Aircraft engine sector input constraint robust control method based on space reconstruction

Abstract

The invention discloses an aero-engine sector input constraint robust control method based on spatial reconstruction, which comprises the following steps of: 1) establishing an aero-engine nonlinear system containing sector input constraint, modeling uncertainty and noise, and converting a sector constraint problem by utilizing spatial reconstruction; step 2), calculating a maximum boundary value of an uncertainty item in the system; step 3), designing a sector constraint robust controller; and 4) verifying the global actual stability of the system. According to the invention, the constraint problem of two sectors distributed in different quadrants is converted into the constraint problem of a single sector in a single quadrant through spatial reconstruction, and the robust control method is designed based on the converted constraint condition. The method effectively solves the problem that the control effect is reduced and even a closed-loop system is unstable due to uncertainty of sector input constraint, modeling error, unknown bounded noise and the like in an aero-engine nonlinear system at the same time.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft engine control, and in particular relates to an aircraft engine sector input constraint robust control method based on space reconstruction. Background Art

[0002] Aircraft engines are core components of aircraft, providing the necessary propulsion for flight. The extreme complexity and sophistication of their thermodynamic systems inevitably lead to significant technical challenges, long research cycles, and high investment costs. As the crown jewel of modern industry, aircraft engines embody a nation's industrial, national defense, and economic capabilities. For such multivariable, highly nonlinear, and uncertain systems, the performance of aircraft engine control systems not only directly impacts aircraft flight safety and economics, but can even endanger the lives of pilots. Therefore, research on advanced engine control technologies holds both practical and theoretical significance. Designing robust aircraft engine control systems that meet the requirements of real-time performance, reliability, speed, and economy, while fully considering the complex and variable external environments and strong noise interference encountered during actual aircraft engine operation, has always been a goal of aircraft engine control system design. Ensuring that the engine operates smoothly within its safe operating boundaries while meeting wide-ranging rapid response requirements remains a key challenge in engine control system design.

[0003] Since the control system will be affected by external disturbances, the controlled object has physical limitations, or due to factors such as system safety and environmental protection, the actual control system is inevitably subject to some constraints. Sector input constraints refer to the fact that the characteristics of the actuator are unknown and cannot be accurately described by mathematical functions, but can be considered to be limited to a sector area. For a complex system such as an aircraft engine with strong nonlinearity and a wide range of operating point changes, due to factors such as aging and wear of components, the output of the actuator, such as the angle of the actuator's adjustable blades, will inevitably have sector constraint nonlinear problems. This constraint runs through the entire operating cycle, causing uncertainty in the system's control input within a certain range, and as the input increases, the impact of this uncertainty will also increase, the system's control quality will gradually decline, and then have a serious impact on system performance. Therefore, the present invention proposes a robust control method for aircraft engine sector input constraints based on spatial reconstruction. Summary of the Invention

[0004] Purpose of the Invention: To address the inevitable sector input constraints in nonlinear aeroengine systems, this invention proposes a robust control method for sector input constraints in aeroengines based on spatial reconstruction. This spatial reconstruction transforms the two sector constraints distributed in different quadrants into a single-quadrant, single-sector constraint problem. Based on the transformed constraints, a robust control method is designed to ensure both uniform boundedness and uniform ultimate boundedness of the aeroengine nonlinear system.

[0005] Technical solution: To achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A method for robust control of sectors of an aircraft engine with input constraints based on spatial reconstruction comprises the following steps:

[0007] Step 1) Establish an aero-engine nonlinear system with sector input constraints, modeling uncertainty and noise, and use spatial reconstruction to transform the two-quadrant sector constraint into a single-quadrant single-sector constraint problem;

[0008] Step 2), based on the reconstructed system model, calculate the maximum limit value of the uncertainty term in the system;

[0009] Step 3), based on the maximum limit, design a sector constrained robust controller;

[0010] Step 4) Based on the controller, verify the actual global stability of the system.

[0011] Furthermore, the specific steps in step 1) are as follows:

[0012] Step 1.1) Establish a class of aero-engine nonlinear systems with sector input constraints, modeling uncertainty and noise

[0013]

[0014] in, Indicates status, Indicates the jth x states,j x =1,2,…,n; Indicates input, Indicates the jth u Input,j u =1,2,…,m; Represents sector-constrained input represents the i-th input affected by the sector constraint, and Indicates that there is a maximum upper bound on the noise, Indicates the jth g Noise, j g =1,2,…,p; represents the uncertainty parameter, n, m, p and l represent the dimensions of state, input, noise and uncertainty parameter respectively, f(x(t),t), Δf(x(t),σ(t),t), B(x(t),t) and B0(x(t),t) are dimensionally appropriate vectors or matrices, f(·), Δf(·), B(·), B0(·) and σ(·) are continuous functions; σ(t) is in the compact set middle;

[0015] In step 1.2), the appropriate operating conditions are selected using the component-level model of the aircraft engine, and f(x(t),t), B(x(t),t), and B0(x(t),t) in system (1) are obtained based on the engine characteristics.

[0016] Step 1.3), input constraint model for the sector

[0017]

[0018] Among them, β 1i and β 2i Indicates input u i The sector constraints of are bounded; using the space reconstruction scheme, the constraints are transformed into a single quadrant problem through matrix transformation, that is,

[0019]

[0020] The sector-constrained input is converted to

[0021] u T β1u≤u T φ(u)≤u T β2u (4)

[0022] Step 1.4), using the Rayleigh-Ritz minimax formula, we get

[0023] λ min [β1]||u|| 2 ≤u T φ(u)≤λ max [β1]||u|| 2 (5)

[0024] Among them, λ max [·], λ min [·] represent the solution of the maximum and minimum eigenvalues, respectively, thereby reformulating the two-quadrant sector constraint into a single-quadrant constraint problem.

[0025] Furthermore, the specific steps in step 2) are as follows:

[0026] Step 2.1), design function Satisfy

[0027] Δf(x,σ,t)=B(x,t)h(x,σ,t) (6)

[0028] and

[0029]

[0030] Among them, ρ h (x, t) represents the maximum norm of h(x, σ, t) affected by uncertainty.

[0031] Step 2.2), design function Satisfy

[0032] B0(x,t)=B(x,t)J(x,t) (8)

[0033] Step 2.3), define the total uncertainty in the system as a function Right now

[0034] κ(x,σ,t)=h(x,σ,t)+J(x,t)g (9)

[0035] Where g represents the noise with a maximum upper bound. System (1) can be written as

[0036]

[0037] Step 2.4), κ(x,σ,t) has an upper bound Combined with formula (7), the threshold value is determined to be

[0038] ρ(x,t)=ρ h (x,t)+||J(x,t)g|| (11)

[0039] Furthermore, the specific steps in step 3) are as follows:

[0040] Step 3.1), design a continuous function For any satisfy

[0041]

[0042] Step 3.2), design the controller u(t) = p(x(t), t), where p(x, t) is a Carathedory function, and For a given positive constant ε,

[0043]

[0044] in, μ(x,t):=α(x,t)ρ(x,t), V(x,t) is the Lyapunov equation, and

[0045] Furthermore, the specific steps in step 4) are as follows:

[0046] Step 4.1) for autonomous systems

[0047]

[0048] Construct the Lyapunov function V(x,t) and functions γ1, γ2 and γ3 to satisfy

[0049] γ i (0)=0,i=1,2,3 (15)

[0050]

[0051] And for any

[0052] γ1(||x||)≤V(x,t)≤γ2(||x||) (17)

[0053]

[0054] Step 4.2), take the derivative of the Lyapunov equation of system (1) and get

[0055]

[0056] When ||μ(x,t)||>ε, take τ(x,t)=η(ρ(x,t))ρ(x,t) / ||μ(x,t)||, p(x,t)=-τ(x,t)α(x,t), we get

[0057]

[0058] Combined with (19), we get

[0059]

[0060] When ||μ||≤ε, if α≠0 and p(x,t)≠0, combined with (13), we can get

[0061]

[0062] Combined with (19), we get

[0063]

[0064] If p(x,t)=0, then αT (x,t)φ(p(x,t))=0,

[0065]

[0066] If α(x,t)=0, then α T (x,t)φ(p(x,t))=α T (x,t)κ(x,σ,t)=0,

[0067]

[0068] In summary, combining (21), (23), (24) and (25), we can get All

[0069]

[0070] Therefore, when ||x|| is large enough, For must be negative;

[0071] Step 4.3), combined with (26), verify that system (1) is uniformly bounded, that is, if x(t0)=x0, then

[0072]

[0073] in,

[0074]

[0075] and

[0076] Step 4.4), combined with (26), verify that system (1) has uniform final boundedness, that is, if x(t0)=x0, and ||x0||<r, then for the given have

[0077]

[0078] in,

[0079]

[0080] and

[0081]

[0082] The beneficial effects of the present invention are:

[0083] (1) For a dual-sector constraint problem where the sector input constraint spans two quadrants, the present invention utilizes spatial reconstruction theory to transform the two-sector problem distributed in different quadrants into a single-sector problem in a single quadrant through matrix transformation, thereby simplifying the constraint problem.

[0084] (2) While addressing the uncertainty issues of sector nonlinearity, modeling nonlinearity, and noise in aircraft engine systems, the present invention can ensure the actual stability of the system—uniformly bounded and uniformly ultimately bounded.

[0085] (3) The present invention is universal and can help solve sector constraint problems in other systems in engineering and society. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 Schematic diagram of the process of the present invention.

[0087] Figure 2 Enter the constraint diagram for the sector.

[0088] Figure 3 Schematic diagram of the variable cycle engine structure and cross-sectional identification in an embodiment of the present invention.

[0089] Figure 4 Schematic diagram comparing the response results of the control method of the present invention and the SMC method x1.

[0090] Figure 5 Schematic diagram comparing the response results of the control method of the present invention and the SMC method x2.

[0091] Figure 6 Schematic diagram comparing the response results of the control method of the present invention and the SMC method x3.

[0092] Figure 7 Schematic diagram comparing the u1 response results of the control method of the present invention and the SMC method.

[0093] Figure 8 Schematic diagram comparing the u2 response results of the control method of the present invention and the SMC method.

[0094] Figure 9 Schematic diagram comparing the u3 response results of the control method of the present invention and the SMC method. DETAILED DESCRIPTION

[0095] A method for robust control of sector input constraints of an aircraft engine based on spatial reconstruction comprises the following steps: Step 1), establishing an aircraft engine nonlinear system containing sector input constraints, modeling uncertainty and noise, and using spatial reconstruction to convert the two-quadrant sector constraints into a single-quadrant single-sector constraint problem; Step 2), based on the reconstructed system model, calculating the maximum limit of the uncertainty term in the system; Step 3), based on the maximum limit, designing a sector constraint robust controller; Step 4), based on the controller, verifying the global actual stability of the system.

[0096] The present invention converts two sector constraint problems distributed in different quadrants into a single-quadrant single-sector constraint problem through spatial reconstruction, and designs a robust control method based on the converted constraint conditions. It effectively solves the problem of reduced control effect and even closed-loop system instability caused by uncertainties such as simultaneous existence of sector input constraints, modeling errors, and unknown bounded noise in the nonlinear system of aircraft engines.

[0097] A robust control method for aero-engine sector input constraints based on spatial reconstruction, such as Figure 1 The following steps are included:

[0098] Step 1) establishes an aero-engine nonlinear system with sector input constraints, modeling uncertainty, and noise, and uses spatial reconstruction to transform the two-quadrant sector constraint into a single-quadrant single-sector constraint problem;

[0099] Step 1.1) Establish a class of aero-engine nonlinear systems with sector input constraints, modeling uncertainty and noise

[0100]

[0101] in, Indicates status, Indicates the jth x states,j x =1,2,…,n; Indicates input, Indicates the jth u Input,j u =1,2,…,m; Represents sector-constrained input represents the i-th input affected by the sector constraint, and Indicates that there is a maximum upper bound on the noise, Indicates the jth g A noise, represents the uncertainty parameter, n, m, p and l represent the dimensions of state, input, noise and uncertainty parameter respectively, f(x(t),t), Δf(x(t),σ(t),t), B(x(t),t) and B0(x(t),t) are dimensionally appropriate vectors or matrices, f(·), Δf(·), B(·), B0(·) and σ(·) are continuous functions; σ(t) is in the compact set middle;

[0102] In step 1.2), the appropriate operating conditions are selected using the component-level model of the aircraft engine, and f(x(t),t), B(x(t),t), and B0(x(t),t) in system (1) are obtained based on the engine characteristics.

[0103] Step 1.3), input constraint model for the sector

[0104]

[0105] Among them, β 1i and β 2i Indicates input u i The sector constraints of are bounded; using the space reconstruction scheme, the constraints are transformed into a single quadrant problem through matrix transformation, that is,

[0106]

[0107] The sector-constrained input is converted to

[0108] u T β1u≤u T φ(u)≤u T β2u (4)

[0109] Step 1.4), using the Rayleigh-Ritz minimax formula, we get

[0110] λ min [β1]||u|| 2 ≤u T φ(u)≤λ max [β1]||u|| 2 (5)

[0111] Among them, λ max [·], λ min [·] represent the solution of the maximum and minimum eigenvalues, respectively, thereby reformulating the two-quadrant sector constraint into a single-quadrant constraint problem.

[0112] Step 2), based on the reconstructed system model, calculate the maximum bound of the uncertainty term in the system;

[0113] Step 2.1), design function Satisfy

[0114]

[0115] and

[0116]

[0117] Among them, ρ h (x, t) represents the maximum norm of h(x, σ, t) affected by uncertainty.

[0118] Step 2.2), design function Satisfy

[0119] B0(x,t)=B(x,t)J(x,t) (8)

[0120] Step 2.3), define the total uncertainty in the system as a function Right now

[0121] κ(x,σ,t)=h(x,σ,t)+J(x,t)g (9)

[0122] Where g represents the noise with a maximum upper bound. System (1) can be written as

[0123]

[0124] Step 2.4), κ(x,σ,t) has an upper bound Combined with formula (7), the threshold value is determined to be

[0125] ρ(x,t)=ρ h (x,t)+||J(x,t)g|| (11).

[0126] Step 3), designing a sector constrained robust controller based on the maximum limit;

[0127] Step 3.1), design a continuous function η(0)=0, for any satisfy

[0128]

[0129] Step 3.2), design the controller u(t) = p(x(t), t), where p(x, t) is a Carathedory function, and For a given positive constant ε,

[0130]

[0131] in, μ(x,t):=α(x,t)ρ(x,t), V(x,t) is the Lyapunov equation, and

[0132] Step 4), based on the controller, verifying the actual global stability of the system;

[0133] Step 4.1) for autonomous systems

[0134]

[0135] Construct the Lyapunov function V(x,t) and functions γ1, γ2 and γ3 to satisfy

[0136] γ i (0)=0,i=1,2,3 (15)

[0137]

[0138] And for any

[0139] γ1(||x||)≤V(x,t)≤γ2(||x||) (17)

[0140]

[0141] Step 4.2), take the derivative of the Lyapunov equation of system (1) and get

[0142]

[0143] When ||μ(x,t)||>ε, take τ(x,t)=η(ρ(x,t))ρ(x,t) / ||μ(x,t)||, p(x,t)=-τ(x,t)α(x,t), we get

[0144]

[0145] Combined with (19), we get

[0146]

[0147] When ||μ||≤ε, if α≠0 and p(x,t)≠0, combined with (13), we can get

[0148]

[0149] Combined with (19), we get

[0150]

[0151] If p(x,t)=0, then αT (x,t)φ(p(x,t))=0,

[0152]

[0153] If α(x,t)=0, then α T (x,t)φ(p(x,t))=α T (x,t)κ(x,σ,t)=0,

[0154]

[0155] In summary, combining (21), (23), (24) and (25), we can get All

[0156]

[0157] Therefore, when ||x|| is large enough, For must be negative;

[0158] Step 4.3), combined with (26), verify that system (1) is uniformly bounded, that is, if x(t0)=x0, then

[0159]

[0160] in,

[0161]

[0162] and

[0163] Step 4.4), combined with (26), verify that system (1) has uniform final boundedness, that is, if x(t0)=x0, and ||x0||<r, then for the given have

[0164]

[0165] in,

[0166]

[0167] and

[0168]

[0169] Example

[0170] The present invention will be further described below with reference to the accompanying drawings and examples.

[0171] The present invention can be better understood with reference to the following examples. Figure 3 As an example of a variable cycle engine, based on the component-level model of the variable cycle engine aerodynamic thermodynamics, the state variables and control variables are selected as

[0172] x(t)=[x1(t) x2(t) x3(t)] T =[Δn L (t) Δn H (t) ΔEPR(t)] T (32)

[0173] u(t)=[u1(t) u2(t) u3(t)] T =[ΔW f (t) ΔA8(t) ΔA 163 (t)] T (33)

[0174] Among them, n L Indicates the low-pressure rotor speed, n H Indicates the high-pressure rotor speed, EPR indicates the engine pressure ratio, W f Indicates the fuel flow rate of the main combustion chamber, A8 indicates the throat area of ​​the tail nozzle, A 163 represents the area of ​​the rear adjustable duct ejector, and Δ represents the increment of the variable.

[0175] The system model of the variable cycle engine in single bypass mode at an altitude of h = 5 km and a Mach number of Ma = 0.6 is established, that is, f(x(t),t), B(x(t),t) and B0(x(t),t) are:

[0176]

[0177]

[0178] Choose the modeling uncertainty Δf(x(t),t) as

[0179] Δf(x(t),σ(t),t)=ι(t)f(x(t),t) (37)

[0180] Where ι(t) is a random function and ||ι(t)||≤0.1. The noise g(t) satisfies and ||g(t)||≤2.5×10 -4 The sector constraint boundary value is chosen as

[0181]

[0182] Then λ min [β1]=0.7, and the function Can be selected as

[0183]

[0184] Select ε=0.01, Figure 4-Figure 9 It shows that [0.05 0.05 0.05] is applied to the system in 0.025s. T The response curves of state variables and control variables after the initial disturbance are calculated, and the sliding mode controller (SMC) is selected for comparison with the sector-boundedness constraint robust control (SCRC) designed by the present invention. The simulation results show that when the system is disturbed, the SCRC designed by the present invention can make the system with sector input nonlinearity return to steady state within 0.1s, and the steady-state error is almost 0. In contrast, the system state under SMC control diverges and oscillates and cannot return to steady state. Therefore, it is concluded that for the nonlinear system of aircraft engines with sector constraints, the controller designed by the present invention performs better than SMC, further highlighting its robustness and practical applicability in complex nonlinear systems.

Claims

1. A robust control method for aircraft engine sectors with input constraints based on spatial reconstruction, characterized by: The following steps are involved: Step 1) Establish an aero-engine nonlinear system with sector input constraints, modeling uncertainty and noise, and use spatial reconstruction to transform the two-quadrant sector constraint into a single-quadrant single-sector constraint problem; Step 2), based on the reconstructed system model, calculate the maximum limit value of the uncertainty term in the system; Step 3), based on the maximum limit, design a sector constrained robust controller; Step 4) Based on the controller, verify the actual global stability of the system.

2. The method for robust control of aircraft engine sectors with input constraints based on spatial reconstruction according to claim 1, characterized in that: The specific steps of step 1) are as follows: Step 1.1) Establish the aero-engine nonlinear system with sector input constraints, modeling uncertainty and noise in, Indicates status, Indicates the jth x states,j x =1,2,…,n; Indicates input, Indicates the jth u Input,j u =1,2,…,m; Represents sector-constrained input represents the i-th input affected by the sector constraint, and Indicates that there is a maximum upper bound on the noise, Indicates the jth g Noise, j g =1,2,…,p; represents the uncertainty parameter, n, m, p and l represent the dimensions of state, input, noise and uncertainty parameter respectively, f(x(t),t), Δf(x(t),σ(t),t), B(x(t),t) and B0(x(t),t) are dimensionally appropriate vectors or matrices, f(·), Δf(·), B(·), B0(·) and σ(·) are continuous functions; σ(t) is in the compact set middle; In step 1.2), the appropriate operating conditions are selected using the component-level model of the aircraft engine, and f(x(t),t), B(x(t),t), and B0(x(t),t) in system (1) are obtained based on the engine characteristics. Step 1.3), input constraint model for the sector Among them, β 1i and β 2i Indicates input u i The sector constraints of are bounded; using the space reconstruction scheme, the constraints are transformed into a single quadrant problem through matrix transformation, that is, The sector-constrained input is converted to you T β1u≤u T φ(u)≤u T b2u (4) Step 1.4), using the Rayleigh-Ritz minimax formula, we get l min [β1]||u|| 2 ≤u T φ(u)≤λ max [β1]||u|| 2 (5) Among them, λ max [·], λ min [·] represent the solution of the maximum and minimum eigenvalues, respectively, thereby reformulating the two-quadrant sector constraint into a single-quadrant constraint problem.

3. The method for robust control of aircraft engine sectors with input constraints based on spatial reconstruction according to claim 2, characterized in that: The specific steps of calculating the maximum limit value of the uncertainty term in the system in step 2) are as follows: Step 2.1), design function h(·): Satisfy Δf(x,σ,t)=B(x,t)h(x,σ,t) (6) and Among them, ρ h (x, t) represents the maximum norm of h(x, σ, t) affected by uncertainty; Step 2.2), design function J(·): Satisfy B0(x,t)=B(x,t)J(x,t) (8) In step 2.3), define the lumped uncertainty in the system as a function κ(·): Right now κ(x,σ,t)=h(x,σ,t)+J(x,t)g (9) Where g represents the noise with a maximum upper bound; system (1) can be written as Step 2.4), κ(x,σ,t) has an upper bound ρ(·): Combined with formula (7), the threshold value is determined to be ρ(x,t)=ρ h (x,t)+||J(x,t)g|| (11)。 4. The method for robust control of aircraft engine sectors with input constraints based on spatial reconstruction according to claim 2, characterized in that: The specific steps of designing the sector-constrained robust controller in step 3) are as follows: Step 3.1), design the continuous function η(·): η(0)=0, for any satisfy Step 3.2) Design the controller u(t) = p(x(t), t), where p(x, t) is a Carathedory function and p(·): For a given positive constant ε, in, μ(x,t):=α(x,t)ρ(x,t), V(x,t) is the Lyapunov equation, and V(·):

5. The method for robust control of aircraft engine sectors with input constraints based on spatial reconstruction according to claim 4, characterized in that: The specific steps for verifying the global actual stability of the system in step 4) are as follows: Step 4.1) for autonomous systems Construct the Lyapunov function V(x,t) and functions γ1, γ2 and γ3 to satisfy c i (0)=0,i=1,2,3 (15) And for any γ1(||x||)≤V(x,t)≤γ2(||x||) (17) Step 4.2), take the derivative of the Lyapunov equation of system (1) and get When ||μ(x,t)||>ε, take τ(x,t)=η(ρ(x,t))ρ(x,t) / ||μ(x,t)||, p(x,t)=-τ(x,t)α(x,t), we get Combined with (19), we get When ||μ||≤ε, if α≠0 and p(x,t)≠0, combined with (13), we can get Combined with (19), we get If p(x,t)=0, then α T (x,t)φ(p(x,t))=0, If α(x,t) = 0, then we get α T (x,t)φ(p(x,t)) = α T (x,t)κ(x,σ,t) = 0, In summary, combining (21), (23), (24) and (25), we can get All Therefore, when ||x|| is large enough, For must be negative; Step 4.3), combined with (26), verify that system (1) is uniformly bounded, that is, if x(t0)=x0, then in, and Step 4.4), combined with (26), verify that system (1) has uniform final boundedness, that is, if x(t0)=x0, and ||x0||<r, then for the given have in, and

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