CN114156510B - Fuel cell power tracking control method based on model predictive control - Google Patents
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- 230000008569 process Effects 0.000 claims abstract description 6
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- 229910052760 oxygen Inorganic materials 0.000 claims description 11
- 125000000864 peroxy group Chemical group O(O*)* 0.000 claims description 11
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- 150000002978 peroxides Chemical class 0.000 claims description 4
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Abstract
The invention discloses a fuel cell power tracking control method based on model predictive control. It comprises the following steps: A. the controller acquires a control target; B. the data acquisition module transmits data required by the control strategy to the controller; C. the controller establishes an observer to estimate the internal state of the fuel cell stack; D. linearizing a nonlinear state space model of the fuel cell stack, and discretizing the linearization model; E. predicting the state quantity and the output quantity to obtain a predicted sequence of the state quantity and the output quantity; F. searching a minimum value of an objective function through quadratic programming to obtain a control sequence; G. the first item of the control sequence is sent as a control signal to the corresponding actuator. The advantages are that: the fuel cell system can be controlled to rapidly provide required power within a safe range, the calculation load is greatly reduced, and the minimum value of the current of the electric pile is sought in the optimization process, so that the hydrogen consumption of the electric pile is reduced.
Description
Technical Field
The invention relates to a proton exchange membrane fuel cell technology, in particular to a fuel cell power tracking control method based on model predictive control.
Background
The increasing environmental pollution and energy shortage have forced the automotive industry to develop new energy solutions, proton Exchange Membrane (PEM) fuel cells have great potential in driving future automotive decarbonization and electrification; in recent years, some automobile manufacturers have begun to provide Fuel Cell Hybrid Electric Vehicles (FCHEV) on the market, which have the characteristics of short start-up time, high specific energy, no pollution, and low operating temperature, and have become an important development direction of new automobile power sources, however, without electrochemical reaction of reactants, the fuel cell stack cannot directly operate in an electric circuit, and the fuel cell stack must be dynamically operated in a wide load range to meet the power requirements of the automobile, so that an automobile fuel cell system generally includes a PEM fuel cell stack, an oxygen supply system, a hydrogen supply system, and reactant supply, power response control systems.
The power response of the fuel cell system has important influence on the whole vehicle energy management and the performance of the fuel cell system, under the condition of meeting the power requirement of the whole vehicle, the aims of reducing the hydrogen consumption and prolonging the service life of the electric pile are needed to be realized, when the fuel cell electric pile is faced with the change of the required power with rapid change and large range, the air supply system and the power response control are needed to ensure that enough air is provided for electrochemical reaction under the premise of not surging an air compressor, the peroxy ratio of the system is controlled in a reasonable range, and the required power is rapidly and accurately output, however, various control methods are proposed in the prior art, but because various defects exist, and particularly, the system constraint is not taken into consideration, the electric pile current is taken into account, the electric pile cannot be directly applied to the control of the proton exchange membrane fuel cell, the control requirement of the fuel cell electric pile with large range is difficult to be realized, the hydrogen consumption is very serious, and the service life of the electric pile is short.
Disclosure of Invention
The technical problem to be solved by the invention is to provide the fuel cell power tracking control method based on model prediction control, which can realize tracking control of the fuel cell stack with larger range of required power, realize the goal of reducing hydrogen consumption and prolong the service life of the stack.
In order to solve the technical problems, the fuel cell power tracking control method based on model predictive control of the invention comprises the following steps:
A. the controller acquires a control target;
B. the data acquisition module transmits data required by the control strategy to the controller;
C. the controller establishes an observer to estimate the internal state of the fuel cell stack, and a nonlinear state space model is established in advance for the fuel cell stack in a control strategy;
D. linearizing the nonlinear state space model of the fuel cell stack at the working point aiming at a pre-established nonlinear state space model of the fuel cell stack, and discretizing the linearization model;
E. predicting the state quantity and the output quantity in the set prediction step length to obtain a prediction sequence of the state quantity and the output quantity;
F. searching a minimum value of an objective function through quadratic programming to obtain a control sequence;
G. the first item of the control sequence is sent as a control signal to the corresponding actuator.
The nonlinear state space model is a fourth-order state space model, and the fourth-order state space model specifically comprises:
the output of the fuel cell stack nonlinear state space model is the stack net power and the peroxy ratio:
wherein P is net Lambda is the fuel cell stack cathode peroxide ratio for the fuel cell stack net power.
And D, linearizing the nonlinear state space model of the fuel cell stack at different current working points by utilizing a jacobian matrix of a dynamic system to obtain a state space equation:
and D, discretizing the fuel cell linearization model to obtain:
the predicted sequence of the state quantity and the output quantity obtained in the step E:
X(k+m|k)＝A m X(k)+A m-1 BU(k)+A m-2 BU(k+1)+...+BU(k+m-1)
Y(k+m|k)＝C d X(k+m|k)+D d U(k+m)
where m is a prediction step length, and k is a current time.
In the step F, the minimum value of the sum of objective functions of all prediction step sizes is sought through quadratic programming, and the control voltage of the air compressor and the current of the electric pile are obtained, wherein the objective functions are as follows:
the stack current is calculated by the following formula:
in which W is in For air flow into the stack, χ o2,in The oxygen fraction in the cathode inlet gas is F, F is Faraday constant, M air Is the molar mass of air, lambda is the peroxy ratio.
In the objective function, I ref Set to 0, the objective function first term becomes:
F 1 ＝Q P [P ref (k+i|k)-P(k+i|k)] 2 +Q I [I(k+i|k)] 2
the quadratic programming in said step F sets constraints on the fuel cell part parameters, the values of which are controlled between maximum and minimum values.
After the first item of the control sequence is sent as a control signal to the corresponding actuator in step G, the above steps are repeated at the next sampling time.
The invention has the following beneficial effects:
(1) The invention adopts model predictive control to control the power of the fuel cell and the cathode end air supply system, and can control the fuel cell system to rapidly provide required power in a safe range in consideration of control constraint.
(2) The fuel cell model is linearized at each operating point, the basis of the control strategy is linear adaptive MPC, the linear model of the fuel cell and the cost function of optimal control of the fuel cell are used, and the optimization process adopts a formula with only optimal quadratic problem, so that compared with nonlinear MPC, the calculation load is greatly reduced.
(3) The weight of the current of the electric pile is set in the cost function of the optimal control, and the current reference value is set to be 0, so that the minimum value of the current of the electric pile is sought in the optimization process, and the hydrogen consumption of the electric pile is reduced.
Drawings
FIG. 1 is a flow chart of a fuel cell power tracking control method based on model predictive control of the present invention;
fig. 2 is a block diagram of the fuel cell power tracking control method based on model predictive control of the present invention.
Detailed Description
The invention aims to realize the tracking control of the fuel cell stack with larger range of required power, realize the aim of reducing hydrogen consumption and prolong the service life of the stack, and further describe the fuel cell power tracking control method based on model predictive control in detail with reference to the attached drawings and the detailed description.
As shown in fig. 1-2, the fuel cell power tracking control method based on model predictive control of the present invention introduces air compressor voltage as a control variable, uses fuel cell cathode end oxygen partial pressure, nitrogen partial pressure, cathode intake manifold pressure and air compressor rotational speed as state variables, uses fuel cell system net power and peroxy ratio as output, establishes a nonlinear model of the fuel cell system, adopts a linear adaptive model predictive control algorithm to search for an optimal solution of quadratic programming through real-time linearization of the model, and realizes power tracking control of the fuel cell, and specifically comprises the following steps:
A. the controller obtains a control target, and particularly the MPC controller receives the control requirement of the electric pile power;
B. the data acquisition module transmits data required by a control strategy to the controller, wherein the data comprise the rotating speed of the air compressor, the pressure of an air inlet manifold, the inlet and outlet pressure of a fuel cell stack, the voltage and the current of the stack.
C. The controller establishes an observer to estimate the internal state of the fuel cell stack, a nonlinear state space model is established in advance for the fuel cell stack in a control strategy, and the estimated content comprises partial pressures of oxygen and nitrogen at the cathode end of the stack.
D. B, linearizing the nonlinear state space model of the fuel cell stack at the working point according to the state quantity of the fuel cell stack obtained in the step B and the step C and aiming at the nonlinear state space model of the fuel cell stack, and discretizing the linearization model;
E. predicting the state quantity and the output quantity in the set prediction step length to obtain a prediction sequence of the state quantity and the output quantity;
F. searching a minimum value of an objective function through secondary planning to obtain a control sequence (air compressor flow and pile current);
G. and sending the first item of the control sequence as a control signal to a corresponding executing mechanism, repeating the steps at the next sampling time, updating the state quantity and the predicted sequence of the output quantity at each sampling time, updating the control sequence, and taking the new first item of the control sequence as the control signal.
The above control method is described in further detail below.
The MPC controller in step A receives the control requirement of the pile power, namely the required power P ref This data serves as a power reference in the quadratic programming algorithm.
And B and C, the controller acquires state variables required by a control strategy and is used for the nonlinear state space model of the fuel cell stack in the step D.
The nonlinear state space model of the fuel cell stack in the step D is a fourth-order state space model,
wherein, X1, X2, X3, X4 respectively represent the partial pressure P of oxygen at the cathode end of the fuel cell stack O2 Partial pressure P of nitrogen N2 Rotational speed omega of air compressor cp Partial pressure P of intake manifold sm U is the control quantity, the voltage of the air compressor, and I is the current of the fuel cell.
Specifically, the state equation is:
wherein k is ca,in Is the flow coefficient of the inlet of the cathode flow channel, R is the gas constant, T atm At ambient temperature, M air Is the air molar mass, V sm For the volume of the air supply pipeline W cp Is the flow of the air compressor, T is the temperature of the electric pile, V ca For fuel cell cathode flow channel volume, M o2 X is the molar mass of oxygen o2 Omega is the mass fraction of oxygen in air atm For air-to-humidity ratio, M N2 Is nitrogen molar mass, F is FaradayNumber, P sat At saturated steam pressure, C p Constant pressure specific heat capacity, eta of air cp For air compressor efficiency, J cp Is the rotational inertia, k of the air compressor v ，k t Is the related parameter of the air compressor, R cm Is the resistance of the driving motor.
Further, the output of the fuel cell stack state space model is the net power of the stack and the peroxide ratio:
wherein P is net Lambda is the fuel cell stack cathode peroxide ratio for the fuel cell stack net power.
The specific formula is as follows:
further, the stack voltage is calculated from the equation to be fitted as follows:
wherein N is the single-chip number of the cells in the pile, and P 02 Is the oxygen partial pressure at the cathode end, i is the current density, T is the temperature of the electric pile, alpha 1 、α 2 、α 3 、α 4 Is a fitting parameter.
And D, linearizing the nonlinear state space model of the fuel cell stack at different current working points by utilizing a jacobian matrix of the dynamic system to obtain a state space equation:
wherein:
further, in the step D, discretizing the fuel cell linearization model to obtain:
wherein:
C d ＝C
D d ＝D
wherein T is s For sampling time, X o 、U o The state quantity and the control quantity of the current working point.
In the step E, the state quantity and the output quantity are predicted in the set prediction step length, and a predicted sequence of the state quantity and the output quantity is obtained:
X(k+m|k)＝A m X(k)+A m-1 BU(k)+A m-2 BU(k+1)+...+BU(k+m-1)
Y(k+m|k)＝C d X(k+m|k)+D d U(k+m)
where m is a prediction step length, and k is a current time.
In the step F, the minimum value of the sum of objective functions of all prediction step sizes is sought through quadratic programming, and the control voltage of the air compressor and the current of the electric pile are obtained, wherein the objective functions are as follows:
wherein:
E(k+i|k)＝Y ref (k+i|k)-Y(k+i|k)
ΔU(k+i-1|k)＝U(k+i|k)-U(k+i-1|k)
R＝R u
q in P 、Q I 、R U The weights of the pile power, the current and the control voltage of the air compressor are respectively. P (P) ref 、I ref 、λ ref Respectively the reference values of pile power, current and peroxy ratio.
Further, the stack current can be calculated by the following formula:
in which W is in For air flow into the stack, χ o2,in The oxygen fraction in the cathode inlet gas is F, F is Faraday constant, M air Is the molar mass of air, lambda is the peroxy ratio.
In the objective function, I ref Set to 0, then targetThe first term of the function becomes:
F 1 ＝Q P [P ref (k+i|k)-P(k+i|k)] 2 +Q I [I(k+i|k)] 2 in the process of searching for the optimal solution, the current reference value I ref Set to 0, the controller will reduce the stack current value within the constraint range, which will reduce the fuel cell hydrogen loss since the hydrogen consumption is positively correlated to the current level.
And F, setting constraint on partial parameters of the fuel cell by using the quadratic programming in the step, wherein the numerical value of the constraint is between the maximum value and the minimum value, and the constraint comprises stack voltage, a peroxy ratio and air compressor torque, wherein the stack voltage, the peroxy ratio and the air compressor torque are in soft constraint, and the air compressor torque is limited by the performance of the air compressor and is in hard constraint.
Claims (7)
1. A fuel cell power tracking control method based on model predictive control includes the following steps:
A. the controller acquires a control target;
B. the data acquisition module transmits data required by the control strategy to the controller;
C. the controller establishes an observer to estimate the internal state of the fuel cell stack, and a nonlinear state space model is established in advance for the fuel cell stack in a control strategy;
D. linearizing the nonlinear state space model of the fuel cell stack at a working point aiming at a pre-established nonlinear state space model of the fuel cell stack, and discretizing the linearization model;
E. predicting the state quantity and the output quantity in the set prediction step length to obtain a prediction sequence of the state quantity and the output quantity;
F. searching a minimum value of an objective function through quadratic programming to obtain a control sequence;
G. transmitting a first item of the control sequence as a control signal to a corresponding actuator;
in the step F, the minimum value of the sum of objective functions of all prediction step sizes is sought through quadratic programming, and the control voltage of the air compressor and the current of the electric pile are obtained, wherein the objective functions are as follows:
in the method, in the process of the invention, in (1) the->，/>，/>The weight of the control voltage of the pile power, the current and the air compressor is respectively +.>，/>，/>Respectively the reference values of pile power, current and peroxy ratio;
the stack current is calculated by the following formula:
in the method, in the process of the invention,W in for air flow into the stack, χ o2,in The oxygen fraction in the cathode inlet gas is F, F is Faraday constant, M air Is the air molar mass, lambda is the peroxy ratio;
the nonlinear state space model is a fourth-order state space model, and the fourth-order state space model specifically comprises:
χ 1 , χ 2 , χ 3 , χ 4 respectively represents the cathode oxygen partial pressure P of the fuel cell stack O2 Partial pressure P of nitrogen N2 Rotational speed omega of air compressor cp Partial pressure P of intake manifold sm U is the control quantity;
in the objective function, I ref Set to 0, the objective function first term becomes:
。
2. the model predictive control-based fuel cell power tracking control method according to claim 1, wherein: the output of the fuel cell stack nonlinear state space model is the stack net power and the peroxy ratio:
wherein P is net Lambda is the fuel cell stack cathode peroxide ratio for the fuel cell stack net power.
3. The model predictive control-based fuel cell power tracking control method according to claim 1 or 2, characterized in that: and D, linearizing the nonlinear state space model of the fuel cell stack at different current working points by utilizing a jacobian matrix of a dynamic system to obtain a state space equation:
wherein:
wherein X is o 、U o The state quantity and the control quantity of the current working point.
4. A fuel cell power tracking control method based on model predictive control according to claim 3, characterized in that: and D, discretizing the fuel cell linearization model to obtain:
wherein:
wherein T is s For sampling time, X o 、U o The state quantity and the control quantity of the current working point.
5. The model predictive control-based fuel cell power tracking control method according to claim 4, wherein: the predicted sequence of the state quantity and the output quantity obtained in the step E:
where m is a prediction step length, and k is a current time.
6. The model predictive control-based fuel cell power tracking control method according to claim 1, 2, 4, or 5, characterized in that: the quadratic programming in said step F sets constraints on the fuel cell part parameters, the values of which are between maximum and minimum values.
7. The model predictive control-based fuel cell power tracking control method according to claim 6, wherein: after the first item of the control sequence is sent as a control signal to the corresponding actuator in step G, the above steps are repeated at the next sampling time.
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