A sliding mode control method for aircraft engines with preset time under dwell time

Abstract

The present invention belongs to the field of aircraft engine control technology, and proposes a preset time sliding mode control method for aircraft engines under residence time. The method uses residence time analysis to clarify the minimum interval between two adjacent modes of the engine, thereby ensuring the stability of the engine closed-loop control system. Secondly, in order to ensure the robustness and rapid response capability of the control system, the present invention obtains a control law that is more suitable for each working mode through the design of a modal-dependent sliding surface. Then, based on the preset time theoretical analysis, by incorporating the mode switching process into the parameter design of the controller, the upper limit of the sliding surface arrival time can be preset in advance. The designed preset time sliding mode controller can not only ensure the accessibility of the sliding surface of each engine control system within the modal operating range, ensure the robustness of the system, but also has a faster response speed.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft engine control, and in particular to an aircraft engine preset time sliding mode control method under a dwell time. Background Art

[0002] Modern flight missions and flight environment constraints place more and more stringent requirements on aircraft engines. First, during large-scale, full-envelope flights, aircraft engines need to continuously switch between multiple design points within the flight envelope. When the design point changes, the engine's operating state will also change accordingly, resulting in the engine's operating process having multi-modal characteristics. When the mode transition occurs, the safety of the engine's operating process should be guaranteed. Secondly, the engine's control system should have strong robustness to ensure control accuracy in response to interference from the flight environment, such as temperature and airflow. In addition, when the design point changes, the engine should have a rapid response capability to ensure the real-time nature of the task. In response to the above three requirements, an ideal aircraft engine control system should simultaneously have modal transition safety guarantees, strong robustness, and rapid response capabilities. Therefore, the present invention proposes an aircraft engine preset time sliding mode control method based on dwell time, which is applied to the speed control of a twin-rotor turbofan aircraft engine. Summary of the Invention

[0003] In order to ensure the stability of the engine mode switching process and the robustness of the control system, the present invention proposes an aircraft engine preset time sliding mode control method under dwell time, which is applied to the speed control of aircraft turbofan engines.

[0004] The technical solution of the present invention:

[0005] A sliding mode control method for an aircraft engine with preset time under dwell time, comprising the following steps:

[0006] Step 1: Model the switching system of the engine's multimodal working process using input-output data. The established engine switching system model is as follows:

[0007]

[0008] Where, e=[ΔN l ΔN h ] T , u=ΔW f ;ΔN l Indicates the per-unit error of the engine low-pressure rotor speed relative to the engine design point, ΔN h Indicates the per-unit error of the engine high-pressure rotor speed relative to the engine design point, ΔW frepresents the per-unit error of the fuel-air ratio relative to the engine design point, σ(t) represents the operating mode of the engine system at time t, σ(t): N is the total number of engine operating modes. In the interval [0, t], the switching moment of the system is defined as belonging to the set And satisfy t0=0 and A σ(t) and B σ(t) is the system matrix, f represents the system input uncertainty, f: satisfying ||f(e,t)||≤ξ,

[0009] Step 2: Design the sliding mode surface that the working mode depends on and calculate the sliding mode system equation; for the engine in the i-th working mode, design the sliding mode function as follows:

[0010]

[0011] in, is the controller gain to be solved;

[0012] Define the sliding surface as S i (t) = 0; Calculated;

[0013]

[0014] Then the equivalent control law is calculated:

[0015] u eq (t) = K i e(t)-f(e,t)

[0016] and the sliding mode system equations,

[0017]

[0018] in,

[0019] Step 3: Perform stability analysis and optimize controller parameters in the dwell time frame; for sliding mode systems, when there is a Lyapunov function V i (e) and real numbers α>0 and μ>1, such that,

[0020]

[0021] V i (e(t k ))≤μV j (e(t k )),i≠j∈X

[0022] Then the following inequality holds,

[0023]

[0024] Among them, N σ (t0,t) represents the total number of mode switching in the interval [t0,t);

[0025] When there is τ d >0, so that the engine switching process satisfies When , the engine mode satisfies the dwell time switching, and,

[0026]

[0027] At this time, when the residence time meets

[0028]

[0029] Then when time t approaches infinity, V σ(t) (e(t)) approaches 0, at which point the engine control system is stable;

[0030] In order to obtain the controller gain that satisfies the above stability conditions, a Lyapunov function is constructed for the sliding mode system equation.

[0031] V i (e) = e T U i e

[0032] Among them, U i >0;

[0033] make At this time, when there is a matrix P i >0 and When the following matrix inequality holds,

[0034]

[0035] P i ≤μP j

[0036] Then the engine mode conversion process is stable and the controller gain is expressed as K i =L i P i -1 ;

[0037] Step 4: Design the sliding mode control law and analyze the accessibility of the sliding surface; Design the control law

[0038] u(t)=K i e(t)-g(t)sign(S i(t))

[0039] Where g(t)=ξ+ρ||S i (t)|| 1-ε +κ||S i (t)|| 1+ε , ε is a given parameter, satisfying 0<ε<1.

[0040] In order to verify the accessibility of the sliding surface, a Lyapunov function is constructed.

[0041]

[0042] get,

[0043]

[0044] Therefore, in each mode operation range, the maximum arrival time of the sliding surface does not exceed τ d ; The system state can reach the designed sliding surface within each modal operation range.

[0045] Finally, an aviation turbofan engine speed simulation experiment is conducted to analyze the control performance.

[0046] In order to ensure the safety of the engine mode conversion process, the present invention uses residence time analysis to clarify the minimum interval between two adjacent engine modes and ensure the stability of the engine closed-loop control system. Secondly, in order to ensure the robustness and rapid response capability of the control system, the present invention obtains a control law that is more suitable for each working mode through the design of a mode-dependent sliding surface. Then, based on the preset time theoretical analysis, by incorporating the mode switching process into the parameter design of the controller, the upper limit of the sliding surface arrival time can be preset in advance. The designed preset time sliding mode controller can not only ensure the accessibility of the sliding surface of each engine control system within the modal operating range, ensure the robustness of the system, but also has a faster response speed.

[0047] Beneficial Effects of the Invention: This invention studies multi-modal switching control for aircraft engines and proposes a preset-time sliding mode control method for aircraft engines with dwell time. This method ensures the accessibility of the sliding mode surface under each engine mode, enhancing the robustness of the engine control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is the turbofan engine working mode switching signal;

[0049] Figure 2 is the high-pressure rotor speed curve of the turbofan engine;

[0050] Figure 3 is the oil-gas ratio change curve;

[0051] Figure 4 is the trajectory curve of the sliding mode function. DETAILED DESCRIPTION

[0052] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0053] Specific implementation steps:

[0054] 1) Modeling of the engine switching system in the multi-modal working process of the engine,

[0055] The engine's operating process is highly nonlinear and heavily coupled, making direct mechanistic modeling difficult. This paper considers the engine's multimodal operation between multiple design points. Using real-time input-output data and system identification methods, the multimodal engine operation is described as a switching system:

[0056]

[0057] Where, e=[ΔN l ΔN h ] T , u=ΔW f ΔN l Indicates the per-unit error of the engine low-pressure rotor speed relative to the engine design point, ΔN h Indicates the per-unit error of the engine high-pressure rotor speed relative to the engine design point, ΔW f Represents the per-unit error of the fuel-air ratio relative to the engine design point. σ(t) represents the operating mode of the engine system at time t, σ(t): N is the total number of engine operating modes. In the interval [0, t], the switching moment of the system is defined as belonging to the set And satisfy t0=0 and A σ(t) and B σ(t) is the system matrix, f represents the system input uncertainty, f: satisfying ||f(e,t)||≤ξ,

[0058] 2) Sliding surface design and sliding mode system equation calculation

[0059] In order to ensure the robustness and rapid response capability of the engine working process, the present invention designs a preset sliding mode controller for the engine switching system (1). First, in order to reduce the conservatism of the control process, the controller design under the corresponding mode is carried out for different working stages of the engine. For the engine in the i-th working mode, the sliding mode function is designed.

[0060]

[0061] in, are the controller gains to be solved.

[0062] In addition, in order to ensure the robustness of the engine control process, the sliding surface needs to be defined as S i (t) = 0. When the state trajectory of the engine switching system is on the sliding surface, Calculated;

[0063]

[0064] At this time, the equivalent control law can be obtained from formula (3);

[0065] u eq (t) = K i e(t)-f(e,t). (4)

[0066] From Equations (1) and (4), we can obtain the sliding mode system equation where the system trajectory runs on the sliding mode surface;

[0067]

[0068] in,

[0069] 3) Stability analysis and controller parameter optimization under dwell time

[0070] In order to ensure the stability of the state of the switching system (1) when it runs on the sliding mode surface, it is necessary to constrain the engine's mode conversion process and design an optimization rule to solve the controller parameter gain that meets the system stability requirements. First, for the sliding mode system (5), if there is a Lyapunov function V i (e) and real numbers α>0 and μ>1, such that

[0071]

[0072] V i (e(t k ))≤μV j (e(t k )),i≠j∈X, (7)

[0073] Then from formula (6) and formula (7), we can get

[0074]

[0075] Among them, N σ (t0,t) represents the total number of mode switching in the interval [t0,t).

[0076] According to the definition of residence time, when there is τ d > 0, so that the interval between any two adjacent switches is not less than τ d ,Right now The sliding mode system (5) is said to satisfy the dwell time switching, where τ d Represents the residence time. From formula (8), we can get

[0077]

[0078] Therefore, when the dwell time satisfies

[0079]

[0080] Then when time t approaches infinity, V σ(t) (e(t)) approaches 0. At this point, the sliding mode system (5) is stable, thus ensuring the stability of the engine mode conversion process. In order to design a controller that satisfies stability conditions (6) and (7), it is necessary to construct a suitable Lyapunov function and transform conditions (6) and (7) into solvable linear matrix inequalities to optimize the controller parameters.

[0081] For system (5), the Lyapunov function is constructed as follows:

[0082] V i (e) = e T U i e, (11)

[0083] Among them, U i >0. V i Substituting the expression of (e) into the stability conditions (6) and (7), we obtain the following inequality,

[0084]

[0085] V i -μV j =e T {U i -μU j}e≤0.

[0086] From this, it can be concluded that

[0087] (A i+B i K i ) T U i +U i (A i +B i K i )+αU i , (12)

[0088] U i -μU j ≤0. (13)

[0089] In order to achieve the decoupling of control parameters and obtain the optimized controller gain, let Multiply the left and right sides of the nonlinear matrix inequalities (12) and (13) by the matrix P i , and let L i =K i P i , the decoupled linear matrix inequality conditions are as follows:

[0090]

[0091] P i ≤μP j . (15)

[0092] Therefore, if there exists a matrix P i >0 and If inequalities (14) and (15) hold, then stability conditions (6) and (7) hold, and the sliding mode system (5) is stable. The optimized controller gain is calculated as K i =L i P i -1 .

[0093] 4) Control law design and sliding surface reachability analysis

[0094] In addition, on the basis of ensuring the stability of the engine control system, the present invention further considers the accessibility of the designed sliding surface to ensure the robustness of the engine control process. First, the control law is designed as follows:

[0095] u(t)=K i e(t)-g(t)sign(S i (t)), (16)

[0096] Where g(t)=ξ+ρ||S i (t)|| 1-ε +κ||S i (t)|| 1+ε , ε is a given parameter, satisfying 0<ε<1.

[0097] From the sliding mode function (2) and the control law (16), we can get

[0098]

[0099] In order to verify the accessibility of the sliding surface, for system (17), construct the Lyapunov function

[0100]

[0101] Substituting formula (17) into formula (18), we can get

[0102]

[0103] Therefore, according to formula (19), by the preset time theory, for each working mode of the engine, the sliding mode function stays in the preset residence time τ d It converges to 0. In each modal operation range, the state trajectory of system (1) can reach the designed sliding surface, which effectively ensures the robustness of the engine working process.

[0104] 5) Aviation turbofan engine speed control simulation experiment

[0105] The system matrix of the turbofan engine at different design points is obtained by input-output data identification

[0106]

[0107]

[0108] Given the parameters α = 0.8 and μ = 1.5, the dwell time condition (10) is obtained as

[0109] τ d >0.5068s.

[0110] By solving inequalities (14) and (15), we can obtain the optimized controller gain

[0111] K1=[-5.8217 3.5017], K2=[-7.8709 3.2127].

[0112] In addition, the parameter τ is set in the controller d =5 and ε=0.1. The simulation results are shown in Figures 1-4 shown. Figure 1It is the working mode switching signal of the turbofan engine. It can be seen that the interval between two adjacent mode switches is greater than the designed dwell time, which ensures the stability of the switching process. Figure 2 and Figure 3 The curves represent the high-pressure rotor speed curve and the oil-gas ratio variation curve of the engine respectively. Under the action of the designed controller, the high-pressure rotor speed of the engine can quickly and well track the target value in each working mode. Figure 4 The operating trajectory of the sliding mode function is shown. Within each modal operating range, the system state trajectory can reach the designed sliding surface, further enhancing the robustness of the system.

[0113] This paper addresses the multi-design-point switching control problem of turbofan engines by proposing a preset-time sliding mode control method within a dwell time framework. Results demonstrate that this method, with a dwell time framework, ensures the stability of the engine mode switching process, ensures the accessibility of the sliding mode surface within each modal operating range, and effectively enhances the robustness of the engine control system. The control effect exhibits rapid response characteristics.

Claims

1. A sliding mode control method for an aircraft engine with preset time under dwell time, characterized in that: The specific steps are as follows: Step 1: Model the switching system of the engine's multimodal working process using input-output data. The established engine switching system model is as follows: Where, e=[ΔN l ΔN h ] T , u=ΔW f ;ΔN l Indicates the per-unit error of the engine low-pressure rotor speed relative to the engine design point, ΔN h Indicates the per-unit error of the engine high-pressure rotor speed relative to the engine design point, ΔW f represents the per-unit error of the oil-air ratio relative to the engine design point, σ(t) represents the operating mode of the engine system at time t, N is the total number of engine operating modes. In the interval [0, t], the switching moment of the system is defined as belonging to the set And satisfy t0=0 and A σ(t) and B σ(t) is the system matrix, f represents the system input uncertainty, satisfying ||f(e,t)||≤ξ, Step 2: Design the sliding mode surface that the working mode depends on and calculate the sliding mode system equation; for the engine in the i-th working mode, design the sliding mode function as follows: in, is the controller gain to be solved; Define the sliding surface as S i (t) = 0; Calculated; Then the equivalent control law is calculated: u eq (t)=K i e(t)-f(e,t) and the sliding mode system equations, in, Step 3: Perform stability analysis and optimize controller parameters in the dwell time frame; for sliding mode systems, when there is a Lyapunov function V i (e) and real numbers α>0 and μ>1, such that, Then the following inequality holds, Among them, N σ (t0,t) represents the total number of mode switching in the interval [t0,t); When there is τ d >0, so that the engine switching process satisfies When , the engine mode satisfies the dwell time switching, and, At this time, when the residence time meets Then when time t approaches infinity, V σ(t) (e(t)) approaches 0, at which point the engine control system is stable; In order to obtain the controller gain that satisfies the above stability conditions, a Lyapunov function is constructed for the sliding mode system equation. V i (e)=e T U i yes Among them, U i >0; make At this time, when there is a matrix P i >0 and When the following matrix inequality holds, P i ≤μP j Then the engine mode conversion process is stable and the controller gain is expressed as K i =L i P i -1 ; Step 4: Design the sliding mode control law and analyze the accessibility of the sliding surface; Design the control law u(t)=K i e(t)-g(t)sign(S i (t)) Where g(t)=ξ+ρ||S i (t)|| 1-ε +κ||S i (t)|| 1+ε , ε is a given parameter, satisfying 0<ε<1; In order to verify the accessibility of the sliding surface, a Lyapunov function is constructed. get, Therefore, in each mode operation range, the maximum arrival time of the sliding surface does not exceed τ d ; The system state can reach the designed sliding surface within each modal operation range.

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