then, whether the fault exists in a motor system is judged through a residual error, then, the residual error of the system is estimated, finally, the fault is reconstructed according to a residual error estimated value, and finally, the fault compensation is realized, and a schematic diagram of the method is shown in fig. 2.
(1) Modeling
The invention discloses a fault estimation and compensation method for an actuator of an asynchronous motor. Based on the assumption of a linear magnetic circuit, a mathematical model of five-order nonlinear dynamics of an induction motor is as follows:
where ω is the rotor speed, as used hereinThe state vector is represented by a vector of states,which represents the magnetic flux of the rotor,which is representative of the stator current,representing stator voltage and as control system input vectorRepresenting the measurement output. We specify that rotor speed ω is a parameter, such thatIn order to be a new state vector,is the new output vector. It is found from the analysis that the induction motor does have a switching characteristic, and the stator resistance R is caused by a medium change in the motor environment, particularly a temperature changesVariation of (2) causing rotor resistance R when speed is regulated by switching different selectorsrChange, so that the mathematical model of the system is modified to switch the control system pair as follows when taking into account the switching phenomena
wherein
And the rotor speed range is omega epsilon [ omega ]min,ωmax]=[-110,110]rad/s。a1=npLsr/(DmLr),a2=-Rm/Dm,a3=-1/Dm, a4,i=-1/Tr,i,a5,i=Lsr/Tr,i,a6,i=Lsr/(Tr,iσLsLr),a7=npLsr/(σLsLr),a8=1/(σLs), wherein LsIs a stator inductance, LrIs the rotor inductance, LsrFor mutual inductance, σ is the leakage factor, Rs,iIs stator resistance, Rr,iIs rotor resistance, DmIs the moment of inertia, RmIs a viscous damping constant, npIs the number of pole pairs. Parameters of the induction machine are shown in the table below, forFor the system, the sampling period is TsDiscretization was performed 0.002s and p was introduced1(ω)=(ω-ωmin)/(ωmax-ω),p2(ω)=1-p1(ω) results in a switched Linear Parameter Variation (LPV) system in the discrete time domain, hence M-2 is directly obtained. The system mathematical model is as follows:
where x (k) represents system state, y (k) represents system output, u (k) represents control input, d (k) represents unknown input, f (k) represents fault input,fl(k)(l=1,2,...,m2) Corresponding to a particular fault. Matrix Aσk(ρk),Bσk(ρk),Cσk(ρk) Is a known function of p, the measurable parameter variable, bounded at a given tight set Θ. B isdIs a given constant matrix of appropriate dimensions, BfIs a matrix representing the impact of each fault on the system. Among all the classes of possible faults, actuator faults are one of the most difficult faults to handle, since actuators can cause great disturbances to the final control result. From the time-dependent behavior, it is assumed that the switching signal σkThe residence time constraint is satisfied and,n represents the number of subsystems in the system (3), when sigma iskWhen the system (3) is represented by i, respectively Assuming that the parametric variables are in the form of polyhedra, Ai(ρk) Can be rewritten as:
where p is[m]:Is a determined continuous function, Ai,mIs a matrix of known constantsM is in the range of { 1. Furthermore, we assume that the mapping p:satisfy the requirement of
Therefore, it is considered that Ai(ρk) Located in convex hull Co { Ai,1,...,Ai,MOn, for convenience, we useIn place of p[m](ρk)。
In the switching sequence to the system (3), the switching time isResidence time of τdAnd satisfy the pairAre all provided withIf presentClass function xi andclass functionAll initial states of the systemAnd all unknown inputsAll satisfyThe nonlinear system x (k +1) ═ f (x (k), d (k)) is called input-state stable (ISS). For the purpose of studying (ISS) of the system (3), it is assumed here that (A)i(ρk), Ci(ρk) Is consistently observable, (A)i(ρk),Bi(ρk) Are consistently calm, areAll holds true, below we perform fault detection, fault estimation and fault compensation on the system.
The method comprises the following steps: the fault detection in the present invention consists of a residual generator and a residual estimator, as shown in the fault tolerant control schematic of fig. 3. The basic idea is to develop a Fault Detection Filter (FDF) that generates a residual signal that is both fault indicator or fault-accentuated, which is sensitive to faults but robust to unknown inputs. When the system has no fault, the residual error is usually zero or close to zero, but when the system has fault, the residual error is obviously different from zero, namely, the value of the residual error is greatly different between fault and non-fault, and the residual error can be well detected. Let σ generate the residual signalkFull-order FDF of i-system (3) such asThe following are shown:
herein, theIs an estimate of x (k) and,is a residual signal, AF,i(ρk),BF,i(ρk),CF,i(ρk),DF,i(ρk) Is the parameter matrix of the designed filter, all in the form of LPV. For faster detection of the fault f (k) the following weighted faults can be constructed,is a given stable weighting matrix.
Without loss of generality, the minimum implementation of (7) is assumed to be:
is a weighted fault condition that is a condition of a fault,is a weighted fault, AW,BW,CW,DWIs a known constant matrix of appropriate dimensions.
Is represented by e (k)The model of the augmentation system (3) generates the following augmentation matrix in states including (6) and (8):
Through the analysis, the fault detection problem of the system (3) can be converted into a classAnd (4) a filtering problem. The main objective here is to design a suitable FDF gain matrix A for the system (3)F,i(ρk),BF,i(ρk),CF,i(ρk),DF,i(ρk) Thereby ensuring that the extended system (9) is progressively stabilized when ω (k) is 0 and that the infimum bound of γ becomes small in the zero initial state, while satisfying:
the residual estimation equation and its critical values are:
where sL is the time window of the residual estimate, k0Representing the initial estimate, it is noted that in practical estimation the length of the time window is limited, so that estimation of the residual is not realistic over time, and it is always desirable to detect actuator failure as early as possible. Referring to the system (3), whether the system is malfunctioning is determined based on the logic:
secondly, the step of: the above work completes the detection of system faults, and the following estimation of system states and faults is realized based on the LPV observer, as shown in fig. 4, and when a fault alarm is triggered in the fault detection stage, the following synchronous state and fault estimator is introduced:
here, theIn order to be able to estimate the state,in order to be able to estimate the fault,andis the observer gain matrix. The dynamic estimation error is:
the state estimation error and fault estimation error are thus derived based on systems (3) and (13) as:
wherein Further to the simplification of (15), an extended estimation error system is established as follows:
here, the By (16) obtaining a gain matrix of a state and fault estimation observer of an augmented system
③: finally, the actuator fault is compensated through fault reconstruction, a schematic diagram of a reconstruction structure is shown in fig. 5, and it is assumed that:
rank(Bi(ρk),Bf)=rank(Bi(ρk)) (17)
in case of activation of an alarm, a Fault Tolerant Control (FTC) is established containing fault compensation based on the estimation of the state and fault as follows:
u herer(k) Is a reference input, Ki(ρk) Is the LPV feedback gain matrix to be determined,is used for compensatingThe impact of the fault on the system. Assume reference input ur(k) Is equal to 0 and has The system (3) thus switches the LPV system at discrete times including fault compensation as:
in order to overcome the defects of the multiple Lyapunov equation, the invention adopts an ISS Lyapunov equation with LPV dependent residence time, thereby obtaining a satisfactory ISS gain performance index as follows:
wherein
(2) Solving for
The method comprises the following steps: when tau isdAnd gamma is a normal number, and gamma is,in the case of a positive timing matrix, the FDF parameter matrix in (4) can be made to be:
secondly, the step of: assume (22) that the following conditions are satisfied:
by (27), when k is 0 and k is z-1, and applying formula (23) we have:
ISS gain ofTo obtain the minimum value of the gain, conversion is made into a solution such asThe convex optimization problem of the following form:
and the above convex optimization needs to satisfy the following matrix inequalities (30) to (32):
while Where P isi,l,m,Gi,l,m,Zi,l,mAre all positive definite matrices, scalarsAnd delta represents the mutual transposition of the symmetric positions in the matrix. And system (16)The associated ISS gain isFurthermore, the gain matrix obtained from the observer estimator is:
here, theM, n ∈ {1,..., M }. The optimal solutions under the constraints (30) - (32) of the above Linear Matrix Inequalities (LMIs) can be solved with the MATLAB LMI toolbox.
③: the optimal solution satisfying the conditions of the closed-loop ISS system (18) and the fault-tolerant control system (19) is solved, and the Liya Ponuff equation (20) is consideredAnd m, n ∈ {1,. said, M } satisfies the following (33) - (36) matrix inequalities:
||x(k)||2≤Vi,l(x(k),ρk)≤κ-1||x(k)||2 (34)
||x(k)||2≤Vi,τd(x(k),ρk)≤κ-1||x(k)||2 (35)
Qi,l,m≥κI,Qi,τd,m≥κI (40)
here, theTo pair M, n ∈ {1,..., M } are all satisfied, solving for system (19) concerns d (k), ef(k),ex(k) ISS gain ofAnd the gain matrix for the corresponding controller is obtained as follows:
Analyzing the parameters of the Fault Detection Filter (FDF) and obtaining the gain matrix based on the observer estimatorAnd fault tolerant controller gain matrix Ki(ρk)。
The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.
Claims (7)
1. A method for estimating and compensating for faults of an asynchronous motor actuator is characterized by comprising the following steps:
building a five-order nonlinear mathematical model of the asynchronous induction motor based on the assumption of a linear magnetic circuit, improving the built mathematical model of the asynchronous induction motor according to the switching characteristic of the asynchronous motor to obtain an improved nonlinear mathematical model of the asynchronous induction motor, and discretizing the improved nonlinear mathematical model of the asynchronous induction motor;
establishing a fault detection filter, generating a residual signal through the fault detection filter, and judging whether the motor has an actuator fault according to the value of the residual signal;
designing a fault estimator for estimating the fault size of the actuator;
and compensating the actuator fault through fault reconstruction.
2. The method for estimating and compensating the fault of the asynchronous motor actuator according to claim 1, wherein a five-order nonlinear mathematical model of the asynchronous induction motor is constructed on the basis of the assumption of a linear magnetic circuit, and the established squirrel-cage induction motor mathematical model is improved according to the switching characteristic of the asynchronous motor to obtain the improved nonlinear mathematical model of the asynchronous induction motor; the method specifically comprises the following steps:
a five-order nonlinear mathematical model of the asynchronous induction motor is constructed on the assumption of a linear magnetic circuit, and the mathematical model comprises the following steps:
the nonlinear mathematical model of the improved asynchronous induction motor is as follows:
where ω is the rotor speed, the letters are marked ". cndot." andrespectively representing the differential of the corresponding letter physical quantity and defining the left side as the right side; tau isLRepresenting a load moment disturbance;the state vector is represented by a vector of states,which represents the magnetic flux of the rotor,which is representative of the stator current,representing the stator voltage and as a control system input vector; the upper right hand "T" indicates transpose.
And the rotor speed range is omega epsilon [ omega ]min,ωmax]=[-110,110]rad/s;a1=npLsr/(DmLr),a2=-Rm/Dm,a3=-1/Dm,a4,i=-1/Tr,i,a5,i=Lsr/Tr,i,a6,i=Lsr/(Tr,iσLsLr),a7=npLsr/(σLsLr),a8=1/(σLs), wherein LsIs a stator inductance, LrIs the rotor inductance, LsrIs mutual inductanceσ is the leakage factor, Rs,iIs stator resistance, Rr,iIs rotor resistance, DmIs the moment of inertia, RmIs a viscous damping constant, npIs the number of pole pairs.
3. The method for estimating and compensating for the fault of the asynchronous motor actuator according to claim 2, wherein the improved nonlinear mathematical model of the asynchronous induction motor is discretized, and specifically:
where x (k) represents system state, y (k) represents system output, u (k) represents control input, d (k) represents unknown input, f (k) represents fault input, and matrix Aσk(ρk),Bσk(ρk),Cσk(ρk) Is a known function of p of a measurable parameter variable, BdIs a given constant matrix of appropriate dimensions, BfIs a matrix representing the impact of each fault on the system; switching signal sigmakThe residence time constraint is satisfied and,n represents the number of subsystems in the system; let σ for conveniencekI.e. i
4. The method for estimating and compensating for faults of an asynchronous motor actuator according to claim 3, wherein a fault detection filter is established, and a residual signal is generated by the fault detection filter, specifically:
5. The method for estimating and compensating for the actuator fault of the asynchronous motor according to claim 4, wherein whether the actuator fault exists in the motor is judged according to the magnitude of the residual signal value, and specifically, the method comprises the following steps:
the residual estimation equation and its critical values are:
sLis the time window of the residual estimate, k0Representing an initial estimated value, f and d representing a fault and an external disturbance respectively; l2Represents the euclidean 2 norm with values of 0, ∞; sup denotes the supremum, i.e. the minimum upper bound.
6. The method for estimating and compensating the fault of the asynchronous motor actuator according to claim 5, wherein a fault estimator is designed to estimate the fault magnitude of the actuator, and specifically comprises the following steps:
7. The method for estimating and compensating for the fault of the asynchronous motor actuator according to claim 6, wherein the fault of the actuator is compensated through fault reconstruction, specifically:
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