A Robust Control Method for the Full Envelope of a Variable Cycle Engine Based on Fuzzy Gain Scheduling

Abstract

The present invention discloses a full - envelope robust control method for a variable - cycle engine based on fuzzy gain scheduling, which includes the following steps: Step 1) Design the dynamic and steady - state performance characteristic parameters of the variable - cycle engine under the full envelope; Step 2) Use the intelligent clustering algorithm to optimize the number of rules of the fuzzy scheduling model and the nominal controller design points; Step 3) Use the SQP algorithm to optimize the robust controller gain at the nominal operating point; Step 4) Design a full - envelope fuzzy gain - scheduling robust controller based on the fuzzy scheduling rules and the nominal - point robust controller. The present invention considers the problem of designing a full - envelope controller in the variable - cycle engine control system. By designing the dynamic and steady - state performance characteristic parameters of the variable - cycle engine, using the intelligent clustering algorithm to optimize the number of rules of the fuzzy scheduling model and the nominal controller design points, and using the SQP algorithm to optimize the robust controller gain at the nominal operating point, a full - envelope fuzzy gain - scheduling robust controller is obtained, realizing the full - envelope control of the variable - cycle engine.

Description

Technical Field

[0001] The present invention belongs to the technical field of aeroengine control, and particularly relates to a full-envelope robust control method for a variable cycle engine based on fuzzy gain scheduling. Background Art

[0002] An aeroengine is a complex strongly nonlinear control object, and it is difficult to design an engine control system with a nonlinear control method. The traditional control methods for an aeroengine are designed based on a linear model, such as the PI / PID control method based on a transfer function model and the multivariable control method based on a state space model. However, with the development of electronic information technology and the increase in the complexity of combat missions, the operating range of an aeroengine is becoming wider and the flight missions are more complex and changeable, which poses challenges to the design of full-envelope control for the engine.

[0003] The traditional method for full-envelope control of an aeroengine is a gain scheduling method, that is, linear mathematical models are established at multiple steady-state operating points within the flight envelope, and a controller for the current steady-state operating point is designed based on this mathematical model. By selecting a relatively large number of steady-state operating points to establish corresponding controllers, the controller gain is designed as an interpolation table, and the controller gain under the current state is obtained by interpolation of the current flight state during full-envelope simulation. The control performance of the traditional interpolation table form gain scheduling method depends on the selected interpolation steady-state points, and it is rather troublesome to index the interpolation range during actual calculation. In addition, the method of online designing a controller based on an onboard model has also received certain attention. For an aeroengine, an onboard model within the full-envelope is first designed. This onboard model is usually a mathematical model designed for a controller or fault diagnosis, and commonly used ones include LPV models, balanced flow models, etc. Based on this type of linear onboard model, a linear state space model of the engine under the current flight state is obtained, and a controller is solved online based on this linear model. Since this method is a model-based method, it has high requirements for the accuracy of the onboard model, and this method solves the controller online, and has certain requirements for the algorithm complexity of solving the controller so as to meet the real-time performance of the control system.

[0004] Due to its intrinsically nonlinear characteristics, the fuzzy method has inherent advantages and shows good performance in solving such objects with complex structures and strong nonlinearity. Therefore, considering the design problem of a full-envelope controller for a variable cycle engine, a full-envelope robust control method for a variable cycle engine based on fuzzy gain scheduling is proposed. Summary of the Invention

[0005] Objective of the Invention: To overcome the problem of complex design of the full-envelope controller under complex operating conditions of a variable cycle engine, the present invention proposes a full-envelope robust control method for a variable cycle engine based on fuzzy gain scheduling. Considering the design problem of the full-envelope controller under complex operating conditions of a variable cycle engine, a full-envelope robust controller based on gain scheduling is obtained by combining a scheduling rule based on a T-S fuzzy model with an LQR robust controller. By using the above method, the design of the full-envelope controller under complex operating conditions of a variable cycle engine can be realized.

[0006] A full-envelope robust control method for a variable cycle engine based on fuzzy gain scheduling, comprising the following steps:

[0007] Step 1): Design the dynamic and steady-state performance characteristic parameters of the variable cycle engine under the full envelope.

[0008] Step 2): Optimize the number of rules of the fuzzy scheduling model and the nominal controller design points by using an intelligent clustering algorithm.

[0009] Step 3): Optimize the gain of the robust controller at the nominal operating point by using the SQP algorithm.

[0010] Step 4): Design a full-envelope fuzzy gain scheduling robust controller based on the fuzzy scheduling rule and the nominal point robust controller.

[0011] Further, the specific steps of the said Step 1) are as follows:

[0012] Step 1.1): Select the state variables as the high-pressure rotor speed n H , the low-pressure rotor speed n L , and the engine pressure ratio EPR; the control variables are the main combustion chamber fuel flow rate W f , the nozzle throat area A8, and the area A of the rear adjustable ejector 163 ; According to the component-level model of the variable cycle engine, use the small perturbation method to establish a three-input three-output state space model of the variable cycle engine, and the mathematical expression form of the model is as follows:

[0013]

[0014] Δy = CΔx + DΔu

[0015] where, the system coefficient matrix is a constant matrix A ∈ R of a known dimension 3×3 , B ∈ R 3×3 , C ∈ R 3×3 , D ∈ R 3×3 ;

[0016] Step 1.2): Obtain the transfer function model of the system according to the three-input three-output state space model, and the model is as follows:

[0017]

[0018] Step 1.3), according to Step 1.1) and Step 1.2), obtain the dynamic and steady-state performance characteristic parameters of the variable cycle engine designed based on the state space model and transfer function model; the transfer function matrix of the above three-input three-output state space model can be expressed as:

[0019]

[0020]

[0021] where A ij ∈R 3×3 is the adjoint matrix of matrix A, and |sI - A| is the determinant of matrix (sI - A); define the eigenvalue of matrix A close to the imaginary axis as the dominant eigenvalue λ:

[0022]

[0023] Describe the dynamic characteristics of the engine object with the dynamic characteristic parameter λ;

[0024] The steady-state gain of the transfer function is expressed as:

[0025]

[0026] Define the steady-state characteristic parameter Θ characterizing the steady-state performance of the system:

[0027]

[0028] Step 1.4), according to Step 1.1), establish a state space model with multiple steady-state points within the full envelope and calculate the engine dynamic and steady-state performance parameters defined in Step 1.3).

[0029] Furthermore, the specific steps in Step 2) are as follows:

[0030] Step 2.1), disassemble the real part and imaginary part of the dynamic characteristic parameter λ, and combine with the steady-state characteristic parameter Θ to form a three-dimensional characteristic space characterizing the engine characteristics;

[0031] Step 2.2), use the data in this three-dimensional characteristic space as the data set to be clustered, and use the AP algorithm to optimize the number of fuzzy rules in the envelope space;

[0032] Step 2.3), obtain the result after the iteration of the AP algorithm, and determine the number of fuzzy rules and the nominal operating point of the T-S fuzzy model.

[0033] Furthermore, the specific steps in Step 2.2) are as follows:

[0034] Step 2.2.1), calculate the similarity information between the i-th and j-th data points (x1, x2, x3,.......x n-1 , x n ) in the three-dimensional feature space, and the similarity is defined as the negative value of the Euclidean distance;

[0035] s(i,j) = -||x i - x j || 2 , i ≠ j, i = 1, 2,..., n, j = 1, 2,..., n

[0036] The similarity characterizes whether point j is suitable as the clustering center of point i; when i = j, the elements on the main diagonal of the similarity matrix are set to the same bias parameter, indicating that each data point has the same probability of becoming the clustering center at the initial moment; the bias parameter is generally set to the median of the elements of the similarity matrix or the minimum element of the similarity matrix;

[0037] Step 2.2.2), calculate the representative information r(i,j) sent from point i to point j, which characterizes the degree to which point i selects point j as its clustering center after considering other potential clustering centers;

[0038]

[0039] At the initial moment, the candidate information is set to zero;

[0040] Step 2.2.3), when data point j receives the information r(i,j) sent from point i, point j will give feedback to point i the candidate information a(i,j), which characterizes the ability of point j to prove itself as the clustering center of point i after receiving the information r(i,j);

[0041]

[0042] When i = j, the information a(j,j) is calculated as

[0043]

[0044] Step 2.2.4), set the damping coefficient θ ∈ [0, 1], and update the candidate matrix R k and the representative matrix A k , where R k , A k are the matrices composed of the representative information r(i,j) and the candidate information a(i,j) in the k-th iteration process respectively; the weighted update formula is as follows:

[0045] R k = (1 - θ) × R k + θ × R k-1

[0046] A k = (1 - θ) × A k + θ × A k-1

[0047] Step 2.2.5), the AP algorithm continuously transmits the above two types of information between data points until a stable clustering center is generated or the maximum number of iterations is reached, and then the algorithm is considered to converge to obtain the clustering result; the judgment condition for generating a stable clustering center is: r(i, j) + a(i, j) remains stable in several consecutive iterations; point j needs to meet the condition to be the clustering center of point i;

[0048]

[0049] That is, the potential center with the largest sum of the information transmitted between all potential centers and point i is taken as the clustering center of point i.

[0050] Furthermore, the specific steps in step 3) are as follows:

[0051] Step 3.1), design an LQR robust controller using the nominal operating point;

[0052] Step 3.2), design an SQP optimization performance index for the LQR robust controller at the nominal operating point. The performance index is as follows:

[0053]

[0054] where θ is a relatively large constant, and δ i (t) aims to suppress the overshoot problem in the dynamic process of the controller;

[0055] Step 3.3), optimize the LQR robust controller at the nominal point using the SQP algorithm according to the performance index defined in step 3.2).

[0056] Furthermore, the specific steps in step 3.1) are as follows:

[0057] Step 3.1.1), based on step 1.1), obtain the state - space model for the nominal operating point, augment the error between the tracking command and the output signal into the state variable, and establish the augmented state - space model;

[0058]

[0059]

[0060] where, Define

[0061] Step 3.1.2), design an LQR controller based on the augmented state-space model above. The form of the controller is as follows:

[0062]

[0063] Solve the Riccati equation by selecting appropriate Q and R matrices to obtain the controller gain. The Riccati equation is as follows:

[0064]

[0065] where the controller gain is:

[0066]

[0067] Partition the K matrix to obtain K X , K e .

[0068] Furthermore, the specific steps in step 4) are as follows:

[0069] Step 4.1), design the antecedent variables, membership functions, and consequent variables of the if-then rules in the T-S fuzzy scheduling model;

[0070] Step 4.2), based on the number of if-then rules and the optimal nominal point controller gain, establish an envelope-covering robust controller scheduled based on the T-S fuzzy model.

[0071] Beneficial effects: A variable cycle engine envelope-covering robust control method based on fuzzy gain scheduling provided by the present invention has the following technical effects compared with the prior art by adopting the above technical solutions:

[0072] (1) The purpose of the present invention is to perform envelope-covering control on a variable cycle engine. Based on the original dynamic and steady-state characteristics of the engine, an intelligent clustering algorithm is used in combination with a T-S fuzzy model to obtain a gain scheduling robust controller design method for a large range of the envelope. The designed controller is applicable to the entire envelope, multiple working conditions, and has good control effects.

[0073] (2) The present invention adopts an if-then rule number optimization method based on dynamic and steady-state characteristic parameters, which has the following advantages:

[0074] 1) The defined dynamic and steady-state parameters can fully characterize the dynamic and steady-state characteristics of the engine under the current working conditions;

[0075] 2) The if-then rule number optimization method based on the intelligent clustering algorithm can quickly and efficiently divide the data characteristics through an iterative method, obtaining good optimization effects;

[0076] 3) The result of the if-then rule number optimization method based on dynamic and steady-state characteristic parameters depends on the characteristics of the engine at different operating points. Compared with the traditional envelope characteristic division based on flight altitude, flight speed, or envelope range, the envelope characteristic extraction of this method is more scientific and has a theoretical basis. Description of the Drawings

[0077] Figure 1 Schematic diagram of the method flow of the present invention.

[0078] Figure 2 Object diagram of the method of the present invention.

[0079] Figure 3 Object operating envelope diagram of the method of the present invention.

[0080] Figure 4 Three-dimensional dynamic and steady-state performance characteristic parameter space diagram of the engine in the embodiment of the present invention.

[0081] Figure 5 Three-dimensional characteristic parameter space clustering result diagram of the engine in the embodiment of the present invention.

[0082] Figure 6 For the method of the present invention at H = 0m, Ma = 0, n Lc = 97% SQP optimized LQR control simulation diagram after optimization.

[0083] Figure 7 For the method of the present invention at H = 13000m, Ma = 1.2, n Lc = 93% SQP optimized LQR control simulation diagram after optimization.

[0084] Figure 8 Nominal controller low-pressure rotor speed loop regulation time diagram of the method of the present invention.

[0085] Figure 9 Nominal controller high-pressure rotor speed loop regulation time diagram of the method of the present invention.

[0086] Figure 10 Nominal controller engine pressure ratio loop regulation time diagram of the method of the present invention.

[0087] Figure 11 For the non-nominal point H = 2000m, Ma = 0.3, n in the embodiment of the present invention Lc = 95% control simulation diagram.

[0088] Figure 12 For the non-nominal point H = 4000m, Ma = 0.6, n in the embodiment of the present invention Lc = 97% control simulation diagram.

[0089] Figure 13In the embodiment of the present invention, the non-nominal point is H = 16000m, Ma = 1.2, and the control simulation diagram at n Lc = 95%.

[0090] Figure 14 The full-envelope simulation flight mission diagram in the embodiment of the present invention.

[0091] Figure 15 The full-envelope simulation result diagram in the embodiment of the present invention. Detailed implementation manners

[0092] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0093] According to Figure 1 , 2 , 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, the present embodiment proposes a full-envelope robust control method for a variable cycle engine based on fuzzy gain scheduling, including the following steps:

[0094] Step 1) Design the dynamic and steady-state performance characteristic parameters of the variable cycle engine under the full envelope. The specific design steps are as follows:

[0095] Step 1.1), select the state variables as the high-pressure rotor speed n H , the low-pressure rotor speed n L , and the engine pressure ratio EPR; the control variables are the main combustion chamber fuel flow rate W f , the nozzle throat area A8, and the area A of the rear adjustable ejector 163 ; based on the component-level model of the variable cycle engine, use the small perturbation method to establish a three-input three-output state space model of the variable cycle engine. The mathematical expression form of the model is as follows:

[0096]

[0097] Δy = CΔx + DΔu

[0098] Among them, the system coefficient matrix is a constant matrix A ∈ R with a known dimension 3×3 , B ∈ R 3×3 , C ∈ R 3×3 , D ∈ R 3×3 ;

[0099] Step 1.2), obtain the transfer function model of the system according to the three-input three-output state space model. The model is as follows:

[0100]

[0101] Step 1.3), based on Step 1.1) and Step 1.2), obtain the dynamic and steady-state performance characteristic parameters of the variable cycle engine designed by the state space model and the transfer function model; the transfer function matrix of the above three-input three-output state space model can be expressed as:

[0102]

[0103]

[0104] where A ij ∈R 3×3 is the adjoint matrix of matrix A, and |sI - A| is the determinant of matrix (sI - A); define the eigenvalue of matrix A close to the imaginary axis as the dominant eigenvalue λ:

[0105]

[0106] Describe the dynamic characteristics of the engine object with the dynamic characteristic parameter λ;

[0107] The steady-state gain of the transfer function is expressed as:

[0108]

[0109] Define the steady-state characteristic parameter Θ characterizing the steady-state performance of the system:

[0110]

[0111] Step 1.4), based on Step 1.1), establish a state space model with multiple steady-state points within the full envelope and calculate the engine dynamic and steady-state performance parameters defined in Step 1.3).

[0112] Step 2) Use the intelligent clustering algorithm to optimize the number of rules and the nominal controller design points of the fuzzy scheduling model. The specific steps are as follows:

[0113] Step 2.1), preprocess the engine dynamic and steady-state performance parameters obtained in Step 1.4), disassemble the real and imaginary parts of the dynamic characteristic parameter λ, and combine the steady-state characteristic parameter Θ to form a three-dimensional characteristic space characterizing the engine characteristics;

[0114] Step 2.2), use the data in this three-dimensional characteristic space as the data set to be clustered, and use the AP algorithm to optimize the number of fuzzy rules in the envelope space. The specific steps are as follows:

[0115] Step 2.2.1), calculate the n groups of data points (x1, x2, x3,.......x n-1 , x n) The similarity information between the midpoint i and the point j, where the similarity is defined as the negative of the Euclidean distance;

[0116] s(i,j) = -||x i -x j || 2 , i ≠ j, i = 1,2,...,n, j = 1,2,...,n

[0117] The similarity characterizes whether the point j is suitable as the clustering center of the point i; when i = j, the elements on the main diagonal of the similarity matrix are set to the same bias parameter, indicating that each data point has the same probability of becoming the clustering center at the initial moment; the bias parameter is generally set to the median of the elements of the similarity matrix or the minimum element of the similarity matrix;

[0118] Step 2.2.2), calculate the representative information r(i,j) sent from the point i to the point j, which characterizes the degree to which the point i selects the point j as its clustering center after considering other potential clustering centers;

[0119]

[0120] At the initial moment, the suitability information is set to zero;

[0121] Step 2.2.3), when the data point j receives the information r(i,j) sent by the point i, the point j will give feedback on the suitability information a(i,j) to the point i, which characterizes the ability of the point j to prove itself as the clustering center of the point i after receiving the information r(i,j);

[0122]

[0123] When i = j, the information a(j,j) is calculated as

[0124]

[0125] Step 2.2.4), set the damping coefficient θ ∈ [0,1], and update the suitability matrix R k and the representative matrix A k , where R k , A k are the matrices composed of the representative information r(i,j) and the suitability information a(i,j) respectively in the k-th iteration process; the weighted update formula is as follows:

[0126] R k = (1 - θ) × R k + θ × R k-1

[0127] A k = (1 - θ) × A k + θ × Ak-1

[0128] In step 2.2.5), the AP algorithm continuously transmits the above two types of information between data points until a stable clustering center is generated or the maximum number of iterations is reached, at which point the algorithm is considered to converge and the clustering result is obtained. The condition for judging the generation of a stable clustering center is that r(i, j) + a(i, j) remains stable in several consecutive iterations. For point j to be the clustering center of point i, it needs to meet the condition;

[0129]

[0130] That is, the potential center with the largest sum of the information transmitted between all potential centers and point i is taken as the clustering center of point i.

[0131] In step 2.3), obtain the result after the iteration of the AP algorithm, and determine the number of fuzzy rules and the nominal operating point of the T-S fuzzy model.

[0132] In step 3), use the SQP algorithm to optimize the gain of the nominal operating point robust controller. The specific steps are as follows:

[0133] In step 3.1), design an LQR robust controller using the nominal operating point. The specific steps are as follows:

[0134] In step 3.1.1), based on step 1.1), obtain the state-space model for the nominal operating point, augment the error between the tracking command and the output signal into the state variable, and establish the augmented state-space model;

[0135]

[0136]

[0137] Among them, Define

[0138] In step 3.1.2), design an LQR controller based on the above augmented state-space model. The form of the controller is:

[0139]

[0140] By selecting appropriate Q and R matrices and solving the Riccati equation, the controller gain is obtained. The Riccati equation is as follows:

[0141]

[0142] Among them, the controller gain is:

[0143]

[0144] The K matrix is partitioned to obtain KX , K e 。

[0145] Step 3.2), design the SQP optimization performance index for the nominal operating point LQR robust controller. The performance index is as follows:

[0146]

[0147] where θ is a relatively large constant, and δ i (t) aims to suppress the overshoot problem in the dynamic process of the controller;

[0148] Step 3.3), optimize the nominal point LQR robust controller using the SQP algorithm according to the performance index defined in Step 3.2).

[0149] Step 4) Design an all-envelope fuzzy gain-scheduling robust controller based on the fuzzy scheduling rule and the nominal point robust controller. The specific steps are as follows:

[0150] Step 4.1), design the antecedent variables, membership functions, and consequent variables of the if-then rules in the T-S fuzzy scheduling model;

[0151] Step 4.2), establish an all-envelope robust controller scheduled based on the T-S fuzzy model according to the number of if-then rules and the optimal nominal point controller gains.

[0152] For Figure 2 taking the steady-state control of a certain type of variable cycle engine shown as an example, based on the component-level model of the variable cycle engine's aerodynamic thermodynamics, select the state variables as the high-pressure rotor speed n H , the low-pressure rotor speed n L , and the engine pressure ratio EPR. The control variables are the main combustion chamber fuel flow rate W f , the throat area A8 of the nozzle, and the area A 163 of the rear adjustable ejector. Use the small perturbation method to establish a three-input three-output state space model of the variable cycle engine. Design the dynamic and steady-state characteristic characterization parameters of the engine based on this state space model, calculate the dynamic and steady-state characteristic characterization parameters within the three-dimensional envelope space, optimize the number of T-S fuzzy rules according to the intelligent clustering algorithm, and determine the steady-state operating points. For the design of the steady-state operating point controller, design the performance index and use SQP to optimize the performance of the nominal point LQR controller, thereby obtaining an all-envelope fuzzy gain-scheduling robust control method;

[0153] For Figure 2The establishment of a linear model for a certain type of variable cycle engine shown first determines its operating conditions and operating modes. For example, in the single-duct operating mode of the variable cycle engine, under the condition of 100% low-pressure rotor speed at the ground equilibrium point, the three-input three-output state space model established using the small perturbation method is as follows:

[0154]

[0155] C = I 3×3 , D = 0 3×3

[0156] The dominant eigenvalues calculated for this state space model are:

[0157] λ = -0.8596

[0158] Based on the above state space model, it is transformed into a transfer function matrix, and the steady-state gain is calculated as:

[0159] Θ = 1.1214

[0160] Based on Figure 3 the three-dimensional operating space of the variable cycle engine shown, a state space model of the steady-state point is established. In the three-dimensional envelope space, at intervals of 1000 m for altitude H, 0.1 for Ma, and 0.01 for the low-pressure conversion speed n Lc a total of 928 steady-state operating points are selected, and the dynamic and steady-state characteristic parameters of each steady-state operating point are calculated. The three-dimensional space of the dynamic and steady-state characteristic parameters formed is as shown in Figure 4 Using the AP algorithm, the dynamic and steady-state characteristic parameters in this three-dimensional space are clustered to obtain 25 clusters. Taking the two-dimensional plane of the steady-state gain and the real part of the dominant eigenvalue as an example, the distribution of the 25 clusters obtained by the AP algorithm is as shown in Figure 5 The 25 clusters indicate that there are 25 T-S fuzzy scheduling rules, and the operating state at the center of each cluster is the corresponding steady-state operating point. The specific steady-state operating points at the cluster centers are listed in the following table:

[0161] Table 1 Positions of the cluster center points of the full-envelope characteristic parameters

[0162]

[0163] For the above steady-state operating points, a nominal point LQR controller is designed, and the SQP algorithm is used to optimize this controller. By continuously adjusting the values of the Q and R matrices using the SQP algorithm, the following Riccati equation is solved:

[0164]

[0165] Thus, the LQR controller gain is obtained, and a component-level model simulation is carried out for this LQR controller to calculate the performance parameter J during the simulation process,

[0166]

[0167] where θ is a relatively large fixed constant, and the initial Q and R matrices are adjusted according to this performance index and the SQP algorithm, and finally the controller gains with excellent performance are obtained.

[0168] Taking the steady-state operating point of H = 2000m, Ma = 0.2, n Lc = 99% as an example, the controller gains obtained through SQP optimization are:

[0169]

[0170] Perform performance simulation on the optimized nominal point controller. At the ground design point of H = 0m, Ma = 0, n Lc = 97%, the simulation results are as Figure 6 , from Figure 6 it can be seen that the optimized LQR controller has good dynamic and steady-state performance, can quickly track the command signal, and the adjustment time t s is less than 5s, without overshoot and without steady-state error. At the high-altitude steady-state operating point of H = 13000m, Ma = 1.2, n Lc = 93% for simulation, the simulation results are as Figure 7 , Figure 7 also shows that the optimized LQR controller has good dynamic and steady-state performance, can quickly track the command signal, and the adjustment time t s is less than 5s, without overshoot and without steady-state error. Perform simulation on the optimized 25 nominal controllers and calculate their dynamic performance parameter adjustment time t s , the adjustment times of the three outputs are as Figures 8 - 10 , where Figure 8 represents the adjustment time of the nominal point controller of the low-pressure rotor speed n L loop, Figure 9 represents the adjustment time of the nominal point controller of the high-pressure rotor speed n H loop, Figure 10 represents the adjustment time of the nominal point controller of the engine pressure ratio EPR loop. From Figures 8 - 10 it can be seen that compared with the low-pressure rotor speed n L loop and the engine pressure ratio EPR loop, the adjustment time of the high-pressure rotor speed n H loop is longer, indicating that the response of the high-pressure rotor speed n H of this engine is slower, and correspondingly it can be obtained that the pressure ratio EPR of this engine has the fastest response. And at different steady-state operating points, there are also significant differences in the performance of the engine control system. The maximum adjustment time of the low-pressure rotor speed n L loop is 3.725s, and the minimum adjustment time is 2.25s. The high-pressure rotor speed nH The maximum adjustment time of the circuit is 7.075 s, and the minimum adjustment time is 4.05 s. The maximum adjustment time of the engine pressure ratio (EPR) circuit is 3.125 s, and the minimum adjustment time is 1.375 s.

[0171] Based on the nominal operating point controller gains optimized by the above SQP, a scheduling rule based on the T-S fuzzy model is designed. The antecedent variables of the T-S fuzzy model are selected as the total inlet temperature T t1 related to the engine characteristics, and the total inlet pressure P t1 . The designed if-then rules are as follows:

[0172]

[0173] Among them, the subscript 1 represents the first steady-state operating point, and the subscript 25 represents the 25th steady-state operating point. Combining all the above if-then rules, the expression form of the T-S fuzzy scheduling controller is obtained:

[0174]

[0175] Among them, h i (v(t)) represents the weight of the controller gain belonging to the i-th rule under the current antecedent variable v(t), and h i (v(t)) is defined as:

[0176]

[0177] Among them, μ i (v(t)) is the membership function:

[0178]

[0179] Component-level model simulation is carried out for the full-envelope scheduling controller based on the T-S fuzzy model. First, simulation verification is carried out at non-nominal steady-state operating points, and then simulation verification is carried out under a complete flight cycle in the full envelope. At non-nominal steady-state operating points H = 2000 m, Ma = 0.3, n Lc = 95%, H = 4000 m, Ma = 0.6, n Lc = 97%, H = 16000 m, Ma = 1.2, n Lc = 95% for simulation verification. The simulation results are as Figures 11 - 13 . As Figure 11 shown, at the operating point of H = 2000 m, Ma = 0.3, n Lc = 95%, this controller can quickly track the command signal, and the adjustment times of the response are: 3.375 s, 4.675 s, 2.95 s, and there is no steady-state error and overshoot in the response. As Figure 12As shown, at the operating point where H = 4000m, Ma = 0.6, n Lc = 97%, the controller can quickly track the command signal, and the response adjustment times are: 3.275s, 4.75s, 3.025s, with no steady-state error and no overshoot in the response. As Figure 13 shown, at the operating point where H = 16000m, Ma = 1.2, n Lc = 95%, the controller can quickly track the command signal, and the response adjustment times are: 3.175s, 6.275s, 1.825s, with no steady-state error and no overshoot in the response. The above simulations fully demonstrate that the proposed full-envelope control method still has good control quality at non-nominal operating points.

[0180] Next, full-envelope simulation verification is carried out, and the designed full-envelope flight mission is as Figure 14 shown. Based on Figure 14 the flight mission shown, the simulation results of the full-envelope scheduling controller based on the T-S fuzzy model are as Figure 15 . Figure 14 The operating points of the flight mission shown are as follows in the table:

[0181] Table 2 Steady-state operating points of the full-envelope flight mission

[0182]

[0183] It can be seen from Figure 15 that in the full-envelope flight mission simulation, this method still has good control quality and control performance. In the full-envelope flight mission, the controller not only faces external disturbances, but the nonlinearity and uncertainty brought about by the change of the engine operating characteristics will also increase the difficulty of controller design. Figure 15 It can be seen that the full-envelope controller designed by this method can quickly track the command signal. When performing a step simulation in the time period of 140 - 150s of the simulation, the adjustment times of the control system are calculated as: 0.82s, 1.25s, 0.825s. Under the action of external disturbances, there is a certain overshoot and steady-state error in the control system, but this error is small. The maximum tracking error of each loop during the controller simulation is: 0.0032, 0.0023, 0.0048, indicating that the controller still has excellent tracking performance during the rapid dynamic change process. It can be seen from the above simulation results that this method has certain engineering practicability and beneficial effects when facing the full-envelope control of the engine.

[0184] The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and what is described in the above embodiments and the specification is only to illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A full - envelope robust control method for variable - cycle engines based on fuzzy gain scheduling, characterized in that: It includes the following steps: Step 1) Design the dynamic and steady-state performance characteristic parameters of the fully-enveloped variable cycle engine; Step 2) Use the intelligent clustering algorithm to optimize the number of rules of the fuzzy scheduling model and the nominal controller design points; Step 3) Use the SQP algorithm to optimize the gain of the nominal operating point robust controller; Step 4) Design the fully-enveloped fuzzy gain scheduling robust controller based on the fuzzy scheduling rules and the nominal point robust controller; The specific steps of the above-mentioned Step 1) are as follows: Step 1.1), select the state variables as the high-pressure rotor speed n H , the low-pressure rotor speed n L , and the engine pressure ratio EPR; the control variables are the main combustion chamber fuel flow rate W f , the nozzle throat area A8, and the area A of the rear adjustable ejector 163 ; Based on the component-level model of the variable cycle engine, use the small perturbation method to establish a three-input three-output state space model of the variable cycle engine. The mathematical expression of the model is as follows: Δy = CΔx + DΔu Among them, the system coefficient matrix is a constant matrix A ∈ R of known dimension 3×3 , B ∈ R 3×3 , C ∈ R 3×3 , D ∈ R 3×3 ; Step 1.2), Obtain the transfer function model of the system according to the three-input three-output state space model. The model is as follows: Step 1.3), Design the dynamic and steady-state performance characteristic parameters of the variable cycle engine according to the state space model and the transfer function model obtained in Step 1.1) and Step 1.2). The transfer function matrix of the above three-input three-output state space model is expressed as: where A ij ∈R 3×3 is the adjoint matrix of matrix A, and |sI - A| is the determinant of matrix (sI - A); define the eigenvalue of matrix A close to the imaginary axis as the dominant eigenvalue λ: Use the dynamic characteristic parameter λ to describe the dynamic characteristics of the engine object; The steady-state gain of the transfer function is expressed as: Define the steady-state characteristic parameter Θ characterizing the steady-state performance of the system: Step 1.4), Establish the state space model of multiple steady-state points within the full envelope according to Step 1.1) and calculate the engine dynamic and steady-state performance parameters defined in Step 1.3); The specific steps in the above-mentioned Step 2) are as follows: Step 2.1), Decompose the real part and the imaginary part of the dynamic characteristic parameter λ, and combine with the steady-state characteristic parameter Θ to form a three-dimensional characteristic space characterizing the engine characteristics; Step 2.2), Use the data in this three-dimensional characteristic space as the data set to be clustered, and use the AP algorithm to optimize the number of fuzzy rules in the envelope space; Step 2.3), Obtain the result after the AP algorithm iteration, and determine the number of fuzzy rules and the nominal operating points of the T-S fuzzy model; The specific steps in the above-mentioned Step 2.2) are as follows: Step 2.2.1), calculate the similarity information between point i and point j among n groups of data points to be clustered (x1, x2, x3,.......x n-1 , x n ) in the three-dimensional feature space. The similarity is defined as the negative value of the Euclidean distance; s(i,j) = -||x i - x j || 2 , i ≠ j, i = 1, 2, ..., n, j = 1, 2, ..., n The similarity characterizes whether point j is suitable as the clustering center of point i. When i = j, the elements on the main diagonal of the similarity matrix are set to the same bias parameter, indicating that each data point has the same probability of becoming the clustering center at the initial moment. The bias parameter is generally set to the median of the elements of the similarity matrix or the minimum element of the similarity matrix; Step 2.2.2), Calculate the representative information r(i,j) sent from point i to point j, which characterizes the degree to which point i selects point j as its clustering center after considering other potential clustering centers; At the initial moment, the preference information is set to zero; Step 2.2.3), When data point j receives the information r(i,j) sent from point i, point j will give feedback to point i the preference information a(i,j), which characterizes the ability of point j to prove itself as the clustering center of point i after receiving the information r(i,j); When i = j, the information a(j,j) is calculated as Step 2.2.4), set the damping coefficient θ ∈ [0, 1], and update the candidate matrix R for each iteration k and the representative matrix A k , where R k , A k are matrices composed of the representative information r(i, j) and the candidate information a(i, j) in the k-th iteration process respectively; the weighted update formula is as follows: R k = (1 - θ) × R k + θ × R k-1 A k =(1 - θ)×A k + θ×A k-1 Step 2.2.5), The AP algorithm continuously transmits the above two types of information between data points until a stable clustering center is generated or the maximum number of iterations is reached, and then it is considered that the algorithm converges and the clustering result is obtained. The judgment condition for generating a stable clustering center is: r(i,j) + a(i,j) remains stable in several consecutive iterations. Point j needs to meet the conditions to be the clustering center of point i; That is, take the information transmitted between all potential centers and point i and the maximum potential center as the clustering center of point i; The specific steps in step 3) are as follows: Step 3.1), design an LQR robust controller using the nominal operating point; Step 3.2), design an SQP optimization performance index for the LQR robust controller at the nominal operating point. The performance index is as follows: Among them θ is a relatively large constant, δ i (t) is designed to suppress the overshoot problem in the dynamic process of the controller; Step 3.3), optimize the LQR robust controller at the nominal point using the SQP algorithm according to the performance index defined in step 3.2); The specific steps in step 3.1) are as follows: Step 3.1.1), based on the nominal operating point, obtain the state space model according to step 1.1), augment the error between the tracking command and the output signal into the state variable, and establish the augmented state space model; Among them, Define Step 3.1.2), design an LQR controller based on the augmented state space model above. The form of the controller is: Obtain the controller gain by solving the Riccati equation by selecting appropriate Q and R matrices. The Riccati equation is as follows: where the controller gain is: The K matrix is partitioned to obtain K X , K e ; The specific steps in step 4) are as follows: Step 4.1), design the antecedent variable, membership function, and consequent variable of the if-then rule in the T-S fuzzy scheduling model; Step 4.2), based on the number of if-then rules and the optimal nominal point controller gain, establish an envelope-to-envelope robust controller scheduled based on the T-S fuzzy model.

Images