Active aero-engine surge control system based on second-order sliding mode control

Abstract

An active aero-engine surge control system based on second-order sliding mode control. The system involves the establishment of a compressor model which has an actuator, and the design of a second-order sliding mode controller. On the basis of the principle of high-order sliding mode control, the chattering problem during sliding mode control is inhibited while maintaining the advantages of the good robustness of a conventional sliding mode, such that the limitation of a relative order is eliminated, the control precision is improved, and quick active surge control with a strong anti-interference capability and a good robustness is realized. In addition to second-order sliding mode control, a linear item is also provided in a designed quick superhelix second-order sliding mode controller, such that not only is the chattering problem during sliding mode control effectively suppressed, but the convergence speed of the control system is also increased and the robustness of the system against unmatched uncertainty is enhanced. The designed controller can perform effective active anti-surge control and surge removal control, such that a compressor can stably operate in a region beyond a surge boundary, thereby expanding the operation range for the compressor, without the need to know the specified model of the compressor. The designed controller has a good robustness against uncertain factors such as unmodeled dynamics and system disturbances.

Description

An active control system for aircraft engine surge based on second-order sliding mode control Technical Field

[0001] The present invention belongs to the field of aircraft engine modeling and control, and relates to an aircraft engine surge active control system based on second-order sliding mode control. Background Art

[0002] Since the mid-20th century, with the advancement of science and technology and the development of society, the aviation industry has flourished. As the power source of modern aircraft, the performance of aircraft engines directly determines their performance and stability. The level of aircraft engine development is often considered a key indicator of national strength. Currently, aircraft engines are pursuing higher thrust-to-weight ratios and higher speeds, while also placing higher demands on operational stability. The compressor, a key component directly impacting its operational performance, has a stability that constrains the stable operating range of aircraft engines. According to basic compressor principles, the pursuit of high thrust-to-weight ratios and speeds will cause airflow separation within the compressor blade passages, leading to aerodynamic instability. Current research has identified surge and rotating stall as the two most common instabilities in aircraft engines. The occurrence of unstable flow patterns can rapidly reduce engine performance and efficiency. Furthermore, the vibration and temperature rise caused by unstable airflow clusters can place significant stress on the engine structure, significantly shortening its lifespan and increasing maintenance costs. In more severe cases, it can even cause engine failure, resulting in catastrophic consequences. Therefore, in order to effectively improve the thrust-to-weight ratio of the engine and expand its stable operating range, and avoid the occurrence of compressor instability, compressor active stability control technology has gradually become a research hotspot in this field.

[0003] To ensure stable engine operation, traditional engines primarily employ a combination of passive anti-surge control and de-surge control. The key concept of this control approach is to design the compressor away from the unstable operating point, leaving sufficient margin for instability, and to implement measures to bring the compressor out of the state of instability after it enters instability. However, this passive approach, while capable of stabilizing the engine, does so at the expense of engine performance, significantly limiting compressor performance and preventing it from realizing its full potential. The subsequently proposed active compressor stability control theory employs a control mechanism that detects the onset of instability disturbances before or at their initial stages. This controller then actively controls the compressor to suppress the development of these internal stall-initiating disturbances, thereby preventing instability. Compared to traditional passive control methods, active compressor stability control offers numerous advantages, including increasing engine operating speed and thrust-to-weight ratio, and improving performance at different speeds and operating conditions. Current active compressor stability control methods can be categorized into two types: modal-based control and nonlinear control. Modal control decomposes the compressor stall disturbance signal into multi-order modal waves, detects their amplitude and phase, and uses actuators to perform feedback control, thereby preventing the compressor from entering an unstable state. Nonlinear control treats the compressor system as a nonlinear system and uses nonlinear control theory to suppress the compressor stall disturbance, thereby preventing the occurrence of compressor instability. Therefore, a large number of researchers have combined nonlinear control theory with active compressor control for research, producing numerous results. Currently, the most widely used nonlinear control methods include backstepping control, sliding mode variable structure control, and intelligent control.

[0004] In most active control algorithms, the compressor system model is assumed to be known. Unmodeled system dynamics and internal and external disturbances can potentially render active control systems inoperable. Therefore, active control methods that account for various uncertainties have become a major research focus in compressor active stability control. Sliding mode variable structure control (VSC) has garnered widespread attention due to its exceptional robustness. It employs a control switching rule to switch between different control actions, generating a "sliding mode" state trajectory. This sliding mode motion is highly robust to parameter perturbations and external disturbances. However, the variable structure formulation makes sliding mode control susceptible to time and space lags, as well as system inertia, in practical applications. This leads to high-frequency oscillations during the control switching process, a prominent problem in sliding mode control. Chattering not only affects control accuracy and increases energy consumption, but also easily excites high-frequency unmodeled dynamics in the system, impairing system performance and even causing oscillations or instability, potentially damaging controller components. Consequently, research on chattering suppression has progressed alongside the development of sliding mode control theory. The methods are mainly divided into many methods, such as boundary layer method, reaching law method, filtering method, etc. Among them, high-order sliding mode control method, while maintaining the advantages of traditional sliding mode, completely solves the "black box" control problem when only the relative order of the system is known. At the same time, it can eliminate the defects of traditional sliding mode and has become a major research hotspot.

[0005] Summary of the Invention

[0006] Aiming at the poor anti-interference performance of compressor active stability control and the buffeting problem of sliding mode variable structure control in the prior art, the present invention proposes an active control system for aircraft engine surge based on second-order sliding mode control.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] An active control system for aircraft engine surge based on second-order sliding mode control is provided. The active control system mainly includes two parts: establishing a compressor model with an actuator and designing a second-order sliding mode controller. The design process of each part includes the following steps:

[0009] S1 builds a compressor model with an actuator

[0010] The compressor model is the foundation for the design of this aircraft engine's active surge control system. It describes the dynamic changes in pressure ratio, average flow rate, and flow disturbances, providing a basis for analyzing and determining compressor instability and designing control laws within the active stability control system. The compressor actuator is the controller's primary execution unit, applying active control to influence the compressor's pressure rise and flow rate to stabilize the system. The specific implementation process is as follows:

[0011] S1.1 The present invention adopts a first-order spatial Fourier truncated compressor Moore-Gretizer model, the mathematical model of which is shown in the figure below:

[0012] Where Ψ is the total static pressure rise coefficient of the compressor system; Φ is the average flow coefficient, Φ T Represents the average flow coefficient of the throttle valve; A is the square of the stall disturbance amplitude, that is, the axial disturbance velocity coefficient, which is used to describe the circumferential asymmetry of the compressor flow and can reflect the working state and circumferential characteristics of the compressor. C0 ,H,W are the compressor steady-state characteristic parameters, representing the pressure rise when Ψ=0, the half height of the compressor steady-state characteristic curve, and the half width of the compressor steady-state characteristic curve respectively. c ,m,α and B are all compressor structural parameters: B represents the Greitzer-B parameter, which is used to judge the instability state of the compressor; l c represents the effective length of the compressor and its upstream and downstream pipelines; α represents the size of the average lag of the compressor stage; ξ represents the dimensionless time; and m represents the parameter characterizing the length of the outlet pipeline.

[0013] The steady-state characteristic of a compressor refers to the steady-state pressure rise characteristic of the compressor in the absence of rotating stall and other non-uniformity effects. This characteristic is an axisymmetric characteristic of the compressor that is independent of disturbances and can be described by a cubic curve:

[0014] Among them, c represents the axisymmetric characteristic of the compressor that is independent of disturbances, Ψ C0 It represents the pressure rise when Ψ=0; Φ represents the average flow coefficient.

[0015] Φ T is the average flow coefficient of the throttle valve, which can be written as:

[0016] Among them, γ T is the throttle valve parameter.

[0017] From the mathematical model of the compressor, we know that the first equation shown in formula (1) is the balance equation of the local position of the compressor system, the second equation shown in formula (1) is the balance equation of the circumferential average, and the third equation shown in formula (1) is the mass continuity equation from the cavity to the throttle valve. At the same time, according to the basic principles and mathematical models of the compressor, when the derivatives of these three variables are When , the compressor system is in equilibrium. At this time, the equilibrium point of the compressor system is the intersection of the throttle valve characteristic line and the compressor steady-state characteristic line. The throttle valve characteristic line is shown in formula (3), which represents the relationship between the throttle valve pressure rise coefficient and the flow coefficient, as shown in Figure 4; the compressor steady-state characteristic is shown in formula (2), which represents the relationship between the compressor pressure rise coefficient and the flow coefficient in the absence of rotating stall and other non-uniformity effects, as shown in Figure 4.

[0018] S1.2 The present invention uses a close-coupled control valve as the actual actuator of the controller. The close-coupled control valve is a valve that is close to the compressor outlet. The function of the valve is the same as that of the compressor, which is to compress air. It is equivalent to a pure pressure drop at the compressor outlet. By controlling the close-coupled control valve, the pressure rise and flow coefficient of the compressor are changed, thereby affecting the change of the momentum and average flow of the compressor flow field. Ultimately, under the action of the control law, the compressor is prevented from entering an unstable state. Then the close-coupled control valve is introduced into the compressor model of step 1.1, and the compressor system model with the close-coupled control valve is finally derived as follows:

[0019] Among them, v is the pressure drop of the close-coupled valve, which is similar to the throttle valve and can be expressed as the following quadratic curve:

[0020] Among them, γ v It is the opening of the tight-coupled control valve.

[0021] According to the description of the equilibrium state of the compressor system in step 1.1, after the close-coupled control valve is introduced, the equilibrium point of the compressor also changes. Since the distance between the close-coupled control valve and the compressor outlet is short enough, the mass storage between the two can be ignored. Therefore, the present invention can regard the compressor and the close-coupled control valve as an equivalent compressor. In this case, the equivalent compressor pressure rise is equivalent to the compressor pressure rise minus the pressure drop of the close-coupled control valve. The steady-state characteristic Ψ of the equivalent compressor cm (Φ) can be calculated using the compressor steady-state characteristic Ψ c (Φ) and the characteristic Ψ of the close-coupled control valve v (Φ) represents: Ψ cm (Φ)=Ψ c (Φ)-Ψ v (Φ) (6)

[0022] At this point, the balance point of the compressor becomes the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line. The equivalent compressor steady-state characteristic line is shown in formula (6), which represents the relationship between the pressure rise coefficient and the flow coefficient of the equivalent compressor, as shown in Figure 4.

[0023] S1.3 According to the compressor model constructed in step 1.2, when no actuator is introduced, the equilibrium point of the compressor system is the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line:

[0024] According to the basic principles of compressors, when the system equilibrium point is located to the left of the maximum pressure ratio coefficient point in the compressor steady-state characteristic curve, the system will enter an unstable state under the influence of disturbances; when the system equilibrium point is located to the right of the maximum pressure ratio coefficient point in the compressor steady-state characteristic curve, the system will always remain stable. According to the compressor model constructed in step 1.2, after introducing the tightly coupled control valve, it can make the compressor steady-state characteristic line move up to become the equivalent compressor steady-state characteristic line. At this time, the equilibrium point of the compressor system also becomes the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line:

[0025] Among them, c Indicates the axisymmetric characteristics of the compressor that are independent of disturbances; Ψ v Indicates the relationship between the pressure rise coefficient and the flow coefficient of the close-coupled control valve; Ψ cm Represents the steady-state characteristics of the equivalent compressor.

[0026] Figure 4 shows the compressor characteristics for different tight-coupled control valve openings. The figure shows that the introduction of the tight-coupled control valve keeps the system equilibrium point to the right of the maximum point of the equivalent compressor steady-state characteristic line. This also shows that the tight-coupled control valve stabilizes the compressor system constructed in step 1.2.

[0027] S1.4 Like other physical systems, disturbances will occur in the compression system. The presence of disturbances may affect the stability of the compressor and may even cause the controller to malfunction. Therefore, when designing an active controller, disturbance suppression should also be taken into consideration. The disturbances in the compressor are mainly divided into pressure disturbances and flow disturbances. They are also divided into time-varying disturbances and offsets. This patent considers an offset, which is a constant negative mass flow / pressure disturbance that moves the balance of the compression system to the unstable area of ​​the compression diagram, resulting in surge or rotational stall. The pressure offset can be considered as a certain uncertainty in the steady-state characteristics of the compressor; and the mass flow offset can be considered as a certain uncertainty in the throttle valve. When these disturbances are introduced, the compressor system model shown in formula (4) becomes:

[0028] Among them, d ψ represents the external disturbance of the compressor pressure rise; d φ represents the external disturbance of the compressor flow; u represents the output of the tightly coupled control valve, which is also the controller output.

[0029] S2 design of second-order sliding mode controller

[0030] Sliding mode variable structure control is a highly robust control method. It employs a control switching rule and employs a variable structure to switch between different control actions, thereby generating a "sliding mode" state trajectory. This sliding mode motion is highly robust to parameter perturbations and external disturbances. Conventional sliding mode variable structure control can cause chattering due to its variable structure nature. High-order sliding mode control methods, however, maintain the invariance of traditional sliding mode control while suppressing chattering, eliminating relative order limitations and improving control accuracy.

[0031] S2.1 High-order sliding mode is actually a special type of motion on the integral manifold of a discontinuous dynamic system in the sense of Filippov.

[0032] Among them, s is the sliding manifold, that is, the sliding surface; is the first-order derivative of the sliding surface; is the second-order derivative of the sliding surface; s (r-1) is the r-1 derivative of the sliding surface; r is the dimension of the constraints of the dynamic system.

[0033] In other words, the above equation constitutes an r-dimensional constraint for the dynamic system. Our goal is to design a controller that satisfies this constraint so that the r-dimensional sliding set is nonempty. Assume it is a local integral set in the Filippov sense, meaning it consists of Filippov trajectories of the discontinuous dynamic system. In short, if this equation is satisfied, it is called an r-order sliding mode.

[0034] S2.2 Second-order sliding mode

[0035] The second-order sliding mode control method is the most widely used high-order sliding mode control algorithm because of its simple controller structure and the small amount of information required. In the second-order sliding mode control method, the control input explicitly appears in the second-order derivative of the sliding surface. In the control law, the form is based on s and Or the switching law of their sign functions, to ensure that the state of the system is stable on the sliding surface within a finite time The control law itself is continuous, which effectively suppresses chattering. The four most common algorithms in the second-order sliding mode are the Twisting algorithm, the Sub-Optimal algorithm, the Prescribed Convergence Law algorithm, and the Super-Twisting algorithm. The Super-Twisting algorithm in the second-order sliding mode algorithm adopted by the present invention has the following algorithm form:

[0036] Where u is the controller output; λ is a constant, which is the second-order sliding mode control parameter; s is the sliding surface; u1 is the intermediate variable of the second-order sliding mode controller, which is a variable structure form; β is a constant, which is the variable structure control parameter; is the derivative of the intermediate variable;

[0037] When the conditions are met:

[0038] The Super-Twisting algorithm converges. The phase trajectory of the Super-Twisting algorithm is shown in Figure 5. Where C is a constant; K m are constants, C and K m Guarantee the finite time stability of the second-order sliding mode control; λ is the second-order sliding mode control parameter.

[0039] S2.3 Second-order sliding mode controller design

[0040] S2.3.1 For the above system (9), it is divided into a flow subsystem and a pressure rise subsystem. First, the sliding surface s1 is designed for the flow subsystem: s1=Φ-Φ0 (13)

[0041] Among them, Φ is the average flow coefficient; Φ0 is the target flow value;

[0042] Taking the derivative of the sliding surface, we can get:

[0043] Continue to calculate the second-order derivative of the sliding surface:

[0044] The designed control law is:

[0045] Where, σ is the intermediate variable of the second-order sliding mode controller; Δ is the external disturbance of the system;

[0046] Then, a linear term is added to the superhelical algorithm to improve the convergence speed of the controller:

[0047] S2.3.2 Prove the stability of the control law and define the Lyapunov function as: V = 2η3|s| + η4s 2 +0.5σ 2 +0.5(η1|s| 0.5 sgn(s)+η2s-σ) 2 (18)

[0048] Among them, η1, η2, η3, and η4 are constants, representing the parameters of the fast superhelical controller; σ represents the intermediate variable of the controller, which is a variable structure form.

[0049] Written in quadratic form as follows:

[0050] The Lyapunov function satisfies the following relationship:

[0051] Among them, ||Γ||2 is the bi-norm of Γ; λ min {Q},λ max {Q} are the minimum and maximum eigenvalues ​​of the matrix Q, respectively. It can be seen that λ min {Q}>0,λ max {Q}>0. Taking the derivative of the Lyapunov function, we get:

[0052] Among them are The following form:

[0053] From equations (21) and (22), we can get:

[0054] If Γ T (AC)Γ and Γ T BΓ are all positive definite quadratic forms, then The necessary and sufficient condition is that all the ordered principal minors of matrices AC and B are greater than 0, It can be deduced that

[0055] When η1, η2, η3, η4 are constants and their values ​​satisfy equation (24), the eigenvalues ​​of matrices AC and B are both greater than 0. From equation (23), we can get

[0056] Where: coefficients λmin{AC}>0,λmin{B}>0 are the minimum eigenvalues ​​of matrices AC and B respectively. From formula (20), we can get

[0057] From equations (20), (25) and (26), we can get:

[0058] Since the parameters ξ1 and ξ2 in equation (27) are both greater than 0, it can be seen that the system state converges to s = 0, σ = 0 in a finite time. From expression (17), we can know that The perturbed fast super twisting algorithm converges to And the convergence time satisfies

[0059] Therefore, the system state can converge to the target equilibrium point in a finite time. Therefore, it can be concluded that the designed controller can make the entire compressor system stable.

[0060] From formula (27), we can see that when the Lyapunov function is close to the equilibrium point, the nonlinear term ξ1V 0.5 is much larger than the linear term ξ2V, and the convergence rate is mainly determined by the nonlinear term ξ1V 0.5 The Lipschitz property makes the system converge quickly. When the Lyapunov function is far away from the equilibrium point, the linear term ξ2V is much larger than the nonlinear term ξ1V 0.5 , the convergence rate is mainly determined by the linear term ξ2V, which is exponential convergence. The combination of nonlinear terms and linear terms makes the fast super twisting algorithm in this paper have a very fast convergence rate.

[0061] The above is the main design and calculation process of the aircraft engine surge active control system based on inverse sliding mode control designed by the present invention. The aircraft engine surge active control system designed by the present invention adopts a second-order sliding mode control method, which not only increases the system's robustness to mismatched uncertainty but also weakens the impact of the chattering problem in the sliding mode control. Then, a linear term is added to the super twisting algorithm, which has better convergence characteristics than the ordinary super twisting algorithm. It solves the chattering problem existing in the sliding mode controller, overcomes the compressor surge problem caused by chattering, and expands the effective operating range of the surge active controller, thereby achieving stable operation of the aircraft engine axial flow compressor within a wider operating range. This method greatly improves the success rate of active surge control and the stability of the compressor, and enhances the safety and reliability of the aircraft engine. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is a flow chart of the design of an active control system for aircraft engine surge based on second-order sliding mode control;

[0063] FIG2 is a schematic diagram of the structure of an aircraft engine surge active control system based on second-order sliding mode control;

[0064] FIG3 is a structural diagram of an aircraft engine surge active control system based on second-order sliding mode control in an embodiment of the present invention;

[0065] Figure 4 is a schematic diagram of the compressor characteristics under different injection flow coefficients after the introduction of the tight-coupled control valve. The solid line represents the steady-state characteristic curve of the compressor without the introduction of the tight-coupled control valve; the dot-dash line represents the steady-state characteristic curve of the compressor after the introduction of the tight-coupled control valve and the tight-coupled control valve opening γ v =1.6 when the equivalent steady-state characteristic curve of the compressor; the dotted line represents the compressor after the introduction of the close-coupled control valve, and the close-coupled control valve opening γv =2.16 The equivalent steady-state characteristic curve of the compressor; the two dotted lines indicate that the throttle valve opening is γ T =0.7 and γ T =0.62 when the throttle valve characteristic curve.

[0066] Figure 5 shows the active control process of surge under undisturbed conditions, wherein Figure (a) shows the change process of the local compressor flow coefficient when the fast super-helical second-order controller and the spiral algorithm second-order controller proposed in the present invention implement control under undisturbed conditions; Figure (b) shows the change process of the total pressure rise coefficient of the compressor when the fast super-helical second-order controller and the spiral algorithm second-order controller proposed in the present invention implement control under undisturbed conditions; Figure (c) shows the change process of the first-order modal amplitude when the fast super-helical second-order controller and the spiral algorithm second-order controller proposed in the present invention implement control under undisturbed conditions.

[0067] Figure 6 shows the active control process of surge under disturbance conditions, wherein Figure (a) shows the change process of the local compressor flow coefficient when the fast super helical second-order controller and the spiral algorithm second-order controller proposed in the present invention implement control under white noise disturbance conditions; Figure (b) shows the change process of the total pressure rise coefficient of the compressor when the fast super helical second-order controller and the spiral algorithm second-order controller proposed in the present invention implement control under white noise disturbance conditions; Figure (c) shows the change process of the first-order modal amplitude when the fast super helical second-order controller and the spiral algorithm second-order controller proposed in the present invention implement control under white noise disturbance conditions. DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the accompanying drawings and embodiments of the present invention.

[0069] An active control system for aircraft engine surge based on second-order sliding mode control is proposed. The control system mainly includes two parts: establishing a compressor model with an actuator and designing a second-order sliding mode controller. The design flow chart of the active control system for aircraft engine surge based on second-order sliding mode control is shown in Figure 1.

[0070] Figure 2 shows the schematic diagram of the active control system for aircraft engine surge based on backstepping sliding mode control. As can be seen from the figure, the controller mainly consists of two parts: establishing a compressor model with an actuator and designing a second-order sliding mode controller.

[0071] FIG3 is a structural diagram of an aircraft engine surge active control system based on second-order sliding mode control in this embodiment.

[0072] The specific implementation process includes the following steps:

[0073] The S1 compressor model is the foundation for the design of this aircraft engine's active surge control system. It describes the dynamic changes in pressure ratio, average flow rate, and flow disturbances, providing a basis for analyzing and determining compressor instability and designing control laws for the active stability control system. The compressor's actuator is the controller's primary execution unit, influencing the compressor's pressure rise and flow rate through active control to stabilize the system. The present invention utilizes an air jet with an independent air source as the actuator, and its specific implementation process is as follows:

[0074] S1.1 The present invention adopts a first-order spatial Fourier truncated compressor Moore-Gretizer model, the mathematical model of which is as follows:

[0075] Where, Φ is the average flow coefficient of the compressor system, Ψ is the total static pressure rise coefficient of the compressor system, A is the first-order modal amplitude, Φ T is the average flow coefficient of the throttle valve. The other parameters in the equation are inherent parameters of the compressor. Here we select the following values: C0 =0.30, H=0.14, W=0.25, l C =8.0, α=1 / 3.5, m=1.75.

[0076] According to the basic principles and mathematical models of the compressor, when the derivatives of these three variables are When , the system is in equilibrium. At this time, the equilibrium point of the compressor system is the intersection of the throttle valve characteristic line and the compressor steady-state characteristic line.

[0077] S1.2 The actuator used in this invention is a close-coupled control valve, a valve located close to the compressor outlet. The valve's function, like the compressor's, is to compress air, equivalent to a pure pressure drop at the compressor outlet. By controlling the close-coupled control valve, the compressor's pressure rise and flow coefficient are changed, thereby affecting the momentum and average flow rate of the compressor flow field. Ultimately, under the control of the control law, the compressor is prevented from entering an unstable state. Therefore, by introducing it into the compressor model of step 1.1, the compressor system model with a close-coupled control valve can be derived as follows:

[0078] where Ψ v The pressure rise effect brought by the jet device.

[0079] Based on the description of the compressor system's equilibrium state in Step 1.1, the introduction of the jet system changes the compressor's equilibrium point. The jet system now acts as a pure pressure rise at the compressor inlet. Therefore, the compressor and jet system can be considered an equivalent compressor. The compressor's equilibrium point now becomes the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line.

[0080] S1.3 According to the basic principles and mathematical models of compressors, without the introduction of an actuator, the equilibrium point of the compressor system is the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line. When the system equilibrium point is to the left of the maximum pressure ratio coefficient point on the compressor steady-state characteristic curve, the system is unstable; otherwise, the system is stable. The system equilibrium point is the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line. When the system equilibrium point intersects to the left of the maximum pressure ratio coefficient point on the compressor steady-state characteristic curve, the system enters an unstable state; otherwise, the system is stable. After the introduction of a tight-coupled control valve, it can shift the compressor steady-state characteristic line upward to the equivalent compressor steady-state characteristic line. At this time, the equilibrium point of the compressor system also becomes the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line. Figure 4 shows the compressor characteristics under different tight-coupled control valve openings. As can be seen from the figure, the introduction of the close-coupled control valve keeps the system equilibrium point to the right of the maximum point of the equivalent compressor steady-state characteristic line, which shows that the close-coupled control valve can stabilize the compressor system constructed in step 1.2.

[0081] S1.4 Like other physical systems, disturbances will occur in the compression system. Disturbances in the compressor are mainly divided into pressure disturbances and flow disturbances. They are also divided into time-varying disturbances and offsets. The present invention considers an offset, which is a constant negative mass flow / pressure disturbance that causes the balance of the compression system to move to the unstable area of ​​the compression diagram, resulting in surge or rotating stall. The pressure offset can be considered as a certain uncertainty in the steady-state characteristics of the compressor; and the mass flow offset can be considered as a certain uncertainty in the throttle valve.

[0082] S2 sliding mode variable structure control is a highly robust control method. It uses a control switching rule to switch between different control actions, thereby generating a "sliding mode" state trajectory. This sliding mode motion is highly robust to parameter perturbations and external disturbances. Conventional sliding mode variable structure control produces chattering due to its variable structure nature. High-order sliding mode control methods effectively suppress chattering based on traditional sliding mode control, so a high-order sliding mode algorithm is used to design the controller. The specific implementation process is as follows:

[0083] S2.1 High-order sliding mode is actually a special type of motion on an integral manifold of a discontinuous dynamic system in the sense of Filippov. The purpose of high-order sliding mode controller design is to ensure that the r-dimensional sliding set is non-empty, also known as r-order sliding mode. When r = 2, it is a second-order sliding mode. The Super-Twisting algorithm, a second-order sliding mode algorithm used in this embodiment, has the following algorithm form:

[0084] Then, a sliding surface is designed for the flow error, and a fast Super-Twisting control law is designed. That is, a linear term is added to improve the convergence speed of the controller. The algorithm is as follows:

[0085] The specific parameters are as follows: η1=10,η2=10,η3=20,η4=5 (33)

[0086] The simulation calculation results of this embodiment are shown in Figures 5 and 6: Figure 5 shows the surge active control process under undisturbed conditions, wherein Figure 5(a) shows the change process of the local compressor flow coefficient when the fast super-helical second-order controller and the spiral algorithm second-order controller proposed by the present invention are implemented under undisturbed conditions; Figure 5(b) shows the change process of the compressor total pressure rise coefficient when the fast super-helical second-order controller and the spiral algorithm second-order controller proposed by the present invention are implemented under undisturbed conditions; Figure 5(c) shows the change process of the first-order modal amplitude when the fast super-helical second-order controller and the spiral algorithm second-order controller proposed by the present invention are implemented under undisturbed conditions. Comparing the fast super-helical second-order controller proposed by the present invention with the spiral algorithm second-order controller, it can be seen from the figure that the fast super-helical second-order controller effectively improves the convergence speed of each state.

[0087] Figure 6 shows the surge active control process under disturbance conditions, where Figures 6(a), 6(b), and 6(c) have the same meanings as those described in Figure 5. The disturbance is a white noise disturbance. Under the influence of this disturbance, neither the fast superhelical second-order controller nor the spiral algorithm second-order controller experiences chattering. Both controllers can prevent the compressor from entering surge. Compared with the spiral algorithm second-order controller, the designed fast superhelical second-order controller effectively improves the convergence speed of each variable. At the same time, it is less affected by disturbances and has a smaller stability error. Therefore, it can be seen that the designed fast superhelical second-order controller improves the system's convergence speed and steady-state tracking accuracy, and has stronger anti-interference and robustness.

[0088] The above-described embodiments merely express the implementation methods of the present invention, but should not be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. An active control system for aircraft engine surge based on second-order sliding mode control, characterized in that: The active control system for aircraft engine surge includes two parts: establishing a compressor model with an actuator and designing a second-order sliding mode controller. The design process of each part includes the following steps: Step S1: establishing a compressor model with an actuator; Step S2 designs a second-order sliding mode controller.

2. The active control system for aircraft engine surge based on second-order sliding mode control according to claim 1, characterized in that: The steps S1 and S2 are specifically as follows: Step S1 establishes a compressor model with an actuator, as follows: S1.1 uses the first-order spatial Fourier truncated compressor Moore-Gretizer model, which is shown below: Where Ψ is the total static pressure rise coefficient of the compressor system; Φ is the average flow coefficient, Φ T Represents the average flow coefficient of the throttle valve; A is the square of the stall disturbance amplitude, that is, the axial disturbance velocity coefficient, which is used to describe the circumferential asymmetry of the compressor flow and can reflect the working state and circumferential characteristics of the compressor; Ψ C0 , H, W are the compressor steady-state characteristic parameters, representing the pressure rise when Ψ=0, the half-height of the compressor steady-state characteristic curve, and the half-width of the compressor steady-state characteristic curve respectively; l c ,m,α and B are all compressor structural parameters: B represents the Greitzer-B parameter, which is used to judge the instability state of the compressor; l c represents the effective length of the compressor and its upstream and downstream pipelines; α represents the size of the average lag of the compressor stage; ξ represents the dimensionless time; m represents the parameter characterizing the length of the outlet pipeline; The steady-state characteristics of the compressor are axisymmetric characteristics that are independent of disturbances and are described by cubic curves: Among them, c represents the axisymmetric characteristics of the compressor that are independent of disturbances, Ψ C0 It represents the pressure rise when Ψ=0; Φ represents the average flow coefficient; Φ T is the average flow coefficient of the throttle valve, which can be written as: Among them, γ T is the throttle valve parameter; From the above compressor model, it can be seen that the first equation in formula (1) is expressed as the balance equation of the local position of the compressor system, the second equation in formula (1) is expressed as the balance equation of the circumferential average, and the third equation in formula (1) is the mass continuity equation from the cavity to the throttle valve; at the same time, when the derivatives of the three variables are When , the compressor system is in equilibrium. At this time, the equilibrium point of the compressor system is the intersection of the throttle valve characteristic line and the compressor steady-state characteristic line; the throttle valve characteristic line is shown in formula (3), which represents the relationship between the throttle valve pressure rise coefficient and the flow coefficient; the compressor steady-state The characteristic is shown in formula (2), which represents the relationship between the pressure rise coefficient and the flow coefficient of the compressor without rotating stall and other non-uniformity effects; S1.2 uses a tightly coupled control valve as the actual actuator of the controller. By controlling the tightly coupled control valve, the pressure rise and flow coefficient of the compressor are changed, thereby affecting the change of the momentum and average flow of the compressor flow field, and finally preventing the compressor from entering an unstable state under the action of the control law; the tightly coupled control valve is introduced into the compressor model of step S 1.1, and finally the compressor system model with a tightly coupled control valve is derived as follows: Among them, v is the pressure drop of the close-coupled valve, which is similar to the throttle valve and can be expressed as the following quadratic curve: Among them, γ v It is the opening of the close-coupled control valve; According to the description of the equilibrium state of the compressor system in step 1.1, after the close-coupled control valve is introduced, the equilibrium point of the compressor also changes; the compressor and the close-coupled control valve are regarded as an equivalent compressor. At this time, the equivalent compressor pressure rise is equivalent to the compressor pressure rise minus the pressure drop of the close-coupled control valve; the steady-state characteristic of the equivalent compressor Ψ cm (Φ) Compressor steady-state characteristic Ψ c (Φ) and the characteristic Ψ of the close-coupled control valve v (Φ) means: P cm (F)=P c (F)-P v (F) (6) At this time, the balance point of the compressor becomes the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line; the equivalent compressor steady-state characteristic line is shown in formula (6), which represents the relationship between the pressure rise coefficient and the flow coefficient of the equivalent compressor; S1.3 According to the compressor model constructed in step 1.2, when no actuator is introduced, the equilibrium point of the compressor system is the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line: According to the compressor model constructed in step 1.2, after the close-coupled control valve is introduced, the compressor steady-state characteristic line moves up to become the equivalent compressor steady-state characteristic line. At this time, the balance point of the compressor system also becomes the intersection of the throttle valve characteristic line and the equivalent compressor steady-state characteristic line: Among them, c Indicates the axisymmetric characteristics of the compressor that are independent of disturbances; Ψ v Indicates the relationship between the pressure rise coefficient and the flow coefficient of the close-coupled control valve; Ψ cm represents the steady-state characteristics of the equivalent compressor; S1.4 When these disturbances are introduced, the compressor system model shown in formula (4) becomes: Among them, d ψ represents the external disturbance of the compressor pressure rise; d φ represents the external disturbance of the compressor flow; u represents the output of the close-coupled control valve, which is also the output of the controller; S2 designs a second-order sliding mode controller as follows: S2.1 uses formula (10) to form the r-dimensional constraint condition of the dynamic system. If the designed controller satisfies the constraint condition, it is called r-order sliding mode; Among them, s is the sliding manifold, that is, the sliding surface; is the first-order derivative of the sliding surface; is the second-order derivative of the sliding surface; s (r-1) is the r-1 derivative of the sliding surface; r is the dimension of the constraint condition of the dynamic system; S2.2 Second-order sliding mode The Super-Twisting algorithm in the second-order sliding mode algorithm is used, and its algorithm form is as follows: Among them, u is the controller output; λ is a constant, which is the second-order sliding mode control parameter; s is the sliding surface; u1 is the intermediate variable of the second-order sliding mode controller, which is a variable structure form; β is a constant, which is the variable structure control parameter; is the derivative of the intermediate variable; When the conditions are met: Then the Super-Twisting algorithm converges; Among them, C is a constant; K m are constants, C and K m Guarantee the finite time stability of the second-order sliding mode control; λ is the second-order sliding mode control parameter; S2.3 Second-order sliding mode controller design S2.3.1 For the compressor system model shown in formula (9), it is divided into a flow subsystem and a pressure rise subsystem. First, the sliding surface s1 is designed for the flow subsystem: s1=Φ-Φ0 (13) Among them, Φ is the average flow coefficient; Φ0 is the target flow value; After successively taking the derivative of the sliding surface and the second-order derivative of the sliding surface, the designed control law is: Among them, σ is the intermediate variable of the second-order sliding mode controller; Δ is the external disturbance of the system; Adding linear terms to the superhelical algorithm improves the convergence speed of the controller: S2.3.2 By verifying the stability of the control law, the system state can converge to the target equilibrium point in a finite time, and the designed controller can ensure the stability of the entire compressor system.

Images