CN109524693A - Fuel battery air feed system model predictive control method - Google Patents
Fuel battery air feed system model predictive control method Download PDFInfo
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- 239000000446 fuel Substances 0.000 title claims abstract description 97
- 238000000034 method Methods 0.000 title claims abstract description 24
- 150000002978 peroxides Chemical class 0.000 claims abstract description 25
- 239000001301 oxygen Substances 0.000 claims description 59
- 229910052760 oxygen Inorganic materials 0.000 claims description 59
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 claims description 57
- IJGRMHOSHXDMSA-UHFFFAOYSA-N Atomic nitrogen Chemical compound N#N IJGRMHOSHXDMSA-UHFFFAOYSA-N 0.000 claims description 26
- 239000012528 membrane Substances 0.000 claims description 25
- 239000007789 gas Substances 0.000 claims description 18
- 238000005070 sampling Methods 0.000 claims description 16
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- 238000013461 design Methods 0.000 claims description 11
- 230000007246 mechanism Effects 0.000 claims description 10
- 238000006243 chemical reaction Methods 0.000 claims description 9
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- 230000008569 process Effects 0.000 claims description 9
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 3
- 230000008878 coupling Effects 0.000 claims description 3
- 238000010168 coupling process Methods 0.000 claims description 3
- 238000005859 coupling reaction Methods 0.000 claims description 3
- 230000005518 electrochemistry Effects 0.000 claims description 3
- 238000013178 mathematical model Methods 0.000 claims description 3
- 239000011159 matrix material Substances 0.000 claims description 3
- -1 oxygen peroxide Chemical class 0.000 claims description 2
- 238000005516 engineering process Methods 0.000 abstract description 3
- 206010013975 Dyspnoeas Diseases 0.000 abstract 1
- 235000003642 hunger Nutrition 0.000 description 5
- 230000037351 starvation Effects 0.000 description 5
- 238000011161 development Methods 0.000 description 4
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 description 3
- 230000009471 action Effects 0.000 description 3
- 238000011217 control strategy Methods 0.000 description 3
- 239000001257 hydrogen Substances 0.000 description 3
- 229910052739 hydrogen Inorganic materials 0.000 description 3
- 238000005259 measurement Methods 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 238000004364 calculation method Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000003487 electrochemical reaction Methods 0.000 description 2
- 238000010248 power generation Methods 0.000 description 2
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 2
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000033228 biological regulation Effects 0.000 description 1
- 230000007248 cellular mechanism Effects 0.000 description 1
- 239000000306 component Substances 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 239000008358 core component Substances 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
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- 230000003071 parasitic effect Effects 0.000 description 1
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- 230000009467 reduction Effects 0.000 description 1
- 238000005096 rolling process Methods 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
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- H01M8/04305—Modeling, demonstration models of fuel cells, e.g. for training purposes
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- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
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Abstract
A kind of fuel battery air feed system model predictive control method, belongs to control technology field.The purpose of the present invention is the peroxide ratios to proton exchange film fuel battery system to be adjusted, and avoids air hunger, to realize the fuel battery air feed system model predictive control method of system even running.Step of the present invention is: step 1: establishing the fuel battery air feed system dynamic model of high-precision Control-oriented；Step 2: determine that the peroxide of proton exchange film fuel battery system compares reference value；Step 3: cathode internal pressure value and system disturbance are estimated using extended mode observer；Step 4: the peroxide for designing proton exchange film fuel battery system compares controller.The present invention is adjusted output estimation error using extended mode observer in real time, while output error can realize the accurate estimation to immeasurability value cathode pipe pressure in Finite-time convergence to zero.
Description
Technical Field
The invention belongs to the technical field of control, and particularly relates to a proton exchange membrane fuel cell technology.
Background
The new energy electric automobile is energy-saving and environment-friendly, and is a necessary trend of automobile industry development. Therefore, the development of new automobiles with low energy consumption and low emission becomes the development direction of automobiles in the world today. The proton exchange membrane fuel cell is used as the most important core component of an electric automobile, and influences the performances of the automobile such as dynamic property, safety, endurance mileage and the like. The proton exchange membrane fuel cell is a power generation device which directly converts chemical energy of hydrogen and oxygen into electric energy through electrochemical reaction, and has the characteristics of high efficiency, low noise, capability of adapting to different power requirements, capability of rapidly supplementing energy, abundant hydrogen sources, no pollution and the like. Currently, the development of vehicle-mounted fuel cells is receiving extremely wide attention all over the world.
The fuel cell air supply system is an important subsystem for ensuring the normal and stable operation of the fuel cell system. However, due to the time lag of the gas supply system, the required gas flow of the cell stack cannot quickly follow the change of the load. When the load is suddenly increased, the electrochemical reaction consumes more oxygen, and if the air supply is insufficient, oxygen starvation, i.e. oxygen starvation, is generated, which directly results in the decline of the output voltage of the cell, the water flooding of the cell stack, and even damages the service life of the fuel cell. When the oxygen flow is far higher than the demand, the power consumption (parasitic power consumption) of the compressor is overlarge, and the net power output by the electric pile is not obviously improved, so that the efficiency of the whole system is reduced. The fuel cell vehicle has complex operation condition and constantly changing load, so the oxygen flow must be quickly and accurately controlled, and the system oxygen ratio is always kept in an ideal range.
Researchers at home and abroad have made a lot of work aiming at the control problem of the oxygen ratio of the air supply system of the fuel cell. At present, the existing control methods include linear quadratic gaussian control, linear control of feedback linearization, neural network control, sliding mode control and the like. The various control strategies described above have advantages over the regulation of oxygen ratio, but are not fully applicable to non-linear, multiple-input, strongly coupled fuel cell systems. Moreover, the above control strategy does not adequately take into account the uncertainty of the actual operation of the fuel cell system and the effects of external disturbances, such as sensor-induced measurement disturbances or environment-induced perturbation of system model parameters. Therefore, the existing control strategy does not have good noise immunity and robustness.
Disclosure of Invention
The invention aims to adjust the peroxide ratio of a proton exchange membrane fuel cell system, avoid oxygen starvation and realize a fuel cell air supply system model predictive control method for stable operation of the system.
The method comprises the following steps:
the method comprises the following steps: establishing a mechanism model of the internal reaction of the proton exchange membrane fuel cell according to the principles of electrochemistry, thermodynamics and hydrodynamics, analyzing the characteristics of parameter coupling, time variation, nonlinear characteristics, model uncertainty and the like of the mechanism model of the fuel cell, and establishing a high-precision control-oriented dynamic model of the air supply system of the fuel cell;
step two: determining a reference value of the peroxide ratio of the proton exchange membrane fuel cell system;
step three: in view of the fact that in the control-oriented fuel cell air supply system model established in the step one, the internal pressure of the state variable cathode cannot be directly measured, and uncertainty and external interference exist in the fuel cell system, an extended state observer is adopted to estimate the internal pressure value of the cathode and system disturbance;
step four: based on a nonlinear model predictive control algorithm, with the output voltage of an air compressor as a control variable, designing a peroxide ratio controller of a proton exchange membrane fuel cell system: a nonlinear model predictive control algorithm is selected, the output voltage of an air compressor is used as a control variable, a peroxide ratio tracking reference value is used as a control target, and the flow constraint and the pressure constraint existing in the system are considered at the same time, so that the design of the controller is completed;
(1) modeling an air supply system of the exchange membrane fuel cell: respectively establishing mathematical models of an air compressor, an air supply manifold and cathode airflow of an air inlet system according to the working mechanism and physical characteristics of the system
① air compressor model:
angular velocity w of compressorcpIs a dynamic model of
Wherein, JcpIs the moment of inertia, τ, of the compressorcmAnd τcpRespectively is the driving torque of the permanent magnet synchronous motor and the load torque of the compressor;
τcmand τcpThe expression is as follows
In the formula, kt，RcmAnd kvIs the motor constant, ηcmIs the mechanical efficiency of the motor, vcmIs terminal voltage of the machine, CpIs the constant pressure coefficient of heat capacity of air, gamma is the heat ratio coefficient of air, ηcpIs the air compressor efficiency, psmIs the supply manifold pressure, TatmAnd patmIs the inlet air temperature and pressure, WcpIs the air mass flow at the compressor outlet;
② gas manifold model:
supply manifold pressure psmIs a dynamic model of
In the formula, VsmIs the volume of the gas supply manifold,is the air gas constant, Ma,atmIs the molar mass of air, TcpIs the temperature of the air leaving the compressor, kca,inIs the supply conduit orifice constant, pcaIs the cathode internal pressure, expressed as follows
Wherein p issatIs cathode vapor pressure, temperature T of air leaving the compressorcpCan be calculated by
③ cathode gas flow model
Cathode oxygen and nitrogen pressureAre respectively as
Wherein,andis the molar mass of oxygen and nitrogen, TstIs the temperature of the stack, VcaIs the volume of the cathode, and,respectively the mass flow of oxygen and nitrogen entering the cathode,respectively the oxygen and nitrogen mass flows leaving the cathode,is the oxygen mass flow consumed by the reaction;
④ according to the formula (1-8), selecting the state quantity x ═ x1,x2,x3]T＝[wcp,psm,pca]TA three-step control-oriented fuel cell air supply system model can be obtained, namely
u represents the input voltage of the air compressor, d represents the stack current; system state quantity x1Indicating the speed w of the compressor motorcp，x2Indicating the supply manifold pressure psm，x3Represents the cathode internal pressure pca；ci(i ═ 1,2,3L 12) is a constant;
⑤ the system can measure the output matrix as
y＝[y1,y2,y3]T＝[Wcp(x1,x2),x2,Vfc]T(12)
Wherein, y1＝Wcp(x1,x2) Is the mass flow of air at the outlet of the compressor, y2＝x2Is the supply manifold pressure, y3＝VfcIs the stack voltage;
⑥ due to compressor speed wcpSupply manifold pressure psmCan be directly measured, so that the rotating speed w of the compressor can be directly measured by using a speed sensor and a pressure sensorcpAnd supply manifold pressure psmA value of (d);
(2) determining a reference value for a peroxide ratio of a PEM fuel cell system
Ratio of excess oxygenIs defined as follows:
in the formula,andthe cathode oxygen intake and the reaction consumption, c13And c14Is a constant;
ratio of excess oxygenIndicating that the oxygen supply and the oxygen peroxide ratio of the fuel cell system need to be maintained at the optimum reference operating pointControl of the air supply system of the fuel cellTrackingWhen the system oxygen ratio is between 1.9 and 2.5, the net power of the system reaches the maximum value;
(3) disturbance observer design
① use a linear extended state observer to estimate x3A value of (d); formula (10) is written as
Wherein,θ(x2,x3,t)＝c8g(x2)x3；θ(x2,x3and t) is internal to the systemLumped disturbances of uncertainty and external disturbances, h (t) is the rate of change of the system uncertainty, the observer equation is
Wherein l1，l2Is the observer gain;
② define the observer error asThe observer error is
Writing equations (18) and (19) as state space expressions
Therefore, the unmeasurable variable x3Is estimated as
③ due to lumped perturbation theta (x)2,x3T) has a constant value in a steady state, h (t) may be obtainedt→∞0; the condition sufficient for convergence is l1＞0，l2Greater than 0, the characteristic polynomial of equation (20) is (s + ω)0)2＝s2+l1s+l2(ii) a Then l1＝2ω0，Wherein observer bandwidth ω0Is the only performance setting parameter of the observer, omega0Selecting to balance the influence of estimation precision and noise;
(4) controller design based on nonlinear model predictive control
① the discrete time system model obtained by discretizing equations (9-11) and (13) by using Euler's equation is as follows:
wherein,
k denotes the sampling instant, TsIn order to be the time of sampling,estimated value, x, representing the state quantity of the system at time k1(k) Representing the state quantity x at time k1Value of (a), x2(k) Representing the state quantity x at time k2The value of (a) is,representing the state quantity x at time k3U (k) represents the control input at time k, d (k) represents the current at time k, fkIndicates the rate of change of the state quantity at time k, yc(k) A control output representing time k;
② defining the prediction time domain as NpControl time domain as Nc，Np≥NcNot less than 1; suppose the current time of the fuel cell system is k, at [ k +1, k + Np]The dynamics in the prediction time domain can be obtained based on the current state of the system and a prediction model;
③ at the k sample time, the control input sequence of the system is
④ System oxygen ratio at time kThe prediction output sequence of (2) can be obtained from the following equations (24) and (25)
⑤ corresponding to the predicted output sequence (27), reference input oxygen ratioShould be updated in real time in each prediction time domain, the reference input sequence of the system is
⑥ by the expression Δ u (k) -u (k-1), the variation sequence of the control input is
⑦ at the sampling time instant k,as a starting point of the prediction, a value equal to the value at the start of the prediction process, i.e.The updating process of the system prediction state variable and the prediction output variable is shown in the formula (30) and the formula (31)
(5) Control of fuel cell air supply systems requires consideration of multiple constraints
① constraint of fuel cell system state quantity
Psm,min≤x2(k)≤Psm,max(32)
At the same time the input voltage v of the air compressorcmCannot be greater than its rated voltage, i.e.
0≤u(k)≤Vcm_r(33)
Wherein Vcm_rIs the rated voltage of the air compressor;
② the objective function of the controller is
Γy，ΓuRespectively controlling the output sequence and the variation of the control signalA weight coefficient;
(6) the control problem of the air supply system of the proton exchange membrane fuel cell is converted into an optimization problem with restriction:
satisfy Psm,min≤x2(k)≤Psm,max
0≤u(k)≤Vcm_r
And (3) solving the optimization problem of the formula (35) on line by adopting an fmincon function in a Matlab tool box to obtain a control input sequence of the system.
The invention has the beneficial effects that:
1. the invention analyzes the mechanism model of the proton exchange membrane fuel cell and establishes a three-order nonlinear dynamic model for describing the air supply system of the fuel cell. The model has lower order, can reflect the change conditions of internal variables and peroxide ratio of the actual system of the fuel cell, does not need linearization processing, reduces the calculation time and provides a basis for subsequent controller design.
2. The invention utilizes the extended state observer to adjust the output estimation error in real time, and meanwhile, the output error can be converged to zero in limited time, thereby realizing the accurate estimation of the pressure of the cathode pipeline with the non-measurable value.
3. Due to the cost of sensor technology, or due to quantity limitations, particularly in conditions of humidified gas flow within the fuel cell stack, it is not always possible to use sensors for measurements. Observing unmeasured or unmeasured variables in a fuel cell system through an estimation method will greatly reduce hardware costs.
4. The invention utilizes the nonlinear model predictive control algorithm to predict the state of the system in a period of time in the future according to the running state of the current fuel cell system, has simple structure and strong robustness, and can process the multivariable optimization problem with restriction. In addition, the rolling optimization and feedback correction characteristics of the nonlinear model predictive control algorithm can effectively reduce or even eliminate the influence caused by the actual uncertainty of the closed-loop system.
Drawings
FIG. 1 is a block diagram of a proton exchange membrane fuel cell system;
FIG. 2 is a graph of net power of the system at different stack currents and oxygen ratios;
FIG. 3 is a diagram of a fuel cell air supply system control scheme in accordance with the present invention;
FIG. 4 is a graph of fuel cell stack current change;
FIG. 5 shows the non-measurable variable cathode internal pressure pcaThe estimated result map of (1);
FIG. 6 is the peroxide ratioAnd (5) a simulation result graph.
Detailed Description
The model predictive control is an algorithm based on a model and is mainly applied to the tracking control problem of a system. The nonlinear model predictive control method based on the disturbance observer is a feedforward and feedback control algorithm mainly considering system uncertainty and disturbance, and can effectively process explicit constraint and nonlinear programming problems on line.
The invention comprises the following steps:
the method comprises the following steps: according to the principles of electrochemistry, thermodynamics and hydrodynamics, a mechanism model of the internal reaction of the proton exchange membrane fuel cell is established. Analyzing the characteristics of parameter coupling, time variation, nonlinear characteristics, model uncertainty and the like of the fuel cell mechanism model, and establishing a high-precision control-oriented fuel cell air supply system dynamic model;
step two: determining a reference value of the peroxide ratio of the proton exchange membrane fuel cell system;
step three: in view of the fact that in the control-oriented fuel cell air supply system model established in the step one, the internal pressure of the state variable cathode cannot be directly measured, and uncertainty and external interference exist in the fuel cell system, an extended state observer is adopted to estimate the internal pressure value of the cathode and system disturbance;
step four: based on a nonlinear model predictive control algorithm, with the output voltage of an air compressor as a control variable, designing a peroxide ratio controller of a proton exchange membrane fuel cell system: and (3) selecting a nonlinear model predictive control algorithm, taking the output voltage of the air compressor as a control variable, taking the peroxide ratio tracking reference value as a control target, and considering flow constraint and pressure constraint existing in the system to complete the design of the controller.
The technical solution proposed by the present invention will be further explained and explained with reference to the accompanying drawings.
1. Proton exchange membrane fuel cell air supply system modeling
The proton exchange membrane fuel cell system is composed of a galvanic pile, an air compressor, a humidifier, a cooler, a high-pressure hydrogen tank and the like, and the system structure is shown in figure 1. And respectively establishing mathematical models of an air compressor, an air supply manifold and cathode airflow of the air inlet system according to the working mechanism and physical characteristics of the system.
Before the fuel cell system model is built, the following assumptions are made for the model:
1) assuming that all gases satisfy the ideal gas law;
2) the intake air is assumed to be air at standard atmospheric pressure;
3) assuming that the inlet air temperature and the outlet air temperature of the air supply manifold are the same;
4) assuming that the gas inside the cathode is perfectly humidified and the humidity is 100%;
5) assuming that the only components of the drying gas are nitrogen and oxygen.
a. Air compressor model
The air compressor is driven by a torque-controlled permanent magnet synchronous motor for supplying oxygen to the cathode of the fuel cell system. Angular velocity w of compressorcpIs a dynamic model of
Wherein, JcpIs the moment of inertia, τ, of the compressorcmAnd τcpRespectively the driving torque of the permanent magnet synchronous motor and the load torque of the compressor. Tau iscmAnd τcpThe expression is as follows
In the formula, kt，RcmAnd kvIs the motor constant, ηcmIs the mechanical efficiency of the motor, vcmIs terminal voltage of the machine, CpIs the constant pressure coefficient of heat capacity of air, gamma is the heat ratio coefficient of air, ηcpIs the air compressor efficiency, psmIs the supply manifold pressure, TatmAnd patmIs inlet airTemperature and pressure, WcpIs the mass flow of air at the outlet of the compressor, wherein the compressor outlet flow WcpAnd supply manifold pressure psmAnd angular speed w of the compressorcpIt is related.
b. Air supply manifold model
The manifold represents the lumped volume of piping between the air compressor and the stack. According to the law of conservation of energy, the law of ideal gas and the thermodynamic properties of air, the pressure p of the supply manifoldsmIs a dynamic model of
In the formula, VsmIs the volume of the gas supply manifold,is the air gas constant, Ma,atmIs the molar mass of air, TcpIs the temperature of the air leaving the compressor, kca,inIs the supply conduit orifice constant, pcaIs the cathode internal pressure, expressed as follows
Wherein p issatIs the cathode water vapor pressure. Temperature T of air leaving compressorcpCan be calculated by
c. Cathode airflow model
Cathode oxygen and nitrogen pressures according to the principle of mass flow continuityAre respectively as
Wherein,andis the molar mass of oxygen and nitrogen, TstIs the temperature of the stack, VcaIs the volume of the cathode, and,respectively the mass flow of oxygen and nitrogen entering the cathode,respectively the oxygen and nitrogen mass flows leaving the cathode,is the mass flow of oxygen consumed by the reaction.
According to the formula (1-8), selecting the state quantity x ═ x1,x2,x3]T＝[wcp,psm,pca]TA three-step control-oriented fuel cell air supply system model can be obtained, namely
u represents the input voltage of the air compressor, d represents the stack current; system state quantity x1Indicating the speed w of the compressor motorcp，x2Indicating the supply manifold pressure psm，x3Represents the cathode internal pressure pca；ci(i ═ 1,2,3L 12) is a constant.
The system can measure an output matrix of
y＝[y1,y2,y3]T＝[Wcp(x1,x2),x2,Vfc]T(12)
Wherein, y1＝Wcp(x1,x2) Is the mass flow of air at the outlet of the compressor, y2＝x2Is the supply manifold pressure, y3＝VfcIs the stack voltage.
Due to the rotation speed w of the compressorcpSupply manifold pressure psmCan be directly measured, so that the rotating speed w of the compressor can be directly measured by using a speed sensor and a pressure sensorcpAnd supply manifold pressure psmThe value of (c).
2. Determining a reference value for a peroxide ratio of a PEM fuel cell system
Ratio of excess oxygenIs defined as follows:
in the formula,andthe cathode oxygen intake and the reaction consumption, c13And c14Is a constant.
Ratio of excess oxygenThe oxygen supply amount of the fuel cell system is an important performance index of the fuel cell system, which is related to the efficiency of the fuel cell system. If the ratio of excess oxygen is higher than the ratio of excess oxygenSmaller, fuel cell systems suffer from oxygen starvation. Oxygen starvation can lead to reduced system performance, membrane surface damage and reduced power generation. And the ratio of peroxide to oxygenHigher would increase the power consumption of the air supply system accessories, resulting in a reduction in the net power of the system. Under high load conditions, the fuel cell air supply system consumes up to 20% of the total stack output power. Therefore, the peroxide ratio needs to be maintained at the optimum reference operating point
The control of the air supply system of the fuel cell is mainly the control of the oxygen ratioTrackingFigure 2 shows that the net system power reaches a maximum for different stack currents when the system oxygen ratio is between 1.9 and 2.5.
3. Disturbance observer design
By the formula (13)Calculation of the oxygen ratio and variable x3Related, and x3For non-measurable variables, the present invention employs a linear extended state observer to estimate x3The value of (c). The formula (10) can be written as
Wherein,θ(x2,x3,t)＝c8g(x2)x3。θ(x2,x3t) is the collective disturbance of the internal uncertainty and external disturbance of the system, h (t) is the rate of change of the system uncertainty, the observer equation is
Wherein l1，l2Is the observer gain.
Defining observer error asThe observer error is
Writing equations (18) and (19) as state space expressions
Therefore, the unmeasurable variable x3Is estimated as
Due to lumped disturbance theta (x)2,x3T) has a constant value in a steady state, h (t) may be obtainedt→∞0. The condition sufficient for convergence is l1＞0，l2Greater than 0, the characteristic polynomial of equation (20) is (s + ω)0)2＝s2+l1s+l2. Then l1＝2ω0，Wherein observer bandwidth ω0Is the only performance setting parameter of the observer. When bandwidth ω0The larger the value, the higher the estimation accuracy of the observer, but at the same time the system noise increases. Therefore, ω0Is chosen to balance the effects of estimation accuracy and noise.
4. Controller design based on nonlinear model predictive control
The model predictive control algorithm can be adopted to solve the nonlinear problem by considering the characteristics of nonlinearity, flow, pressure constraint, parameter time variation and the like of the fuel cell system. When the stack current of the fuel cell changes, the input voltage of the air compressor is calculated by a designed nonlinear model predictive controller, so that the peroxide ratio of the proton exchange membrane fuel cell system is enabled to be higher than that of the air compressorCan track the set reference value
Discretizing equations (9-11) and (13) by using an Euler formula to obtain a discrete time system model as follows:
wherein,
k denotes the sampling instant, TsIn order to be the time of sampling,estimated value, x, representing the state quantity of the system at time k1(k) Representing the state quantity x at time k1Value of (a), x2(k) Representing the state quantity x at time k2The value of (a) is,representing the state quantity x at time k3U (k) represents the control input at time k, d (k) represents the current at time k, fkIndicates the rate of change of the state quantity at time k, yc(k) Indicating the control output at time k (i.e., the oxygen ratio at time k))。
In the invention, a prediction time domain is defined as NpControl time domain as Nc，Np≥NcNot less than 1. Suppose the current time of the fuel cell system is k, at [ k +1, k + Np]The dynamics in the prediction time domain can be obtained based on the current state of the system and a prediction model.
Thus at the time of k samples, the control input sequence of the system is
System oxygen ratio at time kThe prediction output sequence of (2) can be obtained from the following equations (24) and (25)
Corresponding to the predicted output sequence (27), referring to the input oxygen ratioShould be updated in real time in each prediction time domain, the reference input sequence of the system is
When the sampling time is greater than the control time domain, the control input is held constant until the prediction time domain, i.e.
u(k+Nc-1)＝u(k+Nc)＝u(k+Nc+1)＝L u(k+Np-1). By the expression Δ u (k) -u (k-1), the variation sequence of the control input is
At the time of sampling the time k, the sampling time k,as a starting point of the prediction, a value equal to the value at the start of the prediction process, i.e.The updating process of the system predicted state variables and the predicted output variables is shown in the formula (30) and the formula (31).
After a sampling time, the state quantity and input of the system are calculated and updated according to the state variable value at the current moment and the system input value at the previous moment, and the solved control quantity (voltage) acts on the system at the next sampling moment. And at the next sampling moment, the controller solves a new optimization control problem according to the new state measurement value. Therefore, the condition that only the initial state value at the current sampling moment is solved is avoided, and the condition of the future sampling moment is solved.
Control of the fuel cell air supply system requires consideration of a number of constraints. First, the state quantity of the fuel cell system is restricted
At the same time the input voltage v of the air compressorcmCannot be greater than its rated voltage, i.e.
0≤u(k)≤Vcm_r(33)
Wherein Vcm_rIs the rated voltage of the air compressor.
The invention aims to design the nonlinear model predictive controller to adjust the system oxygen ratio so as to quickly track the set reference valueAnd the action change of the air compressor of the actuating mechanism is as small as possible, so that the excessive vibration is avoided, and the objective function of the controller is
Γy，ΓuRespectively, the weight coefficients that control the output sequence and the change of the control signal. When gamma isyWhen the actual peroxide ratio of the fuel cell system is relatively large, the actual peroxide ratio of the fuel cell system has a better tracking effect than the reference value of the fuel cell system, namely the tracking deviation is close to zero. When gamma isuWhen the voltage is relatively large, the change of the control input voltage is small, and the control action is small.
Γ in an objective functiony，ΓuThe weights of the fuel cell system for the control accuracy and the control action magnitude are represented respectively, and have relative meanings, so the requirements of the actual system need to be considered in the adjustment process, and the two are considered in a trade-off manner.
The control problem of the air supply system of the proton exchange membrane fuel cell is converted into an optimization problem with restriction:
satisfy Psm,min≤x2(k)≤Psm,max(35)
0≤u(k)≤Vcm_r
And (3) solving the optimization problem of the formula (35) on line by adopting an fmincon function in a Matlab tool box to obtain a control input sequence of the system.
Verification example:
for ease of understanding, the invention is illustrated below in a specific example:
proton exchange membrane fuel cell System parameter c in equations (9-11) and (13)i(i ═ 1,2,3L 14) is shown in table 1.
TABLE 1 Fuel cell System parameter Table
| c1＝5.6227 | c2＝7.4795×109 | c3＝101325 |
| c4＝0.2857 | c5＝367.5 | c6＝15.5889 |
| c7＝1.25 | c8＝0.3629×10-5 | c9＝34.6185 |
| c10＝31.0596 | c11＝1.6754×105 | c12＝289.745 |
| c13＝7.1113×10-7 | c14＝3.159×10-5 |
And under the Matlab/Simulink simulation environment, a controller simulation model for realizing the control scheme is built. The stack current variation of the fuel cell is shown in fig. 4, in which the current variation range is 130A to 300A. Selecting observer bandwidth omega01000, observer gain is l1＝2000，l21000000, system sample time Ts0.02s, reference value of peroxide ratioIs the desired target value, the results are shown in fig. 5-6. As can be seen from FIG. 5, the disturbance observer designed by the invention can accurately estimate the cathode internal pressure p of the unmeasured variablecaThe value of (c). Meanwhile, as can be seen from fig. 6, the model predictive control method designed by the invention can enable the peroxide ratio of the fuel cell system to quickly track the upper reference value and has good anti-interference capability.
Claims (1)
1. A fuel cell air supply system model predictive control method characterized by: the method comprises the following steps:
the method comprises the following steps: establishing a mechanism model of the internal reaction of the proton exchange membrane fuel cell according to the principles of electrochemistry, thermodynamics and hydrodynamics, analyzing the characteristics of parameter coupling, time variation, nonlinear characteristics, model uncertainty and the like of the mechanism model of the fuel cell, and establishing a high-precision control-oriented dynamic model of the air supply system of the fuel cell;
step two: determining a reference value of the peroxide ratio of the proton exchange membrane fuel cell system;
step three: in view of the fact that in the control-oriented fuel cell air supply system model established in the step one, the internal pressure of the state variable cathode cannot be directly measured, and uncertainty and external interference exist in the fuel cell system, an extended state observer is adopted to estimate the internal pressure value of the cathode and system disturbance;
step four: based on a nonlinear model predictive control algorithm, with the output voltage of an air compressor as a control variable, designing a peroxide ratio controller of a proton exchange membrane fuel cell system: a nonlinear model predictive control algorithm is selected, the output voltage of an air compressor is used as a control variable, a peroxide ratio tracking reference value is used as a control target, and the flow constraint and the pressure constraint existing in the system are considered at the same time, so that the design of the controller is completed;
(1) modeling an air supply system of the exchange membrane fuel cell: respectively establishing mathematical models of an air compressor, an air supply manifold and cathode airflow of an air inlet system according to the working mechanism and physical characteristics of the system
① air compressor model:
angular velocity w of compressorcpIs a dynamic model of
Wherein, JcpIs the moment of inertia, τ, of the compressorcmAnd τcpRespectively is the driving torque of the permanent magnet synchronous motor and the load torque of the compressor;
τcmand τcpThe expression is as follows
In the formula, kt，RcmAnd kvIs the motor constant, ηcmIs a mechanical effect of the motorRate, vcmIs terminal voltage of the machine, CpIs the constant pressure coefficient of heat capacity of air, gamma is the heat ratio coefficient of air, ηcpIs the air compressor efficiency, psmIs the supply manifold pressure, TatmAnd patmIs the inlet air temperature and pressure, WcpIs the air mass flow at the compressor outlet;
② gas manifold model:
supply manifold pressure psmIs a dynamic model of
In the formula, VsmIs the volume of the gas supply manifold,is the air gas constant, Ma,atmIs the molar mass of air, TcpIs the temperature of the air leaving the compressor, kca,inIs the supply conduit orifice constant, pcaIs the cathode internal pressure, expressed as follows
Wherein p issatIs cathode vapor pressure, temperature T of air leaving the compressorcpCan be calculated by
③ cathode gas flow model
Cathode oxygen and nitrogen pressureAre respectively as
Wherein,andis the molar mass of oxygen and nitrogen, TstIs the temperature of the stack, VcaIs the volume of the cathode, and,respectively the mass flow of oxygen and nitrogen entering the cathode,respectively the oxygen and nitrogen mass flows leaving the cathode,is the oxygen mass flow consumed by the reaction;
④ according to the formula (1-8), selecting the state quantity x ═ x1,x2,x3]T＝[wcp,psm,pca]TA three-step control-oriented fuel cell air supply system model can be obtained, namely
u denotes an input voltage of the air compressor,d represents a stack current; system state quantity x1Indicating the speed w of the compressor motorcp，x2Indicating the supply manifold pressure psm，x3Represents the cathode internal pressure pca；ci(i ═ 1,2,3L 12) is a constant;
⑤ the system can measure the output matrix as
y＝[y1,y2,y3]T＝[Wcp(x1,x2),x2,Vfc]T(12)
Wherein, y1＝Wcp(x1,x2) Is the mass flow of air at the outlet of the compressor, y2＝x2Is the supply manifold pressure, y3＝VfcIs the stack voltage;
⑥ due to compressor speed wcpSupply manifold pressure psmCan be directly measured, so that the rotating speed w of the compressor can be directly measured by using a speed sensor and a pressure sensorcpAnd supply manifold pressure psmA value of (d);
(2) determining a reference value for a peroxide ratio of a PEM fuel cell system
Ratio of excess oxygenIs defined as follows:
in the formula,andthe cathode oxygen intake and the reaction consumption, c13And c14Is a constant;
ratio of excess oxygenIndicating that the oxygen supply and the oxygen peroxide ratio of the fuel cell system need to be maintained at the optimum reference operating pointControl of the air supply system of the fuel cellTrackingWhen the system oxygen ratio is between 1.9 and 2.5, the net power of the system reaches the maximum value;
(3) disturbance observer design
① use a linear extended state observer to estimate x3A value of (d); formula (10) is written as
Wherein,θ(x2,x3,t)＝c8g(x2)x3；θ(x2,x3t) is the collective disturbance of the internal uncertainty and external disturbance of the system, h (t) is the rate of change of the system uncertainty, the observer equation is
Wherein l1，l2Is the observer gain;
② define the observer error asThe observer error is
Writing equations (18) and (19) as state space expressions
Therefore, the unmeasurable variable x3Is estimated as
③ due to lumped perturbation theta (x)2,x3T) has a constant value in a steady state, h (t) may be obtainedt→∞0; the condition sufficient for convergence is l1＞0，l2Greater than 0, the characteristic polynomial of equation (20) is (s + ω)0)2＝s2+l1s+l2(ii) a Then l1＝2ω0，Wherein observer bandwidth ω0Is the only performance setting parameter of the observer, omega0Selecting to balance the influence of estimation precision and noise;
(4) controller design based on nonlinear model predictive control
① the discrete time system model obtained by discretizing equations (9-11) and (13) by using Euler's equation is as follows:
wherein,
k denotes the sampling instant, TsIn order to be the time of sampling,estimated value, x, representing the state quantity of the system at time k1(k) Representing the state quantity x at time k1Value of (a), x2(k) Representing the state quantity x at time k2The value of (a) is,representing the state quantity x at time k3U (k) represents the control input at time k, d (k) represents the current at time k, fkIndicates the rate of change of the state quantity at time k, yc(k) A control output representing time k;
② defining the prediction time domain as NpControl time domain as Nc，Np≥NcNot less than 1; suppose the current time of the fuel cell system is k, at [ k +1, k + Np]The dynamics in the prediction time domain can be obtained based on the current state of the system and a prediction model;
③ at the k sample time, the control input sequence of the system is
④ System pass at time kOxygen ratioThe prediction output sequence of (2) can be obtained from the following equations (24) and (25)
⑤ corresponding to the predicted output sequence (27), reference input oxygen ratioShould be updated in real time in each prediction time domain, the reference input sequence of the system is
⑥ by the expression Δ u (k) -u (k-1), the variation sequence of the control input is
⑦ at the sampling time instant k,as a starting point of the prediction, a value equal to the value at the start of the prediction process, i.e.
The updating process of the system prediction state variable and the prediction output variable is shown in the formula (30) and the formula (31)
(5) Control of fuel cell air supply systems requires consideration of multiple constraints
① constraint of fuel cell system state quantity
Psm,min≤x2(k)≤Psm,max(32)
At the same time the input voltage v of the air compressorcmCannot be greater than its rated voltage, i.e.
0≤u(k)≤Vcm_r(33)
Wherein Vcm_rIs the rated voltage of the air compressor;
② the objective function of the controller is
Γy，ΓuThe weight coefficients of the control output sequence and the control signal change respectively;
(6) the control problem of the air supply system of the proton exchange membrane fuel cell is converted into an optimization problem with restriction:
satisfy Psm,min≤x2(k)≤Psm,max
0≤u(k)≤Vcm_r
And (3) solving the optimization problem of the formula (35) on line by adopting an fmincon function in a Matlab tool box to obtain a control input sequence of the system.
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| CN115347218A (en) * | 2022-07-22 | 2022-11-15 | 浙大宁波理工学院 | Cascade control method of air supply system of proton exchange membrane fuel cell |
| CN115188999B (en) * | 2022-07-22 | 2024-04-16 | 吉林大学 | Control method of air supply loop of fuel cell system |
| CN115390459A (en) * | 2022-10-28 | 2022-11-25 | 浙江中控技术股份有限公司 | Model prediction control method and device |
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