Method for predicting internal temperature distribution in planar solid oxide fuel cell stacks

Abstract

This invention discloses a method for predicting the internal temperature distribution of a planar solid oxide fuel cell stack, belonging to the field of fuel cell technology. The method includes the following steps: establishing a nonlinear stack temperature model based on a mass conservation model, an energy conservation model, and an electrical characteristic model; linearizing the obtained nonlinear stack temperature model to obtain a linear stack temperature model; designing a Luenberger-sliding mode observer for monitoring the stack temperature based on the obtained linear stack temperature model; and collecting peripheral measurement data of the stack and inputting it into the Luenberger-sliding mode observer to obtain an estimated state of the internal temperature distribution of the stack. This invention predicts the internal temperature distribution of the stack using a Luenberger-sliding mode stack temperature observer, which has stronger error correction capabilities and faster convergence speed compared to existing temperature observers, significantly reducing the monitoring cost of the internal temperature distribution of the stack and ensuring efficient and stable operation of the stack.

Description

Technical Field

[0001] This invention relates to the field of fuel cell technology, and more specifically to a method for predicting the internal temperature distribution of a planar solid oxide fuel cell stack. Background Technology

[0002] Energy and environmental issues are two major challenges facing humanity today, and countries around the world are actively seeking reliable and clean energy conversion methods. Solid oxide fuel cells (SOFCs) offer high energy conversion efficiency, are not limited by the carnot cycle, and have a wide availability of fuel sources, making them one of the most attractive power generation methods after thermal power, hydropower, and nuclear power. However, many technical challenges remain to be overcome in the commercialization of SOFCs, the most notable of which is predicting the temperature distribution inside the stack.

[0003] The optimal operating temperature for SOFCs is generally around 750℃. Maintaining a suitable operating temperature is crucial for achieving high power generation performance and reducing degradation rates. Large temperature gradients within the stack can cause severe deformation or even breakage of the cells, affecting the stack's output performance. However, the high-temperature operating environment of the stack imposes extremely strict limitations on airtightness, and directly installing thermocouples inside the stack to obtain temperature information can lead to stack damage and high installation costs. Therefore, predicting the internal temperature distribution of the stack using limited and easily measurable external parameters is a highly effective solution.

[0004] Existing research has limited findings on predicting the internal temperature distribution of fuel cell stacks. Therefore, there is an urgent need to develop new prediction methods to accurately predict the internal temperature distribution of fuel cell stacks. Summary of the Invention

[0005] In view of this, the present invention provides a method for predicting the internal temperature distribution of a planar solid oxide fuel cell stack, which is used to accurately predict the internal temperature distribution of the stack.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for predicting the internal temperature distribution of a planar solid oxide fuel cell stack includes the following steps:

[0008] S1. Establish a nonlinear stack temperature model based on the mass conservation model, energy conservation model, and electrical characteristic model;

[0009] S2. Linearize the nonlinear stack temperature model obtained in step S1 to obtain a linear stack temperature model.

[0010] S3. Based on the linear stack temperature model obtained in step S2, design a Luenberger-sliding mode observer for observing the stack temperature.

[0011] S4. Collect peripheral measurement data of the fuel cell stack and input them into the Luneburg sliding mode observer to obtain the estimated state of internal temperature distribution of the fuel cell stack.

[0012] Preferably, step S1 specifically includes:

[0013] S11. Divide the single cell of the fuel cell stack into nodes according to the airflow direction, and perform mechanism modeling according to the nodes. Each node mechanism model consists of a mass conservation model, an energy conservation model, and an electrical characteristic model.

[0014] S12. Simplify the mechanism model of each node, including:

[0015] The mass conservation model is simplified by using the quasi-false state assumption method;

[0016] The energy conservation model is simplified by using the solid layer temperature equivalence method;

[0017] The electrical characteristic model is simplified using the equivalent resistance method;

[0018] S13. A nonlinear stack temperature model is constructed based on a simplified node mechanism model.

[0019] Preferably, step S2 specifically includes:

[0020] S21. Convert the nonlinear stack temperature model into a state-space model;

[0021] S22. Perform a Taylor series expansion at the steady-state operating point of the state-space model to obtain a linear stack temperature model.

[0022] Preferably, in step S3, the structural expression of the Lumberjack-sliding mode observer is as follows:

[0023]

[0024]

[0025]

[0026] In the formula: For the Romberg + sliding mode observer on temperature state variables The estimated value; This serves as the input for the linear fuel cell stack temperature model; Observation variables for linear fuel cell stack temperature model The estimated value, Here is the feedback gain matrix of the Luneburg observer. This is the feedback gain matrix of the sliding mode observer; Let be a nonlinear discontinuous term, where Indicates a positive scalar, Represents a symbolic function; , , All of these represent the coefficient matrix obtained from the state-space model.

[0027] Preferably, the feedback gain matrix of the Luneburg observer The solution is obtained through the following steps:

[0028] The estimated value of the Lundberg observer and temperature state variables By subtracting the values, we obtain the error dynamic equation of the Romberg observer:

[0029]

[0030] in, Observational bias The estimated value, ;

[0031] Solve the feedback gain matrix of the Lumberger observer based on the error dynamic equation of the Lumberger observer. .

[0032] Preferably, the feedback gain matrix of the Lumberjack observer is solved based on the error dynamic equation of the Lumberjack observer. Specifically, this includes using the pole placement algorithm to solve... , making Its eigenvalues ​​are negative.

[0033] Preferably, the feedback gain matrix of the sliding mode observer The solution is obtained through the following steps:

[0034] S311. Constructing a sliding mode observer:

[0035]

[0036]

[0037] In the formula, For sliding mode observers to the temperature state variable The estimated value; Observation variables for linear fuel cell stack temperature model The estimated value; This represents the nonlinear discontinuity term corresponding to the sliding mode observer;

[0038] The The specific expression is as follows:

[0039]

[0040] S312. Construct the state estimation error equation based on the sliding mode observer. and output estimation error ,in,

[0041]

[0042]

[0043] S313, Using the state estimation error equation The error system equations are obtained, and their expressions are as follows:

[0044]

[0045] S314, Error System Equation Based on Column Vector Pairs Decompose the system and obtain the decomposed error system equations:

[0046]

[0047]

[0048] in, This represents the design degrees of freedom of the sliding mode observer. , , , Represents the coefficient matrix Matrix parameters after coordinate transformation;

[0049] S315, will Substitute the expression , obtain Component expressions:

[0050]

[0051] in: Represents matrix parameters The OK, Represents matrix parameters The OK, express The One component;

[0052] S316, according to The component expression, when When each component converges to zero, the equivalent expression of the error system equation is obtained.

[0053]

[0054]

[0055] In the formula: Injecting equivalent error;

[0056] S317. Obtain the dynamic error equation of the sliding mode observer based on the equivalent expression of the error system equation:

[0057] ;

[0058] S318, Solve using the pole placement algorithm ,make The eigenvalue is negative, and through and relational expressions Get ,in It is an identity matrix.

[0059] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for predicting the internal temperature distribution of a planar solid oxide fuel cell stack, which has the following beneficial effects:

[0060] This invention designs a Luneburg-sliding mode fuel cell stack temperature observer to predict the internal temperature distribution of the fuel cell stack. Compared with existing temperature observers, this temperature observer has stronger error correction capabilities and faster convergence speed, which will greatly reduce the monitoring cost of the internal temperature distribution of the fuel cell stack and ensure the efficient and stable operation of the fuel cell stack. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0062] Figure 1 This is a schematic diagram of the overall process of the method provided in the embodiments of the present invention;

[0063] Figure 2 This is a schematic diagram illustrating the structure and working principle of a single SOFC cell provided in an embodiment of the present invention;

[0064] Figure 3 This is a schematic diagram of the same-direction flow node partitioning provided in an embodiment of the present invention;

[0065] Figure 4 Observation variables provided for embodiments of the present invention A flowchart illustrating the selection process;

[0066] Figure 5 A schematic diagram of the Luneburg-sliding mode observer system provided in an embodiment of the present invention. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] like Figure 1 As shown in the figure, an embodiment of the present invention discloses a method for predicting the internal temperature distribution of a planar solid oxide fuel cell stack, comprising the following steps:

[0069] S1. Establish a nonlinear stack temperature model based on the mass conservation model, energy conservation model, and electrical characteristic model;

[0070] S2. Linearize the nonlinear stack temperature model obtained in step S1 to obtain a linear stack temperature model.

[0071] S3. Based on the linear stack temperature model obtained in step S2, design a Luenberger-sliding mode observer for observing the stack temperature.

[0072] S4. Collect peripheral measurement data of the fuel cell stack and input them into the Luneburg sliding mode observer to obtain the estimated state of internal temperature distribution of the fuel cell stack.

[0073] This invention presents a Luenberger-sliding mode fuel cell stack temperature observer designed to predict the internal temperature distribution of the fuel cell stack. Compared with existing temperature observers, it has stronger error correction capabilities and faster convergence speed. Each step of this invention is further described below.

[0074] SOFCs are expensive, and conducting various tests on them directly carries significant risks. Therefore, it is necessary to establish a mathematical model that can accurately reflect the actual working condition of the stack. In this embodiment of the invention, the entire stack is divided into nodes, and a mass conservation sub-model, an energy conservation sub-model, and an electrical characteristic model are established for each node. The three sub-models are simplified by using quasi-false state assumptions, equivalent solid layer temperature, and equivalent resistance, respectively. The stack model is linearized at the steady-state operating point of the stack, and the state-space representation of the stack is obtained through a simple coordinate transformation.

[0075] A single solar cell consists of a PEN (cathode, electrolyte, anode), connectors, air channels, and fuel channels. Its structure and principle are illustrated in the diagram below. Figure 2 As shown.

[0076] Furthermore, such as Figure 3 As shown, the single cell nodes are divided. The unidirectional flow stack is divided into 5 nodes at equal intervals according to the direction of gas introduction. The mechanism model of each node consists of 3 sub-models: mass conservation, energy conservation, and electrical characteristics.

[0077] The three sub-models of mass conservation, energy conservation, and electrical properties will be explained separately below.

[0078] a. Mass conservation model

[0079] In the mass conservation sub-model, since the reaction rate of gas within the flow channel is extremely rapid, the chemical reaction can be considered to reach equilibrium instantaneously. Therefore, a quasi-static assumption is used for the nodes. The specific mathematical model expression for modeling is as follows:

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] In the formula: , , , They are the first Nodes ( The mole fractions of hydrogen, water, oxygen, and nitrogen in the gas. and The first Anode molar velocity and cathode molar velocity at each node , This represents the number of moles of substance participating in the reaction within the flow channel.

[0085] b. Energy conservation model

[0086] Each part of a single solar cell has different temperature dynamic response characteristics. The temperatures of the metal interconnect, PEN layer, and anode flow channel are unified as the solid layer temperature to establish a temperature dynamic model, while the air layer is established separately. The specific temperature dynamic models of the air layer and the solid layer are as follows:

[0087] No. The dynamic model of air layer temperature at each node is shown below:

[0088]

[0089] In the formula: For nodes The number of air moles inside, The average volumetric specific heat capacity of air. For nodes air temperature, and These represent the heat carried by the air flowing in and out of the preceding and following nodes, respectively. This represents the total amount of heat transferred between the air node and its adjacent nodes.

[0090] Solid layer The temperature dynamics model for each node is shown below:

[0091] ;

[0092] In the formula: , , These represent the density, volume, and specific heat capacity corresponding to the solid layer nodes. For nodes The temperature of the solid layer, For nodes The total amount of heat conducted between the node and its adjacent nodes. The total energy of the electrochemical reaction. The electrical energy released by the reaction.

[0093] c. Electrical characteristic model

[0094] In the electrical characteristic sub-model, the voltage at each node of a SOFC single cell is equal, which is equal to the open-circuit voltage minus the three polarization losses. The equivalent resistance replaces the three losses, and its specific expression is as follows:

[0095] ;

[0096] in the formula and These represent the operating voltage and node of a single cell, respectively. Operating voltage; The first Ohmic loss, activation loss, and concentration loss at each node. Indicates the first The equivalent resistance of each node. For nodes Total loss, For nodes The open-circuit voltage.

[0097] The simplified node mechanism model constructed by the above method constitutes a nonlinear stack temperature model, which needs to be converted into a linear stack temperature model.

[0098] First, the model is converted into a state-space model, whose abstract expression is as follows:

[0099] ;

[0100] ;

[0101] in, and These are the state variables and input variables of the fuel cell stack system, respectively:

[0102] ;

[0103] ;

[0104] In the formula: and These are the cathode gas inlet velocity and the anode gas inlet velocity, respectively.

[0105] As can be seen from the previously established fuel cell stack mechanism model, the different sub-models are highly coupled and exhibit strong nonlinearity, making them unsuitable for direct use in the design of temperature observers, especially at the steady-state operating point of the fuel cell stack. Expanding the model using a Taylor series and ignoring higher-order terms, its abstract expression is as follows:

[0106] ;

[0107] ;

[0108] in, , , , , Given the coefficient matrix after linearization, and after a simple coordinate transformation, the above model can be represented in the following state-space form:

[0109]

[0110]

[0111] in, , and Represent , and .

[0112] After obtaining the linear stack temperature model, a Luneburg-sliding mode observer was designed to monitor the stack temperature.

[0113] The selection of observed variables involves choosing an optimal set of parameters from readily measurable parameters surrounding the fuel cell stack and inputting them into the stack temperature observer. This selection directly impacts the overall performance of the temperature observer; different combinations of observed variables can significantly affect its prediction accuracy and overall performance. High performance of the temperature observer and the ease of measurement of the observed variables in practical engineering are two crucial criteria for selection. Therefore, studying how to select observed variables is an important prerequisite for ensuring good overall performance. The selection of observed variables for the stack temperature observer only requires considering measurable input variables. and output variables The selection of the input for the fuel cell stack temperature observer. The selection of the cathode gas flow rate is necessary because the model is linearized near the steady-state operating point of the fuel cell stack. Therefore, the fuel cell stack needs to operate in a specific state, which requires a specific cathode gas flow rate. and anode gas flow rate The input variable must be a definite value for the internal state of the fuel cell stack to be determined; therefore, the input variable... Select and Observed variables The selection process is as follows: Figure 4 As shown.

[0114] For observed variables The selection of the observation variables involves screening all combinations of observation variables from two perspectives: system observability and practical engineering significance. The observability of the fuel cell stack system is the primary consideration in the design of a fuel cell stack temperature observer. , Is it possible to completely observe the system matrix? , The decision, as can be seen from the state-space model, is that the system matrix... The value is fixed; the matrix The value of an uncertain observed variable Its value is uncertain, therefore the observed variable y determines the observability of the fuel cell system, and the matrix After the value is determined, the observability rank criterion is used to determine whether the system is observable. Once the system is observable, the optimal combination of output variables is determined based on the actual engineering significance and the condition number of the evaluation index for observation performance. The final observed variable Selecting the temperature state variable at the end of the fuel cell stack and .

[0115] The fuel cell stack temperature observer designed in this embodiment combines the feedback terms of the Luneburg observer and the sliding mode observer to form a new feedback term, constructing a novel Luneburg + sliding mode observer. This newly combined feedback term has stronger error correction capabilities and faster convergence speed. When applied to the observation subsystem, it improves the overall performance of the observer, especially significantly enhancing the robustness of the temperature observer. A schematic diagram of the observer control structure designed in this embodiment is shown below. Figure 5 As shown, it has the following structure expression:

[0116] ;

[0117] ;

[0118] ;

[0119] In the formula: For the Romberg + sliding mode observer on temperature state variables The estimated value; This serves as the input for the linear fuel cell stack temperature model; Observation variables for linear fuel cell stack temperature model The estimated value, Here is the feedback gain matrix of the Luneburg observer. This is the feedback gain matrix of the sliding mode observer; Let be a nonlinear discontinuous term, where Indicates a positive scalar, Represents a symbolic function; , , All of these represent the coefficient matrix obtained from the state-space model.

[0120] The parameter solving in the Luneburg + sliding mode observer designed in this implementation is crucial, as the matching of observer parameters directly determines the overall performance of the observer. The key parameter that needs to be solved is the Luneburg feedback gain matrix. Sliding mode feedback gain matrix and positive scalars in sliding mode feedback terms These key parameters need to be selected appropriately to ensure good observer performance, including the Lumberjack feedback gain matrix. As long as it makes If the eigenvalue is negative, then convergence is guaranteed. The specific calculation can be solved using the pole placement algorithm, positive scalar As long as it meets the requirements This ensures that sliding mode motion occurs, thus obtaining the equivalent error system. As long as you choose the right one make If the eigenvalue is negative, then the sliding mode observer estimate can be guaranteed. Converging to the actual value Find the right Then, through construction get The above method is used to obtain and Then, the Luneburg+ sliding mode observer was constructed.

[0121] Luneberger feedback gain matrix and sliding mode feedback gain matrix The specific solution process is as follows:

[0122] 1) Luneberg feedback gain matrix The pursuit

[0123] The estimated value of the Lundberg observer and system actual value Taking the difference yields the error dynamic equation:

[0124] ;

[0125] in, Observational bias The estimated value, Choose an appropriate feedback gain matrix. This makes the error dynamic equation globally stable and the state error tend to zero, while the system's poles and stability margin can be determined by giving different values. To adjust, just choose the appropriate make If the eigenvalue is negative, then the estimate of the Lundberg observer can be guaranteed. Converging to the actual value , The specific calculation can be solved using the pole placement algorithm.

[0126] (b) Sliding mode feedback gain matrix and the positive scalar in the sliding mode feedback term The pursuit

[0127] First, the coefficient matrix is ​​obtained based on the state-space model of the fuel cell stack. , , Apply coordinate transformation matrix For the coefficient matrix , , The coordinate transformation is performed, and the coordinate transformation matrix and expression are as follows:

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] in, The column spans the null space of C. It is an identity matrix.

[0133] The basic form of the sliding mode observer is as follows:

[0134] ;

[0135] ;

[0136] In the formula: for The estimated value, It is a nonlinear discontinuous term, specifically expressed as follows: ,in It is a positive scalar. It is a symbolic function.

[0137] definition and These are the state estimation error and the output estimation error, respectively. Defined in component form as:

[0138]

[0139] in: It is a positive real scalar. express The Each component.

[0140] design The purpose of this project is to make the system more sensitive to the sliding surface. Perform discontinuous switching, and make The motion trajectory tends to the sliding surface, let the sliding gain be... It has the following structure

[0141]

[0142] In the formula: This represents the design degrees of freedom of the observer. It is an identity matrix.

[0143] use The following error system can be obtained:

[0144] ;

[0145] Bundle Decompose into column vectors In this form, the error system is further... Decomposed into the following two equations:

[0146] ;

[0147] ;

[0148] Based on the expression for discontinuous phases, the above equation is... Transform into a component-based expression

[0149]

[0150] in: , They are respectively and No. OK.

[0151] Based on the component form above, we can obtain

[0152]

[0153] If scalar Large enough to satisfy:

[0154]

[0155] That would make This can guarantee It converges to zero in a finite amount of time, when When each component converges to zero, sliding motion occurs. Therefore, the error system can be equivalently written in the following form:

[0156] ;

[0157] ;

[0158] In the formula: To inject equivalent error, rearranging the two equations above, we obtain the following expression:

[0159] .

[0160] Select an appropriate feedback gain matrix This makes the above error dynamic equation globally stable, with the state error approaching zero, while the system's poles and stability margin can be determined by giving different... To adjust, just choose the appropriate make If the eigenvalue is negative, the estimated value of the sliding mode observer can be guaranteed. Converging to the actual value , The specific solution is obtained by using the pole placement algorithm. After passing It can be obtained The specific value.

[0161] In summary, the sliding mode feedback gain matrix and the positive scalar in the sliding mode feedback term The determination of has the following conclusion: regarding the positive scalar of sliding mode, as long as satisfies This ensures that sliding mode motion occurs, thus obtaining the equivalent error system. As long as you choose the right one make If the eigenvalue is negative, the estimated value of the sliding mode observer can be guaranteed. Converging to the actual value Find the right Then, through construction get The above method is used to obtain and Then, the Luneburg-sliding mode observer was constructed.

[0162] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0163] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of predicting temperature distribution inside a planar solid oxide fuel cell stack, characterized by, The method comprises the following steps: S1, establishing a nonlinear stack temperature model according to a mass conservation model, an energy conservation model and an electrical characteristic model; S2, linearizing the nonlinear stack temperature model obtained in step S1 to obtain a linear stack temperature model; S3, designing a Luenberger-sliding mode observer for observing the stack temperature based on the linear stack temperature model obtained in step S2; the structural expression of the Luenberger-sliding mode observer is as follows: where: is the estimate of the temperature state variable by the Luenberger + sliding mode observer; is the input to the linear stack temperature model; is the estimate of the observation variable of the linear stack temperature model, is the feedback gain matrix of the Luenberger observer, is the feedback gain matrix of the sliding mode observer; is a nonlinear discontinuous term, where represents the positive forward scalar, represents the sign function; , , all represent the coefficient matrices obtained from the state space model;​​ S4, collecting stack peripheral measurement data to input the Luenberger-sliding mode observer to obtain an estimated state of the stack internal temperature distribution.

2. The planar solid oxide fuel cell stack internal temperature distribution prediction method according to claim 1, characterized by Step S1 specifically comprises: S11, dividing a stack single cell into nodes according to an airflow direction, and modeling a mechanism according to the nodes; each node mechanism model is composed of a mass conservation model, an energy conservation model and an electrical characteristic model; S12, simplifying each node mechanism model, comprising: simplifying the mass conservation model by using a quasi-false state assumption method; simplifying the energy conservation model by using a solid layer temperature equivalent method; simplifying the electrical characteristic model by using an equivalent resistance method; S13, constructing a nonlinear stack temperature model based on the simplified node mechanism model.

3. The planar solid oxide fuel cell stack internal temperature distribution prediction method according to claim 1, characterized by Step S2 specifically comprises: S21, converting the nonlinear stack temperature model into a state space model; S22, performing Taylor series expansion at a steady state working point of the state space model to obtain a linear stack temperature model.

4. The planar solid oxide fuel cell stack internal temperature distribution prediction method according to claim 1, characterized by , the feedback gain matrix of the Luenberger observer , by solving The estimated value of the Luenberger observer and the temperature state variable Subtracting, the error dynamic equation of the Luenberger observer is obtained: wherein is an estimate of the bias of observation, ; Solving the feedback gain matrix of the Luenberger observer according to the error dynamic equation of the Luenberger observer .

5. The planar solid oxide fuel cell stack internal temperature distribution prediction method according to claim 4, characterized by , according to the error dynamic equation of the Longberg observer, the feedback gain matrix of the Longberg observer is solved , specifically comprising, using the pole placement algorithm to solve , so that The eigenvalue is negative.

6. The planar solid oxide fuel cell stack internal temperature distribution prediction method according to claim 1, characterized by , feedback gain matrix of the sliding mode observer , by solving the following steps: S311, constructing a sliding mode observer: wherein is an estimate of the temperature state variable by the sliding mode observer; is an estimate of the linear stack temperature model observation variable by the sliding mode observer; denotes the corresponding nonlinear discontinuity of the sliding mode observer;​​ The The specific expression is as follows: S312, constructing a state estimation error equation according to the sliding mode observer and an output estimation error wherein, S313, utilize state estimation error equation An error system equation is obtained, which is expressed as follows: S314, based on the column vector, an error system equation decomposition, obtain the error system equation after decomposition: wherein represents the design freedom of the sliding mode observer, , , , represents a coefficient matrix matrix parameters after coordinate transformation; S315, will Substitute the expression , obtain Component expressions: wherein: denotes the matrix parameter of the th row, denotes the matrix parameter of the th row, denotes the th component of ; S316、According to When each component of the component expression converges to zero, an equivalent expression of the error system equation is obtained: When each component of the component expression converges to zero, an equivalent expression of the error system equation is obtained: In the formula: is an equivalent error injection; S317, obtaining a dynamic error equation of the sliding mode observer according to an equivalent expression of an error system equation: S318, solve by pole placement algorithm make the eigenvalue of negative, and through the relationship expression of get where is the unit matrix.​

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