CN111143968A - Method for identifying variable forgetting factor (TFF) deduction space of proton exchange membrane fuel cell - Google Patents
Method for identifying variable forgetting factor (TFF) deduction space of proton exchange membrane fuel cell Download PDFInfo
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Abstract
The invention discloses a proton exchange membrane fuel cell forgetting factor recurrence subspace identification method, which comprises the steps of selecting input and output variables of an identification model, and collecting experimental data on a PEMFC measurement and control platform; constructing a Hankel matrix of input and output data at the current moment, and solving a subspace predictor model at the current moment by using a subspace identification method; constructing a Hankel matrix of input and output data at the next moment, and solving the prediction output at the next moment by using a subspace predictor model at the current moment; and determining actual output data at the next moment according to the control action added by the PEMFC, calculating an output prediction error of actual output and predicted output, if the output prediction error is greater than an allowable error, updating the solution subspace predictor model by using a recursive subspace identification algorithm, and otherwise, not updating the model. The invention adopts a subspace identification algorithm, does not need prior knowledge of a galvanic pile model, and has less model parameters and high identification speed; and a recurrence algorithm of a variable forgetting factor is added, so that the model parameters can be corrected and updated online in real time.
Description
Technical Field
The invention belongs to the field of industrial control, and particularly relates to a proton exchange membrane fuel cell forgetting factor transiting and deducing space identification method.
Background
A Proton Exchange Membrane Fuel Cell (PEMFC) is a power generation device that directly converts chemical energy of hydrogen into electric energy, has the outstanding advantages of low starting temperature, high reliability, high power density, fast response speed, unit modularization, etc., and plays an increasingly important role in the field of new energy. The PEMFC is a multivariable, strong-coupling and time-varying complex system, in order to improve the power generation performance of the PEMFC, the electrical characteristics of the PEMFC in the power generation process need to be controlled, the primary task is to accurately model the electrical characteristics of the PEMFC in real time, and the adopted modeling method not only can accurately describe the dynamic characteristics of the PEMFC, but also can update the model on line in real time.
The existing fuel cell modeling method mainly focuses on mechanism modeling, and models the static/dynamic and electrical characteristics/temperature of the galvanic pile through the energy conservation law, electrochemical reaction equation and other physical and chemical principles, but has the following main problems:
1) clear understanding of the working mechanism of the galvanic pile is needed, and a large amount of prior knowledge is needed.
2) The modeling process is complex and requires a large number of model parameters to be determined.
3) Many conditional assumptions are made and the results may differ significantly from the actual operating conditions.
4) The model cannot be updated on line in real time, and the time-varying characteristic of the fuel cell cannot be met.
In order to overcome the above problems, many scholars have made relevant studies on a modeling method of a fuel cell. An on-line identification and real-time optimal temperature generalized predictive control method for FFRLS of a PEMFC power generation system [ J ] China Motor engineering reports, 2017(11) 169-181+324. the influence of the working temperature of the PEMFC on the output voltage is researched, the temperature of the PEMFC system is modeled and corrected on line by adopting a recursive least square method based on a forgetting factor, but the model only considers the influence of the working temperature on the output performance, ignores the coupling relation among a plurality of parameters influencing the output performance, and has insufficient consideration on the multivariable problem of the PEMFC system. Buchholz M, Esewein M, Krebs V.modeling PEMfuel cell stacks for FDI using linear sub-space identification [ C ]. IEEEInternational reference on Control applications IEEE 2008:341-346. A subspace identification method based on typical variable analysis (CVA) is used for modeling a fuel cell automobile stack and is applied to stack fault detection, but the model is identified offline and cannot be corrected and updated online, so that the time-varying characteristic of the PEMFC is ignored.
Disclosure of Invention
The invention aims to provide a method for identifying a forgetting factor transfer subspace of a proton exchange membrane fuel cell.
The technical solution for realizing the purpose of the invention is as follows: a proton exchange membrane fuel cell forgetting factor deduction subspace identification method comprises the following steps:
step 1, selecting input and output variables of an identification model, and collecting experimental data on a PEMFC measurement and control platform;
step 3, constructing a Hankel matrix of input and output data at the next moment, and solving the prediction output at the next moment by using a subspace predictor model at the current moment;
step 4, determining actual output data at the next moment according to the control action added by the PEMFC, calculating output prediction errors of actual output and predicted output, if the output prediction errors are larger than the allowable errors, updating a solution subspace predictor model by using a recursive subspace identification algorithm, and otherwise, not updating the model;
and 5, repeating the steps 3 and 4, and updating the subspace predictor model in real time.
Compared with the prior art, the invention has the remarkable advantages that: 1) by adopting a subspace identification algorithm, the prior knowledge of the galvanic pile model is not needed, the model parameters are less, and the identification speed is high; 2) and a recurrence algorithm of a variable forgetting factor is added, so that the model parameters can be corrected and updated online in real time.
Drawings
Fig. 1 is a flow chart of the method for identifying the forgetting factor transfer subspace of the pem fuel cell of the present invention.
Fig. 2 is a PEMFC hydrogen flow rate input graph.
Fig. 3 is a PEMFC load current input graph.
FIG. 4 is a graph of the predicted control desired electrical characteristics of the PEMFC recursive subspace model.
FIG. 5 is a graph of the PEMFC recursive subspace predictor model identification forgetting factor.
FIG. 6 is a graph of the identification result of the PEMFC recursive subspace estimator model.
FIG. 7 is a graph of model predictive control results for PEMFC based on recursive subspace identification
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings.
A proton exchange membrane fuel cell forgetting factor deduction subspace identification method comprises the following steps:
step 1, selecting input and output variables of an identification model, and collecting experimental data on a PEMFC measurement and control platform.
Selection of output variables: as a new power generation device, ensuring the electrical characteristic output of the PEMFC to be stable is a primary task, and the output voltage and power are important indexes for measuring the power generation performance of the fuel cell and are selected as output variables of an electrical characteristic model of the fuel cell. However, there are many factors that affect the electrical characteristics of the PEMFC, such as load current, stack temperature, stack humidity, hydrogen/oxygen flow, hydrogen/oxygen pressure, and the like.
Selection of input variables: the fuel cell parameters are more, strong coupling exists between variables, and if all the variables are used as identification model inputs, the model structure is inevitably overstaffed, and the modeling complexity is increased. Therefore, the main input variables of the model identification need to be selected;
1) among many factors affecting the output electrical characteristics of the stack, the influence of the load current on the output electrical characteristics is the most direct and obvious, so the load current is taken into consideration as an input variable of the identification model.
2) During the power generation of the fuel cell, the electrical characteristics thereof are sensitive to changes in the hydrogen gas flow rate and pressure. The higher the hydrogen flow and pressure, the faster the stack electrochemical reaction rate and thus higher power output. However, the hydrogen flow rate only needs to be controlled by the flow valve of the hydrogen bottle, and the testability and controllability of the hydrogen flow rate are obviously superior to those of the hydrogen pressure, so that the hydrogen flow rate is selected as a modeling input variable.
In summary, the hydrogen flow and the load current are used as input variables of the identification model, and the stack voltage and the power are used as output variables. The experimental data is collected on the PEMFC measurement and control platform without control action, and the experimental data is preferably 500-1000 groups. And carrying out data integrity analysis on the acquired experimental data, and rejecting a part of experimental data with the change rate exceeding the actual work of the PEMFC measurement and control system.
And 2, constructing a Hankel matrix by using the acquired input and output data, and solving a subspace predictor model at the k moment by using a subspace identification method.
Assuming that at a certain sampling time k, the Hankel matrix is constructed by using the collected input and output data, including the future input Hankel matrix (U)f)kFuture output Hankel matrix (Y)f)kAnd a past input and output Hankel matrix (W)p)kWherein (W)p)kFrom the past, input into the Hankel matrix (U)p)kAnd a past output Hankel matrix (Y)p)kThe structure of each matrix is as follows:
(Wp)k＝[YpUp]T|k
in the formula: n is the number of sets of sampled data,
in order to input the variables of the device,
in order to output the variable, the output variable,
wherein m is the number of input variables, l is the number of output variables, p is the dimension of the past Hankel matrix, and f is the dimension of the future Hankel matrix.
The subspace predictor model is a model for describing the future output of the system by using the past input and output data and the future control input, and the expression is as shown in formula (1):
(Yf)k＝Lw|k(Wp)k+Lu|k(Uf)k(1)
in the formula: matrix Lw|kAnd Lu|kIs the subspace linear predictor model coefficient at the k moment.
For input and output data Hankel matrix [ W ]pUfYf]T|kRQ decomposition to obtain Rk：
R is calculated from the formula (2)kThen, subspace estimator coefficient matrix Lw|kAnd Lu|kL can be calculated from equation (3)kObtaining:
in formula (3):
upper label
Is Moore-Penrose pseudoinverse.
Step 3, constructing an input and output data Hankel matrix at the moment k +1, and solving the prediction output at the moment k +1 by using a subspace predictor model at the moment k;
the Hankel matrix of input and output data with new data added is constructed as follows:
in the formula: (U)f)k+1Is the future input Hankel matrix at time k +1, (Y)f)k+1Is the future output Hankel matrix at the time of k +1, (W)p)k+1Is a past input and output Hankel matrix at the time of k +1, and is composed of a past input Hankel matrix (U) at the time of k +1p)k+1And future input Hankel matrix (Y)p)k+1Forming;
the predicted output at time k +1 is:
in formula (4):
and
is the coefficient matrix L of the subspace predictor at the k momentw|kAnd Lu|kLast row of (1).
Step 4, according to the control action u added by the PEMFCk+1Determining the actual output data y at the time k +1k+1Calculating the output prediction error of the actual output and the prediction output, if the output prediction error is greater than the allowable error, updating the solution subspace predictor model by using a recursive subspace identification algorithm, and otherwise, not updating the model;
output prediction error e for time k +1k+1As defined below:
in formula (5): y isk+1Is the actual output of the system at time k +1,
is the predicted output of the system at time k +1, and sets the allowable error to be epsilon if ek+1If the coefficient is more than epsilon, the coefficient matrix L of the subspace predictor model is solved again by using a recursive subspace identification algorithmw|k+1And Lu|k+1Otherwise, Lw|k+1＝Lw|k，Lu|k+1＝Lu|k；
The recursive subspace identification algorithm specifically comprises:
forgetting factor lambda to variablek+1As defined below:
in formula (6): epsilon is an allowable error, ek+1To output a prediction error, λk+1The value range of (A) is more than 0 and less than lambdak+1＜1。
Updating Hankel matrix containing new data to [ WpUfYf]T|k+1Obtained by RQ decomposition
Matrix:
subsequent elimination using Givens transform
The rightmost column of (2), for ease of derivation, will be the matrix
Redefined as:
in formula (8):
the indices i and j in (a) are denoted as rows and columns of elements, respectively.
Assuming that the j-th column is the current column, s is calculated from the first column (j equals 1) by using equations (9) and (10)iAnd ci：
Calculating and updating the matrix according to equations (11) and (12)
Each row element in the jth column is
And each row element in the rightmost column is
Finally, the matrix is divided into
After each column of (1) is updated, R is obtainedk+1Comprises the following steps:
removing Rk+1In the last row, the coefficient matrix L of the subspace predictor model is obtained through the calculation of the formula (13)w|k+1And Lu|k+1。
And 5, repeating the steps 3 and 4, and updating the subspace predictor model in real time.
Examples
To verify the validity of the inventive scheme, the following simulation experiment was performed.
The fuel cell stack adopted by the experimental PEMFC measurement and control platform is a 50W air-cooled PEMFC stack, the input and output data are collected, the subspace predictor model is identified on line and updated in real time, and meanwhile, the electrical characteristic output of the PEMFC is controlled to track an expected electrical characteristic curve.
1) Collecting experimental data and establishing an initial subspace predictor model
The input variables of the identification model are hydrogen flow and load current, and the output variables are stack voltage and power, so that the number of the input variables is set to be m-2, and the number of the output variables is set to be l-2. Firstly, input data is given on a PEMFC measurement and control platform, 500 groups of output data are collected, variation curves of hydrogen flow and load current are set as shown in figures 2 and 3, and the number of sampling data groups is N id500. Then, a Hankel matrix of input/output data is constructed, the dimension of the past Hankel matrix is set as p 1, and H in the futureThe dimension of the ankel matrix is f-5 (p < f). And finally, identifying an initial PEMFC electrical characteristic subspace predictor model by adopting a subspace identification algorithm.
2) Setting an electrical characteristic curve expected to be tracked, exerting control action on the PEMFC and obtaining new data
The control method used in this experiment is model predictive control, which obtains the control input by optimizing the future output of the system, i.e. at each sampling time an optimization problem is solved, with the goal of finding the appropriate input signal such that the error objective function is minimized. Fig. 4 shows an electrical characteristic curve to be tracked, and the number of simulation data sets N is 500. And the model prediction controller obtains control input through rolling optimization and applies the control input to the PEMFC to obtain output data, so that new input and output data are obtained for the online updating of the subspace predictor model in the next step.
3) Constructing an input and output Hankel matrix with new data addition, and judging whether to solve the subspace predictor model again
And constructing an input and output Hankel matrix with new data addition, wherein N is 500, p is 1, and f is 5. And calculating the current prediction output through the subspace predictor model solved at the last moment, and calculating the difference between the current prediction output and the actual measurement output to obtain an output prediction error. Setting the tolerance as 10 ∈-3If the output prediction error is larger than the allowable error, solving the subspace predictor model again; otherwise, directly performing model prediction control at the next moment.
4) And calculating a variable forgetting factor, and calculating a solved subspace predictor model again by using a recursion subspace identification method to obtain the variable forgetting factor lambda by calculating an output prediction error and an allowable error, wherein the value range of the variable forgetting factor lambda is more than 0 and less than 1.
And adding a variable forgetting factor, updating the R matrix by using a Givens transformation method, and solving the subspace predictor model coefficient matrix again.
5) Recalculating output prediction error by using newly solved subspace predictor model, and judging whether to update model
Recalculating an output prediction error by using the newly solved subspace predictor model, if the error value becomes smaller, updating the model, and performing model prediction control at the next moment; otherwise, directly performing model prediction control at the next moment.
6) Results of the experiment
When the expected electrical characteristic output tracking proceeds to 250 sets, a model mismatch condition is made, and the stack temperature of the PEMFC is adjusted from 40 ℃ to 50 ℃, causing the subspace estimator model to mutate. At the moment, the system can correct and update the subspace predictor model in real time on line, so that the controller can quickly adjust the parameter tracking electrical characteristic curve. After the 500 groups of expected electrical characteristic output traces are completed, in the process of updating the subspace predictor model in a recursion manner, the variation curve of the forgetting factor is shown in fig. 5, and the identification result is shown in fig. 6. Finally, as shown in fig. 7, the electrical characteristic control result of the PEMFC system is that the model predictive control method based on recursive subspace identification can quickly and accurately track the desired electrical characteristic curve.
Claims (5)
1. A proton exchange membrane fuel cell forgetting factor deduction subspace identification method is characterized by comprising the following steps:
step 1, selecting input and output variables of an identification model, and collecting experimental data on a PEMFC measurement and control platform;
step 2, constructing a Hankel matrix of input and output data at the current moment, and solving a subspace predictor model at the current moment by using a subspace identification method;
step 3, constructing a Hankel matrix of input and output data at the next moment, and solving the prediction output at the next moment by using a subspace predictor model at the current moment;
step 4, determining actual output data at the next moment according to the control action added by the PEMFC, calculating output prediction errors of actual output and predicted output, if the output prediction errors are larger than the allowable errors, updating a solution subspace predictor model by using a recursive subspace identification algorithm, and otherwise, not updating the model;
and 5, repeating the steps 3 and 4, and updating the subspace predictor model in real time.
2. The pem fuel cell forgetting factor recurrence subspace identification method according to claim 1, wherein in step 1, hydrogen flow and load current are used as input variables of the identification model, and stack voltage and power are used as output variables.
3. The pem fuel cell forgetting factor recurrence subspace identification method according to claim 1, wherein in step 2, the specific method for constructing the subspace predictor model comprises:
at a certain sampling time k, constructing a Hankel matrix including a future input Hankel matrix (U) by using the collected input and output dataf)kFuture output Hankel matrix (Y)f)kAnd a past input and output Hankel matrix (W)p)kWherein (W)p)kFrom the past, input into the Hankel matrix (U)p)kAnd a past output Hankel matrix (Y)p)kThe structure of each matrix is as follows:
(Wp)k＝[YpUp]T|k
in the formula: n is the number of sets of sampled data,
in order to input the variables of the device,
in order to output the variable, the output variable,
wherein m is the number of input variables, l is the number of output variables, p is the dimension of the past Hankel matrix, and f is the dimension of the future Hankel matrix;
the subspace predictor model is a model for describing the future output of the system by using the past input and output data and the future control input, and the expression is as shown in formula (1):
(Yf)k＝Lw|k(Wp)k+Lu|k(Uf)k(1)
in formula (1): matrix Lw|kAnd Lu|kIs the subspace linearity predictor model coefficient at the time k;
for input and output data Hankel matrix [ W ]pUfYf]T|kRQ decomposition to obtain Rk：
R is calculated from the formula (2)kThen, subspace estimator coefficient matrix LwkAnd Lu|kL can be calculated from equation (3)kObtaining:
in formula (3):
upper label
Is Moore-Penrose pseudoinverse.
4. The pem fuel cell forgetting factor recurrence subspace identification method according to claim 1, wherein in step 3, the specific method for solving the prediction output at the next moment is:
the Hankel matrix of input and output data with new data added is constructed as follows:
in the formula: (U)f)k+1Is the future input Hankel matrix at time k +1, (Y)f)k+1Is the future output Hankel matrix at the time of k +1, (W)p)k+1Is a past input and output Hankel matrix at the time of k +1, and is composed of a past input Hankel matrix (U) at the time of k +1p)k+1And future input Hankel matrix (Y)p)k+1Forming;
the predicted output at time k +1 is:
in formula (4):
and
is the coefficient matrix L of the subspace predictor at the k momentw|kAnd Lu|kTo lastl lines.
5. The pem fuel cell forgetting factor recursive subspace identification method according to claim 1, wherein in step 4, the specific method for updating the solution subspace predictor model by using the recursive subspace identification algorithm comprises:
forgetting factor lambda to variablek+1As defined below:
in formula (6): epsilon is an allowable error, ek+1To output a prediction error, λk+1The value range of (A) is more than 0 and less than lambdak+1＜1；
Updating Hankel matrix containing new data to [ WpUfYf]T|k+1Obtained by RQ decomposition
Matrix:
subsequent elimination using Givens transform
The rightmost column of (2), for ease of derivation, will be the matrix
Redefined as:
in formula (8):
subscripts i and j of (1)Rows and columns, respectively, denoted as elements;
assuming that the j-th column is the current column, s is calculated from the first column (j equals 1) by using equations (9) and (10)iAnd ci：
Calculating and updating the matrix according to equations (11) and (12)
Each row element in the jth column is
And each row element in the rightmost column is
Finally, the matrix is divided into
After each column of (1) is updated, R is obtainedk+1Comprises the following steps:
removing Rk+1In the last row, the coefficient matrix L of the subspace predictor model is obtained through the calculation of the formula (13)wk+1And Luk+1：
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| CN112507526A (en) * | 2020-11-20 | 2021-03-16 | 武汉船用电力推进装置研究所（中国船舶重工集团公司第七一二研究所） | Performance prediction method and system for proton exchange fuel cell system |
| CN113625555A (en) * | 2021-06-30 | 2021-11-09 | 佛山科学技术学院 | Adaptive inverse control AGV rotation speed control method based on recursive subspace identification |
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Application publication date: 20200512 |