Sliding Mode Control Method for Aeroengine Based on Linear Variable Parameter Model

Abstract

The present invention discloses a sliding mode control method for an aircraft engine based on a linear variable parameter model, including establishing a high-precision linear variable parameter model based on an aircraft engine component-level model and a state space model; designing a multivariable sliding mode speed tracking controller for realizing large-range tracking control; and digital simulation of the multivariable sliding mode speed tracking control method. The present invention realizes real-time updating of the state space coefficient matrix of the control system by establishing a linear variable parameter model of the aircraft engine, so as to solve the problem that the traditional sliding mode controller cannot realize large-range speed tracking. In this method, the method of updating the coefficient matrix using a linear variable parameter model is applicable to various main controllers, and has universal applicability to power mechanical systems with multiple adjustable variables.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft engine control, and in particular relates to an aircraft engine sliding mode control method based on a linear variable parameter model. Background Art

[0002] An aircraft engine is a highly complex nonlinear controlled object. Its working process is an extremely complex aerodynamic and thermodynamic process, and the engine characteristics will change greatly with changes in environmental conditions and working conditions. Therefore, the engine control system not only needs to have good robust performance within the full envelope, but also needs to achieve fast and high-precision tracking of instructions.

[0003] At present, sliding mode control is one of the control methods to solve the problem of aircraft engine tracking control. As a variable structure control method with strong robustness and strong anti-interference ability, it can not only ensure the stability of the system, but also achieve good control performance. However, since the design of the sliding mode control system requires the linear model of the engine in steady state to provide parameters, it can only have a good tracking effect on a small range of tracking instructions near the steady point, and cannot ensure that the system can achieve high-precision and high-reliability tracking when the instructions change in a large range, which greatly limits the application prospects of the sliding mode control method in aircraft engines. The sliding mode control method of aircraft engines based on the linear variable parameter model adds the linear variable parameter model to the sliding mode control system. While retaining the superior performance of the sliding mode controller such as strong robustness, the parameters in the control system are updated through the linear variable parameter model, ensuring that the system can also achieve fast and reliable tracking of large-range engine instruction changes, broadening the application scope of the aircraft engine multivariable sliding mode controller. Summary of the invention

[0004] Purpose of the invention: In order to solve the problem that a large range of speed tracking cannot be achieved in the multivariable sliding mode speed tracking control of aircraft engines, the present invention proposes an aircraft engine sliding mode control method based on a linear variable parameter model. On the basis of a main controller with good stability, robustness and tracking control response speed, a linear variable parameter model is established and added to update the state space coefficient matrix in the control system in real time to achieve a large range of rapid tracking of aircraft engine speed.

[0005] To achieve the above object, an aircraft engine sliding mode control method based on a linear variable parameter model comprises the following steps:

[0006] Step 1: Establish a linear variable parameter model;

[0007] Step 2: Design a speed tracking control system including a reference model and a sliding mode controller;

[0008] Step 3: Carry out digital simulation of multivariable sliding mode speed tracking control method.

[0009] Furthermore, the specific steps in step 1 are as follows:

[0010] Step 1-1: Under ground conditions, determine the normalized fuel flow rate W fsc and normalized nozzle throat area A 8sc The working range is shown in (1)

[0011]

[0012] In the formula, A 8sc,min , A 8sc,max are the minimum and maximum values ​​of the normalized tail nozzle throat area, W fsc,min , W fsc,max are the minimum and maximum values ​​of the normalized fuel flow rate, respectively. Several points are selected at equal intervals within the working range of the normalized tail nozzle throat area. At each tail nozzle throat area working point, within the working range of the normalized fuel flow rate, a normalized fuel flow rate W is selected at equal intervals. fsc , as a nominal point;

[0013] Step 1-2: Using the component-level model, at each nominal point, the aircraft engine state space model is established using the small perturbation method and the fitting method, and the model is normalized, as shown in formula (2):

[0014]

[0015] Where A, B, C, and D are dimensionally appropriate matrices, and Δx(t) = x(t) - x 0 (t), Δy(t)=y(t)-y 0 (t), Δu(t)=u(t)-u 0 (t). x(t), y(t), and u(t) are the actual state, output, and control quantities of the system. 0 (t), y 0 (t),u 0 (t) is the state quantity, output quantity and control quantity of the steady-state operating point. The state quantity of the aircraft engine includes the low-pressure rotor speed N L , high pressure rotor speed N H , the input includes the fuel flow W f , tail nozzle throat area A 8 , the output includes the low pressure rotor speed N L , high pressure rotor speed N H ;

[0016] Step 1-3: Select the high-pressure rotor speed N at the equilibrium point Hs and normalized nozzle throat area A 8scAs the scheduling parameter, the linear model between the operating points is calculated using the polynomial fitting method and the interpolation method to establish the linear variable parameter model of the aircraft engine. The form of the model is shown in (3)

[0017]

[0018] make

[0019]

[0020] In the formula, ρ is the scheduling parameter, x s (ρ), y s (ρ),u s (ρ) is the state quantity, output quantity and control quantity of the model at the steady-state operating point.

[0021] Step 1-4: Design a set of input signals within the range of the system control variables, input the input signals into the component-level model and the established linear variable parameter model, compare the output signals, and verify the accuracy.

[0022] Further, the specific steps of steps 1-3 are as follows:

[0023] Step 2-1: Establish the dimensions of the coefficient matrices A, B, C, and D in equation (3), and record the value of each element in each coefficient matrix at each normalized fuel flow operating point;

[0024] Step 2-2: Use polynomial fitting methods of different orders to fit each element in the coefficient matrix, and use the residual sum of squares as the fitting accuracy measure, combined with the fitting time considerations, to determine the polynomial fitting order;

[0025] Step 2-3: Fit each element of the coefficient matrix according to the established order to obtain the polynomial expression of each element of the coefficient matrix at each normalized tail nozzle throat area operating point.

[0026] Furthermore, the specific steps in step 2 are as follows:

[0027] Step 3-1: According to the design requirements of the sliding mode control method, consider augmenting the state quantity and input quantity. The augmented model is shown in (5)

[0028]

[0029] In the formula, is the augmented state quantity, C a =[CD] is the coefficient matrix after augmentation, I 2 is a 2×2 identity matrix;

[0030] Step 3-2: Design sliding mode function according to control objectives

[0031] s(t)=G(ρ)(x a (t)-x a_ref ) (6)

[0032] Where G(ρ) is the sliding mode coefficient matrix, x a_ref is the augmented state command signal. Design a uniform convergence law including the saturation function

[0033]

[0034] Where η i , i=1,2 is the switching gain, φ i , i=1,2 is the boundary layer thickness, sat(·) is the saturation function. Using the sliding mode control theory, the control rate expression of the speed tracking control system is obtained:

[0035]

[0036] In the formula, After integration, the control law of the sliding mode speed tracking control system is obtained;

[0037] Step 3-3: Design reference model

[0038]

[0039] In the formula, A, B, C, D are matrices of appropriate dimensions, x m (t) = [N Lm N Hm ] T ,u m (t) = [W fm A 8m ] T ,y m (t) = [N Lm N Hm ] T , the subscript m represents the variables of the reference model.

[0040] u m (t) = -Kx m (t)+Pr (10)

[0041] In the formula, K is the feedback gain matrix, P is the static filter gain matrix, and r is the target speed to be tracked. Let P be

[0042] P=[D-(C-DK)(A-BK) -1 B] -1 (11)

[0043] Step 3-4: Use the pole placement method to give the initial sliding mode coefficient matrix and feedback gain matrix, use the trial and error method to give the switching gain and boundary layer thickness, and calculate the static filter gain matrix by equation (11).

[0044] Furthermore, the specific steps of using the pole placement method to solve the initial sliding mode coefficient matrix in step 3-4 are as follows:

[0045] Step 4-1: Use similarity change to degrade the state space model. Introduce a reversible similarity change matrix T, so that

[0046]

[0047] The state space model of the aircraft engine under the z coordinate is shown in (13)

[0048]

[0049] Step 4-2: The sliding mode function (6) is expressed as (14) in the z coordinate

[0050] s(t)=G(ρ)x a (t) = G(ρ)T -1 z(t)=G z1 (ρ)z 1 (t)+G z2 (ρ)z 2 (t) (14)

[0051] In the formula, GT -1 =[G z1 G z2 ]. In sliding mode, G z2 As the scale factor, select G z2 = I. The form of the control rate (8) in the z coordinate is shown in (15)

[0052]

[0053] Step 4-3: Using the control rate (15) under the z coordinate and the aircraft engine state space model (13), the system dynamics model under the sliding mode is obtained as shown in (16):

[0054]

[0055] Based on (A 11 ,A 12 ) to obtain G z1 , we can get the expected sliding mode coefficient matrix G = [G z1 I]T.

[0056] Furthermore, the specific steps in step 3 are as follows:

[0057] Step 5-1: Obtain the flight altitude, Mach number and working state at the initial moment, and give the appropriate step tracking instruction r, simulation time k and simulation step t s , and initialize the simulation time t = 0;

[0058] Step 5-2: Obtain the state space model of the aircraft engine at the initial moment, set the pole position, and calculate the reference model feedback gain, static filter gain, and sliding mode coefficient;

[0059] Step 5-3: Use the reference model to solve the augmented state quantity instruction, calculate the control quantity according to the control law of the sliding mode controller, and obtain the output quantity after inputting the component level model;

[0060] Step 5-4: Obtain the control quantity solved by the sliding mode controller at the current moment and the high-pressure rotor speed output by the aircraft engine component-level model, normalize the control quantity, and input it into the linear variable parameter model;

[0061] Step 5-5: Calculate the elements of the coefficient matrix using the linear variable parameter model, update the coefficient matrix in the reference model and the sliding mode controller, and update the feedback gain and sliding mode coefficient according to the pole placement method;

[0062] Step 5-6: t = t + t s , repeat steps 5-2 to 5-5 until t=k.

[0063] Beneficial effects: The invention provides an aero-engine sliding mode control method based on a linear variable parameter model, which has the following technical effects compared with the prior art by using the above technical solution:

[0064] (1) The present invention adopts a single-loop control architecture to replace a multi-loop switching control architecture, and the control system architecture is simple and the design is simpler;

[0065] (2) The present invention adopts the technical means of introducing a linear variable parameter model to realize the large-range speed tracking control of the aircraft engine. Compared with the traditional sliding mode control technical means, it not only retains the strong robustness of the sliding mode control system, but also realizes the high-precision tracking control of the large-range speed changes of the aircraft engine through the real-time update of the control system parameters by the linear variable parameter model. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is the structural diagram of the aircraft engine sliding mode control system based on the linear variable parameter model.

[0067] Figure 2 It is the input signal of the linear variable parameter model under the flight conditions of H=0km and Ma=0.

[0068] Figure 3It is the low-pressure rotor speed response diagram of the linear variable parameter model under the flight conditions of H=0km, Ma=0.

[0069] Figure 4 It is the high pressure rotor speed response diagram of the linear variable parameter model under the flight conditions of H=0km, Ma=0.

[0070] Figure 5 Yes A 8sc =1 when a 11 Polynomial fitting results at different orders.

[0071] Figure 6 It is the tracking result of large-range changes in low-pressure rotor speed by sliding mode controller based on LPV model under flight conditions of H=0km, Ma=0.

[0072] Figure 7 It is the tracking result of large-range changes in high-pressure rotor speed by the sliding mode controller based on the LPV model under the flight conditions of H=0km, Ma=0. DETAILED DESCRIPTION

[0073] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0074] In order to solve the problem that the traditional multivariable sliding mode tracking control method of aircraft engines cannot achieve tracking control of large-scale instruction changes, the present invention proposes an aircraft engine sliding mode control method based on a linear variable parameter model. On the basis of a sliding mode control system with good stability, robustness and tracking control response speed, by adding a linear variable parameter model, the control system parameters are updated in real time, and high-precision and high-reliability tracking of large-scale instruction changes of aircraft engines is achieved.

[0075] Figure 1 The structure diagram of the aircraft engine sliding mode control system based on the linear variable parameter model used by the method of the present invention is shown. The specific implementation method of the present invention takes the design of the aircraft engine sliding mode control method based on the linear variable parameter model of a certain type of turbofan engine as an example. The design of the aircraft engine sliding mode control method based on the linear variable parameter model includes the following steps:

[0076] Step 1: Establish a linear variable parameter model;

[0077] Step 2: Design a speed tracking control system including a reference model and a sliding mode controller;

[0078] Step 3: Carry out digital simulation of multivariable sliding mode speed tracking control method.

[0079] Taking the initial working state of a certain type of turbofan engine at a ground state (H=0km, Ma=0) of 80.7% of the low-pressure rotor speed and 90.9% of the high-pressure rotor speed as an example, further, the specific steps in step 1 are as follows:

[0080] Step 1-1: Under ground conditions, determine the normalized fuel flow rate W fsc and normalized tail nozzle throat area A 8sc The working range is shown in (1)

[0081]

[0082] In the normalized tail nozzle throat area A 8sc In the working range, a point is selected every 0.1, that is, 6 working points of the tail nozzle throat area are selected. Under these 6 working points, a normalized fuel flow rate W is selected every 2%. fsc , as a nominal point, that is, each normalized tail nozzle throat area A 8sc 42 nominal points were selected under each working point;

[0083] Step 1-2: When the flight altitude is 0 km, the Mach number is 0, the low-pressure rotor speed is 80.7%, and the high-pressure rotor speed is 90.9%, the aircraft engine state space model is established by using the small perturbation and fitting method, and the model is normalized, as shown in formula (2):

[0084]

[0085] Where A, B, C, and D are dimensionally appropriate matrices, and Δx(t) = x(t) - x 0 (t), Δy(t)=y(t)-y 0 (t), Δu(t)=u(t)-u 0 (t). x(t), y(t), and u(t) are the actual state, output, and control quantities of the system. 0 (t), y 0 (t),u 0 (t) is the state quantity, output quantity and control quantity of the steady-state operating point. The state quantity of the aircraft engine includes the low-pressure rotor speed N L , high pressure rotor speed N H , the input includes the fuel flow W f , tail nozzle throat area A 8 , the output includes the low pressure rotor speed N L , high pressure rotor speed N H The coefficient matrices are shown in formula (2):

[0086]

[0087] Step 1-3: Select the high-pressure rotor speed N at the equilibrium point Hs and normalized tail nozzle throat area A 8sc As the scheduling parameter, the linear model between the operating points is calculated using the polynomial fitting method and the interpolation method to establish the linear variable parameter model of the aircraft engine. The form of the model is shown in (4)

[0088]

[0089] make

[0090]

[0091] In the formula, ρ is the scheduling parameter, x s (ρ), y s (ρ),u s (ρ) is the state quantity, output quantity and control quantity of the model at the steady-state operating point;

[0092] Step 1-4: Design a set of sinusoidal input signals with a period of 8s within the range of the system control variables. Set the value range of the normalized tail nozzle throat area in the control variable to 1-1.4, and the value range of the normalized fuel flow rate to 0.3-0.7. Input the input signal into the component-level model and the established linear variable parameter model, compare the output signal, and verify the accuracy.

[0093] The accuracy verification of the linear variable parameter model is as follows Figures 2 to 4 As shown in the figure, we can see that Figure 2 Under the input signal shown, the absolute value of the modeling error of the low-pressure rotor speed of the linear variable parameter model is less than 2%, and the absolute value of the modeling error of the high-pressure rotor speed is less than 3%, which has good modeling accuracy.

[0094] Furthermore, the specific steps in steps 1-3 are as follows:

[0095] Step 2-1: Confirm that the dimensions of the coefficient matrices A, B, C, and D in equation (4) are all 2-dimensional square matrices, and the coefficient matrices C and D satisfy set up Normalized tail nozzle throat area A 8sc =1 as an example, record the value of each element in the coefficient matrix A and B at each normalized fuel flow rate operating point;

[0096] Step 2-2: Use polynomial fitting methods of order 3, 4, and 5 to fit each element in the coefficient matrix, calculate the residual sum of squares of the fitting under each order, and consider the fitting time to determine that the polynomial fitting order is 4;

[0097] Step 2-3: Use a fourth-order polynomial to fit each element of the coefficient matrix, and obtain the polynomial expression of each element of the coefficient matrix at each normalized tail nozzle throat area operating point as shown in (6):

[0098]

[0099] Take element a in coefficient matrix A 11 For example, the fitting results under different order polynomials are as follows Figure 5 As shown. Taking a in the coefficient matrix 11 、a 12 、b 11 、b 12 Take as an example, the residual sum of squares of each element and each order is shown in Table 1. Figure 5 From Table 1, we can see that the higher the order, the higher the accuracy of the polynomial fitting. 12 In the fitting results of , the accuracy of the fitting results of each order is not much different. 11 In the fitting results, the third-order polynomial fitting result is poor, but the fourth-order and fifth-order polynomial fitting accuracy are close. Therefore, out of comprehensive consideration of fitting accuracy and time, the fourth-order polynomial is finally selected for fitting.

[0100] Table 1

[0101]

[0102] Furthermore, the specific steps in step 2 are as follows:

[0103] Step 3-1: According to the design requirements of the sliding mode control method, consider augmenting the state quantity and input quantity. The augmented model is shown in (7)

[0104]

[0105] In the formula, is the augmented state quantity, C a =[CD] is the coefficient matrix after augmentation, I 2 is a 2×2 unit matrix. In the initial working state, the augmented coefficient matrix is ​​shown in (8)

[0106]

[0107] Step 3-2: Design sliding mode function according to control objectives

[0108] s(t)=G(ρ)(x a (t)-x a_ref ) (9)

[0109] Where G(ρ) is the sliding mode coefficient matrix, x a_ref is the augmented state command signal. Design a uniform convergence law including the saturation function

[0110]

[0111] Where η i , i=1,2 is the switching gain, φ i , i=1,2 is the boundary layer thickness, sat(·) is the saturation function. Using the sliding mode control theory, the control rate expression of the speed tracking control system is obtained:

[0112]

[0113] In the formula, After integration, the control law of the sliding mode speed tracking control system is obtained.

[0114] Step 3-3: Design reference model

[0115]

[0116] In the formula, A, B, C, D are matrices of appropriate dimensions, x m (t) = [N Lm N Hm ] T ,u m (t) = [W fm A 8m ] T ,y m (t) = [N Lm N Hm ] T , the subscript m represents the variables of the reference model.

[0117] u m (t) = -Kx m (t)+Pr (13)

[0118] In the formula, K is the feedback gain matrix, P is the static filter gain matrix, and r is the target speed to be tracked. Let P be

[0119] P=[D-(C-DK)(A-BK) -1 B] -1 (14)

[0120] Step 3-4: The poles for solving the feedback gain matrix using the pole placement method are set to p 1 =[-7±5i], the pole point for solving the sliding mode coefficient is set to p 2 =[-5±5i], and the static filter gain matrix is ​​calculated by equation (10). The solution results of the three parameters in the initial state are shown in (15)

[0121]

[0122] The switching gain and boundary layer thickness results given by the trial and error method are shown in (16).

[0123]

[0124] Furthermore, the steps of using the pole placement method to solve the initial sliding mode coefficient matrix in step 3-4 are as follows:

[0125] Step 4-1: Use similarity change to degrade the state space model. Introduce the reversible similarity change matrix T as shown in (17)

[0126]

[0127] At this time, the coefficient matrix of the aircraft engine state space model under the z coordinate is shown in (18)

[0128]

[0129] Step 4-2: The sliding mode function (5) is expressed as (19) in the z coordinate

[0130] s(t)=G(ρ)x a (t) = G(ρ)T -1 z(t)=G z1 (ρ)z 1 (t)+G z2 (ρ)z 2 (t) (19)

[0131] In the formula, GT -1 =[G z1 G z2 ]. In sliding mode, G z2 is the proportional factor, which will not affect the dynamic characteristics of the system, so G is selected z2 =I. The form of the control rate in the z coordinate is shown in (20)

[0132]

[0133] Step 4-3: Use the control rate under the z coordinate and the aircraft engine state space model to obtain the system dynamics model under the sliding mode as shown in (21)

[0134]

[0135] Based on (A 11 ,A 12 ), set the pole to p 2 =[-5±5i], we get The expected sliding mode coefficient matrix can be obtained

[0136] Furthermore, the specific steps in step 3 are as follows:

[0137] Step 5-1: Obtain the flight altitude, Mach number and working status at the initial moment, given the simulation time k = 10s and the simulation step t s = 0.025s, and initialize the simulation time t = 0, and give the step tracking instruction at t = 2s

[0138] Step 5-2: Obtain the state space model of the aircraft engine at the initial moment, set the pole position, and calculate the reference model feedback gain, static filter gain, and sliding mode coefficient;

[0139] Step 5-3: Use the reference model to solve the augmented state quantity instruction, calculate the control quantity according to the control law of the sliding mode controller, and obtain the output quantity after inputting the component level model;

[0140] Step 5-4: Obtain the control quantity solved by the sliding mode controller at the current moment and the high-pressure rotor speed output by the aircraft engine component-level model, normalize the control quantity, and input it into the linear variable parameter model;

[0141] Step 5-5: Calculate the elements of the coefficient matrix using the linear variable parameter model, update the coefficient matrix in the reference model and the sliding mode controller, and update the feedback gain and sliding mode coefficient according to the pole placement method;

[0142] Step 5-6: t = t + t s , repeat steps 5-2 to 5-5 until t=k.

[0143] Digital simulation of sliding mode control of aircraft engines based on linear variable parameter model Figure 5 to Figure 6 As shown in the figure, it can be seen that the sliding mode control method of aircraft engines based on linear variable parameter models can achieve fast and high-precision tracking of large-range command signal changes of aircraft engines. Compared with the traditional aircraft engine multivariable sliding mode tracking control method, the sliding mode control method of aircraft engines based on linear variable parameter models retains the strong robustness and strong anti-interference ability of the sliding mode control method on the one hand, and on the other hand, the addition of the linear variable parameter model enables the reference model and sliding mode controller parameters in the control system to be updated in real time, thereby achieving high-precision tracking control of large-range engine speed changes.

[0144] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A sliding mode control method for aircraft engines based on a linear variable parameter model. Features: The following steps are involved: Step 1: Establish a linear variable parameter model; Step 2: Design a speed tracking control system including a reference model and a sliding mode controller; Step 3: Carry out digital simulation of multivariable sliding mode speed tracking control method; The specific steps of establishing the linear variable parameter model in step 1 are as follows: Step 1-1: Under ground state, normalize the fuel flow rate W fsc and the normalized nozzle throat area A 8sc whose working range is shown in (1) In the formula, A 8sc,min , A 8sc,max are the minimum and maximum values ​​of the normalized tail nozzle throat area, W fsc,min , W fsc,max are the minimum and maximum values ​​of the normalized fuel flow rate, respectively; several points are selected at equal intervals within the working range of the normalized tail nozzle throat area; at each tail nozzle throat area working point, within the working range of the normalized fuel flow rate, a normalized fuel flow rate W is selected at equal intervals fsc , as a nominal point; Step 1-2: Using the component-level model, at each nominal point, the aircraft engine state space model is established using the small perturbation method and the fitting method, and the model is normalized, as shown in formula (2): Where A, B, C, and D are dimensionally appropriate matrices, and Δx(t) = x(t) - x 0 (t), Δy(t)=y(t)-y 0 (t), Δu(t)=u(t)-u 0 (t); x(t), y(t), u(t) are the actual state quantity, output quantity and control quantity of the system, x 0 (t), y 0 (t),u 0 (t) is the state quantity, output quantity and control quantity of the steady-state operating point; the state quantity of the aircraft engine includes the low-pressure rotor speed N L , high pressure rotor speed N H , the input includes the fuel flow W f , tail nozzle throat area A 8 , the output includes the low pressure rotor speed N L , high pressure rotor speed N H ; Step 1-3: Select the high-pressure rotor speed N at the equilibrium point Hs and normalized tail nozzle throat area A 8sc As the scheduling parameter, the linear model between the operating points is calculated using the polynomial fitting method and the interpolation method to establish the linear variable parameter model of the aircraft engine. The form of the model is shown in (3) make In the formula, ρ is the scheduling parameter, x s (ρ), y s (ρ),u s (ρ) is the state quantity, output quantity and control quantity of the model at the steady-state operating point; Step 1-4: Design a set of input signals within the range of the system control variables, input the input signals into the component-level model and the established linear variable parameter model, compare the output signals, and verify the accuracy; The specific steps of designing a speed tracking control system including a reference model and a sliding mode controller in step 2 are as follows: Step 3-1: According to the design requirements of the sliding mode control method, consider augmenting the state quantity and input quantity. The augmented model is shown in (5) In the formula, is the augmented state quantity, C a =[CD] is the coefficient matrix after augmentation, I 2 is a 2×2 identity matrix; Step 3-2: Design sliding mode function according to control objectives s(t)=G(ρ)(x a (t)-x a_ref ) (6) Where G(ρ) is the sliding mode coefficient matrix, x a_ref For the augmented state command signal; design a uniform reaching law including a saturation function Where η i , i=1,2 is the switching gain, φ i , i=1,2 is the boundary layer thickness, sat(·) is the saturation function; using the sliding mode control theory, the control rate expression of the speed tracking control system is obtained In the formula, After integration, the control law of the sliding mode speed tracking control system is obtained; Step 3-3: Design reference model In the formula, A, B, C, D are matrices of appropriate dimensions, x m (t) = [N Lm N Hm ] T ,u m (t) = [W fm A 8m ] T ,y m (t) = [N Lm N Hm ] T , the subscript m represents the variables of the reference model; u m (t)=-Kx m (t)+Pr (10) Where K is the feedback gain matrix, P is the static filter gain matrix, and r is the target speed to be tracked; Let P be P=[D-(C-DK)(A-BK) -1 B] -1 (11) Step 3-4: Use the pole placement method to give the initial sliding mode coefficient matrix and feedback gain matrix, use the trial and error method to give the switching gain and boundary layer thickness, and calculate the static filter gain matrix by equation (11); The specific steps of carrying out digital simulation of the multivariable sliding mode speed tracking control method in step 3 are as follows: Step 5-1: Obtain the flight altitude, Mach number and working state at the initial moment, and give the appropriate step tracking instruction r, simulation time k and simulation step t s , and initialize the simulation time t = 0; Step 5-2: Obtain the state space model of the aircraft engine at the initial moment, set the pole position, and calculate the reference model feedback gain, static filter gain, and sliding mode coefficient; Step 5-3: Use the reference model to solve the augmented state quantity instruction, calculate the control quantity according to the control law of the sliding mode controller, and obtain the output quantity after inputting the component level model; Step 5-4: Obtain the control quantity solved by the sliding mode controller at the current moment and the high-pressure rotor speed output by the aircraft engine component-level model, normalize the control quantity, and input it into the linear variable parameter model; Step 5-5: Calculate the elements of the coefficient matrix using the linear variable parameter model, update the coefficient matrix in the reference model and the sliding mode controller, and update the feedback gain and sliding mode coefficient according to the pole placement method; Step 5-6: t = t + t s , repeat steps 5-2 to 5-5 until t=k.

2. The sliding mode control method for an aircraft engine based on a linear variable parameter model according to claim 1, Features: The specific steps of establishing the linear variable parameter model under each normalized tail nozzle throat area in step 1-3 are as follows: Step 2-1: Establish the dimensions of the coefficient matrices A, B, C, and D in equation (3), and record the value of each element in each coefficient matrix at each normalized fuel flow operating point; Step 2-2: Use polynomial fitting methods of different orders to fit each element in the coefficient matrix, and use the residual sum of squares as the fitting accuracy measure, combined with the fitting time considerations, to determine the polynomial fitting order; Step 2-3: Fit each element of the coefficient matrix according to the established order to obtain the polynomial expression of each element of the coefficient matrix at each normalized tail nozzle throat area operating point.

3. The sliding mode control method for an aircraft engine based on a linear variable parameter model according to claim 1, Features: The specific steps of using the pole placement method to give the initial sliding mode coefficient matrix in step 3-4 are as follows: Step 4-1: Use similarity changes to degrade the state space model and introduce a reversible similarity change matrix T so that The state space model of the aircraft engine under the z coordinate is shown in (13) Step 4-2: The sliding mode function (6) is expressed as (14) in the z coordinate s(t)=G(ρ)x a (t)=G(ρ)T -1 z(t)=G z1 (ρ)z 1 (t)+G z2 (ρ)z 2 (t) (14) In the formula, GT -1 =[G z1 G z2 ]; In sliding mode, G z2 As the scale factor, select G z2 =I; the form of the control rate (8) in the z coordinate is shown in (15) Step 4-3: Using the control rate (15) under the z coordinate and the aircraft engine state space model (13), the system dynamics model under the sliding mode is obtained as shown in (16): Based on (A 11 ,A 12 ) to obtain G z1 , we can get the expected sliding mode coefficient matrix G = [G z1 I]T.

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