CN104009735B - Implementation method of the Kalman filter in 300 series of PLC of S7 - Google Patents

Abstract

The invention discloses implementation method and concrete implementation step of a kind of Kalman filter in 300 series of PLC of S7.16 data blocks defined in 300 series of PLC systems of S7, each matrix variables in 14 data blocks therein and Kalman filter iteration formula are corresponded, and remaining two data blocks are used for the temporary of matrix operation.The accessing operation of some variables in Kalman filter iteration formula is converted into into the accessing operation of variable in 300 series of PLC system corresponding data blocks of S7.Using the instruction system of PLC system, plus and minus calculation, multiplying, inverse operation and the Kalman filter iteration formula of matrix are directly realized by.The relative determination of the calculating time of Kalman filter, and each sampling period in practical application mostly is single iteration, by the warning timer for rationally arranging PLC system, the Kalman filter function of expansion does not interfere with the normal scan function of PLC system, and provides new means for its senior application.

Description

Implementation method of the Kalman filter in S7-300 series of PLC

Technical field

The invention belongs to technical field of automation, is related to implementation method of the Kalman filter in S7-300 series of PLC.

Background technology

Programmable controller (PLC), industrial computer (mainly IPC), Distributed Control System (DCS)/scene are total Line control system (FCS) and intelligent control instrument, are four conventional big class control devices of industrial automation.Wherein, PLC with By means of its high reliability and ease for use, being most widely used in industrial automation engineering.Big-and-middle-sized PLC is mainly used in complicated life Producing line control, sequential control, batch control and process industry control.In numerous big-and-middle-sized PLC systems, the S7- of Siemens 300 or S7-400 series of PLC rely on its well-known architecture, network function, integrated technology and technical support, it has also become China One of wide variety of big-and-middle-sized PLC system.

Kalman (Kalman) proposes a kind of filtering and prediction algorithm, i.e. Kalman filter, the algorithm in nineteen sixty Carry out the state of estimation procedure there is provided a kind of efficiently computable method, and make estimate mean square error minimum, extensively should Follow the trail of for robot navigation, process control, data fusion, radar system, guided missile etc., it is pre- for solving parameter Estimation, state The problems such as report and industrial process fault diagnosis.

Be currently being widely used PLC system and programming language and instruction system provided according to IEC61131-3 international standards, respectively PLC system producer not yet provides Kalman filter module or instruction database.Kalman filter is related to the matrix operation of complexity, Current research or many Matlab platforms or C language platform using based on PC of application.Prior art must be first from PLC system etc. Observation data are obtained in control device, the Matlab platforms of PC is then passed through, is completed the complicated calculations of Kalman filter, most Result of calculation formation controlled quentity controlled variable is passed back to into PLC again afterwards, the control of industrial process is realized by PLC system.Prior art needs week And data and transmission optimization information are obtained to PLC system from PLC system with renewing, need by means of communication network and PC platforms, Collaboration completes state estimation or optimal control in advanced control system etc..

Prior art needs between PC systems and PLC system exchange data again and again, need to be equipped with PC, Windows platform, Matlab platforms and communication network.Network failure, the network delay being especially inherently present all will affect card The application effect of Thalmann filter.Additionally, the high request of industrial environment also proposes challenge to the running environment of PC platforms, increase PC platforms also result in system cost increase.

Therefore, how directly to realize that Kalman filter is the target that automation engineering circle is pursued always in PLC system.

The content of the invention

The invention provides implementation method of the Kalman filter in S7-300 series of PLC, solves current Kalman The problem of the method complexity that wave filter is realized in PLC.

By means of the data block in Siemens's S7-300 series of PLC, by all kinds of accesses between Kalman filter matrix And computing, the access and computing of each element between data block are converted to, using the instruction system of Siemens's S7-300 series of PLC Realize adding, subtract, taking advantage of and inverse operation for matrix, then provide according to the iteration formula and S7-300 series of PLC of Kalman filter Module program design method, realizes Kalman filter in PLC by step.

The technical solution used in the present invention is by the accessing operation of some matrix variables in Kalman filter iteration formula The accessing operation of variable in S7-300 series of PLC system corresponding data blocks is converted into, and adding for matrix is realized in PLC system Subtract computing, multiplying and inverse operation.

Further, the step of implementation method of the Kalman filter in S7-300 series of PLC it is：

Step 1：Data block DB1～DB14 is defined, the variable in Kalman filter formula is deposited；DB1～DB6 is deposited respectively Put matrix variables X (k) in Kalman filter iteration formula, Φ (k), Η (k), y (k), ω (k) and v (k), data block DB7 Storage configuration estimate vectorDB8 storage configuration one-step predictions value vectorDB9 is deposited Filtering gain matrix K (k), DB10 storages estimation error covariance matrix P (k-1, k-1), DB11 storage covariance matrix One-step prediction value P (k, k-1), DB12 storage Q, DB13 storage R, DB14 storage unit matrix I；

Step 2：The one-step prediction value of Kalman filter is calculated, is taken out from data block DB7 and DB2 respectivelyWith Φ (k), the one-step prediction value of Kalman filter is calculated as follows

WillIt is stored in data block DB8；

Step 3：State estimation is calculated, is taken out from data block DB8, DB9, DB3, DB4 respectivelyK K (), H (k) and y (k), are calculated as follows state estimation

UseUpdate in DB7

Step 4：Filtering gain matrix are calculated, respectively taking-up P (k, k-1), H (k) from data block DB11, DB3 and DB13 And R, it is calculated as follows filtering gain matrix K (k)：

K (k)=P (k, k-1) H^T(k)[H(k)P(k,k-1)H^T(k)+R]^-1

K (k) is stored in into data block DB9；

Step 5：The one-step prediction value of calculation error covariance matrix, takes out Φ from data block DB2, DB10, DB12 respectively K (), P (k-1, k-1) and Q, are calculated as follows one-step prediction value P (k, k-1) of error covariance matrix：

P (k, k-1)=Φ (k) P (k-1, k-1) Φ^T(k)+Q

P (k, k-1) is stored in into data block DB11；

Step 6：Calculate estimation error covariance matrix, respectively from data block DB14, DB9, DB3 and DB11 take out I, K (k), H (k) and P (k, k-1), are calculated as follows estimation error covariance matrix P (k, k)：

P (k, k)=[I-K (k) H (k)] P (k, k-1)

The P (k-1, k-1) in DB10 is updated using P (k, k), so far, complete an iteration computing of Kalman filter.

The invention has the beneficial effects as follows method is simple, low cost.

Description of the drawings

Fig. 1 is the storage exemplary plot of two matrix elements that PLC system carries out plus and minus calculation；

Fig. 2 is the storage exemplary plot of two matrix elements that PLC system carries out multiplying；

Fig. 3 is the matrix element access flow chart in PLC system；

Fig. 4 is the matrix plus and minus calculation flow chart in PLC system；

Fig. 5 is the matrix multiplication operation flow chart in PLC system；

Fig. 6 is the matrix determinant calculation flow chart in PLC system；

Fig. 7 is the adjoint matrix calculation flow chart in PLC system；

Fig. 8 is the matrix inversion operation flow chart in PLC system；

Fig. 9 is the program block and data block figure that the Kalman filter in PLC system is used；

Figure 10 is the Kalman filter tracking bead movement locus figure in PLC system；

Figure 11 is the Kalman filter tracking bead movement locus figure that Matlab is provided.

Specific embodiment

The present invention is described in detail with reference to the accompanying drawings and detailed description.

The present invention realizes Kalman filter first by the definition data block matrix in S7-300 series of PLC systems Interative computation needs to define 14 matrixes or vector, it is contemplated that matrix operation also needs to keep in, and defines 16 matrixes, correspondence altogether 16 data blocks of PLC system, data block numbering is DB1～DB16.Secondly, by the adding, subtract of matrix, take advantage of and be converted to inverse operation The arithmetic of basic matrix element, participates in the matrix of computing, using S7-300 systems by accessing corresponding data block access Adding, subtract, taking advantage of and inverse operation for matrix, is realized in the floating point arithmetic instruction of row PLC respectively.Finally, realize blocking by following six steps The interative computation of Thalmann filter, the wherein first step are only carried out once, and follow-up five step is often to carry out a Kalman filter to change The step of in generation, calculates.

Kalman filter realizes that step is as follows in S7-300 series of PLC systems：

Step 1：Data block DB1～DB14 is defined, the variable in Kalman filter formula is deposited.

1. using the definition data block matrix in PLC system：

The most soft element of S7-300 series of PLC internal system quantity is data block, its quantity up to 1024, per number It is 64KB to the maximum according to the capacity of block.S7-300 series of PLC supports single precision floating datum (taking 4 bytes, type is Real), if Using each data block one matrix of correspondence, then the square formation of matrix maximum definable 128 × 128, meets most actual works enough The demand of journey system.After by each data block one matrix of correspondence, the mutual operation between matrix then switchs between data block Operation.

(1) two matrixes for participating in plus and minus calculation have identical line number and columns, and each element of two matrixes is at two Structure in data block is identical, using being defined by row successively, as shown in Figure 1 (by taking 3 × 3-dimensional matrix as an example).Two m × The element ai of n matrix_jAnd bi_jAddress pointer calculated by following formula：

Ptr=[(i-1) n+ (j-1)] × 4

(2) if two matrixes for participating in multiplying still enter row element storage successively by row, need to calculate respectively Address pointer, causes amount of calculation double；For this purpose, multiplicand matrix is carried out the storage of data element by leu, as shown in Figure 2 (by taking 3 × 3-dimensional matrix as an example).One m × n dimension matrix A is multiplied by n × p dimension matrix B, obtains a m × p and ties up Matrix C.

When data structure as shown in Figure 2 deposits two matrixes, then element a_ikAnd bk_jAddress in two data blocks refers to Pin is identical, only need to calculate 1 time as the formula described in (1).

2. the computing of matrix is realized in S7-300 series of PLC systems：

Matrix operation is realized in S7-300 series of PLC systems, the access of solving matrix element, the plus-minus fortune of matrix is needed The problems such as calculation, matrix multiplication operation and inverse of a matrix computing.

(1) access of matrix element：

The access of matrix element includes the read and write operation of matrix element, is both for given matrix and is operated, because This, the read-write operation of matrix element can be realized by same program module which realizes that flow process is as shown in Figure 3.Program number is FC1, its |input paramete is：Data block numbering DBno, matrix line number m, columns n, the be expert at i of read-write element and row j, read-write mark WR (1 is write operation, and 0 is read operation)；Input/output argument is：(WR=1, dat are data to be written to dat；During WR=0, dat is The data read).

(2) plus and minus calculation of matrix：

The plus and minus calculation rule of matrix is similar, therefore the plus and minus calculation of matrix can be designed as a module, its title For FC2, which realizes that flow process is as shown in Figure 4.|input paramete is：Data block numbering DBNo1, DBNo2, DBNo3, line number m of matrix, Columns n；Plus-minus mark PorM (1：Addition, 0：Subtraction)；Without output parameter.

(3) multiplication of matrices computing：

The flow process of multiplication of matrices computing is as shown in figure 5, module title is FC3.|input paramete is：Data block is numbered DBNo1, DBNo2, DBNo3, line number m of multiplicand matrix, columns n, line number n of multiplicand matrix, columns p；Without output parameter.One Individual m × n dimensions matrix A is multiplied by n × p dimension matrix B, obtains a m × p and ties up Matrix C, each element ci in Matrix C_jPress Row formula is calculated：

N multiplication and (n-1) sub-addition computing are needed altogether, therefore, multiplication of matrices computing needs larger calculation process Amount, needs rationally to arrange the warning timer of S7-300 series of PLC systems.

(4) inverse of a matrix computing：

Inverse of a matrix operation program module title be FC4, |input paramete：Data block DBno1, DBNo2, matrix line number m, row Number n；Without output parameter.The matrix inversion operation of PLC system is carried out as follows：

The first step：By the determinant A of elementary transformation angle calculating matrix A, program circuit is as shown in Figure 6；

Second step：The adjoint matrix A of A is calculated using algebraic complement^*, program circuit is as shown in Figure 7；

3rd step：Inverse matrix A of A is calculated by following equation^-1, program circuit is as shown in Figure 8.

Based on the above-mentioned matrix definition having been carried out and its computing, according to the iterative formula of Kalman filter, circulation is adjusted With the above-mentioned matrix operation class method module having been carried out, you can Kalman filter is realized in PLC system.Number is defined first According to block DB1～DB14, the variable in Kalman filter formula is deposited

By following shown linear system discrete state equations, DB1～DB6 deposit respectively its corresponding matrix variables X (k), Φ (k), Η (k), y (k), ω (k) and v (k).

X (k) is state vector；Y (k) is observation vector；ω (k) is system noise；V (k) is observation noise vector；Φ K () is nonsingular state-transition matrix；H (k) is observing matrix.ω (k) and v (k) are orthogonal zero-mean, variance difference For the white Gaussian noise of Q and R.

Data block DB7 storage configuration estimate vectorDB8 storage configuration one-step predictions value vectorDB9 storages filtering gain matrix K (k), DB10 storage estimation error covariance matrix P (k-1, k-1), DB11 deposits one-step prediction value P (k, k-1) of covariance matrix, DB12 storage Q, DB13 storage R, DB14 storage unit matrix I.

Step 2：Calculate the one-step prediction value of Kalman filter：

Take out from data block DB7 and DB2 respectivelyWith Φ (k), Kalman filtering is calculated as follows The one-step prediction value of device

WillIt is stored in data block DB8.

Step 3：Calculate state estimation：

Take out from data block DB8, DB9, DB3, DB4 respectivelyK (k), H (k) and y (k), are counted as the following formula Calculate state estimation

UseUpdate in DB7

Step 4：Calculate filtering gain matrix：

P (k, k-1), H (k) and R are taken out from data block DB11, DB3 and DB13 respectively, filtering gain square is calculated as follows Battle array K (k)：

K (k)=P (k, k-1) H^T(k)[H(k)P(k,k-1)H^T(k)+R]^-1

K (k) is stored in into data block DB9.

Step 5：The one-step prediction value of calculation error covariance matrix：

Φ (k), P (k-1, k-1) and Q are taken out from data block DB2, DB10, DB12 respectively, error covariance is calculated as follows One-step prediction value P (k, k-1) of battle array：

P (k, k-1)=Φ (k) P (k-1, k-1) Φ^T(k)+Q

P (k, k-1) is stored in into data block DB11.

Step 6：Calculate estimation error covariance matrix

I, K (k), H (k) and P (k, k-1) are taken out from data block DB14, DB9, DB3 and DB11 respectively, is calculated as follows Estimation error covariance matrix P (k, k)：

P (k, k)=[I-K (k) H (k)] P (k, k-1)

The P (k-1, k-1) in DB10 is updated using P (k, k).

So far, an iteration computing of Kalman filter, program module, the tissue of data block and its incidence relation are completed As shown in Figure 9.

Specific embodiment is set forth below, and the present invention will be described：

Embodiment 1：Kalman filter application example in PLC system, in order to verify the Kalman realized in PLC system Wave filter, plan estimate the height and speed of the bead of a movement of falling object with Kalman filtering algorithm.The 20 of bead height Secondary measured value is as shown in table 1.If the measure error of height is the white Gaussian noise that zero-mean variance is 1, the initial height of the object Degree h₀With speed V₀And the stochastic variable of Gaussian Profile, i.e.,

The state equation of bead motion is as follows：

In formula,

Filtering initial value：

In order to intuitively show the implementation effect of Kalman filter in PLC, will using the trend control of WinCC configuration softwares Its data exports to EXCEL and is depicted as curve, as shown in Figure 10.The picture left above is Height Estimation value, and top right plot is velocity estimation value, Lower-left figure is Height Estimation covariance, and bottom-right graph is velocity estimation covariance.Height change of the table 1 for pellet free falling Value.

Table 1

In order to further verify the Kalman filter realized in PLC system, Figure 11 gives the Matlab cards of offer Thalmann filter realizes the height of bead motion tracking and velocity estimation value, mean square error curve.In Figure 11, the picture left above is height Estimate, top right plot are velocity estimation value, and lower-left figure is Height Estimation covariance, and bottom-right graph is velocity estimation covariance.

By comparing it is known that the Kalman filtering that provides of the Kalman filter realized in PLC system and Matlab Device has similar effects when bead speed and height is estimated.

The above, preferably specific embodiment only of the invention, protection scope of the present invention not limited to this are any ripe Those skilled in the art are known in the technical scope of present disclosure, the letter of the technical scheme that can be become apparent to Altered or equivalence replacement are each fallen within protection scope of the present invention.

Claims (2)

1. implementation method of the Kalman filter in S7-300 series of PLC, it is characterised in that：Kalman filter iteration is calculated In formula, the accessing operation of some matrix variables is converted into the accessing operation of variable in S7-300 series of PLC system corresponding data blocks, And plus and minus calculation, multiplying and the inverse operation of matrix are realized in PLC system.

2. the implementation method according to Kalman filter described in claim 1 in S7-300 series of PLC, it is characterised in that：

Step 1：Data block DB1～DB16 is defined, the variable in Kalman filter formula is deposited；DB1～DB6 deposits card respectively Matrix variables X (k), Φ (k), H (k), y (k), ω (k) and v (k) in Thalmann filter iteration formula, the storage of data block DB7 State estimation vectorDB8 storage configuration one-step predictions value vectorDB9 storage filtering Gain matrix K (k), DB10 storages estimation error covariance matrix P (k-1, k-1), DB11 deposit a step of covariance matrix Predicted value P (k, k-1), DB12 storage Q, DB13 storage R, DB14 storage unit matrix I, DB15 and DB16 are used to keep in；It is based on The data block of definition, realizes plus and minus calculation, multiplying and the inverse operation of matrix in PLC；Wherein, associations of the Q for system noise Variance matrix, covariance matrixes of the R for measurement noise；

Step 2：The one-step prediction value of Kalman filter is calculated, is taken out from data block DB7 and DB2 respectively With Φ (k), the one-step prediction value of Kalman filter is calculated as follows

$\hat{X}(k,k-1)=\mathrm{\Φ}\left(k\right)\hat{X}(k-1,k-1)$

WillIt is stored in data block DB8；

Step 3：State estimation is calculated, is taken out from data block DB8, DB9, DB3, DB4 respectivelyK(k)、H K () and y (k), is calculated as follows state estimation

$\hat{X}(k,k)=\hat{X}(k,k-1)+K\left(k\right)\[y\left(k\right)-H\left(k\right)\hat{X}(k,k-1)\]$

UseUpdate in DB7

Step 4：Filtering gain matrix are calculated, respectively taking-up P (k, k-1), H (k) and R from data block DB11, DB3 and DB13, It is calculated as follows filtering gain matrix K (k)：

K (k)=P (k, k-1) H^T(k)[H(k)P(k,k-1)H^T(k)+R]^-1

K (k) is stored in into data block DB9；

Step 5：The one-step prediction value of calculation error covariance matrix, takes out Φ (k), P from data block DB2, DB10, DB12 respectively (k-1, k-1) and Q, are calculated as follows one-step prediction value P (k, k-1) of error covariance matrix：

P (k, k-1)=Φ (k) P (k-1, k-1) Φ^T(k)+Q

P (k, k-1) is stored in into data block DB11；

Step 6：Estimation error covariance matrix are calculated, respectively taking-up I, K from data block DB14, DB9, DB3 and DB11 K (), H (k) and P (k, k-1), are calculated as follows estimation error covariance matrix P (k, k)：

P (k, k)=[I-K (k) H (k)] P (k, k-1)

The P (k-1, k-1) in DB10 is updated using P (k, k), so far, complete an iteration computing of Kalman filter.