CN108134114B - Proton exchange membrane fuel cell temperature control method - Google Patents

Proton exchange membrane fuel cell temperature control method Download PDF

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CN108134114B
CN108134114B CN201711287557.8A CN201711287557A CN108134114B CN 108134114 B CN108134114 B CN 108134114B CN 201711287557 A CN201711287557 A CN 201711287557A CN 108134114 B CN108134114 B CN 108134114B
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temperature
fuel cell
fuzzy
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control
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CN108134114A (en
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邹见效
谢雨岑
彭超
徐红兵
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
    • H01M8/04694—Processes for controlling fuel cells or fuel cell systems characterised by variables to be controlled
    • H01M8/04701—Temperature
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04007—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids related to heat exchange
    • H01M8/04029—Heat exchange using liquids
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04007—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids related to heat exchange
    • H01M8/04067—Heat exchange or temperature measuring elements, thermal insulation, e.g. heat pipes, heat pumps, fins
    • H01M8/04074—Heat exchange unit structures specially adapted for fuel cell
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
    • H01M8/04694—Processes for controlling fuel cells or fuel cell systems characterised by variables to be controlled
    • H01M8/04701—Temperature
    • H01M8/04708—Temperature of fuel cell reactants
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
    • H01M8/04694—Processes for controlling fuel cells or fuel cell systems characterised by variables to be controlled
    • H01M8/04746—Pressure; Flow
    • H01M8/04768—Pressure; Flow of the coolant
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
    • H01M8/04992—Processes for controlling fuel cells or fuel cell systems characterised by the implementation of mathematical or computational algorithms, e.g. feedback control loops, fuzzy logic, neural networks or artificial intelligence
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/30—Hydrogen technology
    • Y02E60/50—Fuel cells

Abstract

The invention discloses a proton exchange membrane fuel cell temperature control method, which comprises the steps of taking a PID (proportion integration differentiation) controller as a general feedback controller to stabilize the temperature of a fuel cell stack to achieve a primary control effect, then obtaining the change trend of the temperature of a fuel cell system according to the advanced prediction function of a gray model, compensating the uncertainty and the external interference of the system by using the obtained prediction information through a fuzzy controller, and further improving the control precision of the system. The feedforward compensation control and the feedback control act together to realize the accurate control of the temperature of the proton exchange membrane fuel cell.

Description

Proton exchange membrane fuel cell temperature control method
Technical Field
The invention belongs to the technical field of proton exchange membrane fuel cells, and particularly relates to a temperature control method of a proton exchange membrane fuel cell.
Background
Proton Exchange Membrane Fuel Cells (PEMFCs) are devices that directly convert hydrogen energy into electrical energy, have the advantages of high specific energy, low operating temperature, high starting speed, and the like, and are considered to be very attractive power generation devices.
Despite its wide application prospects, the overall popularity of fuel cells is limited by objective reasons, such as control techniques that are not yet fully developed, particularly in terms of temperature control. The internal electrochemical reaction process of the PEMFC during operation is directly reflected in the change of the temperature and the temperature distribution of the stack. Once the temperature control effect is not ideal, the operating temperature is too high or too low, which easily causes a significant decrease in the power generation efficiency of the PEMFC, and more seriously, irreversible damage to the proton exchange membrane. In addition, the temperature difference at the inlet and outlet of the fuel cell stack needs to be controlled within a set range, otherwise, the aging of the proton exchange membrane is accelerated by the large thermal stress in the fuel cell stack, and the service life of the fuel cell is shortened. Therefore, the temperature control of the proton exchange membrane fuel cell comprises the control of the working temperature of the electric pile and the control of the temperature difference of the inlet and the outlet of the electric pile.
Scholars at home and abroad have conducted a series of studies on the temperature control method of the proton exchange membrane fuel cell, and generally, the heat dissipation capacity of the fuel cell cooling system is adjusted by using methods such as PID control, model predictive control, LQR feedback control, fuzzy control and the like according to the error between the real-time temperature and the set temperature of the fuel cell, so that the temperature of the fuel cell is kept near the set value. The proton exchange membrane fuel cell is a complex dynamic system with nonlinearity, strong coupling and large time delay, and the control method can realize the control of the temperature of the fuel cell, but cannot obtain better control effect. PID and LQR feedback control have high requirements on the precision of the model and cannot solve the problem of time delay; the fuzzy control is based on expert experience control, can overcome the problem of model uncertainty, but can not solve the problem of thermal time delay of the fuel cell; the model predictive control can predict the future deviation value to solve the time delay of the temperature control, but the model mismatch problem exists when the system is subjected to uncertain disturbance. Generally, these current temperature control methods are designed according to certain characteristics of the fuel cell, and the consideration is incomplete, which inevitably results in poor temperature control effect of the fuel cell.
Therefore, considering the nonlinearity, time delay and uncertainty of the fuel cell system, the invention provides a gray prediction fuzzy control method, namely, a gray prediction model and a fuzzy controller are combined to be used as a feedforward controller, and a PID feedback controller is added, so that the control of the temperature of the fuel cell is realized. In the feedforward controller, the fuzzy controller is beneficial to the prediction result of the grey prediction model to carry out compensation control on the system in advance, can solve the influence of uncertain disturbance on the system, and has certain robustness and quick response. And the PID feedback controller can correct the system error and further improve the accuracy of the temperature control of the fuel cell. Therefore, the gray prediction fuzzy control method provided by the invention has certain theoretical significance and practical value on the temperature control research of the fuel cell.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a temperature control method of a proton exchange membrane fuel cell, wherein a gray prediction model and fuzzy control are combined to be used as a feedforward controller, and a PID (proportion integration differentiation) feedback controller is combined to realize the control of the working temperature of a fuel cell stack and the control of the temperature difference of an inlet and an outlet of the fuel cell stack, so that the disturbance resistance, the self-adaptive capacity and the control precision of a system are improved.
In order to achieve the above object, the present invention provides a method for controlling temperature of a proton exchange membrane fuel cell, comprising the steps of:
(1) determining a fuzzy controller model
The fuzzy controller consists of a PD type fuzzy controller and a PI type fuzzy controller, and the model expression is as follows:
ufuzzy＝αuPD-fuzzy+βuPI-fuzzy，
wherein u isfuzzyIs a control quantity of a fuzzy controller, uPD-fuzzyFor the output of a PD-type fuzzy controller, uPI-fuzzyα and β are the weighting coefficients of the PD-type and PI-type fuzzy controllers, respectively, for the output of the PI-type fuzzy controller;
(2) the established grey prediction model GM (1,1)
Figure BDA0001498759700000021
Wherein p is the prediction step length, a and b are the development coefficient and the gray action quantity respectively, k represents the time sequence, y(0)Representing a sequence of raw temperature data, y(0)(1) Representing the first data in the original temperature data sequence,
Figure BDA0001498759700000022
a sequence of predicted temperature data is represented,
Figure BDA0001498759700000023
expressed as the predicted temperature value at time (k + p);
(3) establishing a PID controller
Figure BDA0001498759700000031
Wherein, KpIs a proportionality coefficient, KIIs the integral coefficient, KDIs a differential coefficient, e represents the real-time temperature y of the fuel celloutThe difference value with a set temperature value r, wherein t represents time;
(4) setting initial values of parameters of a fuzzy controller, a gray prediction model GM (1,1) and a PID controller; determining simultaneously the modeling dimension n in the grey prediction model, i.e. the original data sequence y(0)The number of data in (1) and a prediction step length p; determining a proportionality coefficient K for a PID controllerpIntegral coefficient KICoefficient of differentiation KD；
(5) Acquiring real-time temperature data y of the cell stack in real time through a sensor in the actual operation of the fuel cell systemoutThen, these temperature data are sampled, and the temperature data obtained at the first n sampling moments form an original temperature data sequence y of the gray prediction model GM (1,1)(0)＝{y(0)(1),y(0)(2),...,y(0)(n) and obtaining the predicted temperature value of the fuel cell by utilizing a GM (1,1) prediction model established by the original temperature data sequence
Figure BDA0001498759700000032
(6) Predicting the future temperature of the fuel cell system in real time by using a grey prediction model GM (1,1), and obtaining the predicted temperature
Figure BDA0001498759700000033
Comparing with the set working temperature value r to obtain the prediction error of the fuel cell temperature
Figure BDA0001498759700000034
And prediction error variation
Figure BDA0001498759700000035
Real-time temperature y of fuel celloutComparing with the set temperature value r to obtain the real-time error e and the real-time error variation of the fuel cell temperature
Figure BDA0001498759700000036
(7) Error of prediction of fuel cell temperature
Figure BDA0001498759700000037
And prediction error variation
Figure BDA0001498759700000038
As input of the fuzzy controller, the control quantity u of the fuzzy controller is obtainedfuzzy(ii) a Real-time error e and real-time error variation of fuel cell temperature
Figure BDA0001498759700000039
As input of PID controller, feedback control quantity u of system is obtainedpid；
(8) Will control the quantity ufuzzyAnd a feedback control amount upidWeighted summation is carried out to obtain the control quantity u of the systemoutThen u is addedoutActing on heat-dissipating actuators in PEM fuel cell systems by varying uoutThe operating state of the heat dissipation actuator is adjusted by the value of the temperature sensor, so that the temperature of the fuel cell is controlled.
The invention aims to realize the following steps:
the invention relates to a proton exchange membrane fuel cell temperature control method, which takes a PID controller as a general feedback controller to stabilize the temperature of a fuel cell stack to achieve a primary control effect, then obtains the change trend of the temperature of a fuel cell system according to the advanced prediction function of a gray model, and a fuzzy controller compensates the uncertainty and the external interference of the system by using the obtained prediction information to further improve the precision of the system control. The feedforward compensation control and the feedback control act together to realize the accurate control of the temperature of the proton exchange membrane fuel cell.
Meanwhile, the temperature control method of the proton exchange membrane fuel cell also has the following beneficial effects:
(1) the advantages of fuzzy control, gray prediction and traditional PID control are utilized, the control performance of the system is improved by adopting a hybrid control mode, wherein the PID control algorithm is simple, and the reliability is high; the fuzzy control does not depend on a control object model, and has strong adaptability and robustness; the grey prediction control is convenient for decision and control in advance by predicting the future change trend of the fuel cell temperature.
(2) The method adopts a mode of combining gray prediction control and fuzzy control, and can improve the disturbance resistance and self-adaptive capacity of the fuel cell system by utilizing the prediction information of the gray model and the robustness of the fuzzy control, thereby obtaining the effects of quick response and small overshoot;
(3) the PID controller can make up the problem of low steady-state precision of the fuzzy control, improve the steady-state performance of the fuzzy controller and further reduce the overshoot.
Drawings
FIG. 1 is a schematic diagram of a method for controlling the temperature of a PEMFC according to the present invention;
FIG. 2 is a block diagram of a PEMFC thermal management system;
FIG. 3 is a block diagram of a metabolic GM (1,1) prediction model;
FIG. 4 is a block diagram of a fuzzy controller;
FIG. 5 is a schematic diagram of a membership function of fuzzy controller input quantities;
FIG. 6 is a schematic diagram of a membership function of the output of the fuzzy controller;
FIG. 7 shows external disturbances during the operation of a PEM fuel cell according to an embodiment of the present invention, (a) current disturbances, and (b) ambient temperature disturbances;
FIG. 8 shows the predicted value and the actual value of the temperature of the fuel cell stack during the operation of the PEMFC according to the embodiment of the present invention;
FIG. 9 shows the predicted value and the actual value of the temperature difference of the fuel cell stack during the operation of the PEMFC according to the embodiment of the present invention;
FIG. 10 is a graph comparing the temperature control effect of a fuel cell stack during the operation of a PEM fuel cell in accordance with an embodiment of the present invention;
FIG. 11 is a graph comparing the temperature difference control effect of the fuel cell stack during the operation of the PEM fuel cell according to the embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a schematic diagram of a method for controlling the temperature of a PEMFC according to the present invention.
In this embodiment, as shown in fig. 1, a system structure of a method for controlling a temperature of a proton exchange membrane fuel cell mainly includes: a grey prediction model GM (1, 1); secondly, a fuzzy controller; and thirdly, a PID controller. The grey prediction module and the fuzzy control are combined to be used as a feedforward controller for compensating the thermal time delay of the fuel cell and processing the problems of parameter uncertainty, external disturbance and the like, the PID feedback controller is used as a feedback controller, the steady-state performance of control can be improved, and the disturbance resistance, the self-adaptive capacity and the control precision of the system are effectively improved by utilizing the advantages of the three types of controllers.
In particular, the qualityAs shown in fig. 2, a water pump drives cooling water to circulate, so as to bring a large amount of heat generated by electrochemical reaction from the fuel cell stack to a radiator, and then a fan is used to force air to convect, so as to improve the heat dissipation capability of the system. Therefore, the cooling water pump voltage is controlled by the temperature difference controller, and the flow rate of the cooling liquid is adjusted so that the temperature difference between the inlet and the outlet of the fuel cell stack is stabilized at a set value (in this example, the set value of the temperature difference of the fuel cell is 6K). Since the influence of the coolant flow rate on the stack temperature is limited, the fan voltage is adjusted by the temperature controller, and the heat dissipation amount is controlled so that the stack temperature is stabilized at a set value (in this example, the stack temperature set value is 340K). Wherein, TstAnd Tst,inRespectively representing the temperature of the fuel cell stack and the temperature of cooling water at the inlet of the cell stack; delta Tst,refAnd Tst,refRespectively representing a temperature difference set value and a temperature set value of the cell stack; wairAnd WclRespectively representing the heat dissipation capacity of the fan and the flow rate of the cooling water. In fig. 2, the temperature controller and the temperature difference controller both adopt the temperature control method in fig. 1, namely, the temperature control method of the proton exchange membrane fuel cell of the invention.
The following will explain in detail a proton exchange membrane fuel cell temperature control method of the present invention with reference to fig. 1 and 2, and specifically includes the following steps:
s1, determining the fuzzy controller model of the fuel cell temperature
The fuzzy controller of proton exchange membrane fuel cell temperature for feedforward control is composed of a PD type fuzzy controller and a PI type fuzzy controller, and the model expression is as follows: u. offuzzy＝αuPD-fuzzy+βuPI-fuzzy，
Wherein u isfuzzyIs the control variable of the fuzzy controller, i.e. the voltage regulation value of the fuel cell heat dissipation actuator (radiator fan or water pump), uPD-fuzzyFor the output of a PD-type fuzzy controller, uPI-fuzzyα and β are the weighting coefficients of the PD-type and PI-type fuzzy controllers, respectively, for the output of the PI-type fuzzy controller;
the following steps of designing the fuzzy controller are specifically described, specifically:
s1.1, determining input and output of fuzzy controller
Two input quantities of the fuzzy controller are determined: prediction error of fuel cell temperature (operating temperature or stack temperature difference)
Figure BDA0001498759700000061
And fuel cell temperature prediction error variation
Figure BDA0001498759700000062
Output quantity: voltage regulation value of heat dissipation actuator (heat dissipation fan or water pump) in proton exchange membrane fuel cell system;
fuzzy control is essentially a nonlinear control that uses human language information to simulate human thinking for control decisions, so the method belongs to the field of intelligent control. When the control characteristics are improved, the control rules, the membership function, the inference method and the decision method only need to be changed for correction, so that the method is easy to understand, simple in design and convenient to maintain. In this embodiment, the fuzzy controller is used as a feedforward controller of the system, is a pre-control focusing on the future behavior of the system, is a control in advance, can compensate the uncertainty of the system and the external interference, and has the effects of fast response and small overshoot. The fuzzy controller designed in the present invention is shown in fig. 4.
S1.2, fuzzifying input quantity and output quantity of fuzzy controller
Input amount 1: prediction error of fuel cell temperature (operating temperature or stack temperature difference)
Figure BDA0001498759700000064
Taking its linguistic variable as E, its fuzzy domain is divided into 7 levels [ -6, -4, -2,0,2,4,6]The fuzzy subset is { NB, NM, NS, ZO, PS, PM, PB }, and the ranges of prediction errors are { big negative, middle negative, small negative, zero, small positive, middle positive, big positive };
input amount 2: prediction error variation of fuel cell temperature (operating temperature or stack temperature difference)
Figure BDA0001498759700000063
Taking its linguistic variable as EC, the fuzzy domain is divided into 7 levels [ -6, -4, -2,0,2,4,6 [ -4 [ -2,0 [ -2, 4 [ -6 [ ]]The fuzzy subset is { NB, NM, NS, ZO, PS, PM, PB }, and the ranges of the prediction error variation are { big negative, middle negative, small negative, zero, small positive, middle positive, big positive };
output quantity: the method comprises the following steps that a linguistic variable U of a voltage adjusting value U of a radiator (a cooling fan or a water pump) in a fuel cell system is taken as U, a fuzzy domain is divided into 7 grades of (-3, -2, -1,0,1,2, 3), fuzzy subsets of the fuzzy subsets are { NB, NM, NS, ZO, PS, PM and PB }, and the ranges of prediction error variation are { minimum, moderate, large and maximum };
in this embodiment, the membership functions of NM, NS, ZO, PS, and PM in the input quantity and the output quantity are all triangular membership functions, and the form and distribution of the membership functions are represented by three parameters (a, b, c), as follows:
Figure BDA0001498759700000071
the membership function of NB in the input quantity and the output quantity adopts a Z-type membership function, and the specific form is as follows:
Figure BDA0001498759700000072
the membership function of PB in the input quantity and the output quantity adopts an S-type membership function, and the specific form is as follows:
Figure BDA0001498759700000073
the membership function for the input quantities is shown in fig. 5 and the membership function for the output quantities is shown in fig. 6. x represents the fuzzified input or output value, and μ (x) represents the corresponding degree of membership.
S1.3, designing a control rule of the fuzzy controller and carrying out fuzzy reasoning
The fuzzy rules are obtained based on the summary of debugging experience of the fuel cell system and are expressed in the form of IF-THEN language, a control rule table of the fuzzy controller is formed by 49 fuzzy rules, as shown in table 1, and the fuzzy reasoning adopts the Mamdani reasoning method;
in this embodiment, for a two-dimensional controller, the control rule may be expressed as:
R1：if E＝NB and EC＝NB,then U＝PB；
R2：if E＝NB and EC＝NM,then U＝PB；
…………
R49：if E＝PB and EC＝PM,then U＝NB；
the overall fuzzy relationship R describing the control rules of the entire system is:
R＝R1∪R2∪...∪R49
Figure BDA0001498759700000081
TABLE 1
S1.4, the fuzzy output value obtained by fuzzy reasoning is a fuzzy subset on an output domain, and can be applied to an object only by converting the fuzzy output value into an accurate control quantity, and the process is called defuzzification. In the invention, a gravity center method is adopted to defuzzify the designed fuzzy controller, namely, the gravity center of the area enclosed by the fuzzy membership function and the horizontal coordinate in the figure 6 is used as the final output value of the fuzzy inference to obtain the output value u of the PD type fuzzy controllerPD-fuzzy(ii) a Namely:
Figure BDA0001498759700000082
s1.5, determining the actual output of the fuzzy controller
The fuzzy controller output obtained after defuzzification is actually the output value of the PD type fuzzy controller, not the output value of the fuzzy controller in the present invention. Considering that the PD type controller has good transient performance but it cannot eliminate static errors, the present invention improves the fuzzy controller and introduces the PI type fuzzy controller. By combining the advantages of the PI type fuzzy controller and the PD type fuzzy controller, the response speed can be increased, the overshoot of the system can be reduced, and no steady-state error can be ensured.
Specifically, the output of the PD type fuzzy controller is subjected to integral operation to obtain an output value u of the PI type fuzzy controllerPI-fuzzyAnd then, obtaining the actual output of the fuzzy controller by the weighted sum of the output values of the PI type fuzzy controller and the PD type fuzzy controller: u. offuzzy＝αuPD-fuzzy+βuPI-fuzzyWherein the weighting factor of the fuzzy controller of PD type is α type and the weighting factor of the fuzzy controller of PD type is β.
S2, established Gray prediction model GM (1,1)
Figure BDA0001498759700000091
Wherein p is the prediction step length, a and b are the development coefficient and the gray action quantity respectively, k represents the time sequence, y(0)Data sequence representing the original PEM fuel cell temperature (stack operating temperature or stack inlet-outlet temperature difference), y(0)(1) Representing the first data in a raw fuel cell temperature (operating temperature or stack temperature differential) data series,
Figure BDA0001498759700000092
represents a predicted fuel cell temperature (operating temperature or stack temperature differential) data series,
Figure BDA0001498759700000093
expressed as the predicted temperature (operating temperature or stack temperature difference) value at time (k + p);
the specific modeling process for gray prediction GM (1,1) is described below.
1. Accumulation generation
Let the original temperature data sequence of the GM (1,1) model be y(0)＝{y(0)(1),y(0)(2),...,y(0)(n), where n is the modeling dimension. Since the original data sequence is a set of grey quantities with incomplete information, in order to weaken the randomness of the original time sequence, the original time sequence needs to be divided into a plurality of data blocksTo y(0)Performing an accumulation generation operation to obtain a new data sequence y(1)Comprises the following steps:
y(1)＝{y(1)(1),y(1)(2),...,y(1)(n)}
Figure BDA0001498759700000094
2. GM (1,1) model building
After one accumulation operation, a new data sequence y is obtained(1)Exhibits exponential growth law and satisfies the gray differential equation:
y(0)(k)+az(1)(k)＝b
Figure BDA0001498759700000095
Figure BDA0001498759700000096
whitening differential equation, namely GM (1,1) model:
Figure BDA0001498759700000097
the solution of the whitening differential equation is:
Figure BDA0001498759700000101
in the formula, a is referred to as a coefficient of progression, and b represents the amount of gray effect. a reflects the development situation of the initial sequence and the primary accumulated sequence value, and the gray acting quantity b reflects the change relation between the data. k is a time series.
3. GM (1,1) model parameter identification
And (3) performing parameter identification on the development coefficient and the gray effect amount by adopting a least square method:
[a,b]T＝(BTB)-1BTY
Figure BDA0001498759700000102
Y＝[y(0)(2),y(0)(3),...,y(0)(n)]T
4. predictive value reduction
Since GM (1,1) is obtained as the primary accumulation, the data obtained from the GM model must be used
Figure BDA0001498759700000103
The predicted value of the original data sequence can be obtained through inverse generation, namely accumulation and subtraction generation
Figure BDA0001498759700000104
Figure BDA0001498759700000105
The prediction in advance of p steps can be realized by only changing the value of the prediction step size p.
By modeling GM (1,1), it can be found that the predicted value of the fuel cell temperature is related to the prediction step length p and the modeling dimension n, and proper gray model parameters are selected, so that the future temperature change of the fuel cell can be more accurately predicted, and the prediction accuracy and the real-time performance are improved.
The invention adopts 5 fuel cell temperature sampling data to predict (namely n is 5), namely the fuel cell temperature data y of five historical sampling points(0)(1),y(0)(2),y(0)(3),y(0)(4),y(0)(5) Inputting the prediction model of GM (1,1) in the form of sequence, the predicted value of the fuel cell temperature at the 5+ p sampling point can be obtained
Figure BDA0001498759700000106
Considering that the thermal time constant of the fuel cell is in the order of hundreds of seconds, the prediction sampling interval of GM (1,1) for fuel cell stack temperature prediction is 1 second, and the prediction step p is 10; the prediction sampling interval of GM (1,1) for the prediction of the temperature difference of the cell stack is 0.5 second, and the prediction step length p is 3.
Because some random disturbance will enter the system continuously with the time passing in the development process of the gray system to influence the development of the system, in order to improve the prediction accuracy, the invention adopts a rolling prediction mechanism to update the historical data sequence for prediction, namely the metabolism method in a mode of adding the latest historical data and removing the oldest historical data. I.e. from the known original data sequence y(0)＝{y(0)(1),y(0)(2),...,y(0)(n) establishing a GM (1,1) model and obtaining a predicted temperature value p sampling moments in advance
Figure BDA0001498759700000111
Then removing the earliest data information y in the original data sequence(0)(1) Adding the newly sampled fuel cell temperature data to the original data sequence to update the data sequence y(0)′＝{y(0)(2),y(0)(3),...,y(0)(n +1) }, based on the sequence y(0)' the GM (1,1) model is built again to predict the next temperature data, then the new sampling data is added into the sequence, and the earliest data in the previous sequence is removed, so that the metabolism is predicted one by one and is successively supplemented. The model for predicting the GM (1,1) metabolism is shown in FIG. 3.
S3 PID controller for establishing fuel cell temperature
Figure BDA0001498759700000112
Wherein, KpIs a proportionality coefficient, KIIs the integral coefficient, KDAs a differential coefficient, e represents a real-time temperature (operating temperature or stack temperature difference) y of the fuel celloutThe difference value with the set temperature (working temperature or cell stack temperature difference) value r of the fuel cell, wherein t represents time;
the PID controller is used as conventional feedback control to stabilize the system, and a preliminary control effect is achieved. Although the fuzzy controller has the characteristics of high robustness, strong adaptive capacity and the like, the problem of low steady-state control precision exists. And the PID control algorithm is simple and has high reliability, and the method can be used for improving the steady-state performance of the fuzzy control.
S4, setting initial values of parameters of a fuzzy controller, a gray prediction model GM (1,1) and a PID controller; determining simultaneously the modeling dimension n in the grey prediction model, i.e. the original data sequence y(0)The number of data in (1) and a prediction step length p; determining a proportionality coefficient K for a PID controllerpIntegral coefficient KICoefficient of differentiation KD；
In a PID controller, the proportionality coefficient KPIntegral coefficient KIAnd a differential coefficient KDThe values of (a) have a great influence on the performance of the controller, and in the embodiment, the values of the three parameters are determined by using a Ziegler-Nichols tuning method. The Ziegler-Nichols method is a method for designing a PID controller based on a frequency domain, and determines parameters of the PID controller according to transient response characteristics of a given object. The specific parameter setting process is that firstly, a unit step response curve of the open loop system of the proton exchange membrane fuel cell is obtained through experiments; then, according to the obtained curve, the delay time L, the amplification factor K and the time constant T can be determined; then, the controller parameters are set according to a Ziegler-Nichols method, and the proportionality of the controller can be obtained theoretically
Figure BDA0001498759700000121
Integration time Ti2.2L, and 0.5L, the theoretical values of the three parameters of PID, i.e., K, can be obtainedP＝δ、
Figure BDA0001498759700000122
And KD＝KPτ. Because the design method based on the frequency domain avoids accurate system modeling to a certain extent, the obtained proportionality coefficient KPIntegral coefficient KIAnd a differential coefficient KDThe values of (a) are not necessarily suitable for the actual fuel cell system, so the values of the three parameters also need to be adjusted according to the actual operation condition of the fuel cell system.
S5, acquiring real-time temperature data y of the cell stack in real time through a sensor in the actual operation work of the fuel cell systemoutBag (bag)Including the operating temperature of the proton exchange membrane fuel cell and the temperature difference data of the inlet and the outlet of the cell stack. Then, the temperature data are sampled, and the temperature data obtained at the first n sampling moments form an original temperature (working temperature or cell stack temperature difference) data sequence y of a gray prediction model GM (1,1)(0)＝{y(0)(1),y(0)(2),...,y(0)(n) and obtaining the predicted temperature value of the fuel cell by utilizing a GM (1,1) prediction model established by the original temperature data sequence
Figure BDA0001498759700000123
And S6, predicting the temperature of the fuel cell system in real time by using the grey prediction model GM (1,1), wherein the temperature comprises the future working temperature of the fuel cell and the temperature difference between the inlet and the outlet of the cell stack. The obtained predicted temperature
Figure BDA0001498759700000124
Comparing with the set fuel cell temperature value r to obtain the prediction error of the fuel cell temperature (working temperature or stack temperature difference)
Figure BDA0001498759700000125
And prediction error variation
Figure BDA0001498759700000126
Real-time temperature y of fuel celloutComparing with the set temperature value r to obtain the real-time error e and the real-time error variation of the fuel cell temperature
Figure BDA0001498759700000127
S7, predicting the prediction error of the fuel cell temperature (working temperature or cell stack temperature difference)
Figure BDA0001498759700000128
And prediction error variation
Figure BDA0001498759700000129
Obtaining the control quantity u of the fuzzy controller as the input of the fuzzy controller of the fuel cell temperaturefuzzy(ii) a The real-time error e and the real-time error variation of the fuel cell temperature (working temperature or stack temperature difference)
Figure BDA00014987597000001210
As input of the PID controller, a feedback control amount u of the fuel cell system is obtainedpid；
(8) Will control the quantity ufuzzyAnd a feedback control amount upidWeighted summation is carried out to obtain the control quantity u of the systemoutThen u is addedoutActing on heat-dissipating actuators in PEM fuel cell systems by varying uoutThe working state of the heat dissipation actuator is adjusted according to the value of the pressure sensor, namely the voltage adjusting value of the heat dissipation actuator, so that the heat dissipation amount of the fuel cell system is adjusted to realize the control of the temperature of the fuel cell.
The invention provides a novel fuel cell temperature control method based on fuzzy control, grey prediction and traditional PID control. Fuzzy control and gray prediction control are combined to be used as a feedforward compensation controller of the system, and the problems of system uncertainty and system thermal time delay are solved. The feedforward controller integrates the characteristics of self-adaption and robustness of the fuzzy controller and prediction time delay and acceleration stability of a grey prediction model, and can obtain better compensation and control effects. The PID controller can improve the steady-state performance of fuzzy control, and can effectively improve the quick tracking capability of the system and greatly reduce the overshoot of the system as a feedback controller of the system. The invention has the advantages of fast response and small overshoot dynamic characteristic, improves the disturbance rejection capability and the self-adaptive capability of the system, and simultaneously improves the control precision of the system.
Examples of the invention
The present invention is further illustrated by way of example of pem fuel cell temperature control. In a thermal management system of a proton exchange membrane fuel cell, as shown in fig. 2, a temperature controller and a temperature difference controller both adopt the temperature control method provided by the invention. In the process of operating the fuel cell, the temperature of the fuel cell is affected by external disturbance, and in order to ensure the stable operation of the proton exchange membrane fuel cell, the temperature of the fuel cell stack needs to be controlled to 340K, and the temperature difference between the inlet and the outlet of the fuel cell stack needs to be controlled to 6K.
The following is the simulation result of the temperature control of the proton exchange membrane fuel cell by applying the control method of the invention. Simulation parameters in the temperature controller and the temperature difference controller are first determined.
A temperature controller: the data sampling time of the gray prediction module GM (1,1) is 1 second, the modeling dimension is n ═ 5, and the prediction step length is p ═ 10; in the fuzzy controller, the error range of temperature prediction is [ -6K,6K]Error change rate of [ -0.15K,0.15K]Output voltage range of 0-12V, α -0.25, β -0.04, PID controller, KP＝1.45,KI＝0.015,KD＝0.01。
A temperature difference controller: the data sampling time of the gray prediction module GM (1,1) is 0.5 seconds, the modeling dimension is n ═ 5, and the prediction step length is p ═ 3; in the fuzzy controller, the error range of temperature difference prediction is [ -6K,6K]Error change rate of [ -0.12K,0.12K]Output voltage range of 0-12V, α -0.11, β -0.02, PID controller, KP＝0.48,KI＝0.0145,KD＝0.008。
The following simulation results verify the superiority of the control method.
FIG. 7 is a diagram illustrating external disturbances including (a) current disturbance and (b) ambient temperature disturbance during the operation of a PEM fuel cell according to an embodiment of the present invention. External disturbances can affect stack temperature, and an increase in current can increase fuel cell temperature, and vice versa. Meanwhile, the continuous rise of the ambient temperature also affects the heat dissipation capacity of the system, and further affects the adjustment effect of the controller. The robustness and the adaptability of the invention can be verified by adding external disturbance.
Fig. 8 is a diagram showing a predicted value and an actual value of the temperature of the fuel cell stack during the operation of the pem fuel cell according to an embodiment of the present invention, and fig. 9 is a diagram showing a predicted value and an actual value of the difference in the inlet and outlet cooling water temperatures of the fuel cell stack. The accuracy of gray prediction is usually checked by adopting a posterior difference ratio and a small error probability, and if the small error probability is more than 95% and the posterior difference ratio is less than 0.35, the gray prediction model has high accuracy. In the metabolic GM (1,1) model designed by the invention and used for predicting the temperature of the fuel cell, the posterior difference ratio is 0.0692, and the small error probability is 99.7%. In a metabolism GM (1,1) model for predicting the temperature difference of the fuel cell stack, the posterior difference ratio is 0.0238, and the small error probability is 99.98%. The calculation result shows that the metabolic GM (1,1) model designed by the invention is effective for the prediction result of the temperature and the temperature difference of the fuel cell, and the accurate prediction value ensures the effectiveness and the reliability of the design of the subsequent fuzzy controller.
Fig. 10 and fig. 11 are a comparison graph of the temperature control effect and the temperature difference control effect of the fuel cell stack during the operation of the pem fuel cell according to the embodiment of the present invention. Comparing the temperature control method with the conventional PID feedback controller, the invention finds that when the fuel cell system is disturbed by the outside, the two control methods can control the temperature and the temperature difference of the fuel cell at set values, but the adjusting time of the method of the invention is shortened by about 100 seconds compared with the conventional feedback controller. The mean square error of the set temperature value and the actual temperature value is introduced to quantitatively describe the control effect, for the temperature control of the electric pile, the mean square error value of the invention is 0.2492, and the PID control is 0.3269; for stack thermoelectric control, the mean square error of the present invention is 0.2481, while the PID control is 0.3289. Obviously, the invention can effectively improve the quick tracking performance of the system, greatly reduce the overshoot of the system, has good disturbance rejection and robustness, and is suitable for the temperature control of the proton exchange membrane fuel cell.
In conclusion, the proton exchange membrane fuel cell temperature control method provided by the invention combines the advantages of fuzzy control, gray prediction and PID control to perform hybrid control, so that the system performance is improved. The grey prediction link compensates the time lag of the system, fuzzy control improves the disturbance resistance and the self-adaptive capacity of the system, PID control improves the stability of the system, and meanwhile, a control mode of feedback and feedforward compensation accelerates the dynamic response of the system, greatly reduces the overshoot of the system, and effectively improves the disturbance resistance, the self-adaptive capacity and the precision of system control.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (5)

1. A proton exchange membrane fuel cell temperature control method is characterized by comprising the following steps:
(1) determining a fuel cell temperature fuzzy controller model
The fuzzy controller consists of a PD type fuzzy controller and a PI type fuzzy controller, and the model expression is as follows:
ufuzzy＝αuPD-fuzzy+βuPI-fuzzy，
wherein u isfuzzyIs a control quantity of a fuzzy controller, uPD-fuzzyFor the output of a PD-type fuzzy controller, uPI-fuzzyα and β are the weighting coefficients of the PD-type and PI-type fuzzy controllers, respectively, for the output of the PI-type fuzzy controller;
(2) establishing a grey prediction model GM (1,1) of the temperature of the fuel cell
Figure FDA0002371299110000011
Wherein p is the prediction step length, a and b are the development coefficient and the gray action quantity respectively, k represents the time sequence, y(0)Representing a sequence of raw temperature data, y(0)(1) Representing the first data in the original temperature data sequence,
Figure FDA0002371299110000012
a sequence of predicted temperature data is represented,
Figure FDA0002371299110000013
expressed as the predicted temperature value at time (k + p);
(3) PID controller for establishing fuel cell temperature
Figure FDA0002371299110000014
Wherein u ispidPID controller, K, indicating the temperature of the fuel cellpIs a proportionality coefficient, KIIs the integral coefficient, KDIs a differential coefficient, e represents the real-time temperature y of the fuel celloutThe difference value with a set temperature value r, wherein t represents time;
(4) setting initial values of parameters of a fuzzy controller, a gray prediction model GM (1,1) and a PID controller; determining simultaneously the modeling dimension n in the grey prediction model, i.e. the original data sequence y(0)The number of data in (1) and a prediction step length p; determining a proportionality coefficient K for a PID controllerpIntegral coefficient KICoefficient of differentiation KD；
(5) Acquiring real-time temperature data y of the cell stack in real time through a sensor in the actual operation of the fuel cell systemoutThen, these temperature data are sampled, and the temperature data obtained at the first n sampling moments form an original temperature data sequence y of the gray prediction model GM (1,1)(0)＝{y(0)(1),y(0)(2),...,y(0)(n) and obtaining the predicted temperature value of the fuel cell by utilizing a GM (1,1) prediction model established by the original temperature data sequence
Figure FDA0002371299110000015
(6) Predicting the future temperature of the fuel cell system in real time by using a grey prediction model GM (1,1), and obtaining the predicted temperature
Figure FDA0002371299110000021
Comparing with the set working temperature value r to obtain the prediction error of the fuel cell temperature
Figure FDA0002371299110000022
And predicting errorsAmount of difference change
Figure FDA0002371299110000023
Real-time temperature y of fuel celloutComparing with the set temperature value r to obtain the real-time error e and the real-time error variation of the fuel cell temperature
Figure FDA0002371299110000024
(7) Error of prediction of fuel cell temperature
Figure FDA0002371299110000025
And prediction error variation
Figure FDA0002371299110000026
As input of the fuzzy controller, the control quantity u of the fuzzy controller is obtainedfuzzy(ii) a Real-time error e and real-time error variation of fuel cell temperature
Figure FDA0002371299110000027
As input of PID controller, feedback control quantity u of system is obtainedpid；
(8) Will control the quantity ufuzzyAnd a feedback control amount upidWeighted summation is carried out to obtain the control quantity u of the systemoutThen u is addedoutActing on heat-dissipating actuators in PEM fuel cell systems by varying uoutThe operating state of the heat dissipation actuator is adjusted by the value of the temperature sensor, so that the temperature of the fuel cell is controlled.
2. The method of claim 1, wherein the fuzzy controller is configured to:
(2.1) determining input and output of fuzzy controller
Two input quantities of the fuzzy controller are determined: prediction error of fuel cell temperature
Figure FDA0002371299110000028
And fuel cell temperature prediction error variation
Figure FDA0002371299110000029
Output quantity: voltage value of a heat dissipation actuator in a proton exchange membrane fuel cell system;
(2.2) fuzzifying the input quantity and the output quantity of the fuzzy controller
Input amount 1: prediction error of fuel cell temperature
Figure FDA00023712991100000210
Taking its linguistic variable as E and its fuzzy domain as [ -6,6 [)]The fuzzy subset is { NB, NM, NS, ZO, PS, PM, PB }, and the ranges of prediction errors are { big negative, middle negative, small negative, zero, small positive, middle positive, big positive };
input amount 2: predicted error variation of fuel cell temperature
Figure FDA00023712991100000211
The linguistic variable is EC, and the domain of ambiguity is [ -6,6]The fuzzy subset is { NB, NM, NS, ZO, PS, PM, PB }, and the ranges of the prediction error variation are { big negative, middle negative, small negative, zero, small positive, middle positive, big positive };
output quantity: the method comprises the following steps that a language variable of a voltage value U of a radiator in a fuel cell system is taken as U, a fuzzy domain is [ -3,3], fuzzy subsets of the voltage value U are { NB, NM, NS, ZO, PS, PM and PB }, and the ranges of prediction error variation are { minimum, small, moderate, large and maximum };
for the input and output of the fuzzy controller, the membership functions of NM, NS, ZO, PS and PM adopt triangular membership functions, the membership function of NB adopts a Z-type membership function, and the membership function of PB adopts an S-type membership function;
(2.3) designing the control rule of the fuzzy controller and carrying out fuzzy reasoning
The fuzzy rules are expressed in the form of IF-THEN language, a control rule table of the fuzzy controller is formed by 49 fuzzy rules, and the fuzzy reasoning adopts a Mamdani reasoning method;
(2.4) defuzzifying the designed fuzzy controller by adopting a gravity center method to obtain an output value u of the PD type fuzzy controllerPD-fuzzy；
(2.5) determining the actual output of the fuzzy controller
Performing integral operation on the output of the PD type fuzzy controller to obtain the output value u of the PI type fuzzy controllerPI-fuzzyAnd then, obtaining the actual output of the fuzzy controller by the weighted sum of the output values of the PI type fuzzy controller and the PD type fuzzy controller: u. offuzzy＝αuPD-fuzzy+βuPI-fuzzyWherein the weighting factor of the fuzzy controller of PD type is α type and the weighting factor of the fuzzy controller of PD type is β.
3. The proton exchange membrane fuel cell temperature control method according to claim 1, wherein the gray prediction model GM (1,1) is designed by the steps of:
(3.1) raw temperature data y of the fuel cell system operation obtained by sampling(0)＝{y(0)(1),y(0)(2),...,y(0)(n) establishing a gray prediction model GM (1,1) and obtaining predicted temperature values of the previous p sampling moments of the fuel cell system
Figure FDA0002371299110000031
(3.2) removing the earliest data information y in the original temperature data sequence(0)(1) New collected fuel cell temperature data y(0)(n +1) adding the temperature data sequence to the original temperature data sequence to obtain an updated original temperature data sequence y(0)′＝{y(0)(2),y(0)(3),...,y(0)(n +1) }, based on the sequence y(0)′Then establishing GM (1,1) model to predict the next temperature data
Figure FDA0002371299110000032
Then newly collected fuel cell temperature data is added into the array, and the last array is removedThe earliest data in the data, thus metabolism, are predicted one by one and successively supplemented.
4. The pem fuel cell temperature control of claim 1 wherein said gray predictive model and fuzzy controller act together as a feed-forward controller and said PID controller acts as a feedback controller.
5. The method of claim 1, wherein the pem fuel cell temperature is a stack operating temperature or a stack inlet-outlet temperature difference.
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