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

Abstract

The application provides an aero-engine optimal safety control method under time-varying temperature boundary, and relates to the technical field of aero-engine control. The method considers safety boundaries faced by multiple controlled variables in the working process of the aero-engine, and can process the aero-engine safety control problem under multiple safety constraints. Firstly, multiple continuous differentiable functions are designed according to a control target, different relative orders of the continuous differentiable functions for the aero-engine system are considered, a soft minimum function is used, and a 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 researched realizes asymptotic tracking; and a corresponding performance index is constructed to realize optimization while meeting the constraint conditions.

Description

Technical Field

[0001] This invention relates to the field of aero-engine control technology, and in particular to an optimal safety control method for aero-engines under time-varying temperature boundaries. Background Technology

[0002] An aero-engine is the power source for an aircraft, its "heart." It involves extremely complex aerodynamic and thermodynamic processes and operates within a wide flight envelope, making it a complex system with strong nonlinearity and coupling. The design of an aero-engine control system is a unique multi-objective control system design process. Within the flight envelope, the goal of the aero-engine control system design is to ensure stable and reliable operation under various environmental conditions and operating states (such as cruise, acceleration, and deceleration), and to fully utilize its performance benefits. Therefore, it is necessary to find a balance between conflicting control objectives such as safety, performance indicators, and tracking performance. However, for aero-engines, safety, performance indicators, and tracking performance are often contradictory.

[0003] First, aero-engines face multiple safety boundaries during operation, such as maximum temperature boundaries, compressor surge boundaries, maximum speed boundaries, and fuel-lean / rich fuel shut-off boundaries. The breach of these safety boundaries would have catastrophic consequences for the engine. Therefore, safety protection measures are essential in engine control design. Second, aero-engines face performance requirements such as propulsion power, fuel efficiency, and thrust-to-weight ratio. Improving performance is crucial for efficient resource utilization and ensuring effective control; therefore, optimizing performance indicators has received widespread attention and research in aero-engine control design. Furthermore, tracking performance is also a very important indicator in control design, demonstrating the aero-engine's ability to rapidly provide the thrust required for aircraft flight maneuvers. However, for aero engines, safety, performance indicators, and tracking performance are often contradictory: if you want to respond quickly to thrust increase commands, you need to quickly increase turbine residual power, quickly raise turbine inlet temperature, and quickly increase fuel supply. But if the fuel supply is increased too quickly, it will lead to dangers such as overheating, surge, and rich fuel shutdown, as well as low performance due to reduced fuel efficiency. If you want to respond quickly to thrust decrease commands, you need to quickly reduce fuel supply, but this will expose the engine to the danger of lean fuel shutdown.

[0004] Most existing aero-engine control methods fail to address both the safety and optimality of the aero-engine during operation. Optimal control design, while improving engine performance, neglects the possibility of controlled variables exceeding safety boundaries, potentially leading to safety accidents. Conversely, safety protection control design ignores performance, potentially resulting in poor performance. Furthermore, existing aero-engine safety protection control methods rarely consider situations where the controlled variables have time-varying safety boundaries, resulting in a discrepancy between their actual operating characteristics and those of aero-engines.

[0005] Control Barrier Function (CBF) is an emerging safety-critical control algorithm whose core theory integrates the concept of set forward invariance into safety research. Inspired by the control Lyapunov function, CBF is used to ensure the safety of dynamic systems. CBF was first proposed in the paper "Controlbarrier function based quadratic programs for safety critical systems" and has since been applied to the control of various safety-critical systems. For example, the paper "Adaptive Cruise Control for Ground Vehicles using Control Barrier Function under Weather based Surface Conditions" proposes a ground vehicle control method based on CBF. Long L et al., in their paper "Safety-critical control and optimization of nonlinear systems based on newforms of CLF-CBF-QP," proposed a new CLF-CBF-QP framework to improve the feasibility of UAV optimization problems. However, many physical systems in reality are high-relative-order systems, such as aircraft, mobile robots, and drones. Methods proposed for low-relative-order systems cannot be directly applied to high-relative-order systems, necessitating a safety control method applicable to arbitrary relative orders. Researchers have conducted extensive work on high-relative-order safety constraints. The concept of a high-relative-order control barrier function was first proposed in the paper "Control barrier function based quadratic programs for safety critical systems." However, the results in that paper only extend to position-based safety constraints with a relative order of two. On the other hand, the results in the paper "Control barrier function based quadratic programs with application to bipedal robotic walking" extend first-order safety constraints to arbitrary relative-order constraints using backstepping. However, for higher-order systems, designing control barrier functions based on backstepping is extremely complex, especially for systems with a relative order greater than two.In their paper "Safety-critical and constrained geometric control synthesis using control Lyapunov and control barrier functions for systems evolving on manifolds," Wu G et al. proposed a high relative order control barrier function, but their results only extended to position-based safety constraints with a relative order of two. Xiao W et al., in their paper "Control barrier functions for systems with high relative degree," proposed a barrier function for high relative order constraints, 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, in their paper "High-order control barrier functions," they proposed a time-varying high relative order control barrier function, considering that the controlled variable has a time-varying safety boundary. However, to date, research using high relative order control barrier functions to solve aero-engine safety protection control problems remains relatively limited; safety protection control methods considering time-varying safety boundaries are few; and multiple safety constraints introduce certain complexities to the construction and solution process of safety control.

[0006] Patent 202410763274.X discloses an acceleration limitation method for aero-engines, specifically for the acceleration limitation plan of a dual-bypass engine. This method provides an application method for the acceleration limitation plan of a dual-bypass engine, anticipating the risks associated with mode transitions during acceleration and implementing protective measures. However, this method does not consider the performance of the aero-engine during operation, potentially leading to poor performance. Patent 202410771470.1 discloses a quadratic optimal controller design method for a variable-cycle engine. This invention uses an augmented state-space description, employing the augmented state as the optimization objective, and determines the optimal controller gain by solving the algebraic Riccati equation. However, this method does not consider situations where the controlled variable exceeds the safety boundary during aero-engine operation, potentially leading to unsafe conditions in control. Patent 202011440326.8 discloses a multivariable limitation and protection control method for aero-engines. This invention uses online linearization and parameter prediction of an airborne model to select and activate the main control loop or the corresponding limitation and protection loop in real time. It 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 variable, which has a certain gap with the working characteristics of aero-engines.

[0007] Currently, research on using high relative order control obstacle functions to solve the safety protection control problem of aero-engines is still relatively limited. Safety protection control methods considering time-varying safety boundaries need further research. Multiple safety constraints also bring certain complexity to the construction and solution process of safety control and engine control methods. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide an optimal safety control method for aero-engines under time-varying temperature boundaries, which addresses the shortcomings of the prior art and aims to simultaneously achieve three control objectives: safety protection, asymptotic tracking, and performance optimization.

[0009] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0010] The optimal safety control method for aero-engines under time-varying temperature boundaries provided by this invention addresses three control objectives: safety protection, asymptotic tracking, and performance index optimization. It considers that the safety function designed for the high-pressure rotor speed increment is of high relative order for the system, and that the low-pressure turbine outlet temperature increment has a time-varying safety boundary. Using a soft minimum function, the system's safety is ensured by utilizing a control barrier function. The second method in Lyapunov stability theory ensures asymptotic tracking of the studied aero-engine error system. Corresponding performance indices are constructed to achieve optimization while satisfying the above constraints. Specifically, the method includes the following steps:

[0011] Step 1: Select the controlled variable based on the aero-engine control task and establish a linearized model of the aero-engine system:

[0012] The increments of high-pressure rotor speed and low-pressure turbine outlet temperature are selected as controlled variables to ensure that neither the increment of high-pressure rotor speed nor the increment of low-pressure turbine outlet temperature exceeds its respective upper limit. and Simultaneously, it enables the aero-engine system to converge from its initial operating point to the target equilibrium point. ;

[0013] The aero-engine system is modeled as a linear model, and the linear model of the aero-engine system at the initial operating point is shown in the following equation:

[0014] (1)

[0015] in, It is a state matrix. It is the input matrix. It is the output matrix. It is a controller. , , and These represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate, and low-pressure turbine outlet temperature, respectively. , , and These 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 at the target equilibrium point Low-pressure rotor speed fuel flow controller and low-pressure turbine outlet temperature The following conditions must be met:

[0017] (2)

[0018] A linearized model of the aero-engine system is established, as shown in the following equation:

[0019] (3)

[0020] in, For state variables, For output variables, the specific form is:

[0021] (4)

[0022] Step 2: Based on the controlled variable selected in Step 1, set the control objective of the aero-engine system, design multiple continuously differentiable functions according to the control objective, give the relative order of each continuously differentiable function with respect to the aero-engine system, define the corresponding safety set according to the designed continuously differentiable functions, establish auxiliary functions, and obtain the relevant set.

[0023] Step 2.1: Set the control objectives of the aero-engine system according to the flight mission of the aircraft;

[0024] To achieve optimal safety control of aero-engines under time-varying temperature boundaries, while simultaneously realizing asymptotic tracking, safety protection, and performance optimization of the aircraft, the following control objectives are set:

[0025] (1) Asymptotic tracking, i.e., the state variables of the aero-engine system Balance point with the target The following conditions must be met:

[0026] (5)

[0027] (2) Safety protection, namely, the increase in high-pressure rotor speed and the increase in low-pressure turbine outlet temperature do not exceed their respective upper limits. and For any At any moment, satisfaction:

[0028] (6)

[0029] (3) Optimization of performance indicators, performance indicators Defined as:

[0030] (7)

[0031] Step 2.2: Design multiple continuously differentiable functions based on the control objectives set in Step 2.1, and give the relative order of each continuously differentiable function with respect to the aero-engine system;

[0032] Step 2.3: Define the corresponding safety set based on the continuously differentiable functions designed in Step 2.2, and establish auxiliary functions for each continuously differentiable function with respect to the relative order of the aero-engine system to obtain the relevant set;

[0033] Based on multiple continuously differentiable functions Define a security set of the following form :

[0034] (8)

[0035] in, Let be the dimension of the state variables. A continuously differentiable function Quantity, From element 1 to The set that constitutes;

[0036] against Continuously differentiable functions of order differentiability Define auxiliary functions , As shown in the following formula:

[0037] (9)

[0038] in, Representation extension Class function, for about Li Daoshu, A function of the state of the aero-engine system;

[0039] According to security set and auxiliary functions To obtain the relevant set As shown in the formula below:

[0040] (10)

[0041] in, ;

[0042] Step 3: Use a soft minimum function to simplify multiple continuously differentiable functions or auxiliary functions into a single control barrier function;

[0043] Step 4: Construct the CBF-QP algorithm using quadratic programming (QP) combined with CBF and Lyapunov stability theory for the synthetic controller to ensure that the aero-engine system achieves the control objective;

[0044] Step 4.1: Construct the CBF-QP algorithm using quadratic programming (QP) combined with CBF to obtain the controller. To ensure that the aero-engine system meets safety constraints and minimizes performance indicators, the safety of the linearized model of the aero-engine system is guaranteed by verifying the forward invariance of the set to the linearized model of the aero-engine system.

[0045] The specific method for verifying the forward invariance of the set to the linearized model of the aero-engine is as follows:

[0046] For aero-engine systems, a continuously differentiable control barrier function is used. The set defined as shown in the following formula :

[0047] (11)

[0048] If an extension exists Class function Make

[0049] (12)

[0050] in, for about Li Daoshu, for about Li Daoshu, , Both are functions of the aero-engine system state; based on this, any Lipschitz continuous controller satisfying formula (14) , Make the set For the forward direction of the aero-engine system, it remains unchanged;

[0051] The controller is obtained by constructing the CBF-QP algorithm using quadratic programming (QP) combined with CBF. The specific method is as follows:

[0052] Define a single control barrier function for:

[0053] (13)

[0054] Define a set and They are respectively:

[0055] (14)

[0056] (15)

[0057] And satisfy The controller obtained by formula (14) , Make the set For a forward-invariant system, the controller That is, to obtain the controller using the CBF-QP algorithm;

[0058] Step 4.2: Determine the stability of the aero-engine system at the equilibrium point using the second method in Lyapunov's stability theory;

[0059] The specific method for determining the stability of an aero-engine system at its equilibrium point is as follows:

[0060] State equations for aero-engine systems ,and If there exists a scalar function with continuous partial derivatives And it meets the following two conditions: (1) It is positive definite, (2) If the equilibrium value is negative definite, then the equilibrium state of the system at the origin is uniformly asymptotically stable.

[0061] For aero-engine systems, scalar functions are selected. for

[0062] (16)

[0063] in, If it is a positive definite matrix, then The first derivative is in the form of:

[0064] (17)

[0065] Step 4.3: Using quadratic programming (QP) combined with CBF and Lyapunov stability theory, the controller for the optimal safety control strategy of the linearized model of the aero-engine system is obtained, as shown in the following equation:

[0066] (18)

[0067] To ensure that the aero-engine system achieves asymptotic tracking while meeting safety constraints, and simultaneously improves performance indicators. To achieve optimal results.

[0068] The beneficial effects of adopting the above technical solution are as follows: The optimal safety control method for aero-engines under time-varying temperature boundaries provided by this invention 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. It constructs a soft minimum function to integrate multiple safety constraints into a single constraint, simultaneously achieving three control objectives: safety protection, asymptotic tracking, and performance index optimization. This invention considers the safety boundaries faced by multiple controlled variables involved in the operation of aero-engines and can handle aero-engine safety control problems under multiple safety constraints. Attached Figure Description

[0069] Figure 1 A flowchart of an optimal safety control method for an aero-engine under time-varying temperature boundaries provided by an embodiment of the present invention;

[0070] Figure 2 This is a schematic diagram illustrating the various safety boundaries faced by an aero-engine as provided in an embodiment of the present invention;

[0071] Figure 3 A high-voltage rotor speed increment curve provided for an embodiment of the present invention;

[0072] Figure 4 This is a low-pressure turbine outlet temperature increment curve provided for an embodiment of the present invention;

[0073] Figure 5 Performance index comparison curves provided for embodiments of the present invention. Detailed Implementation

[0074] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0075] This embodiment presents an optimal safety control method for aero-engines under time-varying temperature boundaries, such as... Figure 1 As shown, it includes the following steps:

[0076] Step 1: Select the controlled variable based on the aero-engine control task and establish a linearized model of the aero-engine system:

[0077] This embodiment provides an optimal safety control method for aero-engines under time-varying temperature boundaries. It selects the high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment as controlled variables, ensuring that the high-pressure rotor speed increment and the low-pressure turbine outlet temperature increment do not exceed their respective upper limits. and Simultaneously, it enables the aero-engine system to converge from its initial operating point to the target equilibrium point. ;

[0078] The aero-engine system is modeled as a linear model, and the linear model of the aero-engine system at the initial operating point is shown in the following equation:

[0079] (1)

[0080] in, It is a state matrix. It is the input matrix. It is the output matrix. For controller, , , and These represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate, and low-pressure turbine outlet temperature, respectively. , , and These 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.

[0081] High-pressure rotor speed at the target equilibrium point Low-pressure rotor speed fuel flow controller and low-pressure turbine outlet temperature The following conditions must be met:

[0082] (2)

[0083] A linearized model of the aero-engine system is established, as shown in the following equation:

[0084] (3)

[0085] in, For state variables, For output variables, the specific form is:

[0086] (4)

[0087] Step 2: Based on the controlled variable selected in Step 1, set the control objective of the aero-engine system, design multiple continuously differentiable functions according to the control objective, give the relative order of each continuously differentiable function with respect to the aero-engine system, define the corresponding safety set according to the designed continuously differentiable functions, establish auxiliary functions, and obtain the relevant set.

[0088] Step 2.1: Set the control objectives of the aero-engine system according to the flight mission of the aircraft;

[0089] Aero engines face multiple safety boundaries during operation, such as Figure 2 As shown, in this embodiment, to achieve optimal safety control of the aero-engine under time-varying temperature boundaries, and simultaneously realize asymptotic tracking, safety protection, and performance optimization of the aircraft, the following control objectives are set:

[0090] (1) Asymptotic tracking, i.e., the state variables of the aero-engine system Balance point with the target The following conditions must be met:

[0091] (5)

[0092] (2) Safety protection, namely, the increase in high-pressure rotor speed and the increase in low-pressure turbine outlet temperature do not exceed their respective upper limits. and For any At any moment, satisfaction:

[0093] (6)

[0094] (3) Optimization of performance indicators, performance indicators Defined as:

[0095] (7)

[0096] Step 2.2: Design multiple continuously differentiable functions based on the control objectives set in Step 2.1, and give the relative order of each continuously differentiable function with respect to the aero-engine system;

[0097] In this embodiment, based on the control objective set in step 2.1, two continuously differentiable functions are designed. and As shown in the following formula:

[0098] (8)

[0099] in, State variables The first component, namely the high-voltage rotor speed increment; a continuously differentiable function. It is a time-varying function;

[0100] Based on a continuously differentiable function designed for the speed increment of the high-voltage rotor For aero-engine systems of high relative order, and where the low-pressure turbine outlet temperature increment has a time-varying upper limit, give a continuously differentiable function. For an aero-engine system, a continuously differentiable function of relative order 2... The relative order of the aero-engine system is 1;

[0101] Step 2.3: Define the corresponding safety set based on the continuously differentiable functions designed in Step 2.2, and establish auxiliary functions for each continuously differentiable function with respect to the relative order of the aero-engine system to obtain the relevant set;

[0102] For aero-engine systems modeled as affine nonlinear systems:

[0103] (9)

[0104] in, It is the status of the aircraft engine system. It is the control input for aircraft engines. , It is a function of the state of the aero-engine system and is locally Lipschitz continuous;

[0105] Based on multiple continuously differentiable functions Define a security set of the following form :

[0106] (10)

[0107] in, Let be the dimension of the state variables. A continuously differentiable function Quantity, From element 1 to The set that constitutes;

[0108] against Continuously differentiable functions of order differentiability Define auxiliary functions , As shown in the following formula:

[0109] (11)

[0110] in, Representation extension Class function, for about Li Daoshu, It is a function of the state of the aero-engine system;

[0111] Extend The method for determining the type of function is as follows: for continuous functions... ,like Strictly increasing and satisfying Then the function Known as Class function; for continuous functions ,like Strictly increasing and satisfying Then the function is called an extended function. Function-like.

[0112] For continuously differentiable functions ,if , ,in It is an extension Class function, and ,So , .

[0113] According to security set and auxiliary functions To obtain the relevant set As shown in the formula below:

[0114] (12)

[0115] in, ;

[0116] In this embodiment, based on the two continuously differentiable functions designed in step 2.2 and Define a security set of the following form :

[0117] (13)

[0118] For the continuously differentiable function designed in step 2.2 Define auxiliary functions :

[0119] (14)

[0120] in, Representation extension Function-like.

[0121] Based on the continuously differentiable function designed in step 2.2 and and auxiliary functions The relevant set for this embodiment is obtained as shown in the following formula:

[0122] (15)

[0123] Step 3: Use a soft minimum function to simplify multiple continuously differentiable functions or auxiliary functions into a single control barrier function;

[0124] Define the soft minimum function As shown in the formula below:

[0125] (16)

[0126] in, To control the parameters of the soft minimum function, , For function, The number of functions;

[0127] Multiple functions can be simplified into a single function using the soft minimum function, as shown in the following equation:

[0128] (17)

[0129] because ,but

[0130] (18)

[0131] In this embodiment, a soft minimum function is used to combine multiple functions. and Simplify to a single function :

[0132] (19)

[0133] Step 4: Construct the CBF-QP algorithm using quadratic programming (QP) combined with CBF and Lyapunov stability theory for the synthetic controller to ensure that the aero-engine system achieves the control objective;

[0134] Step 4.1: Construct the CBF-QP algorithm using quadratic programming (QP) combined with CBF to obtain the controller. To ensure that the aero-engine system meets safety constraints and minimizes performance indicators, the safety of the aero-engine linearization system is guaranteed by verifying the forward invariance of the set on the aero-engine linearization system.

[0135] Forward invariance means that for an aero-engine system, if any initial state... The system's state trajectory , Then it is called a safe set. For this system, it is forward invariant; if the security set is... If the system is forward invariant, then the system is said to be secure with respect to a set. It is safe;

[0136] In this embodiment, the specific method for verifying the forward invariance of the set to the linearized model of the aero-engine is as follows:

[0137] For aero-engine systems, a continuously differentiable control barrier function is used. The set defined as shown in the following formula :

[0138] (20)

[0139] If an extension exists Class function Make

[0140] (twenty one)

[0141] in, for about Li Daoshu, for about Li Daoshu, , Both are functions of the aero-engine system state; based on this, any Lipschitz continuous controller satisfying formula (21) , Make the set For the forward direction of the aero-engine system, it remains unchanged;

[0142] The controller is obtained by constructing the CBF-QP algorithm using quadratic programming (QP) combined with CBF. The specific method is as follows:

[0143] Define a single control barrier function for:

[0144] (twenty two)

[0145] Define a set and They are respectively:

[0146] (twenty three)

[0147] (twenty four)

[0148] And satisfy The controller obtained by formula (21) , Make the set For a forward-invariant system, the controller That is, the controller obtained using the CBF-QP algorithm;

[0149] Specifically, due to For the forward direction of the aero-engine system to remain unchanged, that is ,Pick According to formula (18), Based on this, due to According to formula (18), we know Repeat the above derivation steps to obtain ,Right now ;because The selection of is arbitrary, resulting in ,and ,get Therefore, the controller is obtained. Make The system remains unchanged forward.

[0150] In this embodiment, based on the control barrier function Define sets separately and ,satisfy The controller of this embodiment is obtained using the CBF-QP algorithm. , where the set As shown in the following formula:

[0151] (25)

[0152] Step 4.2: Determine the stability of the aero-engine system at the equilibrium point using the second method in Lyapunov's stability theory;

[0153] The specific method for determining the stability of an aero-engine system at its equilibrium point is as follows:

[0154] State equations for aero-engine systems ,and If there exists a scalar function with continuous partial derivatives And it meets the following two conditions: (1) It is positive definite, (2) If the equilibrium value is negative definite, then the equilibrium state of the system at the origin is uniformly asymptotically stable.

[0155] For the aero-engine system in this embodiment, a scalar function is selected. for

[0156] (26)

[0157] in, If it is a positive definite matrix, then The first derivative is in the form of:

[0158] (27)

[0159] Step 4.3: Utilize quadratic programming (QP) combined with CBF and Lyapunov stability theory to realize the controller for the optimal safety control strategy of the linearized model of the aero-engine system, as shown in the following equation:

[0160] (28)

[0161] To ensure that the aero-engine system achieves asymptotic tracking while maintaining safety, and simultaneously improves performance indicators. To achieve optimal results.

[0162] In this embodiment, MATLAB is used to simulate the aero-engine system, and a linearized aero-engine model of the following form is established:

[0163] (29)

[0164] in, , , ,Pick The increment of high-pressure rotor speed and the increment of low-pressure turbine outlet temperature are selected as the controlled variables, and the values ​​of each parameter are as follows:

[0165] (30)

[0166] The optimal controller obtained using the optimal safety control method for aero-engines under time-varying temperature boundaries provided in this embodiment is:

[0167] (31)

[0168] High-voltage rotor speed increment Curves Figure 3 As shown, the aircraft tracked to a steady-state value of 715.274. And it never exceeded the upper speed limit of 730 rpm for the high-pressure rotor. Low-pressure turbine outlet temperature increment Curves Figure 4 As shown, the aircraft tracked to a steady-state value of 45.7555. Furthermore, the temperature never exceeded the time-varying upper limit of the low-pressure turbine outlet temperature. Applying the optimal safety control method for aero-engines under the time-varying temperature boundary proposed in this invention, performance indicators were reduced and optimized, such as... Figure 5As shown, the simulation results verify the effectiveness of the optimal safety control method for aero-engines under time-varying temperature boundaries proposed in this invention.

[0169] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions 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 aero-engines under time-varying temperature boundaries, characterized in that: Includes the following steps: Step 1: Select the controlled variable based on the aero-engine control task and establish a linearized model of the aero-engine system: Step 2: Based on the controlled variable selected in Step 1, set the control objective of the aero-engine system, design multiple continuously differentiable functions according to the control objective, give the relative order of each continuously differentiable function with respect to the aero-engine system, define the corresponding safety set according to the designed continuously differentiable functions, establish auxiliary functions, and obtain the relevant set. Step 3: Use a soft minimum function to simplify multiple continuously differentiable functions or auxiliary functions into a single control barrier function; Step 4: Construct the CBF-QP algorithm using quadratic programming (QP) combined with CBF and Lyapunov stability theory for the synthetic controller, ensuring that the aero-engine system achieves the control objectives.

2. The optimal safety control method for aero-engines under time-varying temperature boundaries according to claim 1, characterized in that: Step 1 specifically includes: The increments of high-pressure rotor speed and low-pressure turbine outlet temperature are selected as controlled variables to ensure that neither the increment of high-pressure rotor speed nor the increment of low-pressure turbine outlet temperature exceeds its respective upper limit. and Simultaneously, it enables the aero-engine system to converge from its initial operating point to the target equilibrium point. ; The aero-engine system is modeled as a linear model, and the linear model of the aero-engine system at the initial operating point is shown in the following equation: (1) in, It is a state matrix. It is the input matrix. It is the output matrix. It is a controller. , , and These represent the high-pressure rotor speed, low-pressure rotor speed, fuel flow rate, and low-pressure turbine outlet temperature, respectively. , , and These 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 at the target equilibrium point Low-pressure rotor speed fuel flow controller and low-pressure turbine outlet temperature The following conditions must be met: (2) A linearized model of the aero-engine system is established, as shown in the following equation: (3) in, For state variables, For output variables, the specific form is: (4)。 3. The optimal safety control method for aero-engines under time-varying temperature boundaries according to claim 2, characterized in that: Step 2 specifically includes: Step 2.1: Set the control objectives of the aero-engine system according to the flight mission of the aircraft; Step 2.2: Design multiple continuously differentiable functions based on the control objectives set in Step 2.1, and give the relative order of each continuously differentiable function with respect to the aero-engine system; Step 2.3: Define the corresponding safety set based on the continuously differentiable functions designed in Step 2.2, and establish auxiliary functions for the relative order of each continuously differentiable function with respect to the aero-engine system to obtain the relevant set.

4. The optimal safety control method for aero-engines under time-varying temperature boundaries according to claim 3, characterized in that: Step 2.1 specifically includes: To achieve optimal safety control of aero-engines under time-varying temperature boundaries, while simultaneously realizing asymptotic tracking, safety protection, and performance optimization of the aircraft, the following control objectives are set: (1) Asymptotic tracking, i.e., the state variables of the aero-engine system Balance point with the target The following conditions must be met: (5) (2) Safety protection, namely, the increase in high-pressure rotor speed and the increase in low-pressure turbine outlet temperature do not exceed their respective upper limits. and For any At any moment, satisfaction: (6) (3) Optimization of performance indicators, performance indicators Defined as: (7)。 5. The optimal safety control method for an aero-engine under time-varying temperature boundaries according to claim 4, characterized in that: Step 2.3 specifically includes: Based on multiple continuously differentiable functions , , Define a security set of the following form : (8) in, Let be the dimension of the state variables. A continuously differentiable function Quantity, From element 1 to The set that constitutes; against Continuously differentiable functions of order differentiability , Define auxiliary functions , , As shown in the following formula: (9) in, Representation extension Class function, for about Li Daoshu, A function of the state of the aero-engine system; According to security set and auxiliary functions To obtain the relevant set As shown in the formula below: (10) in, , .

6. The optimal safety control method for an aero-engine under time-varying temperature boundaries according to claim 5, characterized in that: Step 4 specifically includes: Step 4.1: Construct the CBF-QP algorithm using quadratic programming (QP) combined with CBF to obtain the controller. To ensure that the aero-engine system meets safety constraints and minimizes performance indicators, the safety of the linearized model of the aero-engine system is guaranteed by verifying the forward invariance of the set to the linearized model of the aero-engine system. Step 4.2: Determine the stability of the aero-engine system at the equilibrium point using the second method in Lyapunov's stability theory; Step 4.3: Using quadratic programming (QP) combined with CBF and Lyapunov stability theory, the controller of the optimal safety control strategy for the linearized model of the aero-engine system is obtained, which ensures that the aero-engine system achieves asymptotic tracking under the premise of satisfying the control obstacle function, while making the performance index reach the optimal level.

7. The optimal safety control method for aero-engines under time-varying temperature boundaries according to claim 6, characterized in that: Step 4.1 specifically includes: The specific method for verifying the forward invariance of the set to the linearized model of the aero-engine is as follows: For aero-engine systems, a continuously differentiable control barrier function is used. The set defined as shown in the following formula : (11) If an extension exists Class function Make (12) in, for about Li Daoshu, for about Li Daoshu, , Both are functions of the aero-engine system state; based on this, any Lipschitz continuous controller satisfying formula (14) , Make the set For the forward direction of the aero-engine system, it remains unchanged; The controller is obtained by constructing the CBF-QP algorithm using quadratic programming (QP) combined with CBF. The specific method is as follows: Define the control barrier function for: (13) Define a set and They are respectively: (14) (15) And satisfy The controller obtained by formula (14) , Make the set For a forward-invariant system, the controller This means using the CBF-QP algorithm to obtain the controller.

8. The optimal safety control method for aero-engines under time-varying temperature boundaries according to claim 7, characterized in that: Step 4.2 specifically includes: The specific method for determining the stability of an aero-engine system at its equilibrium point is as follows: State equations for aero-engine systems ,and If there exists a scalar function with continuous partial derivatives And it meets the following two conditions: (1) It is positive definite, (2) If the equilibrium value is negative, then the equilibrium state of the system at the origin is uniformly asymptotically stable. For aero-engine systems, scalar functions are selected. for (16) in, If it is a positive definite matrix, then The first derivative is in the form of: (17)。 9. The optimal safety control method for an aero-engine under time-varying temperature boundaries according to claim 8, characterized in that: The controller for the optimal safety control strategy of the linearized model of the aero-engine system obtained in step 4.3 is shown in the following equation: (18)。

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