A Finite-Time Smooth Switching Control Method for Aero Engines

Abstract

This invention belongs to the field of aero-engine control and discloses a finite-time smooth switching control method for aero-engines. Addressing the potential for control oscillations and state variable overshoot during switching between different operating points of an aero-engine, this invention smooths the control signal based on finite-time bounded theory to prevent oscillations. Furthermore, a controller is designed from the perspective of finite-time bounded theory to solve the problem of inadequate control of state variables after the control signal is smoothed, leading to state variable overshoot and excessive transient values. Based on the controller design using low-pass filter smoothing and dynamic output feedback, the overall system is analyzed using finite-time bounded theory, resulting in a linear matrix inequality for solving the controller gain matrix. This invention provides valuable experience for the smooth switching control and transient performance research of aero-engines and also has high practical engineering application value.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aero-engine control, and particularly relates to a limited time smooth switching control method of an aero-engine. BACKGROUND

[0002] An aero-engine is one of the core components of an airplane, and its performance is directly related to the safety, reliability and economy of the airplane. In order to realize accurate control and performance optimization of the aero-engine, more and more control methods are introduced into the field of aero-engine control.

[0003] The working process of an aero-engine has the characteristics of multiple modes. Different needs for different working states require controllers to be designed accordingly. For example, a low fuel consumption index is required in a cruising state, and a large thrust index is required in a take-off state. For an aero-engine system with multiple working states, controllers need to be designed for each state subsystem, and the influence of mode switching on system performance needs to be met to ensure that the overall system has good working states in switching.

[0004] However, the problems caused by switching control in actual engineering cannot be ignored. When the working state of the system changes, the discontinuity of the control output caused by the switching of the controller may cause the system to be subjected to transient impact, and even destroy the stability of the overall system. For example, for an aero-engine, the sudden change in fuel flow caused by the switching of the controller may lead to combustion instability, and then cause phenomena such as rich flameout and lean flameout. Therefore, avoiding the negative effects caused by the switching of the controller has become a very key problem, and the smooth switching method has become one of the popular research schemes for improving the oscillation problem of the control signal in the switching process of the aero-engine.

[0005] In addition, the traditional switching control theory research is based on asymptotic stability, which only guarantees whether the switching system converges, but does not care about the transient performance of the switching system. This means that the state trajectory of the switching system may have a large amplitude in a certain interval, which is not allowed in actual engineering. For example, when the rotor speed of an aero-engine has a very large overshoot, it may exceed the physical limit of the rotor at some time, thereby causing a huge disaster. In order to guarantee the transient state performance of the aero-engine and consider the influence of the switching of the controller on the working process of the engine, the present application studies a smooth switching control method in limited time based on limited time theory. The method can effectively guarantee the boundedness of the rotor speed of the aero-engine in the limited time interval, and improve the smoothness of the fuel flow at the mode switching time, thereby realizing better control effect of the aero-engine. SUMMARY

[0006] In order to avoid state variable overshoot and control quantity oscillation caused by switching of different working states of an aero-engine, the present application provides an aero-engine finite time smooth switching control method.

[0007] The technical solution of the present application is as follows: an aero-engine finite time smooth switching control method, comprising the following steps:

[0008] Step 1: linearized systems of different working points of an aero-engine are established, and the linearized systems of all working points are collectively referred to as aero-engine switching linear systems;

[0009]

[0010] wherein, is an increment of a rotor speed of the aero-engine, is an increment of fuel flow of the aero-engine, is an increment of a controlled rotor speed of the aero-engine, σ is a switching signal for switching of the linearized systems, and is a piecewise constant function, for any switching signal A i ,B i ,C i ,D i is a real matrix of a certain dimension;

[0011] Step 2: a dynamic output feedback controller of the aero-engine switching linear systems is established;

[0012]

[0013] wherein, is a controller state variable, is a real matrix to be determined;

[0014] Step 3: smooth switching of signals is realized through a low-pass filter, and an increment of fuel flow signal u(t) of the output of the dynamic output feedback controller is input into the low-pass filter, and the output is taken as a smooth switching control signal;

[0015]

[0016] wherein, K f is a gain of the low-pass filter, and x f is a low-pass filter state variable;

[0017] Step 4: states of the aero-engine switching linear systems are integrated, and the following is defined:

[0018]

[0019] Δx f (t)=xf (t)-D ci C i x(t)-C ci x c (t),

[0020] Further, the aero-engine switched linear system is represented as:

[0021]

[0022] where the system state matrix A ai is represented as:

[0023]

[0024] where,

[0025] A ai (3,1)=-D ci C i (A i +B i D ci C i )-C ci B ci C i ,

[0026] A ai (3,2)=-D ci C i B i C ci -C ci A ci ,

[0027] A ai (3,3)=-K f -D ci C i B i ,

[0028] Step 5: decoupling the system state matrix to extract all controller pending matrix solution, define the following matrix,

[0029]

[0030] then the system state matrix is represented as:

[0031]

[0032] Step 6: design Lyapunov function of aero-engine switched linear system, and design the condition of finite time boundedness of switched linear system;

[0033] design the following Lyapunov function,

[0034]

[0035] wherein, P σ(t) and Q are positive definite matrices;

[0036] The conditions for finite-time boundedness of the aero-engine switching system are designed as:

[0037] There exist constants a > 0, μ ≥ 1, T, constants c1, c2 satisfying c2 > c1 > 0, positive definite matrices P σ(t) and Q, and continuous functions V σ(t) : and two classes of K ∞ functions κ1 and κ2, such that:

[0038]

[0039] wherein, tk k is the kth switching time;

[0040] The average dwell time τ a of the switching signal satisfies the following condition:

[0041]

[0042] The switching linear system of the aero-engine is finite-time bounded for parameters (c1, c2, T, Q, σ); wherein, λ1 = λ min (P σ(t) ), λ2 = λ max (P σ(0) );

[0043] Step 7: Design linear matrix inequalities for solving the controller undetermined parameter matrices according to the conditions for finite-time boundedness in step 6, as follows:

[0044]

[0045]

[0046]

[0047] wherein, ε and ρ are constants satisfying the Schur complement condition when the Schur complement method is used to decouple the controller undetermined parameter matrices, * is used to omit the lower half of the symmetric matrix; the Schur complement method is represented as follows:

[0048] There exist real constants ε and real matrices W, X, Y, Z such that the following formula is true:

[0049]

[0050] Then the following formula is equivalent to:

[0051] W < 0

[0052] W + X T Y + Y T X < 0

[0053] Step 8: according to the linear matrix inequality designed in step 7, the target matrix R is solved ci And S ci , and finally the controller pending parameter matrix is obtained through , so that the smooth transition switching control of the aero-engine switching system is realized.

[0054] The beneficial effects of the present application: the present application proposes an aero-engine finite time smooth switching control method for the situation that different working point switching of the aero-engine may cause control quantity oscillation and state variable overshoot, based on the finite time bounded theory, the control signal is smoothed to prevent oscillation, and the controller is designed from the perspective of finite time bounded theory to solve the problem that the state variable control is not in place after the control signal is smoothed, thereby causing state variable overshoot and excessive transient value. On the basis of using a low-pass filter to smooth and designing a dynamic output feedback controller, the finite time bounded theory is used to analyze the whole system, so as to design a linear matrix inequality for solving the gain matrix of the controller. The aero-engine aerodynamic thermodynamic model is used for local working point linearization to obtain the linear model of different working points, so as to reasonably verify the control performance of the method. The present application smoothes the aero-engine control input based on a low-pass filter, combines the finite time bounded theory to design the controller, and constrains the transient value range of the state variable, which has high reliability. The present application provides certain experience for the smooth switching control and transient performance research of the aero-engine, and also has high practical engineering application value. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 The switching signal for guiding the switching of the modal of the aero-engine system;

[0056] Figure 2 The response curve of the high-pressure rotor speed and the low-pressure rotor speed of the aero-engine under the action of the controller to be solved; ΔN1 is the high-pressure rotor speed increment; and ΔN2 is the low-pressure rotor speed increment.

[0057] Figure 3 The state trajectory diagram of the high-pressure rotor speed and the low-pressure rotor speed of the aero-engine under the action of the controller to be solved, the trajectory is always within the range included by the dashed line;

[0058] Figure 4 The curve of the controller output fuel flow increment before and after smoothing by the low-pass filter. DETAILED DESCRIPTION

[0059] The application will be further described in conjunction with examples and drawings:

[0060] The specific implementation steps of each step are described in detail below.

[0061] 1) Establish a linear system of different working points of the aero-engine;

[0062]

[0063] wherein, is the rotor speed increment of the aero-engine, is the fuel flow increment of the aero-engine, is the controlled rotor speed increment of the aero-engine, for any A i ,B i ,C i ,D i is a real matrix of appropriate dimension, and σ: is a switching signal, which is a piecewise constant function;

[0064] 2) Establish a dynamic output feedback controller of the switching linear system of the aero-engine;

[0065]

[0066] wherein, is the controller state variable, is a real matrix to be determined;

[0067] 3) Use a low-pass filter to realize smooth switching of the signal, input the control signal of the dynamic output feedback controller into the low-pass filter, and output as the smooth switching control signal;

[0068]

[0069] wherein, K f is the gain of the low-pass filter, and x f is the low-pass filter state variable.

[0070] 4) In order to simplify the analysis, integrate each state of the switching linear system of the aero-engine, and define:

[0071]

[0072] Δx f (t)=x f (t)-D ci C i x(t)-C ci x c (t),

[0073] Further, the aero-engine switching linear system is represented as:

[0074]

[0075] wherein the system state matrix A ai is represented as:

[0076]

[0077] wherein,

[0078] A ai (3,1) = -D ci C i (A i +B i D ci C i )-C ci B ci C i ,

[0079] A ai (3,2) = -D ci C i B i C ci -C ci A ci ,

[0080] A ai (3,3) = -K f -D ci C i B i ,

[0081] 5) Decoupling the system state matrix to extract all controller pending matrices for easy solution, define the following matrix,

[0082]

[0083] then the system state matrix can be represented as:

[0084]

[0085] 6) Design the Lyapunov function of the aero-engine switching linear system, and design the condition of the switching system finite time bounded. Design the following Lyapunov function,

[0086]

[0087] wherein, P σ(t) and Q are positive definite matrices.

[0088] The time-bounded conditions for the aircraft engine switching system can be designed as follows:

[0089] There exist constants α > 0, μ ≥ 1, and a positive definite matrix P. σ(t) And Q, a continuous function V σ(t) : And two types of K ∞ Functions κ1 and κ2 make:

[0090]

[0091] If the average dwell time τ of the switching signal a satisfy:

[0092]

[0093] Therefore, the switching linear system of an aero-engine is finite-time bounded with respect to parameters (c1, c2, T, Q, σ). Where λ1 = λ min (P σ(t) ),λ2=λ max (P σ(0) ).

[0094] Verify the stability of the designed finite-time bounded conditions:

[0095] Integrating condition (8) yields:

[0096]

[0097] So V σ(t) (t) satisfies:

[0098]

[0099] Combining (10) and (11), we can conclude that:

[0100]

[0101] Furthermore, according to the finite time bounded condition (8), we know that:

[0102] ln(λ1c2)-ln(λ2c1)+αT-N0lnμ>0 (13)

[0103] According to the average dwell time condition (9) of the switching signal, we know that:

[0104]

[0105] Substituting (14) into (12) gives:

[0106]

[0107] It can be verified that the designed conditions enable the aero-engine switching system to satisfy the finite-time boundedness of parameters (c1, c2, T, Q, σ).

[0108] 7) Design a linear matrix inequality based on the finite-time bounded condition in step 6 to solve for the undetermined parameter matrix of the controller.

[0109] From condition (8), we can obtain the following matrix inequality:

[0110]

[0111] make Decoupling is achieved using the Schur complement method, and the following matrix is ​​defined:

[0112]

[0113]

[0114] The original matrix inequality can then be equivalent to the following matrix inequality:

[0115]

[0116]

[0117]

[0118] Decoupling is performed again using the Schur complement method, and the following matrix is ​​defined:

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] The original matrix inequality can then be equivalent to the following linear matrix inequality:

[0125]

[0126]

[0127]

[0128] 8) Based on the linear matrix inequality designed in 7), solve for the target matrix R. ci and S ci Finally passed The undetermined parameter matrix of the controller is obtained, thereby realizing the smooth transition switching control of the aero-engine switching system with finite time bounded.

[0129] 9) Simulation and Result Analysis

[0130] In this case, linearized models at two operating points of the aero-engine are selected for verification, as follows:

[0131]

[0132]

[0133] Set c1 to 1, c2 to 1.1, the finite time interval T to 10, N0 to 1, α to 0.5, β to 0.1, μ to 1.1, ε to 1, ρ to 1, and K... f The value is 10. Based on the above parameter settings, the average residence time τ is calculated. a The value is 0.5269s. The controller gain is obtained using the linear matrix inequality from step 8:

[0134]

[0135] A closed-loop system for an aero-engine at different operating points is built in Simulink. The output of a dynamic output feedback controller is connected to a low-pass filter, the output of the low-pass filter is connected to the aero-engine model, and the output of the aero-engine model is connected to the controller input.

[0136] By plotting the controller curve and the state variable trajectory, we can obtain... Figure 2 , Figure 3 , Figure 4 The result.

[0137] From Figure 3 As can be seen, the system's state trajectory is constrained within the range of c2, preventing excessively large transient values. Furthermore, it can be seen from... Figure 4 It can be seen that the system controller trajectory becomes smoother, and when switching is more frequent, the oscillation of the controller output signal is filtered out, effectively avoiding the adverse consequences caused by the oscillation of the aero-engine actuator.

[0138] This invention proposes a finite-time smooth switching control method for aero-engines. Results show that the filter and controller using this method in a linearized aero-engine model exhibit good transient performance and smooth control input. In summary, the method proposed in this invention achieves good application results.

Claims

1. A finite time smooth switching control method for an aeroengine, characterized in that, Specifically comprising the following steps: Step 1: Establish the linearized system of the aero-engine at different operating points, and the linearized systems of all operating points are collectively referred to as the switching linear system of the aero-engine; wherein, is the rotor speed increment of the aero-engine, is the fuel flow increment of the aero-engine, is the controlled rotor speed increment of the aero-engine, is a switching signal that switches each linearized system, and is a piecewise constant function, for any switching signal A i , B i , C i , D i are real matrices of dimension n x n. Step 2: Establish the dynamic output feedback controller of the switching linear system of the aero-engine; wherein, is a controller state variable, is a pending real matrix; Step 3: Realize the smooth switching of signals through a low-pass filter, input the fuel flow increment signal u(t) of the output of the dynamic output feedback controller into the low-pass filter, and output as the smooth switching control signal; where K f is the gain of the low-pass filter, x f is the low-pass filter state variable; Step 4: Integrate each state of the switching linear system of the aero-engine, and define: Δx f (t) = x f (t) - D ci C i x(t) - C ci x c (t) Further express the switching linear system of the aero-engine as: where the system state matrix A ai is represented as: Wherein, A ai (3,1) = -D ci C i (A i +B i D ci C i )-C ci B ci C i A ai (3,2) = -D ci C i B i C ci -C ci A ci A ai (3,3) = -K f -D ci C i B i Step 5: Decouple the system state matrix to extract all controller undetermined matrices for solving, define the following matrix, Then the system state matrix is expressed as: Step 6: Design the Lyapunov function of the switching linear system of the aero-engine, and design the condition for the finite time boundedness of the switching linear system; Design the following Lyapunov function, wherein P σ(t) and Q are positive definite matrices; The condition for the finite time boundedness of the switching linear system of the aero-engine is designed as: There exist constants a > 0, μ ≥ 1, a finite time interval T, constants c1, c2 satisfying c2 > c1 > 0, a positive definite matrix P σ(t) and Q, a continuous function V σ(t) : and two classes of K ∞ functions κ1 and κ2 such that: wherein t k is the kth switching instant; Average dwell time τ of the switching signal a when the following conditions are met: The switching linear system of the aero-engine is finite time bounded for parameters c1, c2, T, Q, σ; wherein λ1 = λ min (P σ(t) ), λ2 = λ max (P σ(0) ). Step 7: Design the linear matrix inequality according to the condition for the finite time boundedness in step 6, which is used to solve the undetermined parameter matrix of the controller, as follows: Wherein, ε and ρ are constants satisfying the Schur complement condition when the undetermined parameter matrix of the controller is decoupled by using the Schur complement method, * is used to omit the lower half of the symmetric matrix; the Schur complement method is expressed as: There exist real constants ε and real matrices W, X, Y, Z such that the following formula is established: Then it is equivalent to the following formula: Step 8: Solve for the target matrix R based on the linear matrix inequalities designed in Step 7. ci and S ci Finally passed The undetermined parameter matrix of the controller is obtained, thereby realizing the smooth transition switching control of the aero-engine switching system with finite time bounded.

Images