CN106849801A - A kind of induction-type bearingless motor method for estimating rotating speed - Google Patents

Abstract

The invention discloses a kind of method for estimating rotating speed of induction-type bearingless motor, Mathematical Models according to asynchronous machine play system state equation and observational equation, determine the covariance matrix and estimation error covariance initial matrix of system noise and observation noise, 2N+1 sigma point and its correspondence weights are produced by Unscented transform and the further predicted value of their point sets is calculated, the one-step prediction and covariance of system state amount and the observed quantity of prediction are calculated, the average and covariance of system prediction are obtained by weighted sum.Calculate kalman gain matrixs and state updates and covariance updates.This new Kalman filtering algorithm sampled point propagates statistics of random processes characteristic rather than as in EKF using the mode of first-order linear, therefore with estimated accuracy higher.And decay factor is introduced when prior uncertainty is calculated, and make wave filter that measured value is more believed in estimation procedure, the probabilistic influence of state estimation is reduced, enhance the robustness of system.

Description

A kind of induction-type bearingless motor method for estimating rotating speed

Technical field

The present invention is a kind of speed estimate of the induction-type bearingless motor based on Attenuation Memory Recursive Unscented kalman filtering algorithm Method.For induction-type bearingless motor provides a kind of new strategy without speed operation, it is adaptable to the high-performance of bearing-free motor Control, belongs to the technical field of electric drive control equipment.

Background technology

Conventional motors spinner velocity generally detected using mechanical speed sensors, but to induction-type bearingless motor Speech, using mechanical speed sensors there are problems that install, connect and.And sensor is mechanically difficult in itself Motor high speed, ultrahigh speed operation are realized, so as to seriously limit the performance of the excellent high speed performance of induction-type bearingless motor.Therefore, nothing Velocity sensor technology turns into the effective means for solving this problem of induction-type bearingless motor.

At present, according to the scope of application of motor operation, sensor-less contro is broadly divided into two kinds:(1) signal note people's method, passes through Apply low-and high-frequency excitation, follow the trail of the space-saliency effect of rotor, the method has to the parameter of electric machine insensitive, robust of change The advantages of property is good, is more suitable for the effective detection for realizing zero-speed and low-speed range internal rotor position.But there is high-frequency signal in the method Process problem, the quality that high-frequency current signal is extracted directly influences the estimation of rotor-position and speed.(2) state observation method, Positional information is directly or indirectly extracted from counter electromotive force of motor.Such as direct computing method, extension counter electromotive force method group is based on mould The estimator of type reference adaptive, algorithm based on sliding mode prediction estimator, estimator based on extended Kalman filter and based on artificial god Through network-evaluated method etc..This kind of method has good dynamic property, more suitable for high speed occasion.

The content of the invention

The invention aims to can quick and precisely estimate turning for induction-type bearingless motor rotor in the range of low high speed Speed, so as to avoid operating speed sensor, makes induction-type bearingless motor give full play to advantage, to promote induction-type bearingless motor Using and a kind of induction-type bearingless motor Speedless sensor building method is provided.

The technical scheme is that：Induction-type bearingless motor rotating speed based on Attenuation Memory Recursive Unscented kalman filtering is estimated Meter, including step:

Step one, constructing system model subsystem (1), including UT conversion modules (11), system changeover module (12), and power Value computing module (13), the original state variable of system is input in UT conversion modules (11), then the factor alpha that will be chosen, and β is defeated Enter to weight computing module (13) in, then output be all input in system changeover module (12).

Step 2, builds observation model subsystem (2), including UG conversion modules (21) and systematic observation module (22). The weighted value of the sigma points that system changeover (12) is produced：And error co-variance matrix：P (k+1 | k) it is input to UT Become mold changing (21) block and produce new sigma point sets, then new sigma point sets are input in systematic observation (21) module.

Step 3, builds parameter Estimation subsystem (3), including covariance meter module (31) is calculated and state update module (32), By the output of covariance computing module (31):System prediction covarianceWithDecay factor γ²Converted with by 3/2 Stator current i_sα,i_sβIt is input to state update module (32).Produce new state vector WhereinIt is respectively the value of electronic current, inductance and rotating speed subsequent time.

Step 4, five outputs that state is updatedIt is input to again and is In system model subsystem (1), the value of subsequent time is calculated, so circulation is gone down, and detects the tachometer value of output.

Further, UT conversion modules module (11) described in step one, weight computing module (13) and system changeover mould The building method of type (12) is：

The UT conversion modules (11) are the five rank state vectors that will be input intoCarry out UT Conversion, produces 2n+1 signma point, whereinIt is respectively that electronic current, inductance and rotating speed are worked as The value at preceding quarter.State vector x is n n-dimensional random variable ns, and known its averageWith covariance P.Can then be become by following UT and got in return To 2n+1 sigma point：

The weight computing module (13) is the corresponding weight value for calculating sigma points.Wherein λ=α²(n+ β)-n is a contracting Scale parameter is put, for reducing total prediction error, α, β are the parameter of selection.

Weights

Weights

Weights

System changeover module (12) is that sigma points are obtained into the further of sigma points after sytem matrix f () is converted Prediction X⁽ⁱ⁾(k+1 | k) and error covariance square P (k+1 | k), f () according to be by the Mathematical Modeling of induction-type bearingless motor come 's.Wherein：

One group of sampled point：

Further predicted value：X⁽ⁱ⁾(k+1 | k)=f [k, X⁽ⁱ⁾(k|k)]

The weighted value of sigma points：

Error co-variance matrix：

Sytem matrix:

Wherein Q is the covariance matrix of system noise. M is sampling time, L_r:Electronic inductance, R_r:Electronic, L_s:Inductor rotor, R_r:Rotor resistance, L_m:Mutual inductance.

Further, systematic observation model (22) building method described in step 2 is as follows：

The observed quantity of prediction：Z⁽ⁱ⁾(k+1 | k)=h [X⁽ⁱ⁾(k+1|k)]

The weighted value of the observation of prediction：

WhereinIt is observing matrix, the Mathematical Modeling construction according to induction-type bearingless motor.

Further, covariance meter module (31) described in step 3 and state update module (32) building method are as follows：

The construction that the covariance calculates mould calculates method：

System prediction covariance：

Wherein R is the covariance matrix of observation noise.

The building method of the state update module (32)：

Kalman gain matrixs：

State updates：

Covariance updates：

The advantage of the invention is that：

1) this new Kalman filtering algorithm sampled point propagates statistics of random processes characteristic rather than as in EKF

Using the mode of first-order linear, therefore with estimated accuracy higher.When process error and measurement error and When prior state is Gaussian Profile, UKF can be accurate to three ranks approximately, and second order at least can be also accurate to for non-gaussian situation Seemingly.

2) Jacobian matrix of linearization procedure equation and measurement equation need not be calculated.

3) decay factor is introduced, makes wave filter that measured value is more believed in estimation procedure such that it is able to state estimation Uncertainty, enhances the robustness of system.

Brief description of the drawings

Fig. 1 is the structural representation of the system.

Fig. 2 is system model subsystem structure schematic diagram.

Fig. 3 is observation model subsystem figure.

Fig. 4 is parameter Estimation subsystem figure.

Specific embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation is described.

1. system model subsystem module (1) as shown in Figure 2, including UT conversion modules (11), system changeover mould are constructed The output of UT conversion modules (11) and weight computing module (13) is all input to system by block (12), weight computing module (13) In conversion module (12).The input of system model subsystem module (1) It is electricity The initial state vector of machine stator electric current, magnetic linkage and rotating speed, is inputted UT conversion (11) modules.The method of UT is：State to Amount x is n n-dimensional random variable ns, and known its averageWith covariance P.Then 2n+1 can be obtained by following UT conversion modules (11) Individual sigma points, UT conversion (11) building method be：

Then the weights of each sigma point, the structure of weight computing module (13) are calculated by weight computing module (13) The method of making is：

Weights

Weights

Weights

Wherein λ=α²(n+ β)-n is a scaling parameter, and for reducing total prediction error, α, β are the ginseng of selection Number.Although its value is without boundary, generally should be ensured that proof (n+ λ) P is positive semidefinite matrix.

After calculating sigma points and weights, by sigma point input systems conversion module (12), system changeover module (12) building method is as follows：

The further prediction X of sigma points is obtained after sytem matrix f () is converted⁽ⁱ⁾(k+1 | k) and error covariance square P(k+1|k).Wherein

One group of sampled point：

Further predicted value：X⁽ⁱ⁾(k+1 | k)=f [k, X⁽ⁱ⁾(k|k)]

The weighted value of sigma points：

Error co-variance matrix：

Wherein f () is sytem matrix, the Mathematical Modeling construction according to induction-type bearingless motor, and Q is system noise Covariance matrix.

WhereinM is sampling time, L_r:Electronic inductance, R_r:Electronic, L_s:Inductor rotor, R_r:Rotor resistance, L_m:Mutual inductance.

2. observation model subsystem (2) is built, is made up of UG conversion modules (21) and systematic observation module (22), by system The weighted value of the output sigma points of conversion module (12)：And error co-variance matrix:P (k+1 | k) it is input to UT Conversion module (11) produces new sigma point sets, then new sigma point sets are input in systematic observation (21) module.

Observation model subsystem shown in Fig. 3 (2), by the weighted value of sigma points：With error covariance square Battle array P (k+1 | k) is input in UG conversion modules (21) the UT conversion that tries again, and produces new sigma point sets.UG conversion modules (21) building method is：

Sigma points input system is observed into observed quantity and average that module (22) obtains premeasuring, i=1,2 ... .., 2n+ 1。

The building method of systematic observation module (22) is：

The observed quantity of premeasuring：Z⁽ⁱ⁾(k+1 | k)=h [X⁽ⁱ⁾(k+1|k)]

The average of premeasuring：

Wherein h () is observing matrix, and Mathematical Modeling according to induction-type bearingless motor is constructed：

3. parameter Estimation subsystem (3) is built, including covariance calculates (31) and state updates (32), by model subsystem (1) it is input in (31) with the output of observation model subsystem (2), is predicted by covariance computing module (31) calculation system and assisted VarianceWithState update module (31) is input to, decay factor γ is added², and by stator current i_sα,i_sβValue It is input in real time as observation in state update module (32).

Parameter Estimation subsystem shown in Fig. 4, by new sigma point sets X⁽ⁱ⁾(k+1 | k) and observational equation obtain premeasuring Observed quantity and average Z⁽ⁱ⁾(k+1 | k),It is input to covariance computing module (31), covariance computing module (31) Building method be：

System prediction covariance

λ²It is that decay factor refers specifically to depend on the forgetting degree to past measurement value, it is generally more bigger than 1.R is The covariance matrix of observation noise.

WillInput state update module (32), calculates the state vector of renewal, state update module (32) building method is：

Kalman gain matrixs：

State updates：

Covariance updates：

4. five outputs for state being updatedSystem model subsystem is input to again (1) in, the value of subsequent time is calculated, circulation is gone down, and detects the tachometer value of output, wherein It is respectively the value of electronic current, inductance and rotating speed subsequent time.

The state renewal that will be calculated and covariance are updated, and constantly circulation is gone down, and the rotational speed omega that real-time detection is exported.

To sum up, the method for estimating rotating speed of a kind of induction-type bearingless motor of the invention, according to the Mathematical Modeling of asynchronous machine System state equation and observational equation are set up, covariance matrix and the association of evaluated error of system noise and observation noise is determined Variance initial matrix, produces 2N+1 sigma point and its correspondence weights and calculates the further of their point sets by Unscented transform Predicted value, calculates the one-step prediction and covariance of system state amount and the observed quantity of prediction, obtains system by weighted sum pre- The average and covariance of survey.Calculate kalman gain matrixs and state updates and covariance updates.This new Kalman filtering Algorithm sampled point propagates statistics of random processes characteristic rather than as in EKF using the mode of first-order linear, therefore has Estimated accuracy higher.And decay factor is introduced when prior uncertainty is calculated, make wave filter that measurement is more believed in estimation procedure Value, reduces the probabilistic influence of state estimation, enhances the robustness of system.

It should be understood that above-mentioned example of applying is only illustrative of the invention and is not intended to limit the scope of the invention, the present invention is being read Afterwards, modification of the those skilled in the art to the various equivalent form of values of the invention falls within the application appended claims and is limited Scope.

Claims (4)

1. a kind of method for estimating rotating speed of induction-type bearingless motor, it is characterized in that using following steps：

Step one, constructing system model subsystem (1), including UT conversion modules (11), system changeover module (12), weight computing Module (13), the output of UT conversion modules (11) and weight computing module (13) is all input in system changeover module (12)；

Step 2, builds observation model subsystem (2), including UG conversion modules (21) and systematic observation module (22), by system The weighted value of the output sigma points of conversion module (12)：And error co-variance matrix：P (k+1 | k) it is input to UG In conversion module (21), new sigma point sets are produced, then new sigma point sets are input to systematic observation module (22) module In；

Step 3, builds parameter Estimation subsystem (3), including covariance computing module (31) and state update module, by model The output of subsystem (1) and observation model subsystem (2) is input in covariance computing module (31), and mould is calculated by covariance Block (31) calculation system predicts covariance：WithState update module (31) is input to, decay factor γ is added², And by stator current i_sα,i_sβValue be input in real time as observation in state update module (32)；

Step 4, five outputs that state is updatedSystem model subsystem is input to again In system (1), the value of subsequent time is calculated, circulation is gone down, and detects the tachometer value of output, wherein ω^k+1It is respectively the value of electronic current, inductance and rotating speed subsequent time.

2. the method for estimating rotating speed of a kind of induction-type bearingless motor according to claim 1, it is characterised in that in step one The construction method of described UT transformation models (11), weight computing module (13) and system changeover model (12) is：

Step 2.1, the building method of the UT conversion modules (11) is the five rank state vectors that will be input intoUT conversion is carried out, 2n+1 signma point is produced, whereinω^k It is respectively value that electronic current, inductance and rotating speed are currently carved, state vector x is n n-dimensional random variable ns, and known its averageAnd association Variance P, then can be converted by following UT and obtain 2n+1 sigma point：

$sigma\left(0\right):X^{\left(0\right)}=\stackrel{\‾}{X},i=0$

$sigma\left(i\right):X^{\left(i\right)}=\stackrel{\‾}{X}+{\left(\sqrt{(n+\mathrm{\λ})P}\right)}_i,i=1~n$

$sigma\left(i\right):X^{\left(i\right)}=\stackrel{\‾}{X}-{\left(\sqrt{(n+\mathrm{\λ})P}\right)}_i,i=n+1~2n$

Step 2.2, the building method of weight computing module (13) is the corresponding weight value for calculating sigma points, wherein λ=α²(n+β)-n It is a scaling parameter, for reducing total prediction error, α, β are the parameter of selection；

Weights

Weights

Weights

Step 2.3, system changeover module (12) building method is that sigma points are obtained after sytem matrix f () is converted The further prediction X of sigma points⁽ⁱ⁾(k+1 | k) and error co-variance matrix P (k+1 | k), f () is according to induction-type bearingless motor Mathematical Modeling construction；Wherein：

One group of sampled point：

Further predicted value：

The weighted value of sigma points：

Error co-variance matrix：

Sytem matrix: Wherein Q is the covariance matrix of system noise；M is sampling Time, L_r:Electronic inductance, R_r:Electronic, L_s:Inductor rotor, R_r:Rotor resistance, L_m:Mutual inductance.

3. the method for estimating rotating speed of a kind of induction-type bearingless motor according to claim 1, it is characterised in that in step 2 Described UG conversion modules (21) are identical with UT conversion modules (11), and systematic observation module (22) construction method is as follows：

The observed quantity of prediction：Z⁽ⁱ⁾(k+1 | k)=h [X⁽ⁱ⁾(k+1|k)]

The weighted value of the observation of prediction：

WhereinIt is observing matrix, the Mathematical Modeling construction according to induction-type bearingless motor.

4. the method for estimating rotating speed of a kind of induction-type bearingless motor according to claim 1, it is characterised in that in step 3 Covariance meter module (31) and state update module (32) construction method are as follows：

Step 4.1, covariance computing module (31) construction method：

System prediction covariance：

$P_{z_k{z}_k}=\underset{i=0}{\overset{2n}{\Σ}}{w}^{\left(i\right)}\[Z^{\left(i\right)}(k+1|k)-\stackrel{\‾}{Z}(k+1|k)\]{\[Z^{\left(i\right)}(k+1|k)-\stackrel{\‾}{Z}(k+1|k)\]}^T+R$

$P_{x_k{z}_k}=\underset{i=0}{\overset{2n}{\Σ}}{w}^{\left(i\right)}\[X^{\left(i\right)}(k+1|k)-\hat{X}(k+1|k)\]{\[Z^{\left(i\right)}(k+1|k)-\stackrel{\‾}{Z}(k+1|k)\]}^T$

Wherein R is the covariance matrix of observation noise；

Step 4.2, the construction method of the state update module (32)：

Kalman gain matrixs：

State updates：

Covariance updates：