CN107870564B - Anti-interference control method for fuel cell with decoupling performance - Google Patents

Anti-interference control method for fuel cell with decoupling performance Download PDF

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CN107870564B
CN107870564B CN201711012272.3A CN201711012272A CN107870564B CN 107870564 B CN107870564 B CN 107870564B CN 201711012272 A CN201711012272 A CN 201711012272A CN 107870564 B CN107870564 B CN 107870564B
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符灏
沈炯
孙立
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Abstract

The invention discloses a fuel cell anti-interference control method with rapid, safe and decoupling performances, aiming at the characteristics of frequent load interference, slow response, easy failure and strong coupling of a solid oxide fuel cell, the optimal control of the solid oxide fuel cell is realized by respectively observing an amplification state, setting operation constraint and a multivariable predictive control algorithm. The problem of slow response of the load disturbance of the fuel cell is solved by amplifying a prediction model of the disturbance state; the air inlet valve amplitude limiting speed limit and the operation constraint of reasonable fuel utilization rate are set, so that valve faults and battery gas shortage are effectively prevented; aiming at the characteristic of strong coupling of fuel utilization rate and output voltage, a multivariable predictive control algorithm is adopted to achieve the decoupling purpose in the dynamic optimization process. The control method provided by the invention can accurately optimize the air inflow of hydrogen and air, quickly inhibit the influence of load disturbance on output voltage, improve the fuel utilization rate and simultaneously ensure the safe operation of a valve and a fuel cell.

Description

Anti-interference control method for fuel cell with decoupling performance
Technical Field
The invention relates to an anti-interference control method for a fuel cell with decoupling performance, and belongs to the technical field of automatic control of new energy utilization.
Background
With the rapid development of economic society, the utilization of resources by people is increased day by day, and the excessive use of conventional energy sources (coal, petroleum and natural gas) causes serious environmental problems. The traditional fossil fuel power generation is limited by Carnot cycle and has low efficiency because chemical energy is converted into heat energy and then mechanical energy is used for acting externally to generate power. The fuel cell is an advanced energy utilization technology, chemical energy in fuel is directly converted into electric energy through electrochemical reaction, and the fuel cell has the characteristics of high efficiency, cleanness and safety. All countries in the world invest manpower and capital to develop stable and reliable fuel cell power generation technology, and promote the commercial application of the fuel cell power generation technology in the energy field.
Scholars at home and abroad carry out a great deal of research work aiming at the aspects of operation optimization, dynamic modeling and the like of the solid oxide fuel cell, but the research on the control strategy is insufficient. Furthermore, due to the fact that the solid oxide fuel cell model has frequent disturbance and strong coupling, a faster and more stable control strategy is needed compared with the traditional control algorithm. Meanwhile, the solid oxide fuel cell has the constraint problems of hydrogen and air inlet valves and fuel utilization rate, so that the traditional control method cannot obtain more satisfactory control effect and economic effect. In addition, the existence of disturbance, measurement noise and uncertainty can generate certain interference effect on the controller, so that the traditional controller is difficult to obtain good control quality.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the fuel cell anti-interference control method with decoupling performance is provided, the influence of load resistance disturbance can be compensated more quickly, and the anti-interference capability and the economic effect of a solid oxide fuel cell model are improved; meanwhile, the constraints of hydrogen flow, air flow and fuel utilization rate are set, so that the conditions of valve failure and battery gas shortage are prevented, and the safe operation of the solid oxide fuel battery is ensured.
The invention adopts the following technical scheme for solving the technical problems:
the anti-interference control method of the fuel cell with the decoupling performance comprises the following steps:
step 1, obtaining a step response model of a fuel cell, respectively carrying out step response tests on hydrogen flow, air flow and load resistance based on a balance point under a steady-state working condition, identifying and obtaining respective corresponding transfer functions, and constructing an augmented state space model with a disturbance term according to the transfer functions;
step 2, setting relevant parameters of a fuel cell controller, including a sampling period, a prediction time domain, a control time domain, an error weight matrix and a control weight matrix; predicting the state quantity, the output quantity, the control increment and the disturbance increment in a future prediction time domain range of the fuel cell controller by adopting an augmented state space model;
step 3, setting interval constraints of the control quantity, the control increment and the controlled quantity of the fuel cell controller;
step 4, taking the actual output value of the fuel cell controller measured under the steady-state working condition as the initial predicted value of the current moment, and initializing the controller;
step 5, according to the interval constraint and the augmented state space model, constructing an optimization problem which enables the performance index of the fuel cell controller to be minimum, and solving the optimization problem to obtain the optimal control increment of the next moment;
step 6, calculating the optimal control quantity of the hydrogen flow and the air flow at the next moment according to the optimal control increment at the next moment;
and 7, calculating and updating an output predicted value at the next moment according to the actual output value at the current moment, and repeatedly executing the steps 4 to 7 in the sampling period.
As a preferred embodiment of the present invention, the augmented state space model with the perturbation term in step 1 is:
Figure GDA0002561825390000021
Figure GDA0002561825390000022
the method is simplified as follows:
x(k+1)＝Ax(k)+BuΔu(k)+BdΔd(k)
y(k)＝Cx(k)
wherein, Δ xd(k+1)＝xd(k+1)-xd(k)，Δxd(k)＝xd(k)-xd(k-1)，Δu(k)＝u(k)-u(k-1)，Δd(k)＝d(k)-d(k-1)，xd(k) Is the state variable at time k, Δ xd(k) Is the relative change of the state variable at the time k, u (k) is the hydrogen flow and the air flow at the time k, Deltau (k) is the relative change of the hydrogen flow and the air flow, d (k) is the system disturbance amount at the time k, Deltad (k) is the relative change of the system disturbance amount at the time k, y (k) is the fuel utilization rate and the output voltage at the time k, A is the fuel consumption rate and the output voltage at the time kd、B1、B2、Cd、D1、D2Respectively are coefficient matrixes, O is a zero matrix, I is a unit matrix, and k +1 and k-1 respectively represent the time of k +1 and k-1.
As a preferred scheme of the present invention, step 2 adopts an augmented state space model to predict state quantity, output quantity, control increment, and disturbance increment in a future prediction time domain range of the fuel cell controller, and the form is as follows:
Y＝F·x(k)+ΦΔU+ΨΔd(k)
wherein the content of the first and second substances,
Figure GDA0002561825390000031
Ψ＝[CBd CABd … CAP-1Bd]T
C＝[O I]，
Figure GDA0002561825390000032
Figure GDA0002561825390000033
Δxd(k) is the relative change of the state variable at the time k, y (k) is the fuel utilization and output voltage at the time k, Δ U is the control quantity, Δ d (k) is the relative change of the disturbance quantity of the system at the time k, Ad、B1、B2、Cd、D1、D2Respectively, coefficient matrixes, O a zero matrix, I an identity matrix, P a prediction time domain, M a control time domain and Y an output prediction.
As a preferred embodiment of the present invention, the optimization problem of minimizing the performance index of the fuel cell controller in step 5 is:
min J＝ΔUT(ΦTQΦ+R)ΔU-2[Yr-F·x(k)-ΨΔd(k)]TQΦΔU
Figure GDA0002561825390000034
wherein the content of the first and second substances,
Figure GDA0002561825390000041
Ψ＝[CBd CABd … CAP-1Bd]T
C＝[O I]，
Figure GDA0002561825390000042
Figure GDA0002561825390000043
Ad、B1、B2、Cd、D1、D2respectively are coefficient matrix, O is zero matrix, I is unit matrix, nu is input control variable number, M is control time domain, delta xd(k) Is the relative change of state variable at time k, Y (k) is the fuel utilization and output voltage at time k, J is the performance index, Δ U is the control quantity, Q is the error weight matrix, R is the control weight matrix, Y is the control weight matrixrFor a given signal,. DELTA.d (k) is the relative change in the amount of disturbance of the system at time k, Umin、UmaxMinimum and large values in the control quantity interval, Ymin、YmaxThe minimum and the maximum values of the controlled quantity interval.
In a preferred embodiment of the present invention, the method uses the hydrogen flow and the air flow of the fuel cell as control quantities, and uses the fuel utilization rate and the output voltage of the fuel cell as controlled quantities, thereby constructing a two-in two-out augmented state space prediction model.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the invention takes the hydrogen and air intake valves of the fuel cell as the control quantity, the fuel utilization rate and the output voltage as the controlled objects, and constructs a multivariable system with two inlets and two outlets as the research object. By controlling the opening of the hydrogen and air inlet valves, the requirements of fuel utilization rate and output voltage are quickly met, and the decoupling performance of the anti-interference controller is realized.
2. According to the invention, the equivalent resistance of the load is introduced as the state observation of the amplified disturbance, so that the problems of frequent disturbance and slow response of the disturbance to the solid oxide fuel cell are quickly eliminated, and the rapidity of the anti-interference controller is realized.
3. The invention simultaneously sets the amplitude and the speed of the air inlet valve and the constraint of the fuel utilization rate to ensure that the system operates under the safe and stable condition, thereby preventing the conditions of valve failure and battery short of gas and realizing the safety of the anti-interference controller.
4. The invention can well process the coupling problem of the system by adopting a dynamically optimized multivariable predictive control method, realizes the coordination control of the fuel utilization rate and the output voltage, can rapidly process the influence caused by frequent disturbance of the resistance at the load side by introducing the equivalent resistance of the load as a predictive model constructed by amplifying the disturbance state, and improves the dynamic regulation quality and the anti-interference capability.
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Fig. 1 is a schematic block diagram of the anti-interference control method of the fuel cell of the present invention.
Fig. 2 is a comparison graph of the controlled quantity change of the control method of the present invention and the conventional PID control method at the time of the load step change.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The invention processes the solid oxide fuel cell into a multivariable object with two inlets and two outlets under the disturbance of load resistance, and dynamically optimizes the opening of the hydrogen and air inlet valves by adopting a multivariable predictive control technology, thereby processing the coupling problem of the fuel utilization rate and the output voltage. By means of the prediction model of the amplification disturbance observation, dynamic deviation caused by load disturbance is eliminated rapidly, and the anti-interference capability of the solid oxide fuel cell is improved. On the other hand, interval constraints are set on the amplitude and the speed of the air inlet valve and the fuel utilization rate of the system, and the optimal opening of the hydrogen valve and the air valve is obtained by adopting constraint quadratic programming to solve, so that the service lives of the gas transmission valve and the pipeline are prolonged, and the safety of a control effect is realized.
As shown in fig. 1, it is a schematic block diagram of a fuel cell interference rejection control method, and the control method includes the following steps:
1) and acquiring a step response curve of the solid oxide fuel cell model. Under the steady-state working condition, the hydrogen flow and the air flow are respectively used as input, the load is used as disturbance, an open-loop step response test is carried out based on a balance point, and the numerical values s of step response models of the hydrogen flow, the air flow and the load resistance are respectively obtainedo,p,qN, where ny, nu are the number of outputs and inputs of the model, respectively, N is the time-domain length of the three step response curves, and N should be selected to ensure that the response at the output side approaches a steady state value.
2) For some future immeasurable disturbances with known change rules, the influence on the output can be predicted, and the disturbance can be compensated through the feed-forward action. Determining an augmented state space model of the fuel cell with the disturbance as follows:
Figure GDA0002561825390000061
in the formula,. DELTA.xd(k+1)＝xd(k+1)-xd(k)，Δxd(k)＝xd(k)-xd(k-1)，Δu(k)＝u(k)-u(k-1)，Δxd(k) The relative change of the state variable at the time k, Δ u (k) the relative change of the hydrogen flow rate and the air flow rate, y (k) the fuel utilization rate and the output voltage, and d (k) the disturbance amount to the system at the time k. A. thed、B1、B2、Cd、D1、D2Respectively corresponding coefficient matrices.
Namely:
Figure GDA0002561825390000062
3) setting controller related parameters. Including the sampling time TsThe method comprises the following steps of predicting a time domain P, controlling the time domain M, an error weight matrix Q and a control weight matrix R. T issThe selection of (A) generally conforms to Shannon's sampling theorem and can be usedRule of thumb T95/TsIs selected from 5 to 15, wherein T95The conditioning time for the transition process to rise to 95%; the prediction time domain P should contain the real dynamic part of the object as much as possible; m is taken as 3-5; q ═ IP×P；R＝IM×M。
After the controller parameters are determined, the future state and output of the solid oxide fuel cell model are predicted by adopting a prediction model shown in formula (2):
Figure GDA0002561825390000063
Figure GDA0002561825390000071
where y (k + i | k), i ═ 1, …, and P denotes the predicted output value at time k to the future time k + i; x (k + i | k), i ═ 1, …, and P denotes the state quantity estimate at time k to the future time k + i.
4) The corresponding control quantity Δ U and disturbance quantity Δ D are:
Figure GDA0002561825390000072
in the equation, Δ u (k + j), j is 1, …, M-1 represents the prediction of the output control increment at time k in the future at time k + j, and Δ d (k + j), j is 1, …, M-1 represents the estimation of the disturbance increment at time k in the future at time k + j.
In actual use, the dynamic response B of the output y (k) to d (k) is generallydD (k) is known and measurable currently, but the future disturbance term d (k + i) is not. The prediction model is modified at this time as follows:
Y＝F·x(k)+ΦΔU+ΨΔd(k) (6)
wherein the content of the first and second substances,
Figure GDA0002561825390000073
Ψ＝[CBd CABd … CAP-1Bd]T
5) the controller is initialized. Namely, under a certain steady-state working condition, the actual output value y (k) measured by the working condition is taken as the initial predicted value at the current moment.
6) The constraints of hydrogen flow and air flow are:
Figure GDA0002561825390000074
wherein the content of the first and second substances,
Figure GDA0002561825390000075
Figure GDA0002561825390000081
i is a nu multiplied by nu order unit matrix, and nu is the number of input control variables;
the hydrogen flow and air flow delta constraints are:
Figure GDA0002561825390000082
wherein the content of the first and second substances,
Figure GDA0002561825390000083
the constraints on fuel utilization are:
Figure GDA0002561825390000084
wherein the content of the first and second substances,
Figure GDA0002561825390000085
ny is the regulated quantity number.
The performance indexes after optimization according to interval constraint are as follows:
Figure GDA0002561825390000086
and selecting the optimal control increment delta u (k) according to the standard quadratic programming problem solved by the performance index.
7) Calculating the optimal control quantity u (k +1) of the hydrogen flow and the air flow at the next moment:
u(k+1)＝u(k)+Δu(k+1) (11)
8) an output prediction value y (k +1| k) at the next time is calculated and updated from the measurement signal. Then, in each sampling period, the steps 6) to 8) are repeatedly performed.
The control method of the present invention is illustrated below by a specific embodiment, and comprises the following steps:
1) and acquiring a step response model of the solid oxide fuel cell. The dynamic characteristics of which can be described by a transfer function model shown in equation (12):
Figure GDA0002561825390000091
wherein u is1,u2Respectively representing hydrogen flow rate (mol/s) and air flow rate (mol/s); y is1,y2Respectively, fuel utilization (. about.100%), output voltage (V).
Let model time domain N be 2400. By performing a step response test on the hydrogen flow, the air flow and the load resistance based on a balance point, the fuel utilization rate and the output voltage of the solid oxide fuel cell are respectively obtained as follows:
[s1,1,1,...,s1,1,2400]＝[0.62536,..0.5847365,0.56053535,..0.5229348],
[s1,2,1,...,s1,2,2400]＝[96.391916,..96.6986,96.823665,..96.72294],
[s2,1,1,...,s2,1,2400]＝[0.62536,..0.625464,0.6255875,..0.606419],
[s2,2,1,...,s2,2,2400]＝[96.3895,..96.44585,96.457231,..93.4703],
[s3,1,1,...,s3,1,2400]＝[0.62536,..0.5920586,0.57957,..0.560721],
[s3,2,1,...,s3,2,2400]＝[96.3895,..102.252341,104.482735,..103.712013],
according to the data identification, the transfer functions are respectively as follows:
Figure GDA0002561825390000092
2) for some disturbances whose output influence is known and which cannot be measured at a future time, they are compensated by a feed forward action. Determining an augmented state space model of the fuel cell with the disturbance as follows:
Figure GDA0002561825390000093
wherein the content of the first and second substances,
Figure GDA0002561825390000094
Figure GDA0002561825390000101
D1＝0,D2＝0；
3) setting controller related parameters. Let a sampling time Ts2s, the prediction time domain P is 100, the control time domain M is 5, and the error weight matrix
Figure GDA0002561825390000102
Control weight matrix
Figure GDA0002561825390000103
4) The corresponding control quantity Δ U and disturbance quantity Δ D are:
Figure GDA0002561825390000104
wherein, the delta u (k + i) is calculated by the optimal performance index, and the delta d (k + i) is input by the outside at the moment of k + i;
the prediction model is modified as follows:
Y＝F·x(k)+ΦΔU+ΨΔd(k) (16)
wherein the content of the first and second substances,
Figure GDA0002561825390000105
Figure GDA0002561825390000106
Ψ＝[-0.095182 16.56095 … 50.6207426]T
5) the state of the controller is initialized. Under a certain steady-state working condition, detecting an output measured value y (k) at the current moment, and taking the output measured value y (k) as an initial predicted value of 100 steps in the future;
6) the constraints of the controlled quantity, the control increment and the controlled quantity are set as follows:
Figure GDA0002561825390000111
after the interval constraint is set, solving a standard quadratic programming problem, and calculating to obtain the optimal control increment delta U of the hydrogen flow and the air flow at the next moment, wherein the optimal control increment delta U meets the following requirements:
Figure GDA0002561825390000112
wherein the content of the first and second substances,
Figure GDA0002561825390000113
7) calculating the optimal control quantity u (k +1) of the hydrogen flow and the air flow at the next moment:
u(k+1)＝u(k)+Δu(k+1) (19)
8) the optimum control amount u (k +1) is output, and the output prediction value y (k +1| k) at the next time is calculated and updated from the measurement signal. Then, in each sampling period, the steps 6) to 8) are repeatedly performed.
The comparison between the control effect of the solid oxide fuel cell anti-interference controller with decoupling performance and the PID control is shown in FIG. 2. The initial steady state operating conditions of the operation are:
u1＝0.0009mol/s,u2＝0.012mol/s,d＝0.8875Ω,y1＝0.625377837970747,
y2＝96.3924825020972V,u1min＝0.00001mol/s,u2min＝0,u1max＝0.001mol/s,
u2max＝0.1mol/s,Δu1min＝-0.01mol/s,Δu2min＝-0.01mol/s,Δu1max＝0.01mol/s,
Δu2max＝0.01mol/s,y1min＝0,y1max＝0.7,y1max＝0.65,y2max＝130,
assuming that the load d changes to 1.065 Ω in 500s step, the dotted line represents the control effect of the solid oxide fuel cell anti-interference controller with decoupling performance, and the solid line represents the control effect of the conventional PID controller. It can be seen that, because the coupling degree of the solid oxide fuel cell system is high, the conventional PID controller cannot stabilize both the fuel utilization rate and the output voltage at the set values at the same time, and the effect is not good. The method provided by the invention can almost simultaneously stabilize the fuel utilization rate and the output voltage in a short time, and compared with the traditional control method, the fuel utilization rate is increased in the system regulation process while the coordination control is ensured; on the output voltage of the system, the control effect of the solid oxide fuel cell anti-interference control method with the decoupling performance can eliminate the influence of disturbance more quickly to reach a set value, and the requirement of the output voltage in actual application is met.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (5)

1. The anti-interference control method of the fuel cell with the decoupling performance is characterized by comprising the following steps:
step 1, obtaining a step response model of a fuel cell, respectively carrying out step response tests on hydrogen flow, air flow and load resistance based on a balance point under a steady-state working condition, identifying and obtaining respective corresponding transfer functions, and constructing an augmented state space model with a disturbance term according to the transfer functions;
step 2, setting relevant parameters of a fuel cell controller, including a sampling period, a prediction time domain, a control time domain, an error weight matrix and a control weight matrix; predicting the state quantity, the output quantity, the control increment and the disturbance increment in a future prediction time domain range of the fuel cell controller by adopting an augmented state space model;
step 3, setting interval constraints of the control quantity, the control increment and the controlled quantity of the fuel cell controller;
step 4, taking the actual output value of the fuel cell controller measured under the steady-state working condition as the initial predicted value of the current moment, and initializing the controller;
step 5, according to the interval constraint and the augmented state space model, constructing an optimization problem which enables the performance index of the fuel cell controller to be minimum, and solving the optimization problem to obtain the optimal control increment of the next moment;
step 6, calculating the optimal control quantity of the hydrogen flow and the air flow at the next moment according to the optimal control increment at the next moment;
and 7, calculating and updating an output predicted value at the next moment according to the actual output value at the current moment, and repeatedly executing the steps 4 to 7 in the sampling period.
2. The anti-interference control method for the fuel cell with the decoupling performance according to claim 1, wherein the augmented state space model with the disturbance term in step 1 is as follows:
Figure FDA0001445719520000011
Figure FDA0001445719520000012
the method is simplified as follows:
x(k+1)＝Ax(k)+BuΔu(k)+BdΔd(k)
y(k)＝Cx(k)
wherein, Δ xd(k+1)＝xd(k+1)-xd(k)，Δxd(k)＝xd(k)-xd(k-1)，Δu(k)＝u(k)-u(k-1)，Δd(k)＝d(k)-d(k-1)，xd(k) Is the state variable at time k, Δ xd(k) Is the relative change of the state variable at the time k, u (k) is the hydrogen flow and the air flow at the time k, Deltau (k) is the relative change of the hydrogen flow and the air flow, d (k) is the system disturbance amount at the time k, Deltad (k) is the relative change of the system disturbance amount at the time k, y (k) is the fuel utilization rate and the output voltage at the time k, A is the fuel consumption rate and the output voltage at the time kd、B1、B2、Cd、D1、D2Respectively are coefficient matrixes, O is a zero matrix, I is a unit matrix, and k +1 and k-1 respectively represent the time of k +1 and k-1.
3. The anti-interference control method for the fuel cell with the decoupling performance according to claim 1, wherein in the step 2, the state quantity, the output quantity, the control increment and the disturbance increment in the future prediction time domain range of the fuel cell controller are predicted by adopting an augmented state space model, and the form is as follows:
Y＝F·x(k)+ΦΔU+ΨΔd(k)
wherein the content of the first and second substances,
Figure FDA0001445719520000021
C＝[O I]，
Figure FDA0001445719520000022
Figure FDA0001445719520000023
Δxd(k) is the relative change of the state variable at time k, y (k) is the fuel utilization and output voltage at time k, Δ U is the control quantity, Δ d (k)Is the relative change of the disturbance quantity of the system at time k, Ad、B1、B2、Cd、D1、D2Respectively, coefficient matrixes, O a zero matrix, I an identity matrix, P a prediction time domain, M a control time domain and Y an output prediction.
4. The anti-interference control method for the fuel cell with the decoupling performance according to claim 1, wherein the optimization problem of minimizing the performance index of the fuel cell controller in the step 5 is as follows:
min J＝ΔUT(ΦTQΦ+R)ΔU-2[Yr-F·x(k)-ΨΔd(k)]TQΦΔU
Figure FDA0001445719520000024
wherein the content of the first and second substances,
Figure FDA0001445719520000031
C＝[O I]，
Figure FDA0001445719520000032
Figure FDA0001445719520000033
Ad、B1、B2、Cd、D1、D2respectively are coefficient matrix, O is zero matrix, I is unit matrix, nu is input control variable number, M is control time domain, delta xd(k) Is the relative change of state variable at time k, Y (k) is the fuel utilization and output voltage at time k, J is the performance index, Δ U is the control quantity, Q is the error weight matrix, R is the control weight matrix, Y is the control weight matrixrFor a given signal,. DELTA.d (k) is the relative change in the amount of disturbance of the system at time k, Umin、UmaxMinimum and large values in the control quantity interval, Ymin、YmaxThe minimum and the maximum values of the controlled quantity interval.
5. The anti-interference control method for the fuel cell with the decoupling performance according to claim 1, wherein the method uses hydrogen flow and air flow of the fuel cell as control quantities, uses fuel utilization rate and output voltage of the fuel cell as controlled quantities, and constructs a two-in two-out augmented state space prediction model.
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