Optimal safety control method for aero-engine under time-varying temperature boundary

Abstract

The invention provides an optimal safety control method for an aero-engine under a time-varying temperature boundary, and relates to the technical field of aero-engine control. According to the method, safety boundaries faced by multiple controlled variables involved in the working process of the aero-engine are considered, and the aero-engine safety control problem under multiple safety constraints can be solved. The method comprises the following steps: firstly, designing a plurality of continuous differentiable functions according to a control target, considering different relative orders of each continuous differentiable function for an aero-engine system, and ensuring the safety of the system by means of a soft minimum function and a control barrier function; it is guaranteed that the researched aero-engine error system achieves asymptotic tracking through a second method in the Lyapunov stability theory; corresponding performance indexes are constructed, and optimization is achieved while constraint conditions are met.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft engine control, and in particular to an optimal safety control method for an aircraft engine under a time-varying temperature boundary. Background Art

[0002] The aircraft engine is a device that provides power for the aircraft. It is the "heart" of the aircraft. It has extremely complex aerodynamic and thermodynamic processes and works in a wide flight envelope. It is a complex system with strong nonlinearity and strong coupling. The design of the aircraft engine control system is a special multi-objective control system design process. Within the flight envelope, the purpose of the aircraft engine control system design is to enable it to operate stably and reliably under various environmental conditions and working conditions (such as cruising, acceleration, and deceleration) and give full play to its performance benefits. Therefore, it is necessary to seek a balance between the conflicting control objectives such as safety, performance indicators, and tracking performance. However, for aircraft engines, safety, performance indicators, and tracking performance are often contradictory.

[0003] First, aircraft engines face multiple safety boundaries during operation, such as the maximum temperature boundary, compressor surge boundary, maximum speed boundary, and lean and rich flameout boundaries. Once these safety boundaries are destroyed, it will be catastrophic for the engine. Therefore, safety protection measures are indispensable in engine control design. Secondly, the performance requirements faced by aircraft engines during operation include propulsion power, fuel efficiency, and thrust-to-weight ratio. Improving performance is of great significance to the rational use of resources and ensuring control effects. Therefore, optimizing performance indicators has received extensive attention and research in aircraft engine control design. In addition, tracking performance is also a very important indicator in control design, which indicates whether the aircraft engine can quickly provide the thrust required for the aircraft's flight actions. However, for aircraft engines, safety, performance indicators and tracking performance are often contradictory: if you want to respond quickly to a thrust increase command, you must quickly increase the turbine residual work, quickly increase the temperature before the turbine, and quickly increase the fuel supply. But if the fuel supply is increased too quickly, it will lead to dangers such as overheating, surge and rich flameout, as well as low performance due to reduced fuel efficiency. If you want to respond quickly to a thrust reduction command, you must quickly reduce the fuel supply, but this will put the engine at risk of lean flameout.

[0004] Most of the existing aircraft engine control methods do not take into account the safety and optimality of aircraft engines in working conditions. Among them, the optimal control design improves the performance of aircraft engines without considering the situation where the controlled quantity exceeds the safety boundary, which may cause safety accidents; the safety protection control design ignores performance, which may lead to poor performance. At the same time, the existing aircraft engine safety protection control methods rarely consider the situation where the controlled quantity has a time-varying safety boundary, which is different from the actual working characteristics of aircraft engines.

[0005] The control barrier function (CBF) is an emerging safety-critical control algorithm. Its core theory is to integrate the idea of ​​collective forward invariance into safety research. Inspired by the control Lyapunov function, the control barrier function is used to ensure the safety of dynamic systems. The control barrier function was first proposed in the paper "Controlbarrier function based quadratic programs for safety critical systems" and was subsequently applied to the control of various safety-critical systems. For example, a ground vehicle control method based on the control barrier function was proposed in the paper "Adaptive Cruise Control for Ground Vehicles using Control Barrier Function under Weather based Surface Conditions". Long L et al. proposed a new CLF-CBF-QP framework in the paper "Safety-critical control and optimization of nonlinear systems based on newforms of CLF-CBF-QP" to improve the feasibility of unmanned aerial vehicle optimization problems. However, in reality, many physical systems are high relative order systems, such as aircraft, mobile robots, drones, etc. The methods proposed for low relative order systems cannot be directly applied to high relative order systems. A safety control method applicable to arbitrary relative order is needed. Researchers have done a lot of work on high relative order safety constraints. High relative order control barrier functions were first proposed in the literature "Control barrier function based quadratic programs for safety critical systems". However, the results in this literature only extend to position-based safety constraints with a relative order of two. On the other hand, the results in the literature "Control barrier function based quadratic programs with application to bipedal robotic walking" use the backstepping method to extend the first-order safety constraints to arbitrary relative order constraints. However, for higher order systems, the design of control barrier functions based on the backstepping method is very complicated, especially for systems with a relative order greater than two.Wu G et al. proposed a high relative order control barrier function in “Safety-critical and constrained geometric control synthesis using control Lyapunov and controlbarrier functions for systems evolving on manifolds”, but the results were only extended to position-based safety constraints with relative order two. Xiao W et al. proposed a barrier function for high relative order constraints in “Controlbarrier functions for systems with high relative degree”, called the High Order Control Barrier Function (HOCBF), whose general form is related to the forward invariance of the intersection of a series of sets. Furthermore, a time-varying high relative order control barrier function was proposed in “High-order control barrier functions”, considering the controlled variable with a time-varying safety boundary. However, so far, the research on solving the safety protection control problem of aircraft engines using high relative order control barrier functions is still relatively limited; there are few safety protection control methods considering time-varying safety boundaries; and multiple safety constraints bring certain complexity to the construction and solution process of safety control.

[0006] Patent 202410763274.X discloses an aircraft engine acceleration limitation method, which is used for the acceleration limitation plan of a dual-spool engine. It provides a method for using the dual-spool engine acceleration limitation plan, predicts the risks brought by mode conversion during acceleration, and takes protective measures for the acceleration process of the dual-spool engine. However, this method does not consider the performance of the aircraft engine during operation, which may lead to poor performance. Patent 202410771470.1 discloses a method for designing a quadratic optimal controller for a variable cycle engine. The invention designs an augmented state space description, takes the augmented state as the optimization target, and determines the optimal controller gain by solving the algebraic Riccati equation. However, this method does not consider the situation where the controlled variable exceeds the safety boundary during the operation of the aircraft engine, which may lead to unsafe conditions in the control. Patent 202011440326.8 discloses a multivariable limiting protection control method for aircraft engines. This invention selects to activate the main control loop or the corresponding limiting protection loop in real time through online linearization and parameter prediction of the airborne model, and uses a multivariable controller to achieve direct control or limitation of unmeasurable variables. However, this method considers the time-varying upper limit of each controlled quantity, which is somewhat different from the operating characteristics of aircraft engines.

[0007] At present, the research on solving the safety protection control problem of aircraft engines by using high relative order control barrier functions is still relatively limited. The safety protection control method considering time-varying safety boundaries needs further research. Multiple safety constraints bring certain complexity to the construction and solution process of safety control and also to the engine control method. Summary of the invention

[0008] The technical problem to be solved by the present invention is to provide an optimal safety control method for aircraft engines under time-varying temperature boundaries in view of the deficiencies of the above-mentioned prior art, aiming to simultaneously achieve the three control objectives of safety protection, asymptotic tracking and performance index optimization.

[0009] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0010] The optimal safety control method for an aero-engine under a time-varying temperature boundary provided by the present invention aims at three control objectives of safety protection, asymptotic tracking and optimization of performance indicators. It is considered that the safety function designed for the high-pressure rotor speed increment is of high relative order for the system, and the low-pressure turbine outlet temperature increment has a time-varying safety boundary. With the help of a soft minimum function, the control barrier function is used to ensure the safety of the system; the second method in the Lyapunov stability theory is used to ensure that the error system of the aero-engine under study achieves asymptotic tracking; the corresponding performance indicators are constructed to achieve optimization while satisfying the above-mentioned constraints, and the method specifically includes the following steps:

[0011] Step 1: Select the controlled variable according to the aircraft engine control task and establish the aircraft engine system linearization model:

[0012] The high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment are selected as the controlled variables to ensure that the high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment do not exceed their respective upper limits, that is, n Hmax and T 6max (t), and at the same time make the aircraft engine system converge from the initial working point to the target equilibrium point x e =[0,0,0] T ;

[0013] The aircraft engine system is modeled as a linearized model. The linearized model of the aircraft engine system at the initial operating point is shown as follows:

[0014]

[0015] Among them, A∈R 3×3 is the state matrix, B∈R 3 is the input matrix, C∈R 1×3 is the output matrix, u∈R is the controller, n H , n L ,qmf and T6 represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate and low-pressure turbine outlet temperature, respectively. H0 , n L0 ,q mf0 and T 60 They represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate and low-pressure turbine outlet temperature at the initial operating point respectively;

[0016] High-pressure rotor speed n at target balance point He , low pressure rotor speed n Le , fuel flow q mfe , controller u and low pressure turbine outlet temperature T 6e The following conditions must be met:

[0017]

[0018] The linear model of the aircraft engine system is established as shown below:

[0019]

[0020] Among them, x is the state variable, y is the output variable, and the specific form is:

[0021]

[0022] Step 2: according to the controlled variable selected in step 1, a control target of the aircraft engine system is set, a plurality of continuously differentiable functions are designed according to the control target, a relative order of each continuously differentiable function for the aircraft engine system is given, a corresponding safety set is defined according to the designed continuously differentiable function, an auxiliary function is established, and a related set is obtained;

[0023] Step 2.1, setting the control target of the aircraft engine system according to the flight mission of the aircraft;

[0024] In order to achieve optimal safety control of the aircraft engine under time-varying temperature boundaries and simultaneously achieve asymptotic tracking, safety protection and performance optimization of the aircraft, the following control objectives are set:

[0025] (1) Asymptotic tracking, that is, the state variable x(t) of the aircraft engine system and the target equilibrium point x e Satisfy between:

[0026]

[0027] (2) Safety protection, i.e. the increment of high-pressure rotor speed and the increment of low-pressure turbine outlet temperature do not exceed their respective upper limits n Hmax and T 6max (t), for any time t ≥ 0, it satisfies:

[0028]

[0029] (3) Performance index optimization, the performance index J(x,u) is defined as:

[0030]

[0031] Step 2.2, designing multiple continuous differentiable functions according to the control objective set in step 2.1, and giving the relative order of each continuous differentiable function with respect to the aero-engine system;

[0032] Step 2.3, defining a corresponding safety set according to the continuously differentiable function designed in step 2.2, establishing an auxiliary function for the relative order of each continuously differentiable function to the aircraft engine system, and obtaining a related set;

[0033] According to multiple continuously differentiable functions Define the security set C(t) as follows:

[0034]

[0035] Where k is the dimension of the state variable and N is the continuous differentiable function h j The number of is a set consisting of elements 1 to N;

[0036] For m j Continuously differentiable functions with differentiable order Defining Helper Functions As shown below:

[0037]

[0038] Among them, α j,i Represents the extended K-type function, L f ψ j,0 (x,t) is ψ j,0 The Lie derivative of (x,t) with respect to f, is a function of the aircraft engine system state;

[0039] According to the safety set C(t) and the auxiliary function ψ j,i , and get the relevant set C j,i (t), as shown in the following formula:

[0040]

[0041] in, i∈{0,1,...,m j -2};

[0042] Step 3, using a soft minimum function to simplify multiple continuously differentiable functions or auxiliary functions into a single function;

[0043] Step 4: Use quadratic programming QP combined with CBF and Lyapunov stability theory to construct a CBF-QP algorithm for synthetic controllers to ensure that the aircraft engine system achieves the control target;

[0044] Step 4.1: Use quadratic programming QP combined with CBF to construct the CBF-QP algorithm to obtain the controller u * (t) To ensure that the aero-engine system meets safety constraints and minimizes performance indicators, and to ensure the safety of the aero-engine system linearization model by verifying the forward invariance of the set to the aero-engine system linearization model;

[0045] The specific method to verify the forward invariance of the set to the linearized model of the aeroengine is as follows:

[0046] For aero-engine systems, a continuously differentiable control obstacle function The set defined as follows

[0047]

[0048] If there exists an extended K-type function α such that

[0049]

[0050] Among them, L f h(x,t) is the Lie derivative of h(x,t) with respect to f, L g h(x,t) is the Lie derivative of h(x,t) with respect to g, are all functions of the aircraft engine system state; on this basis, any Lipschitz continuous controller u(t) that satisfies formula (14) is Make the set S(t) forward invariant to the aircraft engine system;

[0051] Use quadratic programming QP combined with CBF to construct the CBF-QP algorithm to obtain the controller u * The specific method of (t) is:

[0052] Define a single control barrier function for:

[0053]

[0054] Define the sets S(t) and C j (t) are:

[0055]

[0056] And satisfy The controller u obtained by formula (14) * (t), So that the set S(t)∩C s (t) For the system forward unchanged, the controller u * (t) is the controller obtained by using the CBF-QP algorithm;

[0057] Step 4.2, determine the stability of the aircraft engine system at the equilibrium point by the second method in Lyapunov stability theory;

[0058] The specific method for judging the stability of an aircraft engine system at the equilibrium point is:

[0059] The equation of state for an aero-engine system and y(0) = 0, if there exists a scalar function V(x) with continuous partial derivatives that satisfies the following two conditions: (1) V(x) is positive definite, and (2) is negative definite, then the equilibrium state of the system at the origin is uniformly asymptotically stable;

[0060] For the aircraft engine system, the scalar function V(x) is selected as

[0061] V(x)=x T Px (16)

[0062] Where P is a positive definite matrix, the first-order derivative of V(x) is in the form of:

[0063]

[0064] Step 4.3: Use quadratic programming QP combined with CBF and Lyapunov stability theory to obtain the controller of the optimal safety control strategy for the linearized model of the aircraft engine system, as shown in the following formula:

[0065]

[0066] Ensure that the aircraft engine system achieves asymptotic tracking while meeting safety constraints, while making the performance indicator J(x(t),u(t)) optimal.

[0067] The beneficial effects of adopting the above technical solution are: the present invention provides an optimal safety control method for aircraft engines under time-varying temperature boundaries, which considers that the continuously differentiable function designed for the high-pressure rotor speed increment is of high relative order for the system and the continuously differentiable function designed for the low-pressure turbine outlet temperature increment is time-varying, and constructs a soft minimum function to merge multiple safety constraints into a single constraint, while achieving the three control objectives of safety protection, asymptotic tracking and performance index optimization. The present invention considers the safety boundaries faced by multiple controlled quantities involved in the operation of aircraft engines, and can handle aircraft engine safety control problems under multiple safety constraints; BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A flow chart of an optimal safety control method for an aircraft engine under a time-varying temperature boundary provided by an embodiment of the present invention;

[0069] Figure 2 A schematic diagram of various safety boundaries faced by an aircraft engine provided by an embodiment of the present invention;

[0070] Figure 3 A high-pressure rotor speed increment curve diagram provided by an embodiment of the present invention;

[0071] Figure 4 A low-pressure turbine outlet temperature increment curve diagram provided by an embodiment of the present invention;

[0072] Figure 5 A performance indicator comparison curve diagram provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0074] The optimal safety control method of an aircraft engine under a time-varying temperature boundary of this embodiment is as follows: Figure 1 As shown, the following steps are included:

[0075] Step 1: Select the controlled variable according to the aircraft engine control task and establish the aircraft engine system linearization model:

[0076] This embodiment provides an optimal safety control method for an aircraft engine under a time-varying temperature boundary, which selects the high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment as controlled quantities to ensure that the high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment do not exceed their respective upper limits, i.e., n Hmax and T 6max (t), and at the same time make the aircraft engine system converge from the initial working point to the target equilibrium point x e =[0,0,0] T;

[0077] The aircraft engine system is modeled as a linearized model. The linearized model of the aircraft engine system at the initial operating point is shown as follows:

[0078]

[0079] Among them, A∈R 3×3 is the state matrix, B∈R 3 is the input matrix, C∈R 1×3 is the output matrix, u∈R is the controller, n H , n L ,q mf and T6 represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate and low-pressure turbine outlet temperature, respectively. H0 , n L0 ,q mf0 and T 60 They represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate and low-pressure turbine outlet temperature at the initial operating point respectively;

[0080] High-pressure rotor speed n at target balance point He , low pressure rotor speed n Le , fuel flow q mfe , controller u and low pressure turbine outlet temperature T 6e The following conditions must be met:

[0081]

[0082] The linear model of the aircraft engine system is established as shown below:

[0083]

[0084] Among them, x is the state variable, y is the output variable, and the specific form is:

[0085]

[0086] Step 2: according to the controlled variable selected in step 1, a control target of the aircraft engine system is set, a plurality of continuously differentiable functions are designed according to the control target, a relative order of each continuously differentiable function for the aircraft engine system is given, a corresponding safety set is defined according to the designed continuously differentiable function, an auxiliary function is established, and a related set is obtained;

[0087] Step 2.1, setting the control target of the aircraft engine system according to the flight mission of the aircraft;

[0088] Aircraft engines face multiple safety boundaries during operation, such as Figure 2As shown, in this embodiment, in order to achieve optimal safety control of the aircraft engine under the time-varying temperature boundary, and at the same time achieve the asymptotic tracking, safety protection and performance index optimization of the aircraft, the following control objectives are set:

[0089] (1) Asymptotic tracking, that is, the state variable x(t) of the aircraft engine system and the target equilibrium point x e Satisfy between:

[0090]

[0091] (2) Safety protection, i.e. the increment of high-pressure rotor speed and the increment of low-pressure turbine outlet temperature do not exceed their respective upper limits n Hmax and T 6max (t), for any time t ≥ 0, it satisfies:

[0092]

[0093] (3) Performance index optimization, the performance index J(x,u) is defined as:

[0094]

[0095] Step 2.2, designing multiple continuous differentiable functions according to the control objectives set in step 2.1, and giving the relative order of each continuous differentiable function with respect to the aero-engine system;

[0096] In this embodiment, based on the control target set in step 2.1, two continuously differentiable functions h1 and h2 are designed, as shown in the following formula:

[0097]

[0098] Among them, x1 is the first component of the state variable x, that is, the high-pressure rotor speed increment; the continuous differentiable function h2 is a time-varying function;

[0099] According to the fact that the continuously differentiable function h1 designed for the high-pressure rotor speed increment is of high relative order for the aircraft engine system, and the low-pressure turbine outlet temperature increment has a time-varying upper limit, the relative order of the continuously differentiable function h1 for the aircraft engine system is 2, and the relative order of the continuously differentiable function h2 for the aircraft engine system is 1;

[0100] Step 2.3, defining a corresponding safety set according to the continuously differentiable function designed in step 2.2, establishing an auxiliary function for the relative order of each continuously differentiable function to the aircraft engine system, and obtaining a related set;

[0101] For an aero-engine system modeled as an affine nonlinear system:

[0102]

[0103] in, is the aircraft engine system status, is the aircraft engine control input, is a function of the state of the aircraft engine system and is locally Lipschitz continuous;

[0104] According to multiple continuously differentiable functions Define the security set C(t) as follows:

[0105]

[0106] Where k is the dimension of the state variable and N is the continuous differentiable function h j The number of is a set consisting of elements 1 to N;

[0107] For m j Continuously differentiable functions with differentiable order Defining Helper Functions As shown below:

[0108]

[0109] Among them, α j,i Represents the extended K-type function, L f ψ j,0 (x,t) is ψ j,0 The Lie derivative of (x,t) with respect to f, is a function of the aircraft engine system state;

[0110] The method for determining the extended K-type function is as follows: for a continuous function α(r):[0,a)→[0,∞),a>0, if α(r) is strictly increasing and satisfies α(0)=0, then the function α(r) is called a K-type function; for a continuous function α(r):(-b,a)→(-∞,∞),a,b>0, if α(r) is strictly increasing and satisfies α(0)=0, then the function is called an extended K-type function.

[0111] For continuously differentiable functions if Where α is an extended K-type function, and b(t0)≥0, then b(t)≥0,

[0112] According to the safety set C(t) and the auxiliary function ψ j,i , and get the relevant set C j,i (t), as shown in the following formula:

[0113]

[0114] in, i∈{0,1,...,m j -2};

[0115] In this embodiment, based on the two continuously differentiable functions h1 and h2 designed in step 2.2, a safety set C′(t) of the following form is defined:

[0116] C′(t)={x∈R 3 :h1(x)≥0,h2(x,t)≥0} (13)

[0117] For the continuously differentiable function h1(x) designed in step 2.2, define the auxiliary function ψ′:R 3 →R:

[0118]

[0119] Among them, α1 represents the extended K-type function.

[0120] According to the continuously differentiable functions h1 and h2 designed in step 2.2 and the auxiliary function ψ′(x), the relevant set of this embodiment is obtained, as shown in the following formula:

[0121]

[0122] Step 3, using a soft minimum function to simplify multiple continuously differentiable functions or auxiliary functions into a single function;

[0123] Define the soft minimum function As shown in the following formula:

[0124]

[0125] Among them, ρ>0 is the parameter that controls the “softness” of the soft minimum function, b λ ,λ∈[1,W] is a function, W is the number of functions;

[0126] The soft minimum function is used to simplify multiple functions into a single function, as shown in the following formula:

[0127]

[0128] because but

[0129]

[0130] In this embodiment, a soft minimum function is used to simplify multiple functions into a single function.

[0131]

[0132] Step 4: Use quadratic programming QP combined with CBF and Lyapunov stability theory to construct a CBF-QP algorithm for synthetic controllers to ensure that the aircraft engine system achieves the control target;

[0133] Step 4.1: Use quadratic programming QP combined with CBF to construct the CBF-QP algorithm to obtain the controller u * (t) To ensure that the aircraft engine system meets the safety constraints and minimizes the performance indicators, and to ensure the safety of the aircraft engine linearization system by verifying the forward invariance of the set to the aircraft engine linearization system;

[0134] Forward invariance means that for an aircraft engine system, if any initial state y(t0)∈C(t0), the state trajectory of the system y(t)∈C(t), If the security set C(t) is forward invariant to the system, then the system is said to be secure with respect to the security set C(t);

[0135] In this embodiment, the specific method for verifying the forward invariance of the set to the linearized model of the aircraft engine is:

[0136] For aero-engine systems, a continuously differentiable control obstacle function The set defined as follows

[0137]

[0138] If there exists an extended K-type function α such that

[0139]

[0140] Among them, L f h′(x, t) is the Lie derivative of h′(x, t) with respect to f, L g h′(x,t) is the Lie derivative of h′(x,t) with respect to g, are all functions of the aircraft engine system state; on this basis, any Lipschitz continuous controller u(t) that satisfies formula (21) is Make the set S′(t) forward invariant to the aircraft engine system;

[0141] Use quadratic programming QP combined with CBF to construct the CBF-QP algorithm to obtain the controller u * The specific method of (t) is:

[0142] Define a single control barrier function for:

[0143]

[0144] Define the sets S(t) and C s (t) are:

[0145]

[0146] And satisfy The controller u obtained by formula (21) * (t), So that the set S(t)∩C s (t) For the system forward unchanged, the controller u * (t) is the controller obtained using the CBF-QP algorithm;

[0147] Specifically, since S(t) is forward-invariant for the aeroengine system, that is, h′(x(t),t)≥0, Take j * ∈{1,2,...,N}, according to formula (18), On this basis, due to According to formula (18), Repeat the above derivation steps to obtain Right now Because of J * The selection of is arbitrary, and we get x(t)∈C s (t), And x(t)∈S(t), We get x(t)∈S(t)∩C s (t), Therefore, we get the controller u * (t) such that S(t)∩C s (t) is forward-invariant to the system.

[0148] In this embodiment, the sets S′(t) and C are defined based on the control obstacle function h′(x, t). s ′(t), satisfies The controller u of this embodiment is obtained by using the CBF-QP algorithm * ′(t), where the set C s ′(t) is shown as follows:

[0149]

[0150] Step 4.2, determine the stability of the aircraft engine system at the equilibrium point by the second method in Lyapunov stability theory;

[0151] The specific method for judging the stability of an aircraft engine system at the equilibrium point is:

[0152] The equation of state for an aero-engine system and y(0) = 0, if there exists a scalar function V(x) with continuous partial derivatives that satisfies the following two conditions: (1) V(x) is positive definite, and (2) is negative definite, then the equilibrium state of the system at the origin is uniformly asymptotically stable;

[0153] For the aircraft engine system of this embodiment, the scalar function V(x) is selected as

[0154] V(x)=x T Px (26)

[0155] Where P is a positive definite matrix, the first-order derivative of V(x) is in the form of:

[0156]

[0157] Step 4.3: Use quadratic programming QP combined with CBF and Lyapunov stability theory to implement the controller of the optimal safety control strategy of the linearized model of the aircraft engine system, as shown in the following formula:

[0158]

[0159] Ensure that the aircraft engine system achieves asymptotic tracking while ensuring safety, and at the same time makes the performance indicator J(x(t),u(t)) reach the optimal level.

[0160] In this embodiment, MATLAB is used to simulate the aircraft engine system and establish the following aircraft engine linearization model:

[0161]

[0162] Where x = [x1, x2, x3] T ∈R 3 , u∈R, y∈R, ρ=20, select the high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment as the controlled variables, and the values ​​of various parameters are as follows:

[0163]

[0164] The optimal controller obtained by using the optimal safety control method for an aircraft engine under a time-varying temperature boundary provided by this embodiment is:

[0165] u * ′=[9.6303 -21.0434 -490.8718]x (31)

[0166] High pressure rotor speed increment (n H -n H0) Curve such as Figure 3 As shown in Figure 1, the aircraft tracks to a steady-state value of 715.274 r / min and never exceeds the upper speed limit of the high-pressure rotor of 730 r / min. The temperature increment at the outlet of the low-pressure turbine (T6-T 60 ) Curve such as Figure 4 As shown in FIG. 1 , the aircraft tracks to a steady-state value of 45.7555K and never exceeds the time-varying upper limit of the low-pressure turbine outlet temperature. By applying the optimal safety control method for an aircraft engine under a time-varying temperature boundary proposed in the present invention, the performance index is reduced and optimized, such as Figure 5 As shown, the simulation results verify the effectiveness of the optimal safety control method for aircraft engines under time-varying temperature boundaries proposed in the present invention.

[0167] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. An optimal safety control method for an aircraft engine under a time-varying temperature boundary, characterized by: The following steps are involved: Step 1: Select the controlled variable according to the aircraft engine control task and establish the aircraft engine system linearization model: Step 2: according to the controlled variable selected in step 1, a control target of the aircraft engine system is set, a plurality of continuously differentiable functions are designed according to the control target, a relative order of each continuously differentiable function for the aircraft engine system is given, a corresponding safety set is defined according to the designed continuously differentiable function, an auxiliary function is established, and a related set is obtained; Step 3, using a soft minimum function to simplify multiple continuously differentiable functions or auxiliary functions into a single function; Step 4: Use quadratic programming QP combined with CBF and Lyapunov stability theory to construct a CBF-QP algorithm for synthetic controller to ensure that the aircraft engine system achieves the control target.

2. The optimal safety control method for an aircraft engine under a time-varying temperature boundary according to claim 1, characterized in that: The step 1 specifically includes: The high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment are selected as the controlled variables to ensure that the high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment do not exceed their respective upper limits, that is, n Hmax and T 6max (t), and at the same time make the aircraft engine system converge from the initial working point to the target equilibrium point x e =[0,0,0] T ; The aircraft engine system is modeled as a linearized model. The linearized model of the aircraft engine system at the initial operating point is shown as follows: Among them, A∈R 3×3 is the state matrix, B∈R 3 is the input matrix, C∈R 1×3 is the output matrix, u∈R is the controller, n H , n L ,q mf and T6 represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate and low-pressure turbine outlet temperature, respectively. H0 , n L0 ,q mf0 and T 60 They represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate and low-pressure turbine outlet temperature at the initial operating point respectively; High-pressure rotor speed n at target balance point He , low pressure rotor speed n Le , fuel flow q mfe , controller u and low pressure turbine outlet temperature T 6e The following conditions must be met: The linear model of the aircraft engine system is established as shown below: Among them, x is the state variable, y is the output variable, and the specific form is:

3. The optimal safety control method for an aircraft engine under a time-varying temperature boundary according to claim 2 is characterized in that: The step 2 specifically includes: Step 2.1, setting the control target of the aircraft engine system according to the flight mission of the aircraft; Step 2.2, designing multiple continuous differentiable functions according to the control objectives set in step 2.1, and giving the relative order of each continuous differentiable function with respect to the aero-engine system; Step 2.3: Define the corresponding safety set according to the continuously differentiable function designed in step 2.2, establish auxiliary functions for the relative order of each continuously differentiable function to the aircraft engine system, and obtain the relevant set.

4. The optimal safety control method for an aircraft engine under a time-varying temperature boundary according to claim 3 is characterized in that: The step 2.1 specifically includes: In order to achieve optimal safety control of the aircraft engine under time-varying temperature boundaries and simultaneously achieve asymptotic tracking, safety protection and performance optimization of the aircraft, the following control objectives are set: (1) Asymptotic tracking, that is, the state variable x(t) of the aircraft engine system and the target equilibrium point x e Satisfy between: (2) Safety protection, i.e. the increment of high-pressure rotor speed and the increment of low-pressure turbine outlet temperature do not exceed their respective upper limits n Hmax and T 6max (t), for any time t ≥ 0, it satisfies: (3) Performance index optimization, the performance index J(x,u) is defined as:

5. The optimal safety control method for an aircraft engine under a time-varying temperature boundary according to claim 4, characterized in that: The step 2.3 specifically includes: According to multiple continuously differentiable functions Define the security set C(t) as follows: Where k is the dimension of the state variable and N is the continuous differentiable function h j The number of is a set consisting of elements 1 to N; For m j Continuously differentiable functions with differentiable order Defining Helper Functions As shown below: Among them, α j,i Represents the extended K-type function, L f ψ j,0 (x,t) is ψ j,0 The Lie derivative of (x,t) with respect to f, is a function of the aircraft engine system state; According to the safety set C(t) and the auxiliary function ψ j,i , and get the relevant set C j,i (t), as shown in the following formula: in, i∈{0,1,...,m j -2}.

6. The optimal safety control method for an aircraft engine under a time-varying temperature boundary according to claim 5, characterized in that: The step 4 specifically includes: Step 4.1: Use quadratic programming QP combined with CBF to construct the CBF-QP algorithm to obtain the controller u * (t) To ensure that the aero-engine system meets safety constraints and minimizes performance indicators, and to ensure the safety of the aero-engine system linearization model by verifying the forward invariance of the set to the aero-engine system linearization model; Step 4.2, determine the stability of the aircraft engine system at the equilibrium point by the second method in Lyapunov stability theory; Step 4.3: Use quadratic programming QP combined with CBF and Lyapunov stability theory to obtain the controller of the optimal safety control strategy for the linearized model of the aircraft engine system, ensuring that the aircraft engine system achieves asymptotic tracking while satisfying the control obstacle function and making the performance indicators optimal.

7. The optimal safety control method for an aircraft engine under a time-varying temperature boundary according to claim 6 is characterized in that: The step 4.1 specifically includes: The specific method to verify the forward invariance of the set to the linearized model of the aeroengine is: For aero-engine systems, a continuously differentiable control obstacle function The set defined as follows If there exists an extended K-type function α such that Among them, L f h(x,t) is the Lie derivative of h(x,t) with respect to f, L g h(x,t) is the Lie derivative of h(x,t) with respect to g, are all functions of the aircraft engine system state; on this basis, any Lipschitz continuous controller u(t) that satisfies formula (14) is Make the set S(t) forward invariant to the aircraft engine system; Use quadratic programming QP combined with CBF to construct the CBF-QP algorithm to obtain the controller u * The specific method of (t) is: Define a single control barrier function for: Define the sets S(t) and C j (t) are: And satisfy The controller u obtained by formula (14) * (t), So that the set S(t)∩C s (t) For the system forward unchanged, the controller u * (t) is the controller obtained using the CBF-QP algorithm.

8. The optimal safety control method for an aircraft engine under a time-varying temperature boundary according to claim 7, characterized in that: The step 4.2 specifically includes: The specific method for judging the stability of an aircraft engine system at the equilibrium point is: The state equation for the aero-engine system and y(0) = 0, if there exists a scalar function V(x) with continuous partial derivatives that satisfies the following two conditions: (1) V(x) is positive definite, and (2) is negative definite, then the equilibrium state of the system at the origin is uniformly asymptotically stable; For the aircraft engine system, the scalar function V(x) is selected as V(x)=x T Px (18) Where P is a positive definite matrix, the first-order derivative of V(x) is in the form of:

9. The optimal safety control method for an aircraft engine under a time-varying temperature boundary according to claim 8, characterized in that: The controller of the optimal safety control strategy of the linearized model of the aircraft engine system obtained in step 4.3 is shown as follows:

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