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CN110069033B - A double-layer predictive control method for a full-power fuel cell air compressor - Google Patents

A double-layer predictive control method for a full-power fuel cell air compressor Download PDF

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CN110069033B
CN110069033B CN201910373642.9A CN201910373642A CN110069033B CN 110069033 B CN110069033 B CN 110069033B CN 201910373642 A CN201910373642 A CN 201910373642A CN 110069033 B CN110069033 B CN 110069033B
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CN110069033A (en
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王亚雄
陈锦洲
林飞
陈家瑄
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Abstract

本发明涉及一种全功率燃料电池电动汽车的空压机双层预测控制方法。上层预测器通过实时预测车速，计算获取对应车速下燃料电池汽车所需要的功率，将上层预测器计算出的燃料电池所需提供的功率通过燃料电池阴极流量模型计算出燃料电池空压机所需输出的空气流量，并作为底层预测控制器的参考流量。底层预测控制器根据该参考流量，预测燃料电池空压机所需输出的空气流量，同时得到空压机的控制电压，进而实现对空压机输出流量的控制，满足燃料电池堆反应需要的氧气量。本发明可以预测车速和燃料电池空压机所需输出的空气质量流量，利用控制器对燃料电池空压机输出流量进行控制，实现汽车高效稳定运行。

Figure 201910373642

The invention relates to a double-layer predictive control method for an air compressor of a full-power fuel cell electric vehicle. The upper-layer predictor predicts the vehicle speed in real time, calculates and obtains the power required by the fuel cell vehicle at the corresponding vehicle speed, and calculates the required power of the fuel cell air compressor through the fuel cell cathode flow model through the power required by the fuel cell calculated by the upper-layer predictor. The output air flow is used as the reference flow for the underlying predictive controller. The bottom prediction controller predicts the air flow required by the fuel cell air compressor according to the reference flow, and obtains the control voltage of the air compressor, thereby realizing the control of the output flow of the air compressor and satisfying the oxygen required by the fuel cell stack reaction. quantity. The invention can predict the vehicle speed and the air mass flow required by the fuel cell air compressor, and use the controller to control the output flow of the fuel cell air compressor, so as to realize the efficient and stable operation of the vehicle.

Figure 201910373642

Description

Double-layer prediction control method for full-power fuel cell air compressor
Technical Field
The invention relates to the technical field of fuel cell auxiliary systems, in particular to a double-layer prediction control method for a full-power fuel cell air compressor.
Background
The fuel cell converts chemical energy into electric energy through electrochemical reaction, takes fuel and oxygen as raw materials, and has no mechanical transmission part, so the fuel cell has the advantages of high efficiency, no noise, no pollution and the like. From the viewpoint of energy saving and ecological environment protection, fuel cells are the most promising power generation technology. Nowadays, fuel cell power generation is a new generation power generation technology, and its application prospect is very broad, and research as automobile power has made substantial progress. The main accessories of the fuel cell comprise an air compressor, a humidifier, a cooler and a hydrogen circulating pump, wherein the air compressor belongs to the main part of a cathode air supply system of the fuel cell and provides air for the reaction of the fuel cell. When the air supplied by the air compressor is excessive, although the fuel cell can fully react, the power consumed by the air compressor is correspondingly increased, and the power consumption of the air compressor accounts for about 80% of the auxiliary power consumption of the fuel cell, so that the net power of the whole fuel cell is finally reduced. When the air supplied by the air compressor is less than the air amount required by the fuel cell, the fuel cell will be starved by oxygen, so that the service life of the fuel cell is reduced, and in severe cases, the proton exchange membrane is even damaged to scrap the fuel cell, so that the air compressor plays a significant role in the vehicle fuel cell system.
Disclosure of Invention
In view of this, the present invention provides a double-layer prediction control method for a full-power fuel cell air compressor, which obtains the power required to be provided by the fuel cell and the air flow required to be output by the air compressor at a corresponding vehicle speed through calculation of the vehicle speed obtained through prediction, and finally predicts and controls the air flow output by the air compressor, so that the air flow output by the air compressor can adapt to the change of the working condition well, provide a suitable air flow, further improve the efficiency of the fuel cell, and play roles of energy saving, environmental protection, and the like.
In order to achieve the purpose, the invention adopts the following technical scheme:
a double-layer prediction control method for a full-power fuel cell air compressor specifically comprises the following steps:
step S1, constructing a fuel cell cathode flow model;
step S2, constructing a double-layer prediction control system which comprises an upper-layer predictor and a lower-layer prediction controller;
step S3, the upper layer predictor takes the real-time speed V (k) measured by the speed sensor as input, predicts the speed sequences { V (k +1), V (k +2), …, V (k +10) } of ten future moments by the prediction time domain with the step length of 10, and obtains the power { P + needed to be provided by the corresponding moment of the fuel cell through a vehicle dynamics relational expressionr(k+1),Pr(k+2),…,Pr(k+10)}；
Step S4, inputting the power required to be provided by the obtained ten future moments of the fuel cell into a cathode flow model of the fuel cell to obtain an air flow reference value at the corresponding moment;
step S5, the bottom layer prediction controller takes the air flow reference value output by the cathode flow model, the interference parameter and the real-time output flow of the fuel cell air compressor collected by the flow sensor as input, predicts the air flow required to be output by the fuel cell air compressor by using the prediction time domain with the step length of 15, and obtains the control voltage of the fuel cell air compressor at the same time;
and step S6, controlling the output flow of the fuel cell air compressor according to the control voltage.
Further, the disturbance parameter is a linearized state space constant term.
Further, the step S3 is specifically:
and step S31, calculating the predicted vehicle speed according to an exponential prediction method:
V(k+i)＝V(k)·(1+β)i (1)
in the formula: i is 1,2, …,10, V (k + i) is the predicted fuel cell vehicle speed at time k + i, V (k) is the speed at time k, β is an exponential coefficient, where β is taken to be 0.03;
step S32, the vehicle speed sequence of the future ten moments can be predicted by an exponential prediction method, and the power required to be provided by the fuel cell in the corresponding period of time is calculated and obtained according to a dynamic relation formula, as follows:
Figure BDA0002050864810000021
Figure BDA0002050864810000022
in the formula: a (k + i) is the predicted acceleration of the fuel cell vehicle at time k + i, Pr(k + i) is the power required by the fuel cell to predict the time k + i, δ is the vehicle rotating mass conversion factor, G is the total weight of the vehicle, m is the vehicle mass, f is the vehicle rolling resistance factor, α is the vehicle road grade, CDIs the wind resistance coefficient, and a is the windward area.
Further, the step S4 is specifically:
step S41, obtaining the predicted power through the upper layer predictor and the polarization characteristic in the fuel cell cathode flow modelThe characteristic curve can be used for obtaining the current I required to be provided by the corresponding fuel cellst；
Step S42, calculating the air flow required by the air compressor of the fuel cell according to the following formula
Flow rate of oxygen consumed for fuel cell reaction:
Figure BDA0002050864810000031
oxygen flow into the fuel cell cathode:
Figure BDA0002050864810000032
humidity rate of fuel cell:
Figure BDA0002050864810000033
peroxide ratio in fuel cell:
Figure BDA0002050864810000034
in the formula (I), the compound is shown in the specification,
Figure BDA0002050864810000035
is the molar mass of oxygen, MaIs the molar mass of air, ncellIs the number of fuel cells, F is the Faraday constant,
Figure BDA0002050864810000036
is the ratio of the oxygen to the oxygen,
Figure BDA0002050864810000037
is the flow of oxygen into the cathode of the fuel cell,
Figure BDA0002050864810000038
is the flow of oxygen consumed by the fuel cell reaction，WcpIs the output flow of the air compressor of the fuel cell, Psat(Tatm) Is the saturation pressure at atmospheric temperature, PatmIs the pressure of the atmosphere and is,
Figure BDA0002050864810000039
is the relative humidity in the atmosphere.
According to the formulas (4) to (7), if the fuel cell stack current I is determinedstAnd ratio of peroxide to oxygen
Figure BDA00020508648100000310
The air flow required by the fuel cell air compressor to be output can be obtained:
Figure BDA00020508648100000311
in the formula, MvIs the molar mass of the water vapor,
Figure BDA00020508648100000312
is the mass fraction of oxygen in the air.
Further, the bottom layer model controller is specifically constructed as follows:
step S51, constructing a fuel cell air compressor model
Nonlinear air compressor model
Figure BDA0002050864810000041
In the formula, PsmIs the pressure of the supply manifold, Tcp,outIs the temperature at the outlet of the compressor, Wsm,outIs the air flow rate, T, of the supply manifold outputsmIs the temperature of the supply manifold, ωcpIs the rotational speed of the compressor, JcpIs the moment of inertia, tau, of the air compressorcpIs the torque, τ, required to drive the air compressorcmIs the torque of the drive motor. Wherein the torque of the drive motor is calculated as:
Figure BDA0002050864810000042
in the formula of UcmIs the supply voltage, η, of the air compressorcmIs the motor efficiency, KtIs the motor torque coefficient, KvIs the potential coefficient of the motor
② linear air compressor model
For P in formula (9)sm，msm，ωcpThe three state quantities are at point P °sm，m°sm，ω°cpTaylor expansion is adopted to obtain the following equation of state:
Figure BDA0002050864810000043
Y＝CX(t)+DU(t)+W (12)
wherein X is [ P ]sm msm ωcp]TThe method comprises the following steps that (1) state vectors are respectively pressure, mass and rotating speed, U is a control quantity, namely voltage of an air compressor, Y is output flow of the air compressor, d (t) is an interference item, and a linear model of the air compressor is established by utilizing the state equation;
step S52, designing a bottom layer prediction controller according to the linear air compressor model
An objective function:
Figure BDA0002050864810000051
setting a proper prediction time domain p and a proper control time domain m, endowing initial values of state variables and control variables to be zero, calculating a prediction control gain matrix, and calculating an error matrix on line through repeated circulation to enable a prediction controller to perform rolling optimization to obtain an optimal solution
Kmpc＝[I nu×nu 0 …0]1×m(ST uΓT yΓySu+ΓT uΓu)-1ST uΓyΓT y (14)
Δu(k)＝KmpcEp(k+1|k) (15)
In the formula, ycIs the predicted output air flow, r is the flow reference value, Δ u is the control increment, u is the control voltage of the air compressor, Γy，ΓuWeight factor matrices, S, of the manipulated and controlled variables, respectivelyuIs a weighting matrix, KmpcIs a predictive control gain matrix, EpIs an error matrix.
Compared with the prior art, the invention has the following beneficial effects:
1. the index vehicle speed prediction structure is simple;
2. the model predictive control has the characteristics of simple design, strong practicability and the like;
3. the double-layer prediction control system has high response speed and high accuracy;
4. the air flow rate can be properly provided for the fuel cell under different working conditions, and the air flow rate control method has good effects of improving the efficiency of the fuel cell and the like.
According to the invention, the power required to be provided by the fuel cell and the air flow required to be output by the air compressor at the corresponding vehicle speed are obtained through the calculation of the predicted vehicle speed, and the air flow output by the air compressor is finally predicted and controlled, so that the air flow output by the air compressor can be well adapted to the change of working conditions, and a proper air flow is provided, thereby improving the efficiency of the fuel cell, and playing roles of energy conservation, environmental protection and the like.
Drawings
FIG. 1 is a schematic diagram of a dual-layer predictive control architecture of the present invention;
FIG. 2 is a diagram of the dual-layer predictive control concept of the present invention;
FIG. 3 is a schematic diagram of a vehicle speed sequence for predicting ten future times at each speed point by the upper predictor in accordance with an embodiment of the present invention;
FIG. 4 is a schematic vehicle speed diagram illustrating the upper predictor predicting the first and fifth future times at each speed point, according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a verification of the flow of an air compressor of a fuel cell under predictive control by a bottom predictive controller in accordance with an embodiment of the present invention;
fig. 6 is a schematic diagram of the air flow rate required to be output by the fuel cell air compressor when the double-layer predictive control predicts 1046 seconds and 1047 seconds in sequence in accordance with an embodiment of the present invention;
in the figure: the method comprises the following steps of 1-vehicle speed sensor, 2-upper layer predictor, 3-fuel cell cathode flow model, 4-bottom layer prediction controller, 5-fuel cell air compressor and 6-flow sensor.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 1, the present invention provides a double-layer predictive control method for a full-power fuel cell air compressor,
the method specifically comprises the following steps:
step S1, constructing a fuel cell cathode flow model;
step S2, constructing a double-layer prediction control system which comprises an upper-layer predictor and a lower-layer prediction controller;
step S3, the upper layer predictor takes the real-time speed V (k) measured by the speed sensor as input, predicts the speed sequences { V (k +1), V (k +2), …, V (k +10) } of ten future moments by the prediction time domain with the step length of 10, and obtains the power { P + needed to be provided by the corresponding moment of the fuel cell through a vehicle dynamics relational expressionr(k+1),Pr(k+2),…,Pr(k+10)}；
Step S4, inputting the power required to be provided by the obtained ten future moments of the fuel cell into a cathode flow model of the fuel cell to obtain an air flow reference value at the corresponding moment;
step S5, the bottom layer prediction controller takes the air flow reference value output by the cathode flow model, the linearization state space constant term and the real-time output flow of the fuel cell air compressor collected by the flow sensor as input, predicts the air flow required to be output by the fuel cell air compressor by using the prediction time domain with the step length of 15, and obtains the control voltage of the fuel cell air compressor at the same time;
and step S6, controlling the output flow of the fuel cell air compressor according to the control voltage.
In this embodiment, the upper predictor is specifically designed as follows:
and step S31, calculating the predicted vehicle speed according to an exponential prediction method:
V(k+i)＝V(k)·(1+β)i (1)
in the formula: i is 1,2, …,10, V (k + i) is the predicted fuel cell vehicle speed at time k + i, V (k) is the speed at time k, β is an exponential coefficient, where β is taken to be 0.03;
step S32, the vehicle speed sequence of the future ten moments can be predicted by an exponential prediction method, and the power required to be provided by the fuel cell in the corresponding period of time is calculated and obtained according to a dynamic relation formula, as follows:
Figure BDA0002050864810000071
Figure BDA0002050864810000072
in the formula: a (k + i) is the predicted acceleration of the fuel cell vehicle at time k + i, Pr(k + i) is the power required by the fuel cell to predict the time k + i, δ is the vehicle rotating mass conversion factor, G is the total weight of the vehicle, m is the vehicle mass, f is the vehicle rolling resistance factor, α is the vehicle road grade, CDIs the wind resistance coefficient, and a is the windward area.
In the present embodiment, the fuel cell cathode flow model is specifically calculated as follows:
step S41, obtaining the current I needed to be provided by the corresponding fuel cell according to the polarization characteristic curve in the cathode flow model of the fuel cell through the predicted power obtained by the upper layer predictorst；
Step S42, calculating the air flow required by the air compressor of the fuel cell according to the following formula
Flow rate of oxygen consumed for fuel cell reaction:
Figure BDA0002050864810000073
oxygen flow into the fuel cell cathode:
Figure BDA0002050864810000074
humidity rate of fuel cell:
Figure BDA0002050864810000075
peroxide ratio in fuel cell:
Figure BDA0002050864810000076
in the formula (I), the compound is shown in the specification,
Figure BDA0002050864810000077
is the molar mass of oxygen, MaIs the molar mass of air, ncellIs the number of fuel cells, F is the Faraday constant,
Figure BDA0002050864810000078
is the ratio of the oxygen to the oxygen,
Figure BDA0002050864810000079
is the flow of oxygen into the cathode of the fuel cell,
Figure BDA0002050864810000081
is the oxygen flow, W, consumed by the fuel cell reactioncpIs the output flow of the air compressor of the fuel cell, Psat(Tatm) Is the saturation pressure at atmospheric temperature, PatmIs the pressure of the atmosphere and is,
Figure BDA0002050864810000082
is the relative humidity in the atmosphere.
According to the formulas (4) to (7), if the fuel cell stack current I is determinedstAnd ratio of peroxide to oxygen
Figure BDA0002050864810000083
The air flow required by the fuel cell air compressor to be output can be obtained:
Figure BDA0002050864810000084
in the formula, MvIs the molar mass of the water vapor,
Figure BDA0002050864810000085
is the mass fraction of oxygen in the air.
In this embodiment, the bottom layer model controller is specifically constructed as follows:
step S51, constructing a fuel cell air compressor model
Nonlinear air compressor model
Figure BDA0002050864810000086
In the formula, PsmIs the pressure of the supply manifold, Tcp,outIs the temperature at the outlet of the compressor, Wsm,outIs to supply to
Air flow rate, T, due to manifold outputsmIs the temperature of the supply manifold, ωcpIs the rotational speed of the compressor, JcpIs that
Moment of inertia, tau, of air compressorscpIs the torque, τ, required to drive the air compressorcmIs the torque of the drive motor.
Wherein the torque of the drive motor is calculated as:
Figure BDA0002050864810000087
in the formula of UcmIs the supply voltage, η, of the air compressorcmIs the motor efficiency, KtIs the motor torque coefficient, KvIs that
Potential coefficient of motor
② linear air compressor model
For P in formula (9)sm，msm，ωcpThe three state quantities are at point P °sm，m°sm，ω°cpProcessing and mining
Using taylor expansion, the following equation of state is obtained:
Figure BDA0002050864810000088
Y＝CX(t)+DU(t)+W (12)
wherein X is [ P ]sm msm ωcp]TIs the state vector, which is pressure, mass, rotation speed, U, respectively
Is the control quantity, i.e. the voltage of the air compressor, Y is the output flow of the air compressor, d (t) is the interference term, the above-mentioned
Establishing a linear model of the air compressor by using the state equation;
step S52, designing a bottom layer prediction controller according to the linear air compressor model
An objective function:
Figure BDA0002050864810000091
setting a proper prediction time domain p and a proper control time domain m, endowing initial values of state variables and control variables to be zero, calculating a prediction control gain matrix, and calculating an error matrix on line through repeated circulation to enable a prediction controller to perform rolling optimization to obtain an optimal solution
Kmpc＝[Inu×nu 0 … 0]1×m(ST uΓT yΓySu+ΓT uΓu)-1ST uΓyΓT y (14)
Δu(k)＝KmpcEp(k+1|k) (15)
In the formula, ycIs the predicted output air flow rate, and r is the flow rate reference valueΔ u is the control increment, u is the control voltage of the air compressor, Γy，ΓuWeight factor matrices, S, of the manipulated and controlled variables, respectivelyuIs a weighting matrix, KmpcIs a predictive control gain matrix, EpIs an error matrix.
Fig. 5 is a diagram for checking the effect of predictive control of the underlying predictive controller.
As can be seen from fig. 4, the shorter the prediction time domain is, the higher the prediction accuracy is, but the corresponding calculation amount will be larger. The predicted vehicle speed value employed in the present embodiment is the first predicted vehicle speed. In order to verify the effectiveness of the double-layer prediction control, 1045 seconds of the invention are calculated and obtained according to the vehicle speed predicted in the upper-layer predictor for 1046 seconds (the sampling period of the upper-layer predictor is 1 second), the power required to be provided by the fuel cell for 1046 seconds is obtained, the air flow required to be output by the fuel cell air compressor is obtained through a fuel cell cathode flow model (wherein the oxygen ratio is 2), and the air flow required to be output by the fuel cell air compressor is predicted and controlled by the bottom-layer prediction controller according to the air flow to be 0.03729 kg/s. And calculating and obtaining the power required by the fuel cell in 1047 seconds according to the vehicle speed predicted in 1047 seconds in the upper layer predictor in 1046 seconds, obtaining the air flow required to be output by the fuel cell air compressor through a fuel cell cathode flow model (meeting the requirement that the oxygen passing ratio is 2), and predicting and controlling the air flow required to be output by the fuel cell air compressor to be 0.03685kg/s by the bottom layer prediction controller according to the flow. The air flow rate change curve is obtained through simulation, and as shown in fig. 6, the established double-layer predictive control system has good control effect within the acceptable deviation range.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (3)

1. A double-layer prediction control method for a full-power fuel cell air compressor is characterized by comprising the following steps:
step S1, constructing a fuel cell cathode flow model;
step S2, constructing a double-layer prediction control system which comprises an upper-layer predictor and a lower-layer prediction controller;
step S3, the upper layer predictor takes the real-time speed V (k) measured by the speed sensor as input, predicts the speed sequences { V (k +1), V (k +2), …, V (k +10) } of ten future moments by the prediction time domain with the step length of 10, and obtains the power { P + needed to be provided by the corresponding moment of the fuel cell through a vehicle dynamics relational expressionr(k+1),Pr(k+2),…,Pr(k+10)}；
Step S4, inputting the power required to be provided by the obtained ten future moments of the fuel cell into a cathode flow model of the fuel cell to obtain an air flow reference value at the corresponding moment;
step S5, the bottom layer prediction controller takes the air flow reference value output by the cathode flow model, the interference parameter and the real-time output flow of the fuel cell air compressor collected by the flow sensor as input, predicts the air flow required to be output by the fuel cell air compressor by using the prediction time domain with the step length of 15, and obtains the control voltage of the fuel cell air compressor at the same time;
step S6, controlling the output flow of the fuel cell air compressor according to the control voltage;
the step S3 specifically includes:
and step S31, calculating the predicted vehicle speed according to an exponential prediction method:
V(k+i)＝V(k)·(1+β)i (1)
in the formula: i is 1,2, …,10, V (k + i) is the predicted fuel cell vehicle speed at time k + i, V (k) is the speed at time k, and β is an exponential coefficient;
step S32, the vehicle speed sequence of the future ten moments can be predicted by an exponential prediction method, and the power required to be provided by the fuel cell in the corresponding period of time is calculated and obtained according to a dynamic relation formula, as follows:
Figure RE-FDA0003099488990000021
Figure RE-FDA0003099488990000022
in the formula: a (k + i) is the predicted acceleration of the fuel cell vehicle at time k + i, Pr(k + i) is the power required by the fuel cell to predict the time k + i, δ is the vehicle rotating mass conversion factor, G is the total weight of the vehicle, m is the vehicle mass, f is the vehicle rolling resistance factor, α is the vehicle road grade, CDIs the wind resistance coefficient, and a is the windward area.
2. The double-layer prediction control method of the full-power fuel cell air compressor as claimed in claim 1, wherein: the interference parameter is a linearized state space constant term.
3. The double-layer prediction control method of the full-power fuel cell air compressor as claimed in claim 1, wherein: the step S4 specifically includes:
step S41, obtaining the current I needed to be provided by the corresponding fuel cell according to the polarization characteristic curve in the cathode flow model of the fuel cell through the predicted power obtained by the upper layer predictorst；
Step S42, calculating the air flow required by the air compressor of the fuel cell according to the following formula
Flow rate of oxygen consumed for fuel cell reaction:
Figure RE-FDA0003099488990000023
oxygen flow into the fuel cell cathode:
Figure RE-FDA0003099488990000024
humidity rate of fuel cell:
Figure RE-FDA0003099488990000025
peroxide ratio in fuel cell:
Figure RE-FDA0003099488990000026
in the formula (I), the compound is shown in the specification,
Figure RE-FDA0003099488990000031
is the molar mass of oxygen, MaIs the molar mass of air, ncellIs the number of fuel cells, F is the Faraday constant,
Figure RE-FDA0003099488990000032
is the ratio of the oxygen to the oxygen,
Figure RE-FDA0003099488990000033
is the flow of oxygen into the cathode of the fuel cell,
Figure RE-FDA0003099488990000034
is the oxygen flow, W, consumed by the fuel cell reactioncpIs the output flow of the air compressor of the fuel cell, Psat(Tatm) Is the saturation pressure at atmospheric temperature, PatmIs the pressure of the atmosphere and is,
Figure RE-FDA0003099488990000035
is the relative humidity in the atmosphere;
according to the formulas (4) to (7), if the fuel cell stack current I is determinedstAnd ratio of peroxide to oxygen
Figure RE-FDA0003099488990000036
The air flow required by the fuel cell air compressor to be output can be obtained:
Figure RE-FDA0003099488990000037
in the formula, MvIs the molar mass of the water vapor,
Figure RE-FDA0003099488990000038
is the mass fraction of oxygen in the air. The double-layer prediction control method of the full-power fuel cell air compressor as claimed in claim 1, wherein: the bottom layer model controller is specifically constructed as follows:
step S51, constructing a fuel cell air compressor model
Nonlinear air compressor model
Figure RE-FDA0003099488990000039
In the formula, PsmIs the pressure of the supply manifold, Tcp,outIs the temperature at the outlet of the compressor, Wsm,outIs the air flow rate, T, of the supply manifold outputsmIs the temperature of the supply manifold, ωcpIs the rotational speed of the compressor, JcpIs the moment of inertia, tau, of the air compressorcpIs the torque, τ, required to drive the air compressorcmIs the torque of the drive motor;
wherein the torque of the drive motor is calculated as:
Figure RE-FDA00030994889900000310
in the formula of UcmIs the supply voltage, η, of the air compressorcmIs the motor efficiency, KtIs the motor torque coefficient, KvIs the potential coefficient of the motor
② linear air compressor model
For P in formula (9)sm，msm，ωcpThe three state quantities are at point P °sm，m°sm，ω°cpTaylor expansion is adopted to obtain the following equation of state:
Figure RE-FDA0003099488990000041
Y＝CX(t)+DU(t)+W (12)
wherein X is [ P ]sm msm ωcp]TThe method comprises the following steps that (1) state vectors are respectively pressure, mass and rotating speed, U is a control quantity, namely voltage of an air compressor, Y is output flow of the air compressor, d (t) is an interference item, and a linear model of the air compressor is established by utilizing the state equation;
step S52, designing a bottom layer prediction controller according to the linear air compressor model
An objective function:
Figure RE-FDA0003099488990000042
setting a proper prediction time domain p and a proper control time domain m, endowing initial values of state variables and control variables to be zero, calculating a prediction control gain matrix, and calculating an error matrix on line through repeated circulation to enable a prediction controller to perform rolling optimization to obtain an optimal solution
Kmpc＝[Inu×nu 0 … 0]1×m(ST uΓT yΓySu+ΓT uΓu)-1ST uΓyΓT y (14)
Δu(k)＝KmpcEp(k+1|k) (15)
In the formula, ycIs the predicted output air flow, r is the flow reference value, Δ u is the control increment, u is the control voltage of the air compressor, Γy，ΓuWeight factor matrices, S, of the manipulated and controlled variables, respectivelyuIs a weighting matrix, KmpcIs a predictive control gain matrix, EpIs an error matrix.
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