Limit protection control method for aero-engine

Abstract

The invention provides an aero-engine limit protection control method, and belongs to the technical field of aero-engine control. Through the design of the main controller and the limiting controller, the effects of high-pressure rotor rotating speed tracking and turbine outlet temperature limiting are achieved respectively, the Lyapunov function is designed, the stability of a closed-loop system is analyzed under the constraint of the average residence time, controller parameter conditions meeting stability analysis are obtained through solution of an inequality, and the stability of the system is improved. According to the method, the purpose of limiting protection control of the aero-engine in the transition stage can be achieved, the safety of an aero-engine control system is improved, meanwhile, the stability of the aero-engine limiting protection control system is analyzed theoretically, and the reliability of engineering application is improved.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft engine control, and in particular to a novel limiting protection control method. Background Art

[0002] As a propulsion power device, aircraft engines are widely used in important and critical fields. In a public research report by NASA, the control system of aircraft engines is divided into two parts: power management and limit management. Figure 1 As shown in the figure, the power management module is mainly used to realize the closed-loop control of the rotor speed of the aircraft engine and the precise adjustment of the engine thrust, and the limit management is composed of the limit controller and the selection logic. Taking the engine main control system as an example, the monitored quantities include the controlled variables that characterize the engine power (such as fan speed, engine pressure ratio, etc.) and various limit quantities (such as temperature, speed, pressure, etc.). Therefore, a reasonable selection logic is needed for effective switching to ensure safe and stable operation, which not only ensures that the engine works within the limit range, but also ensures good dynamic quality, fast response, small overshoot, less oscillation, and stable and reliable. As early as the 1990s, the PCA program carried out by the NASA Center in the United States first proposed an aircraft engine limit protection control research program, and the backup control system with the engine as the main body was used for flight control in emergency situations. However, existing research results show that the traditional limit protection control method can only ensure that the variable does not exceed the limit in the steady state, and cannot achieve the limit protection effect of the engine in the transient state.

[0003] At present, aircraft engines (such as GE90, PW2000) generally use linear controllers and Max-Min to implement limited protection control. This design can generally meet the FAA's requirements for engine response time. However, many studies in recent years have shown that this limited protection control system has a certain degree of conservatism, especially in emergency situations, and cannot enable the engine to exert its optimal potential. In addition, in existing research results, there is a lack of theoretical research on the stability analysis of aircraft engine limited protection control systems. In order to solve the above problems, the present invention proposes a new type of limited protection control method, the structure of which is as follows: Figure 2 As shown in the figure, it is applied to the temperature limit control of aviation turbofan engines. Not only the performance of the limit protection control in the transition phase is improved by designing a dynamic controller, but also the stability analysis of the aviation engine limit protection control system is carried out by switching the constraint controller, which improves the reliability of practical engineering applications. Summary of the invention

[0004] In order to ensure the safety and stability of the working process of an aircraft engine, the present invention proposes a novel limiting protection control method, which is applied to the temperature limiting control of an aircraft turbofan engine.

[0005] The technical solution of the present invention:

[0006] An aircraft engine limit protection control method, the specific steps are as follows:

[0007] Step 1: Modeling of aircraft engine control system;

[0008] Near the operating point, the linear system identification of the aircraft engine is carried out according to the input-output data, and the system model is established by calculation using the MATLAB software program as follows:

[0009]

[0010] Where n = [n1 n2] T , n1 and n2 represent the increments of the low-pressure rotor speed and the high-pressure rotor speed of the aircraft engine relative to the steady-state operating point, w f represents the fuel increment of the engine, T4 represents the engine turbine outlet temperature increment, A, B, C and D are all the identified system matrices; represents the first-order derivative of n. All the following characters with a dot on them represent the first-order derivative of the character;

[0011] Step 2: Main controller design;

[0012] The system state n and control input w f Augmented to a new state vector x, the speed output augmented system is as follows:

[0013]

[0014] in, represents the derivative of the fuel signal, C1 = [0 1];

[0015] Define the state tracking error as Δx = xx s , where x s Represents the target value to be tracked; the derivative of the fuel signal is designed to meet the conditions:

[0016] u f =k1Θ1Δx,

[0017] Where k1>0 represents the controller gain, 0 2×1 = [0 0];

[0018] The main controller is calculated as follows:

[0019]

[0020] Among them, n 2sIt represents the steady-state operating value of the high-pressure rotor speed, and ε represents the integration factor;

[0021] Step 3: Temperature limit controller design;

[0022] Consider the temperature output augmented system as follows:

[0023]

[0024] in,

[0025] The derivative of the designed fuel signal satisfies the condition:

[0026] u f =k2θ2Δx,

[0027] Where k2>0 represents the controller gain,

[0028] The calculated temperature limit controller is as follows:

[0029]

[0030] Among them, T 4s Indicates the limit value of turbine outlet temperature increment;

[0031] Step 4: Stability analysis;

[0032] Given the residence time constraint, formulate the controller switching rule, analyze the stability of the limited protection control system, and give the stability condition; for the closed-loop control system, when there is a Lyapunov function V σ (Δx), σ(t)∈{1,2} represents the controller switching signal, and the real numbers α>0 and μ>1, satisfying the condition:

[0033] 1) In the main controller operation interval T s (t k , t k+1 )Inside,

[0034]

[0035] 2) In the temperature limit controller operating range T a (t k , t k+1 )Inside,

[0036]

[0037] 3) At the controller switching time t = t k ,

[0038] V i (Δx)≤μVj (Δx),

[0039] Among them, i∈{1, 2}, j∈{1, 2}, i≠j, β represents the upper bound of the system energy growth rate;

[0040] When the above three conditions are met, the following inequality holds:

[0041]

[0042] Among them, N σ (t0, t) represents the total number of switching times in the interval [t0, t); represents the last switching moment in the interval [t0, t);

[0043] Since t-t0=T s (t0, t)+T a (t0, t), we can get

[0044]

[0045] in, Indicates the maximum duration of the temperature limit controller's action;

[0046] When there is τ a >0, so that the controller switching process satisfies When N0∈N, N represents the domain of non-negative integers, the controller switching satisfies the average residence time switching, and,

[0047]

[0048] At this time, when the average residence time meets the condition:

[0049]

[0050] but And the Lyapunov function V σ (Δx) decays to 0; at this point, the aircraft engine limit protection control system is stable;

[0051] In order to obtain the controller parameter conditions that meet the stability analysis, the Lyapunov function is constructed for the closed-loop control system as follows:

[0052] V i (Δx) = Δx T U i Δx,

[0053] Among them, U i =P i -1 , P i represents a given positive definite symmetric matrix;

[0054] For given controller gains k1 and k2, the aircraft engine limit protection control system is stable when there are constants α>0, β>0, μ>1, and positive definite symmetric matrices P1>0, P2>0, so that the following matrix inequalities hold;

[0055]

[0056] P1≤μP2, P2≤μP1;

[0057] Step 5: Conduct aviation turbofan engine control simulation experiments and analyze control performance.

[0058] Beneficial effects of the present invention: In order to ensure the safety and stability of the working process of the aircraft engine, the present invention designs a new type of limiting protection control method. Through the design of the main controller and the limiting controller, the limiting effects of high-pressure rotor speed tracking and turbine outlet temperature are achieved respectively, and the Lyapunov function is designed. The stability of the closed-loop system is analyzed under the constraint of the average residence time. The controller parameter conditions that meet the stability analysis are obtained by solving the inequality. The proposed method can not only achieve the purpose of limiting protection control in the transition stage of the aircraft engine and improve the safety of the aircraft engine control system, but also theoretically analyze the stability of the aircraft engine limiting protection control system and improve the reliability of engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is the control structure diagram of an aircraft engine;

[0060] Figure 2 For the proposed new limit protection control structure;

[0061] Figure 3 Switching signal for the controller;

[0062] Figure 4 is the high pressure rotor speed increment response curve;

[0063] Figure 5 This is the turbine outlet temperature increment response curve. DETAILED DESCRIPTION

[0064] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0065] Specific implementation steps:

[0066] 1) Aircraft engine control system modeling,

[0067] The working process of an aircraft engine has the characteristics of strong nonlinearity, and the coupling relationship between parameters is serious, making it difficult to directly model the engine mechanism. The present invention obtains the following linear system near the engine operating point through real-time input-output data, MATLAB software and system identification calculation program:

[0068]

[0069] Where n = [n1 n2] T , n1 and n2 represent the increments of the low-pressure rotor speed and the high-pressure rotor speed of the aircraft engine relative to the steady-state operating point, w f represents the fuel increment of the engine, T4 represents the engine turbine outlet temperature increment, A, B, C and D are all the identified system matrices;

[0070] 2) Main controller design,

[0071] In order to achieve closed-loop control of the rotor speed and precise adjustment of thrust of the aircraft engine, it is necessary to design the main controller of the limit protection control system. f Augmented to a new state vector x, the speed output augmented system is as follows:

[0072]

[0073] in, represents the derivative of the fuel signal, C1 = [0 1];

[0074] Define the state tracking error as Δx = xx s , where x s Represents the target value to be tracked; the derivative of the fuel signal is designed to meet the conditions:

[0075] u f =k1Θ1Δx, (3)

[0076] Where k1>0 represents the controller gain, 0 2×1 = [0 0];

[0077] From formula (1), we can get:

[0078]

[0079] When the system is in steady state, the following relationship is obtained:

[0080]

[0081] Among them, n 2sIndicates the steady-state operating value of the high-pressure rotor speed;

[0082] From equation (4) and equation (5), we can get:

[0083]

[0084] According to equations (3) and (6), the main controller is calculated as follows:

[0085]

[0086] Among them, ε represents the integration factor;

[0087] 3) Temperature limit controller design,

[0088] In order to limit the turbine outlet temperature of aircraft engines to work within a safe range, it is necessary to carry out the design research of temperature limit controller in the limit protection control, considering the temperature output augmentation system as follows:

[0089]

[0090] in,

[0091] The derivative of the designed fuel signal satisfies the condition:

[0092] u f =k2Θ2Δx, (9)

[0093] Where k2>0 represents the controller gain,

[0094] Similar to the design process of the main controller, the temperature limit controller is calculated as follows:

[0095]

[0096] Among them, T 4s Indicates the limit value of turbine outlet temperature increment;

[0097] 4) Stability analysis,

[0098] In the proposed limiting protection control method, the main controller is used to adjust the engine speed and thrust control, and the temperature limit controller is used to limit the turbine outlet temperature of the engine, constraining the engine to work within a safe range and avoiding over-temperature failures. Therefore, in actual engineering applications, there is a phenomenon of switching between the main controller and the temperature limit controller, which makes it difficult to analyze the stability of the closed-loop control system. To solve this problem, the present invention constrains the switching frequency of the controller based on the average dwell time switching, analyzes the stability of the aircraft engine limiting protection control system, and provides the controller parameter solution inequality that meets the stability conditions.

[0099] First, when the aircraft engine operates in a steady state, the following relationship exists:

[0100]

[0101] Among them, u fs Indicates the fuel w corresponding to the steady-state operation of the engine fs The derivative value of .

[0102] Obviously, there is a relationship From equations (2), (3), (8), (9) and (11), we get the closed-loop control system:

[0103]

[0104] Wherein, i={1,2}, i=1 indicates that the main controller is activated, and i=2 indicates that the temperature limit controller is activated.

[0105] For the closed-loop control system (12), when there exists a Lyapunov function V σ (Δx), σ(t)∈{1,2} represents the controller switching signal, and the real numbers α>0 and μ>1, satisfying the condition:

[0106] 1) In the main controller operation interval T s (t k , t k+1 )Inside,

[0107]

[0108] 2) In the temperature limit controller operating range T a (tk,t k+1 )Inside,

[0109]

[0110] 3) At the controller switching time t = t k ,

[0111] V i (Δx)≤μV j (Δx), (15)

[0112] Among them, i∈{1,2}, j∈{1,2}, i≠j, and β represents the upper bound of the system energy growth rate.

[0113] When the conditions of equations (13) to (15) are met, the following inequality holds:

[0114]

[0115] Among them, N σ(t0, t) represents the total number of switching times in the interval [t0, t); represents the last switching moment in the interval [t0, t);

[0116] In addition, since t-t0=T s (t0, t)+T a (t0, t) and From formula (16), we can get

[0117]

[0118] in, Indicates the maximum duration of the temperature limit controller; when there is τ a >0, so that the controller switching process satisfies When N0∈N, N represents the domain of non-negative integers, the controller switching satisfies the average residence time switching, and,

[0119]

[0120] At this time, when the average residence time meets the condition

[0121]

[0122] but And the Lyapunov function V σ (Δx) decays to 0; at this point, the aircraft engine limit protection control system is stable;

[0123] In order to obtain the controller parameter conditions that meet the stability analysis, the Lyapunov function is constructed for the closed-loop control system as follows:

[0124] V i (Δx) = Δx T U i Δx, (20)

[0125] Among them, U i =P i -1 , P i represents a given positive definite symmetric matrix;

[0126] V i (Δx) is derived and obtained from formula (12):

[0127]

[0128] in,

[0129]

[0130] in,

[0131] Therefore, for given controller gains k1 and k2, when there exist constants α>0, β>0, μ>1, and positive definite symmetric matrices P1>0, P2>0 such that the following matrix inequality holds,

[0132]

[0133]

[0134] P1≤μP2, P2≤μP1, (23)

[0135] Stability conditions (13), (14) and (15) are satisfied. Therefore, the aircraft engine limit protection control system is stable.

[0136] 5) Temperature limit control simulation experiment,

[0137] The system identification of a twin-rotor high bypass ratio turbofan engine is carried out, and the system matrix is ​​obtained as follows:

[0138]

[0139] C=[0.0244-0.2665], D=410.4741;

[0140] The reference value of the high-pressure rotor speed increment is set to 100 r / min, the turbine outlet temperature increment limit is 60 K, the parameters α = 0.2, β = 0.1, μ = 1.1, N0 = 1, and the maximum activation time of the temperature controller is 3 s. The inequality (19) is solved using MATLAB software to obtain the average residence time constraint τ a >4.9766; therefore, in the working range [0,20s], the maximum number of switching times of the controller is N σ =5 times; the controller gains are selected as k1=0.002 and k2=0.03, and the solvability of inequalities (21)-(23) is verified by using the YALMIP function library in MATLAB software; simulation experiments are carried out in SIMULIK software, and the experimental results are shown in Figure 3-Figure 5 shown. Figure 3 It is the controller switching signal of the aircraft engine. It can be seen that the switching frequency of the controller meets the average residence time constraint, which ensures the stability of the limit protection control system. Figure 4 and Figure 5The high-pressure rotor speed increment curve and turbine outlet temperature increment curve of the aircraft engine are shown respectively. Under the action of the designed limiting protection control method, the high-pressure rotor speed of the engine can accurately track the target value. When the turbine outlet temperature of the engine approaches the limit value, the corresponding limiting controller is immediately activated to prevent the further occurrence of over-temperature faults and achieve the function of limiting protection. In addition, compared with the case where the limiting control effect is not applied, the proposed method can effectively reduce the overshoot of the rotor speed control, while avoiding engine overheating and improving the transient control performance.

[0141] Aiming at the problem of aircraft engine safety control, this paper proposes a new type of limit protection control method and applies it to the temperature limit protection control of aircraft turbofan engines. The results show that the proposed method can not only realize the limit protection of the aircraft engine transition process, but also theoretically analyze the stability of the limit protection control system, thus improving the safety of the engine control system and the reliability of engineering applications.

Claims

1. An aircraft engine limit protection control method, characterized in that: The specific steps are as follows: Step 1: Modeling of aircraft engine control system; Near the operating point, the linear system identification of the aircraft engine is carried out according to the input-output data, and the system model is established by calculation using the MATLAB software program as follows: Where n = [n1 n2] T , n1 and n2 represent the increments of the low-pressure rotor speed and the high-pressure rotor speed of the aircraft engine relative to the steady-state operating point, w f represents the fuel increment of the engine, T4 represents the engine turbine outlet temperature increment, A, B, C and D are all the identified system matrices; represents the first-order derivative of n. All the following characters with a dot on them represent the first-order derivative of the character; Step 2: Main controller design; The system state n and control input w f Augmented to a new state vector x, the speed output augmented system is as follows: in, represents the derivative of the fuel signal, C1 = [0 1]; Define the state tracking error as Δx = xx s , where x s Represents the target value to be tracked; the derivative of the fuel signal is designed to meet the conditions: you f =k1Θ1Δx, Where k1>0 represents the controller gain, 0 2×1 = [0 0]; The main controller is calculated as follows: Among them, n 2s It represents the steady-state operating value of the high-pressure rotor speed, and ε represents the integration factor; Step 3: Temperature limit controller design; Consider the temperature output augmented system as follows: in, The derivative of the designed fuel signal satisfies the condition: u f =k2Θ2Δx, Where k2>0 represents the controller gain, The calculated temperature limit controller is as follows: Among them, T 4s Indicates the limit value of turbine outlet temperature increment; Step 4: Stability analysis; Given the residence time constraint, formulate the controller switching rule, analyze the stability of the limited protection control system, and give the stability condition; for the closed-loop control system, when there is a Lyapunov function V σ (Δx), σ(t)∈{1,2} represents the controller switching signal, and the real numbers α>0 and μ>1, satisfying the condition: 1) In the main controller operation interval T s (t k ,t k+1 )Inside, 2) In the temperature limit controller operating range T a (t k ,t k+1 )Inside, 3) At the controller switching time t = t k , V i (Δx)≤μV j (Δx), Among them, i∈{1,2}, j∈{1,2}, i≠j, β represents the upper bound of the system energy growth rate; When the above three conditions are met, the following inequality holds: Among them, N σ (t0,t) represents the total number of switching times in the interval [t0,t); represents the last switching moment in the interval [t0, t); Since t-t0=T s (t0,t)+T a (t0,t), we can get in, Indicates the maximum duration of the temperature limit controller's action; When there is τ a >0, so that the controller switching process satisfies When N0∈N, N represents the domain of non-negative integers, the controller switching satisfies the average residence time switching, and, At this time, when the average residence time meets the condition: but And the Lyapunov function V σ (Δx) decays to 0; at this point, the aircraft engine limit protection control system is stable; In order to obtain the controller parameter conditions that meet the stability analysis, the Lyapunov function is constructed for the closed-loop control system as follows: V i (Δx)=Δx T U i Δx, Among them, U i =P i -1 , P i represents a given positive definite symmetric matrix; For given controller gains k1 and k2, the aircraft engine limit protection control system is stable when there are constants α>0, β>0, μ>1, and positive definite symmetric matrices P1>0, P2>0, so that the following matrix inequalities hold; P1≤μP2,P2≤μP1; Step 5: Conduct aviation turbofan engine control simulation experiments and analyze control performance.

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