CN115128966A - Design method and simulation method of a turbofan engine all-envelope controller - Google Patents

Design method and simulation method of a turbofan engine all-envelope controller Download PDF

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CN115128966A
CN115128966A CN202210375143.5A CN202210375143A CN115128966A CN 115128966 A CN115128966 A CN 115128966A CN 202210375143 A CN202210375143 A CN 202210375143A CN 115128966 A CN115128966 A CN 115128966A
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曾建平
吴盛华
张加劲
余联郴
岳世壮
张家熹
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Abstract

The application provides a design method of a turbofan engine full-envelope controller, which comprises the following steps: s1, establishing an NPV model of the turbofan engine, wherein the NPV model comprises external disturbance, and converting the NPV model into an uncertain model according to the external disturbance; s2, designing a robust controller of a large envelope curve S3 based on the uncertain model, and designing a preset performance parameter matrix in the robust controller of the large envelope curve according to the performance index requirement of a turbofan engine closed-loop system; s4, solving a state feedback gain matrix in the robust controller of the large envelope curve by utilizing an SOS technology, thereby solving the robust controller of the large envelope curve; s5, designing a PI controller of the turbofan engine in a throttling state, and combining the PI controller and the large-envelope linear robust controller into the full-envelope controller by using a switching module. The full-envelope controller can better adapt to the non-linear model of the turbofan engine, so that the full-envelope controller has better control stability.

Description

一种涡扇发动机全包线控制器的设计方法与仿真方法Design method and simulation method of a turbofan engine all-envelope controller

技术领域technical field

本申请涉及航空发动机控制技术领域,具体涉及一种涡扇发动机全包线控制器的设计方法与仿真方法。The present application relates to the technical field of aero-engine control, in particular to a design method and a simulation method of an all-envelope controller of a turbofan engine.

背景技术Background technique

涡扇发动机由于其推力大,推进效率高等优点,目前已经广泛应用在国防和民用领域。但是,由于涡扇发动机的飞行参数和内部参数会在较大范围内变化,且发动机机械结构复杂,使得涡扇发动机系统气动热力学行为复杂,且有显著的非线性、时变、强耦合和不确定性,这给涡扇发动机全包线控制器设计带来极大挑战。Turbofan engines have been widely used in national defense and civil fields due to their advantages of high thrust and high propulsion efficiency. However, due to the fact that the flight parameters and internal parameters of the turbofan engine will change in a large range, and the mechanical structure of the engine is complex, the aerodynamic and thermodynamic behavior of the turbofan engine system is complex, and there are significant nonlinear, time-varying, strong coupling and invariance. Deterministic, which brings great challenges to the design of the turbofan engine all-envelope controller.

在现役的涡扇发动机控制系统中,全包线控制器的设计多采用增益调度方案。通过控制器增益在线调整,以适应系统的非线性和参数变化特性。但是单纯的增益调度缺乏理论上的严密性,其控制效果的有效性依赖于大量的地基和控制飞行模拟实验。且控制器参数以开环方式变更,当调度变量快速变化,难以捕捉被控对象的非线性特征时,系统的稳定性难以保证。随着非线性系统建模方法的发展与完善,用于非线性系统控制的线性变参数(linear parameter-varying,LPV)模型应运而生。然而,LPV模型只是原系统在相应工作点的一阶近似,不能反映系统的完整动态。非线性变参数 (nonlinear parameter-varying,NPV)模型可以描述被控对象的时变和非线性动力学特征。该模型一方面弥补了LPV在刻画被控对象非线性特性的不足,另一方面,借鉴Prajna所提的将非线性系统表示为状态依赖的类线性系统的实现,可以借助成熟的工具处理非线性时变问题。在此基础上,建立这类非线性时变系统的性能分析方法和控制设计理论,可以有效解决涡扇发动机控制相关问题。In the current turbofan engine control system, the design of the full envelope controller mostly adopts the gain scheduling scheme. The controller gain is adjusted online to adapt to the nonlinearity and parameter variation characteristics of the system. However, the simple gain scheduling lacks theoretical rigor, and the effectiveness of its control effect depends on a large number of ground-based and control flight simulation experiments. In addition, the controller parameters are changed in an open-loop manner. When the scheduling variables change rapidly and it is difficult to capture the nonlinear characteristics of the controlled object, the stability of the system is difficult to guarantee. With the development and improvement of nonlinear system modeling methods, the linear parameter-varying (LPV) model for nonlinear system control emerges as the times require. However, the LPV model is only a first-order approximation of the original system at the corresponding operating point, and cannot reflect the complete dynamics of the system. The nonlinear parameter-varying (NPV) model can describe the time-varying and nonlinear dynamic characteristics of the plant. On the one hand, this model makes up for the lack of LPV in describing the nonlinear characteristics of the plant. On the other hand, drawing on Prajna's implementation of representing nonlinear systems as state-dependent quasi-linear systems, mature tools can be used to deal with nonlinearities. time-varying problem. On this basis, the performance analysis method and control design theory of this kind of nonlinear time-varying system are established, which can effectively solve the problems related to turbofan engine control.

基于以上背景,本申请提供一种涡扇发动机全包线控制器的设计方法与仿真方法,针对涡扇发动机全包线稳态和过渡态控制问题,基于涡扇发动机全数字仿真平台设计了全包线鲁棒非线性控制器,保证闭环系统在全包线飞行条件下满足期望的性能指标且具有良好的鲁棒性。Based on the above background, the present application provides a design method and simulation method of a turbofan engine full-envelope controller, aiming at the full-envelope steady-state and transition state control problems of a turbofan engine, based on a turbofan engine full digital simulation platform to design a full The envelope robust nonlinear controller ensures that the closed-loop system meets the desired performance index and has good robustness under full envelope flight conditions.

发明内容SUMMARY OF THE INVENTION

为了解决现有技术中对涡扇发动机全包线控制器的控制稳定性较差的技术问题,本申请提出了一种涡扇发动机全包线控制器的设计方法与仿真方法。In order to solve the technical problem of poor control stability of the turbofan engine all-envelope controller in the prior art, the present application proposes a design method and a simulation method of a turbofan engine all-envelope controller.

根据本申请的第一方面,提出了一种涡扇发动机全包线的设计方法,包括以下步骤:According to the first aspect of the present application, a method for designing an all-envelope of a turbofan engine is proposed, comprising the following steps:

S1、建立所述涡扇发动机包含外部扰动的NPV模型,并根据所述外部扰动将所述NPV模型转化成不确定模型;S1, establishing the NPV model of the turbofan engine including external disturbance, and converting the NPV model into an uncertain model according to the external disturbance;

S2、基于所述不确定模型,设计大包线鲁棒控制器;S2. Based on the uncertainty model, design a robust controller for large envelopes;

S3、根据涡扇发动机闭环系统的性能指标要求,设计所述大包线鲁棒控制器中的预设性能参数矩阵;S3, designing a preset performance parameter matrix in the large-envelope robust controller according to the performance index requirements of the turbofan engine closed-loop system;

S4、利用SOS技术求解出所述大包线鲁棒控制器中的状态反馈增益矩阵,从而求解出所述大包线鲁棒控制器;S4, using SOS technology to solve the state feedback gain matrix in the large-envelope robust controller, so as to solve the large-envelope robust controller;

S5、设计所述涡扇发动机在节流状态下的PI控制器,利用切换模块将所述PI控制器和所述大包线鲁棒控制器组合成所述全包线控制器,以使所述涡扇发动机在节流状态下使用所述PI控制器,在其它状态下通过所述切换模块切换至使用所述大包线鲁棒控制器。S5. Design the PI controller of the turbofan engine in a throttled state, and use a switching module to combine the PI controller and the large-envelope robust controller into the full-envelope controller, so that all The turbofan engine uses the PI controller in a throttled state, and switches to use the large-envelope robust controller through the switching module in other states.

通过上述技术方案,针对涡扇发动机全包线稳态和过渡态控制问题,通过设计大包线鲁棒控制器和PI控制器组合成全包线控制器,涡扇发动机控制系统采用PI-PP(Proportion-Integral&Prescribed-Performance)混合控制策略,即涡扇发动机在节流状态下使用PI控制器,其余飞行状态使用大包线鲁棒控制器,控制系统基于预设性能方法将系统的性能指标转化为控制器的设计指标,使得控制器更好地适应发动机非线性模型,从而具有较好的控制稳定性。Through the above technical solutions, aiming at the full-envelope steady-state and transition-state control problems of the turbofan engine, a large-envelope robust controller and a PI controller are designed to form an all-envelope controller. The turbofan engine control system adopts PI-PP ( Proportion-Integral&Prescribed-Performance) hybrid control strategy, that is, the turbofan engine uses the PI controller in the throttle state, and the large-envelope robust controller is used in the rest of the flight state. The control system converts the performance index of the system based on the preset performance method into The design index of the controller makes the controller better adapt to the nonlinear model of the engine, so that it has better control stability.

优选的,所述包含外部扰动的NPV模型具体为:Preferably, the NPV model including external disturbance is specifically:

Figure RE-GDA0003753661370000031
Figure RE-GDA0003753661370000031

其中,x∈Rn是系统状态,u∈Rn是控制输入,ρ(t)∈Rs是时变参数向量,A(·,·)、B(·,·)和C(·,·)是关于x和ρ(t)的多项式矩阵,ω(t)为外部扰动, E1是合适维数的常数矩阵;where x∈Rn is the system state, u∈Rn is the control input, ρ(t) ∈Rs is the time-varying parameter vector, A(·,·), B(·,·) and C(·,· ) is a polynomial matrix with respect to x and ρ(t), ω(t) is an external disturbance, and E 1 is a constant matrix of suitable dimension;

所述不确定模型具体为:The uncertain model is specifically:

Figure RE-GDA0003753661370000032
Figure RE-GDA0003753661370000032

其中,△F1x(t)是转化后的外部扰动,△是不确定性矩阵,满足△T△≤I, F1,I分别是合适维数的常数矩阵和单位矩阵,满足F1 TF1≥0。Among them, △F 1 x(t) is the external disturbance after transformation, △ is the uncertainty matrix, satisfying △ T △≤I, F 1 ,I are the constant matrix and identity matrix of suitable dimensions, respectively, satisfying F 1 T F 1 ≥ 0.

优选的,所述大包线鲁棒控制器的表达式具体为:Preferably, the expression of the large-envelope robust controller is specifically:

Figure RE-GDA0003753661370000033
Figure RE-GDA0003753661370000033

其中,

Figure RE-GDA0003753661370000034
是待设计的状态反馈增益矩阵,kR是可调系数,
Figure RE-GDA0003753661370000035
是待设计的预设性能参数矩阵。in,
Figure RE-GDA0003753661370000034
is the state feedback gain matrix to be designed, k R is an adjustable coefficient,
Figure RE-GDA0003753661370000035
is the preset performance parameter matrix to be designed.

通过上述技术方案,从式中可以看出,只要选择合适的预设性能参数矩阵

Figure RE-GDA0003753661370000036
就可以使涡扇发动机闭环系统满足给定性能指标的问题。Through the above technical solutions, it can be seen from the formula that as long as an appropriate preset performance parameter matrix is selected
Figure RE-GDA0003753661370000036
Then the closed-loop system of turbofan engine can meet the problem of given performance index.

优选的,所述涡扇发动机的性能指标要求具体为:所述涡扇发动机闭环系统的高压转子转速控制稳态误差、动态超调、阶跃响应时间、喷管闭环控制压比稳态误差以及在高压转子转速扰动下的转速动态超调均在预设阈值内;Preferably, the performance index requirements of the turbofan engine are specifically: the high-pressure rotor speed control steady-state error, dynamic overshoot, step response time, nozzle closed-loop control pressure ratio steady-state error of the turbofan engine closed-loop system, and The dynamic overshoot of the rotational speed under the high-pressure rotor rotational speed disturbance is all within the preset threshold;

所述预设性能参数矩阵的设计过程具体为:基于所述待设计的预设性能参数矩阵,将系统状态在任意时刻的值与预设的期望值作差值运算得到状态误差,引入性能函数并定义误差变换函数,设计得到所述预设性能参数矩阵,所述预设性能参数矩阵的表达式具体为:The design process of the preset performance parameter matrix is specifically: based on the preset performance parameter matrix to be designed, the value of the system state at any time and the preset expected value are calculated by the difference value to obtain the state error, the performance function is introduced and the state error is obtained. An error transformation function is defined, and the preset performance parameter matrix is obtained by design, and the expression of the preset performance parameter matrix is specifically:

Figure RE-GDA0003753661370000041
Figure RE-GDA0003753661370000041

Figure RE-GDA0003753661370000042
Figure RE-GDA0003753661370000042

其中,定义连续函数T为误差变换函数Ti(x,t),

Figure RE-GDA0003753661370000043
为涡扇发动机闭环系统的状态误差,ρi(t)为引入的性能函数。Among them, the continuous function T is defined as the error transformation function T i (x, t),
Figure RE-GDA0003753661370000043
is the state error of the turbofan closed-loop system, and ρ i (t) is the introduced performance function.

通过上述技术方案,通过引入性能函数和定义误差变换函数,构造出预设性能参数矩阵。Through the above technical solution, a preset performance parameter matrix is constructed by introducing a performance function and defining an error transformation function.

优选的,所述状态反馈增益矩阵的求解过程具体包括:Preferably, the solution process of the state feedback gain matrix specifically includes:

设计所述待设计的状态反馈增益矩阵的可解性条件,表达式具体为:The solvability condition of the state feedback gain matrix to be designed is designed, and the expression is specifically:

Figure RE-GDA0003753661370000044
Figure RE-GDA0003753661370000044

Figure RE-GDA0003753661370000045
Figure RE-GDA0003753661370000045

Figure RE-GDA0003753661370000046
Figure RE-GDA0003753661370000046

其中,

Figure RE-GDA0003753661370000047
Figure RE-GDA0003753661370000048
是给定正数,ΦSOS为SOS 多项式集合,in,
Figure RE-GDA0003753661370000047
and
Figure RE-GDA0003753661370000048
is a given positive number, Φ SOS is the set of SOS polynomials,

Figure RE-GDA0003753661370000049
Figure RE-GDA00037536613700000410
是一个n×n维对称多项式矩阵,
Figure RE-GDA00037536613700000411
是一个m×n维多项式矩阵,kR是常数;
Figure RE-GDA0003753661370000049
Figure RE-GDA00037536613700000410
is an n×n-dimensional symmetric polynomial matrix,
Figure RE-GDA00037536613700000411
is an m×n-dimensional polynomial matrix, and k R is a constant;

利用SOS技术求解所述待设计的状态反馈增益矩阵的可解性条件,得到所述状态反馈增益矩阵,所述状态反馈增益矩阵的表达式具体为:Use SOS technology to solve the solvability condition of the state feedback gain matrix to be designed, and obtain the state feedback gain matrix. The expression of the state feedback gain matrix is specifically:

Figure RE-GDA0003753661370000051
Figure RE-GDA0003753661370000051

通过上述技术方案,根据所构造的预设性能参数矩阵,利用SOS技术求解得到状态反馈增益矩阵。Through the above technical solution, according to the constructed preset performance parameter matrix, the state feedback gain matrix is obtained by using the SOS technology to solve.

优选的,所述PI控制器的控制律表达式具体为:Preferably, the control law expression of the PI controller is specifically:

Figure RE-GDA0003753661370000052
Figure RE-GDA0003753661370000052

其中,Kp和Ti为常数,e(t)为系统误差。Among them, K p and T i are constants, and e(t) is the systematic error.

优选的,所述全包线控制器的控制律表达式具体为:Preferably, the control law expression of the all-envelope controller is specifically:

Figure RE-GDA0003753661370000053
Figure RE-GDA0003753661370000053

其中,PLA为油门杆角度,V为常数。where PLA is the throttle stick angle and V is a constant.

通过上述技术方案,由于涡扇发动机的大包线NPV模型没有低工作状态的特征,基于NPV模型设计的大包线鲁棒控制器对于节流状态以下的控制效果不佳,因此涡扇发动机在节流状态下采用PI控制器,PI控制是一种经典的控制算法,它根据给定值与实际输出值构成控制偏差,将偏差的比例和积分通过线性组合构成控制量,对被控对象进行控制。Through the above technical solutions, since the large-envelope NPV model of the turbofan engine does not have the feature of low working state, the large-envelope robust controller designed based on the NPV model has poor control effect under the throttling state, so the turbofan engine is in the throttling state. The PI controller is used in the throttling state. PI control is a classic control algorithm. It forms a control deviation according to the given value and the actual output value. control.

根据本申请的第二方面,提出了一种涡扇发动机全包线控制器的仿真方法,对上述的设计方法中的全包线控制器进行仿真,包括以下步骤:According to the second aspect of the present application, a simulation method for an all-envelope controller of a turbofan engine is proposed, which simulates the all-envelope controller in the above-mentioned design method, including the following steps:

a)在全数字仿真平台上搭建所述全包线控制器;a) building the all-envelope controller on an all-digital simulation platform;

b)采用增益调参的方法优化所述全包线控制器;b) using the method of gain parameter adjustment to optimize the all-envelope controller;

c)对优化后的所述全包线控制器进行全数字仿真;c) performing full digital simulation on the optimized all-envelope controller;

其中,所述步骤b)具体包括:Wherein, the step b) specifically includes:

b1)根据所述涡扇发动机的飞行高度和马赫数确定多个典型工作点,在不同的所述典型工作点以及不同的工作状态下,对所述全包线控制器中的参数采用网格搜索法选择使得所述涡扇发动机闭环系统动态性能表现最优的所述参数,实现对所述参数的整定;b1) Determine a plurality of typical operating points according to the flight height and Mach number of the turbofan engine, and use grids for the parameters in the full-envelope controller under different typical operating points and different operating states The search method selects the parameters that make the dynamic performance of the turbofan engine closed-loop system optimal, and realizes the tuning of the parameters;

b2)采取线性插值方法组合整定的所述参数,使得所述涡扇发动机闭环系统在所有工作点下满足所述性能指标要求,综合成变增益全包线控制器。b2) adopting a linear interpolation method to combine the set parameters, so that the closed-loop system of the turbofan engine meets the performance index requirements at all operating points, and is synthesized into a variable gain full-envelope controller.

通过上述技术方案,针对涡扇发动机非线性部件模型的强非线性特征,运用增益调参的方法对控制器在不同工作点的参数进行调节,使得控制器更好地适应发动机非线性模型,控制效果得到了进一步的提升。Through the above technical solution, in view of the strong nonlinear characteristics of the nonlinear component model of the turbofan engine, the method of gain parameter adjustment is used to adjust the parameters of the controller at different operating points, so that the controller can better adapt to the nonlinear model of the engine and control the The effect has been further improved.

优先的,所述步骤b)中待优化的所述全包线控制器的控制律表达式具体为:Preferably, the control law expression of the all-envelope controller to be optimized in the step b) is specifically:

Figure RE-GDA0003753661370000061
Figure RE-GDA0003753661370000061

其中,Ku,K1,KR,Kp,Ti为待整定的参数。Among them, Ku , K 1 , K R , K p , and T i are parameters to be set.

通过上述技术方案,基于增益调参的方法在不同典型工作点下,整定全包线控制器参数,从而保证在涡扇发动机闭环系统的性能满足给定的控制效果的基础上,设计的全包线控制器对未建模动态有较好的鲁棒性。Through the above technical solution, the method based on gain parameter tuning is used to adjust the parameters of the all-envelope controller under different typical operating points, so as to ensure that the designed all-in The line controller is more robust to unmodeled dynamics.

优选的,还包括:将所述全包线控制器以硬件形式在硬件在环平台和半物理平台上进行稳态实验和动态实验。Preferably, it also includes: performing steady-state experiments and dynamic experiments on the hardware-in-the-loop platform and the semi-physical platform in the form of hardware for the all-envelope controller.

通过上述技术方案,硬件在环仿真系统中拥有真实的I/O接口、控制器硬件设备以及虚拟的被控对象模型,是一种置信度较高的控制算法测试验证手段。半物理仿真具备真实的油路系统,能对控制器与液压机械系统及相关传感器进行综合和试验验证,相比于硬件在环仿真具备更高的逼真。Through the above technical solution, the hardware-in-the-loop simulation system has real I/O interfaces, controller hardware devices and virtual controlled object models, which is a control algorithm test and verification method with high confidence. Semi-physical simulation has a real oil circuit system, which can comprehensively and experimentally verify the controller, hydraulic mechanical system and related sensors. Compared with hardware-in-the-loop simulation, it has higher fidelity.

本申请提出了一种涡扇发动机全包线控制器的设计方法与仿真方法,针对涡扇发动机全包线稳态和过渡态控制问题,基于涡扇发动机全数字仿真平台设计了全包线鲁棒非线性控制器,保证闭环系统在全包线飞行条件下满足期望的性能指标且具有良好的鲁棒性。涡扇发动机控制系统采用 PI-PP混合控制策略,即节流状态下使用PI控制器,其余飞行状态使用大包线鲁棒控制器。控制系统基于预设性能方法将系统的性能指标转化为控制器的设计指标,并运用增益调参的方法对控制器在不同典型工作点的参数进行调节,使得控制器更好地适应发动机非线性模型。将设计的全包线控制器在全数字仿真平台、硬件在环平台(Hardware-in-the-Loop,HIL)和半物理平台上进行了仿真实验,仿真结果表明,所设计的控制器能够保证系统在全包线范围内都具有全局稳定性,满足给定的性能指标,且具有良好的鲁棒性。This application proposes a design method and a simulation method for a turbofan engine full-envelope controller. Aiming at the problem of turbofan engine full-envelope steady-state and transition state control, an all-envelope controller is designed based on a turbofan engine full-digital simulation platform. The robust nonlinear controller ensures that the closed-loop system meets the desired performance index and has good robustness under full-envelope flight conditions. The turbofan engine control system adopts the PI-PP hybrid control strategy, that is, the PI controller is used in the throttle state, and the large-envelope robust controller is used in the other flight states. The control system converts the performance index of the system into the design index of the controller based on the preset performance method, and uses the method of gain parameter adjustment to adjust the parameters of the controller at different typical operating points, so that the controller can better adapt to the nonlinearity of the engine Model. The designed all-in-the-loop controller is simulated on an all-digital simulation platform, a hardware-in-the-loop (HIL) platform and a semi-physical platform. The simulation results show that the designed controller can guarantee The system has global stability in the whole envelope range, meets the given performance indicators, and has good robustness.

附图说明Description of drawings

包括附图以提供对实施例的进一步理解并且附图被并入本说明书中并且构成本说明书的一部分。附图图示了实施例并且与描述一起用于解释本申请的原理。将容易认识到其它实施例和实施例的很多预期优点,因为通过引用以下详细描述,它们变得被更好地理解。附图的元件不一定是相互按照比例的。同样的附图标记指代对应的类似部件。The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The drawings illustrate embodiments and together with the description serve to explain the principles of the application. Other embodiments and many of the intended advantages of the embodiments will be readily recognized as they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale to each other. Like reference numerals designate corresponding similar parts.

图1是根据本申请实施例的涡扇发动机全包线控制器的设计方法流程图;1 is a flowchart of a design method of a turbofan engine all-envelope controller according to an embodiment of the present application;

图2是根据本申请一个具体实施例的涡扇发动机控制系统结构图;2 is a structural diagram of a turbofan engine control system according to a specific embodiment of the present application;

图3是根据本申请实施例的涡扇发动机全包线控制器的仿真方法流程图;3 is a flowchart of a simulation method of a turbofan engine all-envelope controller according to an embodiment of the present application;

图4是根据本申请一个具体实施例的全数字仿真平台主要结构划分示意图;4 is a schematic diagram of the main structure division of an all-digital simulation platform according to a specific embodiment of the present application;

图5是根据本申请一个具体实施例的主燃油量的全包线控制器框图;5 is a block diagram of an all-envelope controller of the main fuel quantity according to a specific embodiment of the present application;

图6是根据本申请一个具体实施例的喉道面积的全包线控制器框图;6 is a block diagram of an all-envelope controller for throat area according to a specific embodiment of the present application;

图7是根据本申请一个具体实施例的涡扇发动机处于节流状态时给定的PLA变化图;7 is a given PLA change diagram when the turbofan engine is in a throttled state according to a specific embodiment of the present application;

图8是根据本申请一个具体实施例的涡扇发动机处于中间状态时给定的PLA变化图;8 is a given PLA change diagram when the turbofan engine is in an intermediate state according to a specific embodiment of the present application;

图9是根据本申请一个具体实施例的涡扇发动机处于加力状态时给定的PLA变化图;9 is a given PLA change diagram when the turbofan engine is in an afterburner state according to a specific embodiment of the present application;

图10是根据本申请一个具体实施例的涡扇发动机包线内飞行高度、马赫数和油门杆角度随时间变化曲线图;10 is a graph showing the variation of flight height, Mach number and throttle stick angle with time in the turbofan engine envelope according to a specific embodiment of the present application;

图11是根据本申请一个具体实施例的飞行轨迹仿真实验得到的高压转子转速变化曲线图;FIG. 11 is a graph showing a high-pressure rotor rotational speed variation curve obtained by a flight trajectory simulation experiment according to a specific embodiment of the present application;

图12是根据本申请一个具体实施例的飞行轨迹仿真实验得到的发动机压比变化曲线图;Fig. 12 is a graph showing the variation of engine pressure ratio obtained by a flight trajectory simulation experiment according to a specific embodiment of the present application;

图13是根据本申请一个具体实施例的单工况仿真实验在工作点(0,0) 节流状态下仿真得到的高压转子转速变化曲线;Fig. 13 is a high-voltage rotor speed variation curve obtained by simulation under the throttling state of the operating point (0, 0) according to a single working condition simulation experiment according to a specific embodiment of the present application;

图14是根据本申请一个具体实施例的单工况仿真实验在工作点(0,0) 中间状态下仿真得到的高压转子转速变化曲线;Fig. 14 is a high-voltage rotor rotational speed variation curve obtained by simulation in the middle state of the operating point (0, 0) according to a single working condition simulation experiment according to a specific embodiment of the present application;

图15是根据本申请一个具体实施例的单工况仿真实验在工作点(0,0) 加力状态下仿真得到的高压转子转速变化曲线;Fig. 15 is a high-voltage rotor speed variation curve obtained by simulation under the applied force state at the working point (0, 0) according to a single-condition simulation experiment according to a specific embodiment of the present application;

图16是根据本申请一个具体实施例的单工况仿真实验在工作点(0,0) 中间状态下仿真得到发动机压比变化曲线;Fig. 16 shows the variation curve of engine pressure ratio obtained by simulation in the middle state of the working point (0, 0) according to a single working condition simulation experiment according to a specific embodiment of the present application;

图17是根据本申请一个具体实施例的单工况仿真实验在工作点(0,0) 加力状态下仿真得到发动机压比变化曲线。FIG. 17 is a simulation experiment of a single working condition according to a specific embodiment of the present application, and a variation curve of the engine pressure ratio obtained by simulation under the applied force state at the working point (0, 0).

具体实施方式Detailed ways

下面将详细描述本申请的各个方面的特征和示例性实施例,为了使本申请的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本申请进行进一步详细描述。应理解,此处所描述的具体实施例仅被配置为解释本申请,并不被配置为限定本申请。对于本领域技术人员来说,本申请可以在不需要这些具体细节中的一些细节的情况下实施。下面对实施例的描述仅仅是为了通过示出本申请的示例来提供对本申请更好的理解。The features and exemplary embodiments of various aspects of the present application will be described in detail below. In order to make the purpose, technical solutions and advantages of the present application more clear, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only configured to explain the present application, and are not configured to limit the present application. It will be apparent to those skilled in the art that the present application may be practiced without some of these specific details. The following description of the embodiments is merely to provide a better understanding of the present application by illustrating examples of the present application.

需要说明的是,在本文中,诸如第一和第二等之类的关系术语仅仅用来将一个实体或者操作与另一个实体或操作区分开来,而不一定要求或者暗示这些实体或操作之间存在任何这种实际的关系或者顺序。而且,术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含,从而使得包括一系列要素的过程、方法、物品或者设备不仅包括那些要素,而且还包括没有明确列出的其他要素,或者是还包括为这种过程、方法、物品或者设备所固有的要素。在没有更多限制的情况下,由语句“包括......”限定的要素,并不排除在包括要素的过程、方法、物品或者设备中还存在另外的相同要素。It should be noted that, in this document, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any relationship between these entities or operations. any such actual relationship or sequence exists. Moreover, the terms "comprising", "comprising" or any other variation thereof are intended to encompass a non-exclusive inclusion such that a process, method, article or device that includes a list of elements includes not only those elements, but also includes not explicitly listed or other elements inherent to such a process, method, article or apparatus. Without further limitation, an element defined by the phrase "comprises..." does not preclude the presence of additional identical elements in the process, method, article, or device that includes the element.

根据本申请的第一方面,提出了一种涡扇发动机全包线控制器的设计方法。According to the first aspect of the present application, a design method for an all-envelope controller of a turbofan engine is proposed.

以下将以某型小涵道比双轴涡扇发动机为研究对象,介绍涡扇发动机全包线控制器的设计方法。The following will take a certain type of small bypass ratio twin-shaft turbofan engine as the research object, and introduce the design method of the turbofan engine all-envelope controller.

图1示出了根据本申请实施例的涡扇发动机全包线控制器的设计方法流程图,如图1所示,该设计方法包括以下步骤:FIG. 1 shows a flowchart of a design method of a turbofan engine all-envelope controller according to an embodiment of the present application. As shown in FIG. 1 , the design method includes the following steps:

S1、建立涡扇发动机包含外部扰动的NPV模型,并根据外部扰动将 NPV模型转化成不确定模型。S1. Establish an NPV model of the turbofan engine including external disturbances, and convert the NPV model into an uncertain model according to the external disturbance.

在具体的实施例中,考虑某型涡扇发动机如下状态变量形式的NPV模型:In a specific embodiment, consider the NPV model of a certain type of turbofan engine in the form of the following state variables:

Figure RE-GDA0003753661370000101
Figure RE-GDA0003753661370000101

其中,x∈Rn是系统状态,u∈Rn是控制输入,ρ(t)∈Rs是时变参数向量,A(·,·)、B(·,·)和C(·,·)是关于x和ρ(t)的多项式矩阵,nL为低压转子转速, nH为高压转子转速,Wf为主燃油量,A8为喉道面积。aij,bij和cij(i,j=1, 2)详细表达式如下:where x∈Rn is the system state, u∈Rn is the control input, ρ(t) ∈Rs is the time-varying parameter vector, A(·,·), B(·,·) and C(·,· ) is a polynomial matrix about x and ρ(t), n L is the low pressure rotor speed, n H is the high pressure rotor speed, W f is the main fuel quantity, and A 8 is the throat area. The detailed expressions of a ij , b ij and c ij (i, j=1, 2) are as follows:

a11=-0.01452H3+0.1052H2+0.7103H-3424.0nH 3-10270.0nH 2nHref+10010.0nH 2 -10270.0nHnHref 2+20010.0nHnHref-9708.0nH-3424.0nHref 3+10010.0nHref 2-9708.0nHref -4.357Ma+3123.0a 11 = -0.01452H 3 +0.1052H 2 +0.7103H-3424.0n H 3 -10270.0n H 2 n Href + 10010.0n H 2 -10270.0n H n Href 2 + 20010.0n H n Href -9708.0n H -3424.0 n Href 3 + 10010.0n Href 2 -9708.0n Href -4.357Ma +3123.0

a12=2.038Ma-0.8023H+200.5Wfref+42500.0A8ref-9708.0nLref-5998.0nHref -413.6WfrefnHref-88810.0A8refnHref+20010.0nLrefnHref+0.007449H2+0.006477H3 +212.1WfrefnHref 2+46220.0A8refnHref 2-10270.0nLrefnHref 2+nH 2(70.71Wfref+15410.0A8ref -3424.0nLref-4646.0nHref+3241.0)-1162.0nH 3-1.0nH(206.8Wfref+44410.0A8ref-10010.0nLref-9724.0nHref-212.1WfrefnHref-46220.0A8refnHref+10270.0nLrefnHref+6969.0nHref 2+2999.0) +9724.0nHref 2-4646.0nHref 3+924.8 3 _ _ _ _ _ _ _ _ _ _ _ _ + 212.1W fref n Href 2 +46220.0A 8ref n Href 2 -10270.0n Lref n Href 2 +n H 2 (70.71W fref +15410.0A 8ref -3424.0n Lref -4646.0n Href +3241.0)-1162.0n H 3 - 1.0n H (206.8W fref +44410.0A 8ref -10010.0n Lref -9724.0n Href -212.1W fref n Href -46220.0A 8ref n Href + 10270.0n Lref n Href + 6969.0n Href 2 +2999.0 ) + 9724.0n Href 2 -4646.0n Href 3 +924.8

a21=-0.01538H3+0.1659H2-0.5276H-817.5nH 3-2452.0nH 2nHref+2347.0nH 2 -2452.0nHnHref 2+4695.0nHnHref-2239.0nH-817.5nHref 3+2347.0nHref 2-2239.0nHref +1.359Ma+708.5a 21 =-0.01538H 3 +0.1659H 2 -0.5276H-817.5n H 3 -2452.0n H 2 n Href + 2347.0n H 2 -2452.0n H n Href 2 + 4695.0n H n Href -2239.0n H -817.5 n Href 3 + 2347.0n Href 2 -2239.0n Href + 1.359Ma +708.5

a22=1.121H-2.098Ma-204.3Wfref-11090.0A8ref-2239.0nLref+10980.0nHref +430.8WfrefnHref+23540.0WfrefnHref+4695.0nLrefnHref-1.0nH2(75.66Wfref+4148.0A8ref +817.5nLref-8143.0nHref+5802.0)-0.3035H2+0.0255H3-227.0WfrefnHref 2-12440.0A8refnHref 2 -2452.0nLrefnHref 2+nH(215.4Wfref+11770.0A8ref+2347.0nLref-17400.0nHref-227.0WfrefnHref -12440.0A8refnHref-2452.0nLrefnHref+12210.0nHref 2+5489.0)+2036.0nH 3-17400.0nHref 2 +8143.0nHref 3-1726.0a 22 =1.121H-2.098Ma-204.3W fref -11090.0A 8ref -2239.0n Lref + 10980.0n Href +430.8W fref n Href + 23540.0W fref n Href + 4695.0n Lref n Href -1.0nH 2 (75.66W fref +4148.0A 8ref +817.5n Lref -8143.0n Href +5802.0)-0.3035H 2 +0.0255H 3 -227.0W fref n Href 2 -12440.0A 8ref n Href 2 -2452.0n Lref n Href 2 +n H ( 215.4W fref +11770.0A 8ref +2347.0n Lref -17400.0n Href -227.0W fref n Href -12440.0A 8ref n Href -2452.0n Lref n Href + 12210.0n Href 2 +5489.0)+ 2036.0n H 3 -17400.0n Href 2 + 8143.0n Href 3 -1726.0

b11=0.0002945H3-0.00616H2+0.01127H+70.71nH 3+212.1nH 2nHref-206.8nH 2 +212.1nHnHref 2-413.6nHnHref+200.5nH+70.71nHref 3-206.8nHref 2+200.5nHref +0.1605Ma-64.06b 11 =0.0002945H 3 -0.00616H 2 +0.01127H+70.71n H 3 +212.1n H 2 n Href -206.8n H 2 + 212.1n H n Href 2 -413.6n H n Href + 200.5n H +70.71n Href 3 -206.8n Href 2 + 200.5n Href + 0.1605Ma -64.06

b12=0.01606H3-0.2997H2+0.6669H+15410.0nH 3+46220.0nH 2nHref-44410.0nH 2 +46220.0nHnHref 2-88810.0nHnHref+42500.0nH+15410.0nHref 3-44410.0nHref 2 +42500.0nHref+5.999Ma-13510.0b 12 =0.01606H 3 -0.2997H 2 +0.6669H+15410.0n H 3 +46220.0n H 2 n Href -44410.0n H 2 + 46220.0n H n Href 2 -88810.0n H n Href + 42500.0n H +15410.0n Href 3 -44410.0n Href 2 + 42500.0n Href +5.999Ma- 13510.0

b21=-0.0003558H3+0.003819H2-0.005397H-75.66nH 3-227.0nH 2nHref+215.4nH 2 -227.0nHnHref 2+430.8nHnHref-204.3nH-75.66nHref 3+215.4nHref 2-204.3nHref -0.01056Ma+64.74b 21 = -0.0003558H 3 +0.003819H 2 -0.005397H-75.66n H 3 -227.0n H 2 n Href + 215.4n H 2 -227.0n H n Href 2 + 430.8n H n Href -204.3n H -75.66 n Href 3 + 215.4n Href 2 -204.3n Href -0.01056Ma +64.74

b22=-0.03469H3+0.4663H2-2.014H-4148.0nH 3-12440.0nH 2nHref+11770.0nH 2 -12440.0nHnHref 2+23540.0nHnHref-11090.0nH-4148.0nHref 3+11770.0nHref 2 -11090.0nHref+2.938Ma+3470.0b 22 = -0.03469H 3 +0.4663H 2 -2.014H-4148.0n H 3 -12440.0n H 2 n Href + 11770.0n H 2 -12440.0n H n Href 2 + 23540.0n H n Href -11090.0n H -4148.0 n Href 3 + 11770.0n Href 2 -11090.0n Href + 2.938Ma +3470.0

c21=0.01922H3-0.1625H2+0.155H+5873.0nH 3+17620.0nH 2nHref-17030.0nH 2 +17620.0nHnHref 2-34060.0nHnHref+16390.0nH+5873.0nHref 3-17030.0nHref 2 +16390.0nHref-0.03688Ma-5236.0c 21 =0.01922H 3 -0.1625H 2 +0.155H+5873.0n H 3 +17620.0n H 2 n Href -17030.0n H 2 + 17620.0n H n Href 2 -34060.0n H n Href + 16390.0n H +5873.0n Href 3 -17030.0n Href 2 + 16390.0n Href -0.03688Ma -5236.0

c22=16390.0nLref-0.04604Ma-0.1191H-31400.0nHref-34060.0nLrefnHref +nH 2(5873.0nLref-22530.0nHref+16320.0)+0.1541H2-0.0185H3+17620.0nLrefnHref 2 -5633.0nH 3+48960.0nHref 2-22530.0nHref 3-1.0nH(17030.0nLref-48960.0nHref -17620.0nLrefnHref+33800.0nHref 2+15700.0)+5011.0c 22 =16390.0n Lref -0.04604Ma-0.1191H- 31400.0n Href -34060.0n Lref n Href +n H 2 (5873.0n Lref -22530.0n Href +16320.0)+0.1541H 2 -0.0185H 3 +17620.0n Lref n Href 2 -5633.0n H 3 + 48960.0n Href 2 -22530.0n Href 3 -1.0n H (17030.0n Lref -48960.0n Href -17620.0n Lref n Href + 33800.0n Href 2 +15700.0) +5011.0

其中,nHref表示高压转子转速的期望值,nLref表示低压转子转速的期望值,Wfref为主燃油量的期望值,A8ref表示喉道面积的期望值,H表示飞行高度,Ma表示马赫数。Among them, n Href represents the expected value of the high pressure rotor speed, n Lref represents the expected value of the low pressure rotor speed, W fref represents the expected value of the main fuel quantity, A 8ref represents the expected value of the throat area, H represents the flight height, and Ma represents the Mach number.

在NPV模型的基础上,引入外部扰动,建立包含外部扰动的NPV模型:On the basis of the NPV model, the external disturbance is introduced, and the NPV model including the external disturbance is established:

Figure RE-GDA0003753661370000111
Figure RE-GDA0003753661370000111

其中,ω(t)为外部扰动,在本实施例中,ω(t)=0.1(nHref-nH(0))sint, nHref=0.9437,nH(0)=0.8632。E1是合适维数的常数矩阵。Wherein, ω(t) is an external disturbance. In this embodiment, ω(t)=0.1(n Href −n H (0))sint, n Href= 0.9437 , and n H (0)=0.8632. E1 is a constant matrix of suitable dimension.

令ω(t)=△F1x(t)。△是不确定性矩阵,满足△T△≤I。F1,I分别是合适维数的常数矩阵和单位矩阵,满足F1 TF1≥0。从而,外部扰动ω(t)转化为系统结构的不确定性。那么,包含外部扰动的NPV模型转化为如下的不确定模型:Let ω(t)=ΔF 1 x(t). △ is the uncertainty matrix, which satisfies △ T △≤I. F 1 , I are a constant matrix and an identity matrix with appropriate dimensions, respectively, satisfying F 1 T F 1 ≥0. Thus, the external disturbance ω(t) is transformed into the uncertainty of the system structure. Then, the NPV model containing external disturbances is transformed into the following uncertainty model:

Figure RE-GDA0003753661370000121
Figure RE-GDA0003753661370000121

继续参照图1,在步骤S1之后,Continuing to refer to FIG. 1, after step S1,

S2、基于不确定模型,设计大包线鲁棒控制器。S2. Based on the uncertainty model, design a robust controller for large envelopes.

在具体的实施例中,对于不确定模型,设计基于预设性能方法的大包线鲁棒控制器,形如:In a specific embodiment, for the uncertain model, a large-envelope robust controller based on a preset performance method is designed, such as:

Figure RE-GDA0003753661370000122
Figure RE-GDA0003753661370000122

其中,

Figure RE-GDA0003753661370000123
是待设计的状态反馈增益矩阵,kR是可调系数,
Figure RE-GDA0003753661370000124
是待设计的预设性能参数矩阵。in,
Figure RE-GDA0003753661370000123
is the state feedback gain matrix to be designed, k R is an adjustable coefficient,
Figure RE-GDA0003753661370000124
is the preset performance parameter matrix to be designed.

继续参照图1,在步骤S2之后,Continuing to refer to FIG. 1, after step S2,

S3、根据涡扇发动机闭环系统的性能指标要求,设计大包线鲁棒控制器中的预设性能参数矩阵。S3. Design the preset performance parameter matrix in the large-envelope robust controller according to the performance index requirements of the turbofan engine closed-loop system.

在具体的实施例中,预设性能方法具体是通过使涡扇发动机闭环系统满足预设的性能指标要求,从而来设计大包线鲁棒控制器。预设性能方法是通过限制系统的动态响应的最大超调量,收敛速度和系统的稳态误差,使得系统满足期望的性能指标。从大包线鲁棒控制器的表达式中可以看出,只要选择合适的预设性能参数矩阵

Figure RE-GDA0003753661370000125
就可以使闭环系统满足给定性能指标的问题。In a specific embodiment, the preset performance method is specifically designed to design a large-envelope robust controller by making the closed-loop system of the turbofan engine meet the preset performance index requirements. The preset performance method is to make the system meet the desired performance index by limiting the maximum overshoot of the dynamic response of the system, the convergence speed and the steady-state error of the system. It can be seen from the expression of the large-envelope robust controller that as long as an appropriate preset performance parameter matrix is selected
Figure RE-GDA0003753661370000125
It is possible to make the closed-loop system meet the given performance index.

在本实施例中,涡扇发动机闭环系统应满足的性能指标是:涡扇发动机的高压转子转速控制稳态误差不大于δ1,动态超调不大于σ1,阶跃响应时间

Figure RE-GDA0003753661370000126
不大于T1。喷管闭环控制压比稳态误差不大于δ2。在高压转子转速扰动
Figure RE-GDA0003753661370000127
下,转速动态超调不大于σ2,即:In this embodiment, the performance indicators that the closed-loop system of the turbofan engine should meet are: the steady-state error of the high-pressure rotor speed control of the turbofan engine is not greater than δ 1 , the dynamic overshoot is not greater than σ 1 , and the step response time is
Figure RE-GDA0003753661370000126
not greater than T 1 . The steady-state error of the nozzle closed-loop control pressure ratio is not greater than δ 2 . rotor speed disturbances at high pressure
Figure RE-GDA0003753661370000127
, the dynamic overshoot of the rotational speed is not greater than σ 2 , namely:

Figure RE-GDA0003753661370000128
Figure RE-GDA0003753661370000128

Figure RE-GDA0003753661370000131
Figure RE-GDA0003753661370000131

Figure RE-GDA0003753661370000132
Figure RE-GDA0003753661370000132

Figure RE-GDA0003753661370000133
Figure RE-GDA0003753661370000133

Figure RE-GDA0003753661370000134
Figure RE-GDA0003753661370000134

其中,nH(0),nH(∞)分别表示高压转子转速的初值和终值,nHref表示高压转子转速的期望值,tp表示超调时刻,π(∞)表示喷管压比的终值,πref表示喷管压比的期望值,δ1、σ1、T1、δ2和σ2分别为本实施例中各性能指标的预设阈值。在本实施例中,取δ1=0.1%,σ1=1%,T1=4s,δ2=0.5%,σ2=1%。Among them, n H (0), n H (∞) represent the initial value and final value of the high pressure rotor speed respectively, n Href represents the expected value of the high pressure rotor speed, t p represents the overshoot time, and π(∞) represents the nozzle pressure ratio The final value of , π ref represents the expected value of the nozzle pressure ratio, δ 1 , σ 1 , T 1 , δ 2 and σ 2 are the preset thresholds of the performance indicators in this embodiment, respectively. In this embodiment, δ 1 =0.1%, σ 1 =1%, T 1 =4s, δ 2 =0.5%, and σ 2 =1%.

预设性能参数矩阵的设计过程具体为:基于待设计的预设性能参数矩阵,将系统状态在任意时刻的值与预设的期望值作差值运算得到状态误差,引入性能函数并定义误差变换函数,设计得到预设性能参数矩阵。设计过程具体如下:The design process of the preset performance parameter matrix is specifically: based on the preset performance parameter matrix to be designed, the difference between the value of the system state at any time and the preset expected value is calculated to obtain the state error, the performance function is introduced and the error transformation function is defined. , and design the preset performance parameter matrix. The design process is as follows:

设状态误差

Figure RE-GDA0003753661370000135
通过引入性能函数,对状态误差的瞬态和稳态性能进行设定,使其满足如下不等式约束:set state error
Figure RE-GDA0003753661370000135
By introducing a performance function, the transient and steady-state performance of the state error are set to satisfy the following inequality constraints:

Figure RE-GDA0003753661370000136
Figure RE-GDA0003753661370000136

其中,ρi(t)为引入的性能函数,t∈[0,∞);

Figure RE-GDA0003753661370000137
给定指数收敛的性能函数如下:Among them, ρ i (t) is the introduced performance function, t∈[0,∞);
Figure RE-GDA0003753661370000137
The performance function for a given exponential convergence is as follows:

Figure RE-GDA0003753661370000138
Figure RE-GDA0003753661370000138

其中,γi>0,ρi(0)表示初始误差界,ρi(∞)表示稳态时允许的最大状态误差。Among them, γ i >0, ρ i (0) represents the initial error bound, and ρ i (∞) represents the maximum allowable state error in steady state.

根据给定的性能指标设计高压转子转速的性能函数:Design the performance function of the high-pressure rotor speed according to the given performance index:

Figure RE-GDA0003753661370000141
Figure RE-GDA0003753661370000141

并令低压转子转速的性能函数ρ1(t)=ρ2(t)。其中,ρ2(∞)≤nHrefδ1

Figure RE-GDA0003753661370000142
α为常数,T1为阶跃响应时间常数。And let the performance function of low pressure rotor speed ρ 1 (t)=ρ 2 (t). where, ρ 2 (∞)≤n Href δ 1 ,
Figure RE-GDA0003753661370000142
α is a constant and T 1 is the step response time constant.

在本实施例中,取ωH=max{0.1(nHref-nH(0))sint}=0.00805,α=1,

Figure RE-GDA0003753661370000143
根据计算可得:In this embodiment, taking ω H =max{0.1(n Href -n H (0))sint}=0.00805, α=1,
Figure RE-GDA0003753661370000143
According to the calculation, we can get:

ρ1(0)=ρ2(0)=0.08,γ1=γ2=1.73,ρ1(∞)=ρ2(∞)=10-3 ρ 1 (0)=ρ 2 (0)=0.08, γ 12 =1.73, ρ 1 (∞)=ρ 2 (∞)=10 −3

从而,thereby,

ρi(t)=0.079e-1.73t+0.001ρ i (t)=0.079e -1.73t +0.001

定义连续函数T为误差变换函数,如果满足以下条件:Define the continuous function T as the error transformation function, if the following conditions are met:

1)

Figure RE-GDA0003753661370000144
1)
Figure RE-GDA0003753661370000144

2)

Figure RE-GDA0003753661370000145
2)
Figure RE-GDA0003753661370000145

那么,给定的误差变换函数为:Then, the given error transformation function is:

Figure RE-GDA0003753661370000146
Figure RE-GDA0003753661370000146

其中,Ti(x,t)为误差变换函数,

Figure RE-GDA0003753661370000147
为涡扇发动机闭环系统的状态误差。Among them, T i (x, t) is the error transformation function,
Figure RE-GDA0003753661370000147
is the state error of the turbofan engine closed-loop system.

那么,预设性能参数矩阵为:Then, the preset performance parameter matrix is:

Figure RE-GDA0003753661370000148
Figure RE-GDA0003753661370000148

在本实施例中,

Figure RE-GDA0003753661370000149
In this embodiment,
Figure RE-GDA0003753661370000149

Figure RE-GDA00037536613700001410
Figure RE-GDA00037536613700001410

继续参照图1,在步骤S3之后,Continuing to refer to FIG. 1, after step S3,

S4、利用SOS技术求解出大包线鲁棒控制器中的状态反馈增益矩阵,从而求解出大包线鲁棒控制器。S4, using the SOS technology to solve the state feedback gain matrix in the large-envelope robust controller, so as to solve the large-envelope robust controller.

在具体的实施例中,设计待设计的状态反馈增益矩阵的可解性条件,表达式具体为:In a specific embodiment, the solvability condition of the state feedback gain matrix to be designed is designed, and the expression is specifically:

Figure RE-GDA0003753661370000151
Figure RE-GDA0003753661370000151

Figure RE-GDA0003753661370000152
Figure RE-GDA0003753661370000152

Figure RE-GDA0003753661370000153
Figure RE-GDA0003753661370000153

其中,

Figure RE-GDA0003753661370000154
Figure RE-GDA0003753661370000155
是给定正数,ΦSOS为SOS 多项式集合,in,
Figure RE-GDA0003753661370000154
and
Figure RE-GDA0003753661370000155
is a given positive number, Φ SOS is the set of SOS polynomials,

Figure RE-GDA0003753661370000156
Figure RE-GDA0003753661370000157
是一个n×n维对称多项式矩阵,
Figure RE-GDA0003753661370000158
是一个m×n维多项式矩阵,kR是常数。
Figure RE-GDA0003753661370000156
Figure RE-GDA0003753661370000157
is an n×n-dimensional symmetric polynomial matrix,
Figure RE-GDA0003753661370000158
is an m×n-dimensional polynomial matrix, and k R is a constant.

利用SOS技术求解状态反馈矩阵

Figure RE-GDA0003753661370000159
的可解性条件,得到状态反馈增益矩阵为:Solving State Feedback Matrix Using SOS Technology
Figure RE-GDA0003753661370000159
The solvability condition of , the state feedback gain matrix is obtained as:

Figure RE-GDA00037536613700001510
Figure RE-GDA00037536613700001510

在本实施例中,取ε1=ε2=ε3=10-6,kR=0.01。利用Matlab中的SOS工具箱求解得到的大包线鲁棒控制器为:K=[k11,k12;k21,k22],其中,In this embodiment, ε 123 =10 −6 , k R =0.01. The large-envelope robust controller obtained by using the SOS toolbox in Matlab is: K=[k 11 , k 12 ; k 21 , k 22 ], where,

k11=0.07907nL 2+1.124*10-10nLnH-1.631*10-8nL+0.000403nH 2-17.55nH-10.21k 11 =0.07907n L 2 +1.124*10 -10 n L n H -1.631*10 -8 n L +0.000403n H 2 -17.55n H -10.21

k12=-0.3095nL 2-4.398*10-10nLnH+6.369*10-8nL-0.001578nH 2+115.4nH-44.61k 12 =-0.3095n L 2 -4.398*10 -10 n L n H +6.369*10 -8 n L -0.001578n H 2 +115.4n H -44.61

k21=-0.0007736nL 2-1.099*10-12nLnH+1.593*10-10nL-3.943*10-6nH 2-0.04534nH+0.2149k 21 = -0.0007736n L 2 -1.099*10 -12 n L n H +1.593*10 -10 n L -3.943*10 -6 n H 2 -0.04534n H +0.2149

k22=0.00412nL 2+5.855*10-12nLnH-8.538*10-10nL+2.1*10-5nH 2-0.5422nH+0.7073k 22 =0.00412n L 2 +5.855*10 -12 n L n H -8.538*10 -10 n L +2.1*10 -5 n H 2 -0.5422n H +0.7073

继续参照图1,在步骤S4之后,Continue to refer to FIG. 1, after step S4,

S5、设计涡扇发动机在节流状态下的PI控制器,利用切换模块将PI 控制器和大包线鲁棒控制器组合成全包线控制器,以使涡扇发动机在节流状态下使用PI控制器,在其它状态下通过切换模块切换至使用大包线鲁棒控制器。S5. Design the PI controller of the turbofan engine in the throttled state, and use the switching module to combine the PI controller and the large-envelope robust controller into a full-envelope controller, so that the turbofan engine can use the PI in the throttled state The controller, in other states, is switched to the robust controller using the large envelope by switching the module.

在具体的实施例中,由于涡扇发动机的大包线NPV模型没有低工作状态的特征,基于NPV模型设计的大包线鲁棒控制器对于节流状态以下的控制效果不佳。因此,节流状态以下采用传统的PI控制器。PI控制是一种经典的控制算法,它根据给定值与实际输出值构成控制偏差,将偏差的比例和积分通过线性组合构成控制量,对被控对象进行控制。PI控制器的控制律表达式如下:In a specific embodiment, since the large-envelope NPV model of the turbofan engine does not have the feature of low working state, the large-envelope robust controller designed based on the NPV model has poor control effect under the throttling state. Therefore, the traditional PI controller is used below the throttle state. PI control is a classic control algorithm. It forms a control deviation according to the given value and the actual output value. The proportion and integral of the deviation are linearly combined to form a control quantity to control the controlled object. The control law expression of the PI controller is as follows:

Figure RE-GDA0003753661370000161
Figure RE-GDA0003753661370000161

其中,Kp和Ti为常数,e(t)为系统误差。在本实施例中,取 Kp=150,Ti=1。Among them, K p and T i are constants, and e(t) is the systematic error. In this embodiment, K p =150 and T i =1.

将设计的大包线鲁棒控制器和PI控制器通过切换模块进行组合,本实施例中,切换模块具体为切换开关。这样一来,采用PI-PP混合控制策略,即涡扇发动机在节流状态以下时使用传统的PI控制器控制,在节流状态以上时采用大包线鲁棒控制器,最终保证了涡扇发动机闭环系统在全包线飞行条件下的控制效果。组合成的全包线控制器的控制律为:The designed large-envelope robust controller and the PI controller are combined through a switching module. In this embodiment, the switching module is specifically a switching switch. In this way, the PI-PP hybrid control strategy is adopted, that is, when the turbofan engine is under the throttle state, the traditional PI controller is used to control, and when the throttle state is above, the large-envelope robust controller is used, which finally ensures the turbofan engine. Control effects of closed-loop engine systems under full-envelope flight conditions. The control law of the combined all-envelope controller is:

Figure RE-GDA0003753661370000162
Figure RE-GDA0003753661370000162

其中,PLA为油门杆角度,V为常数,KR,Kp,Ti为待整定的参数。在本实施例中,取V=41。Among them, PLA is the throttle stick angle, V is a constant, K R , K p , and T i are parameters to be set. In this embodiment, V=41 is taken.

图2示出了根据本申请一个具体实施例的涡扇发动机控制系统结构图,如图2所示,本申请的实施原理为:FIG. 2 shows a structural diagram of a turbofan engine control system according to a specific embodiment of the present application. As shown in FIG. 2 , the implementation principle of the present application is:

针对涡扇发动机全包线稳态和过渡态控制问题,通过设计大包线鲁棒控制器和PI控制器,并利用切换开关组合成全包线控制器。涡扇发动机控制系统基于预设性能方法将系统的性能指标转化为全包线控制器的设计指标,使得全包线控制器更好地适应发动机非线性模型,从而具有较好的控制稳定性。涡扇发动机控制系统采用PI-PP混合控制策略,即涡扇发动机在节流状态下使用PI控制器,其余飞行状态使用大包线鲁棒控制器,最终保证了涡扇发动机闭环系统在全包线飞行条件下的控制效果。Aiming at the full-envelope steady-state and transition-state control problems of turbofan engines, a large-envelope robust controller and a PI controller are designed, and a switch-over switch is used to form an all-envelope controller. The turbofan engine control system transforms the performance index of the system into the design index of the full-envelope controller based on the preset performance method, so that the full-envelope controller can better adapt to the nonlinear model of the engine, so that it has better control stability. The turbofan engine control system adopts the PI-PP hybrid control strategy, that is, the turbofan engine uses the PI controller in the throttle state, and the large-envelope robust controller is used in the rest of the flight state, which finally ensures that the turbofan engine closed-loop system operates in the full package. Control effects in line flight conditions.

根据本申请的第二方面,提出了一种涡扇发动机全包线控制器的仿真方法,该仿真方法用于对上述的全包线控制器的软件部分和硬件部分进行仿真。According to the second aspect of the present application, a simulation method of a turbofan engine full-envelope controller is proposed, and the simulation method is used for simulating the software part and the hardware part of the above-mentioned full-envelope controller.

图3示出了根据本申请实施例的涡扇发动机全包线控制器的仿真方法流程图,如图3所示,该仿真方法包括以下步骤:FIG. 3 shows a flowchart of a simulation method for an all-envelope controller of a turbofan engine according to an embodiment of the present application. As shown in FIG. 3 , the simulation method includes the following steps:

a)在全数字仿真平台上搭建全包线控制器。a) Build an all-envelope controller on an all-digital simulation platform.

在具体的实施例中,全数字仿真平台可以采用Matlab或Simulink。本实施例中,全数字仿真平台具体采用Simulink,Simulink可以实现快速建模与仿真,用Simulink中自带的自动代码生成功能将封装好的部件级实时模型生成C代码,生成的代码可以用来进行硬件在环及半物理仿真验证。In a specific embodiment, the all-digital simulation platform can use Matlab or Simulink. In this embodiment, the all-digital simulation platform specifically uses Simulink, which can realize rapid modeling and simulation, and use the automatic code generation function built in Simulink to generate C code from the packaged component-level real-time model, and the generated code can be used for Perform hardware-in-the-loop and semi-physical simulation verification.

图4示出了根据本申请一个具体实施例的全数字仿真平台主要结构划分示意图,如图4所示,涡扇发动机全数字仿真平台是对涡扇发动机部件级实时模型进行的全数字仿真,主要由飞控指令信号、控制器、执行机构、发动机和观测信号五个模块组成。其中飞控指令信号模块可以实现对飞机飞行高度(H)、马赫数(Ma)和油门杆角度(PLA)的设定,以此来调节飞机的工作状态;控制器是发动机控制算法的实现部分,保证发动机在给定工作状态下平稳运行。FIG. 4 shows a schematic diagram of the main structure division of a full-digital simulation platform according to a specific embodiment of the present application. As shown in FIG. 4 , the turbofan engine full-digital simulation platform is a full-digital simulation of a turbofan engine component-level real-time model, It is mainly composed of five modules: flight control command signal, controller, actuator, engine and observation signal. Among them, the flight control command signal module can realize the setting of the aircraft flight height (H), Mach number (Ma) and throttle stick angle (PLA), so as to adjust the working state of the aircraft; the controller is the realization part of the engine control algorithm , to ensure that the engine runs smoothly under a given working state.

针对控制输入主燃油量和喉道面积,全数字仿真平台中提供了对应的 PI控制模块,实现节流状态以下的闭环控制。在此基础上,将本申请第一方面所设计的大包线鲁棒控制器代入全数字仿真平台的部件级模型进行控制,保证涡扇发动机系统在大包线范围稳定运行。接着,通过切换开关切换进行不同控制器的切换,即节流状态以下使用PI控制器,节流状态以上用大包线鲁棒控制器,组成全包线控制器,保证闭环系统在全包线飞行条件下的控制效果。图5示出了根据本申请一个具体实施例的主燃油量的全包线控制器框图,图6示出了根据本申请一个具体实施例的喉道面积的全包线控制器框图。For controlling the input main fuel quantity and throat area, the corresponding PI control module is provided in the all-digital simulation platform to realize closed-loop control below the throttle state. On this basis, the large-envelope robust controller designed in the first aspect of the present application is substituted into the component-level model of the all-digital simulation platform for control, so as to ensure the stable operation of the turbofan engine system in the large-envelope range. Then, switch between different controllers by switching the switch, that is, the PI controller is used below the throttling state, and the large-envelope robust controller is used above the throttling state to form an all-envelope controller to ensure that the closed-loop system operates in the full-envelope. Control effects in flight conditions. Fig. 5 shows a block diagram of an all-envelope controller of the main fuel quantity according to a specific embodiment of the present application, and Fig. 6 shows a block diagram of an all-envelope controller of the throat area according to a specific embodiment of the present application.

继续参照图3,在步骤a)之后,Continuing to refer to Figure 3, after step a),

b)采用增益调参的方法优化全包线控制器。b) Using the method of gain parameter tuning to optimize the full envelope controller.

具体的,步骤b)具体包括:Specifically, step b) specifically includes:

b1)根据涡扇发动机的飞行高度和马赫数确定多个典型工作点,在不同的典型工作点以及不同的工作状态下,对全包线控制器中的参数采用网格搜索法选择使得涡扇发动机闭环系统动态性能表现最优的参数,实现对参数的整定;b1) Determine multiple typical operating points according to the flight height and Mach number of the turbofan engine. Under different typical operating points and different working conditions, the parameters in the full-envelope controller are selected by grid search method so that the turbofan The parameters with the best dynamic performance of the engine closed-loop system can realize the tuning of the parameters;

b2)采取线性插值方法组合整定的参数,使得涡扇发动机闭环系统在所有工作点下满足性能指标要求,综合成变增益全包线控制器。b2) The linear interpolation method is adopted to combine the set parameters, so that the closed-loop system of the turbofan engine meets the performance index requirements at all operating points, and is integrated into a variable-gain full-envelope controller.

在具体的实施例中,为进一步提高全包线控制器的控制效果,基于增益调参的方法在不同典型工作点下,整定全包线控制器参数,从而保证在闭环系统的性能满足给定的控制效果的基础上,设计的全包线控制器对未建模动态有较好的鲁棒性。增加可调参数Ku、K1,则待优化的全包线控制器的控制律为:In a specific embodiment, in order to further improve the control effect of the all-envelope controller, the parameters of the all-envelope controller are set under different typical operating points based on the method of gain parameter adjustment, so as to ensure that the performance of the closed-loop system meets the given On the basis of the control effect of , the designed all-envelope controller has better robustness to unmodeled dynamics. By adding the adjustable parameters Ku and K 1 , the control law of the full - envelope controller to be optimized is:

Figure RE-GDA0003753661370000181
Figure RE-GDA0003753661370000181

其中,Ku和K1同样为待整定的参数。Among them, Ku and K 1 are also parameters to be set.

在具体的实施例中,按飞行高度H、马赫数Ma选择(0,0)、(8,1.2)、 (3,0.3)、(6,0.6)和(4,0.8)五个典型工作点。分别对五个典型工作点的节流、中间、加力三个工作状态的控制器参数进行网格搜索,选择动态性能最优的参数,优化指标函数变量取为发动机高压转子转速nH和压比π,并分别定义偏差量enH和eπ的归一化偏差,即:In a specific embodiment, five typical operating points (0, 0), (8, 1.2), (3, 0.3), (6, 0.6) and (4, 0.8) are selected according to flight height H and Mach number Ma . Grid search is carried out for the controller parameters of the three working states of throttle, intermediate and afterburner at five typical working points, and the parameters with the best dynamic performance are selected. The optimization index function variables are taken as the engine high-pressure rotor speed n H and pressure. ratio π, and define the normalized deviation of the deviation quantities e nH and e π respectively, namely:

Figure RE-GDA0003753661370000191
Figure RE-GDA0003753661370000191

其中,e* nH(t)为高压转子转速偏差量的归一化偏差,e* π(t)为压比偏差量的归一化偏差,nH(0)、nHref分别表示闭环系统高压转子转速的初值和期望值;π(0)、πref分别表示压比的初值和期望值。Among them, e * nH (t) is the normalized deviation of the high pressure rotor speed deviation, e * π (t) is the normalized deviation of the pressure ratio deviation, n H (0), n Href respectively represent the high pressure of the closed-loop system The initial value and expected value of the rotor speed; π(0), πref represent the initial value and expected value of the pressure ratio, respectively.

继而对高压转子转速和压比分别定义归一化的ITAE指标量:Then, the normalized ITAE index quantities are respectively defined for the high-pressure rotor speed and pressure ratio:

Figure RE-GDA0003753661370000192
Figure RE-GDA0003753661370000192

于是,目标函数归一化形式为:Therefore, the normalized form of the objective function is:

Figure RE-GDA0003753661370000193
Figure RE-GDA0003753661370000193

其中,w1,w2为对应各指标分量的权值系数,是无量纲的。取指标分量的权值系数为:w1=1,w2=1。Among them, w 1 and w 2 are weight coefficients corresponding to each index component, which are dimensionless. The weight coefficients of the index components are taken as: w 1 =1, w 2 =1.

于是,控制器参数优化问题转化为求解最优化

Figure RE-GDA0003753661370000194
问题。根据目标函数归一化形式,利用网格搜索法即可实现对参数的整定。在大包线鲁棒控制器的参数整定中,Ku的搜索范围为(0,1),搜索步长为0.1; K1的搜索范围为(0,0.1),搜索步长为0.01;KR的搜索范围为(-0.1,0),搜索步长为0.01。PI控制器的参数整定中,KP的搜索范围为(0,200),搜索步长为1;Ti的搜索范围为(0,10),搜索步长为0.1,搜索结果如表 1和表2所示。Therefore, the controller parameter optimization problem is transformed into the solution optimization
Figure RE-GDA0003753661370000194
question. According to the normalized form of the objective function, the parameters can be adjusted by grid search method. In the parameter tuning of the large - envelope robust controller, the search range of Ku is (0, 1), and the search step is 0.1; the search range of K 1 is (0, 0.1), and the search step is 0.01; K The search range of R is (-0.1, 0), and the search step is 0.01. In the parameter setting of the PI controller, the search range of K P is (0, 200), and the search step is 1; the search range of T i is (0, 10), and the search step is 0.1. The search results are shown in Table 1 and Table 1. shown in Table 2.

表1大包线鲁棒控制器参数表Table 1 Parameter table of robust controller for large envelope

Figure RE-GDA0003753661370000195
Figure RE-GDA0003753661370000195

Figure RE-GDA0003753661370000201
Figure RE-GDA0003753661370000201

表2 PI控制器参数表Table 2 PI controller parameter table

Figure RE-GDA0003753661370000202
Figure RE-GDA0003753661370000202

整定完参数后,再采取线性插值方法组合整定的参数值,使得涡扇发动机闭环系统在所有工作点下满足性能指标要求,综合成变增益全包线控制器。After the parameters are set, the linear interpolation method is used to combine the set parameter values, so that the closed-loop system of the turbofan engine meets the performance index requirements at all operating points, and is integrated into a variable gain full-envelope controller.

继续参照图3,在步骤b)之后,Continuing to refer to Figure 3, after step b),

c)对优化后的全包线控制器进行全数字仿真。c) Full digital simulation of the optimized all-envelope controller.

d)将全包线控制器以硬件形式在硬件在环平台和半物理平台上进行稳态实验和动态实验。d) Carry out steady-state experiments and dynamic experiments on the hardware-in-the-loop platform and semi-physical platform with the full-envelope controller in the form of hardware.

其中,硬件在环仿真系统中拥有真实的I/O接口、控制器硬件设备以及虚拟的被控对象模型,是一种置信度较高的控制算法测试验证手段。半物理仿真具备真实的油路系统,能对控制器与液压机械系统及相关传感器进行综合和试验验证,相比于硬件在环仿真具备更高的逼真。因此,硬件在环仿真和半物理仿真试验已成为发动机控制系统研制中最重要的试验,新研发的控制系统必须经过硬件在环仿真和半物理仿真试验后才能装机开展台架试车。Among them, the hardware-in-the-loop simulation system has real I/O interfaces, controller hardware devices and virtual controlled object models, which is a high-confidence control algorithm test and verification method. Semi-physical simulation has a real oil circuit system, which can comprehensively and experimentally verify the controller, hydraulic mechanical system and related sensors. Compared with hardware-in-the-loop simulation, it has higher fidelity. Therefore, hardware-in-the-loop simulation and semi-physical simulation test have become the most important tests in engine control system development.

在具体的实施例中,在某型小涵道比双轴涡扇发动机的飞行包线内任意选取飞行轨迹和5个典型工作点,将设计的全包线控制器以软件形式在全数字仿真平台进行实验,将设计的全包线控制器以硬件形式在硬件在环平台(Hardware-in-the-Loop,HIL)和半物理平台上进行实验。在(0,0)、(8, 1.2)、(3,0.3)、(6,0.6)和(4,0.8)五个工作点处分别作油门杆大范围阶跃,根据动态响应曲线来观察控制效果,从而检验所设计的全包线控制器的性能。In a specific embodiment, the flight trajectory and 5 typical operating points are arbitrarily selected within the flight envelope of a certain type of small bypass ratio twin-shaft turbofan engine, and the designed full-envelope controller is simulated in full digital in the form of software. Experiments are carried out on the platform, and the designed all-in-the-loop controller is carried out on the hardware-in-the-Loop (HIL) and semi-physical platforms in the form of hardware. Make a large-scale step of the accelerator lever at the five operating points (0, 0), (8, 1.2), (3, 0.3), (6, 0.6) and (4, 0.8) respectively, and observe according to the dynamic response curve. control effect, so as to test the performance of the designed all-envelope controller.

全数字仿真实验:Full digital simulation experiment:

全数字仿真实验包括任意飞行轨迹仿真实验和单工况仿真实验。单工况仿真实验包括对(0,0)、(8,1.2)、(3,0.3)、(6,0.6)和(4,0.8)五个点的稳态仿真实验和动态仿真实验。稳态仿真试验主要验证在节流状态、中间状态油门杆小阶跃、加力状态时,油门杆小幅度(±5°)阶跃时,控制器性能。动态(或过渡态)仿真试验主要验证慢车进入节流、慢车进入中间、慢车进入全加力、节流进入慢车、中间进入慢车、全加力进入慢车时,油门杆快速大幅度阶跃时,全包线控制器的性能。All-digital simulation experiments include arbitrary flight trajectory simulation experiments and single-condition simulation experiments. Single-condition simulation experiments include steady-state simulation experiments and dynamic simulation experiments for five points (0, 0), (8, 1.2), (3, 0.3), (6, 0.6) and (4, 0.8). The steady-state simulation test mainly verifies the performance of the controller when the throttle lever is stepped with a small amplitude (±5°) in the throttle state, the small step of the throttle lever in the intermediate state, and the afterburner state. The dynamic (or transition state) simulation test mainly verifies that when the slow car enters throttling, the slow car enters the middle, the slow car enters full afterburner, the throttle enters the idle car, the middle enters the idle car, and the full afterburner enters the idle car, when the accelerator lever is rapidly and greatly stepped, Full-coverage controller performance.

图7示出了根据本申请一个具体实施例的涡扇发动机处于节流状态时给定的PLA变化图,图8示出了根据本申请一个具体实施例的涡扇发动机处于中间状态时给定的PLA变化图,图9示出了根据本申请一个具体实施例的涡扇发动机处于加力状态时给定的PLA变化图,如图7-9所示,节流状态的0~20秒和80~100秒为动态仿真实验,20~80秒为稳态仿真实验,中间和加力状态的0~20秒和100~120秒为动态仿真实验,20~100秒为稳态仿真实验。FIG. 7 shows a given PLA change diagram when the turbofan engine is in a throttle state according to a specific embodiment of the present application, and FIG. 8 shows a given PLA change diagram when the turbofan engine is in an intermediate state according to a specific embodiment of the present application Figure 9 shows a given PLA change diagram when the turbofan engine is in the afterburner state according to a specific embodiment of the present application, as shown in Figures 7-9, the 0-20 seconds and 80-100 seconds are dynamic simulation experiments, 20-80 seconds are steady-state simulation experiments, 0-20 seconds and 100-120 seconds in intermediate and afterburning states are dynamic simulation experiments, and 20-100 seconds are steady-state simulation experiments.

(1)包线内任意飞行轨迹仿真实验:(1) Simulation experiment of arbitrary flight trajectory within the envelope:

图10是根据本申请一个具体实施例的涡扇发动机包线内飞行高度、马赫数和油门杆角度随时间变化曲线图,如图10所示,其中,飞行轨迹包括滑跑、起飞、爬升、巡航、加速、爬升、加速等过程。图11示出了根据本申请一个具体实施例的飞行轨迹仿真实验得到的高压转子转速变化曲线图,图12示出了根据本申请一个具体实施例的飞行轨迹仿真实验得到的发动机压比变化曲线图,如图11、12所示,由仿真结果可以看出,随着飞行条件的变化,发动机高压转子的转速和压比能够跟踪控制计划给出的控制目标,且动态响应较好,全包线控制器表现出了较好的鲁棒性和稳定性,能够满足包线内涡扇发动机控制的要求。Fig. 10 is a graph showing the variation of flight height, Mach number and throttle stick angle with time within the envelope of a turbofan engine according to a specific embodiment of the present application, as shown in Fig. 10, wherein the flight trajectory includes rollout, takeoff, climb, Cruise, acceleration, climb, acceleration and other processes. FIG. 11 shows a graph of the high-pressure rotor rotational speed variation curve obtained by a flight trajectory simulation experiment according to a specific embodiment of the present application, and FIG. 12 shows an engine pressure ratio variation curve obtained by a flight trajectory simulation experiment according to a specific embodiment of the present application. As shown in Figures 11 and 12, it can be seen from the simulation results that with the change of flight conditions, the rotational speed and pressure ratio of the high-pressure rotor of the engine can track the control objectives given by the control plan, and the dynamic response is good. The line controller shows good robustness and stability, and can meet the requirements of turbofan engine control within the envelope.

(2)单工况仿真实验:(2) Simulation experiment of single working condition:

全数字仿真试验性能指标要求:高压转子转速控制的调节时间4秒内,稳态误差不大于0.1%,超调量不大于1%;低压转子的稳态误差不大于0.1%。发动机压比的稳态误差不大于0.5%。The performance indicators of the full digital simulation test are: within 4 seconds of the adjustment time of the high-pressure rotor speed control, the steady-state error is not greater than 0.1%, and the overshoot is not greater than 1%; the steady-state error of the low-pressure rotor is not greater than 0.1%. The steady-state error of the engine pressure ratio is not more than 0.5%.

各工作点的稳态实验结果如表3所示。The steady-state experimental results at each operating point are shown in Table 3.

表3稳态实验结果记录表Table 3 Record table of steady state experimental results

Figure RE-GDA0003753661370000221
Figure RE-GDA0003753661370000221

Figure RE-GDA0003753661370000231
Figure RE-GDA0003753661370000231

动态实验中,PLA上升过程的实验结果如表4所示。In the dynamic experiment, the experimental results of the rising process of PLA are shown in Table 4.

表4动态实验(PLA上升过程)结果记录表Table 4 Dynamic experiment (PLA rising process) result record table

Figure RE-GDA0003753661370000232
Figure RE-GDA0003753661370000232

PLA下降过程的实验结果如表5所示。The experimental results of the PLA descending process are shown in Table 5.

表5动态实验(PLA下降过程)结果记录表Table 5 dynamic experiment (PLA descending process) result record table

Figure RE-GDA0003753661370000233
Figure RE-GDA0003753661370000233

Figure RE-GDA0003753661370000241
Figure RE-GDA0003753661370000241

其中,NA表示对应的无法计算。选取(0,0)点的仿真结果图进行展示。Among them, NA indicates that the corresponding cannot be calculated. The simulation result graph of point (0, 0) is selected for display.

图13示出了根据本申请一个具体实施例的单工况仿真实验在工作点 (0,0)节流状态下仿真得到的高压转子转速变化曲线,图14示出了根据本申请一个具体实施例的单工况仿真实验在工作点(0,0)中间状态下仿真得到的高压转子转速变化曲线,图15示出了根据本申请一个具体实施例的单工况仿真实验在工作点(0,0)加力状态下仿真得到的高压转子转速变化曲线;图16示出了根据本申请一个具体实施例的单工况仿真实验在工作点(0,0)中间状态下仿真得到发动机压比变化曲线,图17示出了根据本申请一个具体实施例的单工况仿真实验在工作点(0,0)加力状态下仿真得到发动机压比变化曲线。FIG. 13 shows the high-voltage rotor speed variation curve obtained by simulation under the throttling state at the operating point (0, 0) according to a single working condition simulation experiment according to a specific embodiment of the present application, and FIG. 14 shows a specific implementation according to the present application. Figure 15 shows the simulation experiment of a single working condition according to a specific embodiment of the present application at the working point (0, 0). , 0) the high-pressure rotor speed variation curve obtained by simulation under the afterburner state; Fig. 16 shows the engine pressure ratio obtained by simulation in the middle state of the operating point (0, 0) according to a single working condition simulation experiment according to a specific embodiment of the present application Variation curve, Fig. 17 shows the variation curve of engine pressure ratio obtained by simulation under the state of applying force at the working point (0, 0) according to a single working condition simulation experiment according to a specific embodiment of the present application.

由实验结果记录表可知,在稳态控制实验中,各工作点的控制效果均满足性能指标要求;在动态控制实验中,除了部分状态的高压转子转速调节时间超出了4秒,其它性能均满足指标要求。调节时间较大的原因是当参考状态大幅改变时,由于受到燃油量的物理限制无法大幅改变。It can be seen from the record table of experimental results that in the steady-state control experiment, the control effects of each operating point meet the performance requirements; in the dynamic control experiment, except for the high-voltage rotor speed adjustment time in some states that exceeds 4 seconds, other performances are satisfied. indicator requirements. The reason for the large adjustment time is that when the reference state changes greatly, it cannot be greatly changed due to the physical limitation of the fuel quantity.

由仿真结果可以看到,高压转子转速的稳态误差不大于0.1%,超调量不大于1%;转速能够快速平稳的跟上系统的指令,误差收敛较快。发动机压比的稳态误差不大于0.5%,在慢车及以下状态时,发动机压比为开环控制,因此不跟踪参考值。全数字仿真结果表明:涡扇发动机大包线控制器在全包线范围内能够保证系统的稳定性,满足多性能指标要求,且系统具有良好的动态特性,控制器控制效果良好,具有一定的鲁棒稳定性。It can be seen from the simulation results that the steady-state error of the high-pressure rotor speed is not more than 0.1%, and the overshoot is not more than 1%; the speed can quickly and smoothly keep up with the system command, and the error converges quickly. The steady-state error of the engine pressure ratio is not more than 0.5%. In the idle state and below, the engine pressure ratio is open-loop control, so the reference value is not tracked. The full digital simulation results show that the turbofan engine large-envelope controller can ensure the stability of the system within the full-envelope range, meet the requirements of multiple performance indicators, and the system has good dynamic characteristics. Robust stability.

硬件在环(HIL)仿真和半物理仿真实验:Hardware-in-the-loop (HIL) simulation and semi-physical simulation experiments:

硬件在环仿真和半物理仿真实验除了完成全数字仿真实验中五个工作点的稳态实验和动态实验外,还对(0,0)、(3,0.3)和(8,1.2)三个工作点进行拉偏实验,即高低转子转动惯量全程拉偏10%。由硬件在环仿真实验得到的五个单工况实验点及三个拉偏单工况实验点的动态和稳态的实验结果分别如表6、表7和表8所示。由半物理得到的五个单工况实验点及三个拉偏单工况实验点的过渡态和稳态的实验结果分别如表9、表10和表11所示。The hardware-in-the-loop simulation and semi-physical simulation experiment not only completed the steady-state experiment and dynamic experiment of the five operating points in the full-digital simulation experiment, but also performed three experiments on (0,0), (3,0.3) and (8,1.2) The biasing experiment is carried out at the working point, that is, the rotational inertia of the high and low rotors is biased by 10% in the whole process. The dynamic and steady-state experimental results of the five single-condition experimental points and the three deflection single-condition experimental points obtained from the hardware-in-the-loop simulation experiment are shown in Table 6, Table 7, and Table 8, respectively. The experimental results of the transition state and the steady state of the five single-condition experimental points and the three single-condition experimental points obtained by semi-physics are shown in Table 9, Table 10 and Table 11, respectively.

表6 HIL动态实验(PLA上升过程)结果记录表Table 6 HIL dynamic experiment (PLA rising process) result record table

Figure RE-GDA0003753661370000251
Figure RE-GDA0003753661370000251

Figure RE-GDA0003753661370000261
Figure RE-GDA0003753661370000261

表7 HIL动态实验(PLA下降过程)结果记录表Table 7 HIL dynamic experiment (PLA descending process) result record table

Figure RE-GDA0003753661370000262
Figure RE-GDA0003753661370000262

表8 HIL稳态实验结果记录表Table 8 Record table of HIL steady state experimental results

Figure RE-GDA0003753661370000263
Figure RE-GDA0003753661370000263

Figure RE-GDA0003753661370000271
Figure RE-GDA0003753661370000271

表9半物理动态实验(PLA上升过程)结果记录表Table 9 Semi-physical dynamic experiment (PLA rising process) result record table

Figure RE-GDA0003753661370000272
Figure RE-GDA0003753661370000272

Figure RE-GDA0003753661370000281
Figure RE-GDA0003753661370000281

表10半物理动态实验(PLA下降过程)结果记录表Table 10 Record table of results of semi-physical dynamic experiment (PLA descending process)

Figure RE-GDA0003753661370000282
Figure RE-GDA0003753661370000282

表11半物理稳态实验结果记录表Table 11 Record table of semi-physical steady state experimental results

Figure RE-GDA0003753661370000291
Figure RE-GDA0003753661370000291

由实验结果记录表可知,在动态试验中,五个单工况实验点及三个拉偏单工况实验点的稳态误差和超调量均满足性能指标要求。此外,部分压比调节时间过大、超调过大。调节时间超时的原因是当高压转子转速大幅改变时,由于受到燃油量的限制,转速无法大幅改变。在稳态试验中,五个单工况实验点及三个拉偏单工况实验点的高压转子调节时间、稳态误差和超调量均满足性能指标要求。It can be seen from the experimental result record table that in the dynamic test, the steady-state error and overshoot of the five single-condition experimental points and the three single-biased single-condition experimental points all meet the performance requirements. In addition, the partial pressure ratio adjustment time is too large and the overshoot is too large. The reason for the overtime of the adjustment time is that when the high-pressure rotor speed changes greatly, the speed cannot be greatly changed due to the limitation of the fuel quantity. In the steady-state test, the adjustment time, steady-state error and overshoot of the high-voltage rotor at the five single-condition experimental points and the three pull-off single-condition experimental points all meet the performance requirements.

综上所述,全包线控制器能够满足控制系统的设计要求,在理论上能够保证系统的全局稳定性,使控制系统在整个包线范围内具有良好的性能。实验结果表明,在发动机转速大范围变化的条件下,全包线控制器能够使系统在全包线范围内保持稳定,满足给定的多性能指标要求,并具备较好的动态性能以及鲁棒性。To sum up, the all-envelope controller can meet the design requirements of the control system, and can theoretically ensure the global stability of the system, so that the control system has good performance in the entire envelope range. The experimental results show that under the condition that the engine speed changes in a wide range, the all-envelope controller can keep the system stable in the whole-envelope range, meet the given requirements of multiple performance indicators, and has good dynamic performance and robustness. sex.

本申请提出了一种涡扇发动机全包线控制器的设计方法与仿真方法,在全数字仿真阶段,为克服涡扇发动机NPV模型所设计的控制器对于节流状态以下的控制效果不佳的问题,提出了PI-PP混合控制策略。通过给定设计的全包线控制器切换策略最终保证了涡扇发动机闭环系统在全包线飞行条件下的控制效果。针对涡扇发动机非线性部件模型的强非线性特征,采用增益调参的方法优化全包线控制器,使得全包线控制器更好地适应发动机非线性模型,控制效果得到了进一步的提升。在硬件在环仿真与半物理仿真实验中,基于以上策略搭建的全包线控制器,能够保证系统在全包线范围内都具有全局稳定性,在满足稳态性能的基础上,同时能保证过渡(动态)过程能充分满足给定的多性能指标要求,且涡扇发动机闭环系统有良好的鲁棒性。This application proposes a design method and a simulation method of a turbofan engine full-envelope controller. In the full digital simulation stage, the controller designed to overcome the NPV model of the turbofan engine has poor control effect under the throttle state. problem, a PI-PP hybrid control strategy is proposed. Through the given design of the full-envelope controller switching strategy, the control effect of the turbofan engine closed-loop system under the full-envelope flight condition is finally guaranteed. In view of the strong nonlinear characteristics of the turbofan engine nonlinear component model, the method of gain parameter adjustment is used to optimize the full envelope controller, which makes the full envelope controller better adapt to the engine nonlinear model, and the control effect is further improved. In the hardware-in-the-loop simulation and semi-physical simulation experiments, the all-envelope controller built based on the above strategies can ensure that the system has global stability in the entire envelope range. On the basis of satisfying the steady-state performance, it can also guarantee The transition (dynamic) process can fully meet the given multi-performance index requirements, and the closed-loop system of the turbofan engine has good robustness.

在本申请实施例中,应该理解到,所揭露的技术内容,可通过其它的方式实现。其中,以上所描述的装置/系统/方法实施例仅仅是示意性的,例如所述单元的划分,可以为一种逻辑功能划分,实际实现时可以有另外的划分方式,例如多个单元或组件可以结合或者可以集成到另一个系统,或一些特征可以忽略,或不执行。另一点,所显示或讨论的相互之间的耦合或直接耦合或通信连接可以是通过一些接口,单元或模块的间接耦合或通信连接,可以是电性或其它的形式。In the embodiments of the present application, it should be understood that the disclosed technical content may be implemented in other manners. The apparatus/system/method embodiments described above are only illustrative, for example, the division of the units may be a logical function division, and in actual implementation, there may be other divisions, such as multiple units or components May be combined or may be integrated into another system, or some features may be omitted, or not implemented. On the other hand, the shown or discussed mutual coupling or direct coupling or communication connection may be through some interfaces, indirect coupling or communication connection of units or modules, and may be in electrical or other forms.

所述作为分离部件说明的单元可以是或者也可以不是物理上分开的,作为单元显示的部件可以是或者也可以不是物理单元,即可以位于一个地方,或者也可以分布到多个单元上。可以根据实际的需要选择其中的部分或者全部单元来实现本实施例方案的目的。The units described as separate components may or may not be physically separated, and components shown as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution in this embodiment.

另外,在本申请各个实施例中的各功能单元可以集成在一个处理单元中,也可以是各个单元单独物理存在,也可以两个或两个以上单元集成在一个单元中。上述集成的单元既可以采用硬件的形式实现,也可以采用软件功能单元的形式实现。In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically alone, or two or more units may be integrated into one unit. The above-mentioned integrated units may be implemented in the form of hardware, or may be implemented in the form of software functional units.

所述集成的单元如果以软件功能单元的形式实现并作为独立的产品销售或使用时,可以存储在一个计算机可读取存储介质中。基于这样的理解,本申请的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的全部或部分可以以软件产品的形式体现出来,该计算机软件产品存储在一个存储介质中,包括若干指令用以使得一台计算机设备(可为个人计算机、服务器或者网络设备等)执行本申请各个实施例所述方法的全部或部分步骤。而前述的存储介质包括:U盘、只读存储器(ROM,Read-Only Memory)、随机存取存储器(RAM,Random Access Memory)、移动硬盘、磁碟或者光盘等各种可以存储程序代码的介质。The integrated unit, if implemented in the form of a software functional unit and sold or used as an independent product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the present application can be embodied in the form of software products in essence, or the parts that contribute to the prior art, or all or part of the technical solutions, and the computer software products are stored in a storage medium , including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and other media that can store program codes .

显然,本领域技术人员在不偏离本申请的精神和范围的情况下可以作出对本申请的实施例的各种修改和改变。以该方式,如果这些修改和改变处于本申请的权利要求及其等同形式的范围内,则本申请还旨在涵盖这些修改和改变。词语“包括”不排除未在权利要求中列出的其它元件或步骤的存在。某些措施记载在相互不同的从属权利要求中的简单事实不表明这些措施的组合不能被用于获利。权利要求中的任何附图标记不应当被认为限制范围。It will be apparent to those skilled in the art that various modifications and changes to the embodiments of the present application can be made without departing from the spirit and scope of the present application. In this manner, this application is also intended to cover such modifications and changes if they come within the scope of the claims of this application and their equivalents. The word "comprising" does not exclude the presence of other elements or steps not listed in a claim. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.

Claims (10)

1. A design method of a turbofan engine full-envelope controller is characterized by comprising the following steps:
s1, establishing an NPV model of the turbofan engine, wherein the NPV model comprises external disturbance, and converting the NPV model into an uncertain model according to the external disturbance;
s2, designing a robust controller of the large covered wire based on the uncertain model;
s3, designing a preset performance parameter matrix in the large envelope robust controller according to the performance index requirement of the turbofan engine closed-loop system;
s4, solving a state feedback gain matrix in the robust controller of the large envelope curve by utilizing an SOS technology, thereby solving the robust controller of the large envelope curve;
s5, designing a PI controller of the turbofan engine in a throttling state, and combining the PI controller and the large package wire robust controller into the full package wire controller by using a switching module, so that the PI controller is used by the turbofan engine in the throttling state, and the large package wire robust controller is switched to be used by the switching module in other states.
2. The design method according to claim 1, wherein the NPV model including the external disturbance is specifically:
Figure RE-RE-FDA0003753661360000011
wherein x ∈ R n Is the system state, u ∈ R n Is a control input, rho (t) is ∈ R s Is a time-varying parameter vector, A (-), B (-), and C (-,) are polynomial matrices about x and ρ (t), ω (t) is an external perturbation, E 1 Is a constant matrix of suitable dimensions;
the uncertain model is specifically as follows:
Figure RE-RE-FDA0003753661360000012
wherein, Δ F 1 x (t) is transformed external disturbance, Δ is uncertainty matrix, satisfies Δ T △≤I,F 1 I is a constant matrix and an identity matrix of suitable dimensions, respectively, satisfying F 1 T F 1 ≥0。
3. The design method as claimed in claim 2, wherein the expression of the robust controller for large envelope is as follows:
Figure RE-RE-FDA0003753661360000021
wherein,
Figure RE-RE-FDA0003753661360000022
is the state feedback gain matrix, k, to be designed R Is the adjustable coefficient of the linear motion vector,
Figure RE-RE-FDA0003753661360000023
is a preset performance parameter matrix to be designed.
4. A design method according to claim 3, wherein the performance index requirements of the turbofan engine closed loop system are specified as: the high-pressure rotor rotating speed control steady-state error, the dynamic overshoot, the step response time, the spray pipe closed-loop control pressure ratio steady-state error and the rotating speed dynamic overshoot under the high-pressure rotor rotating speed disturbance of the turbofan engine are all within a preset threshold value;
the design process of the preset performance parameter matrix specifically comprises the following steps: based on the preset performance parameter matrix to be designed, performing difference operation on a value of a system state at any moment and a preset expected value to obtain a state error, introducing a performance function, defining an error transformation function, and designing to obtain the preset performance parameter matrix, wherein an expression of the preset performance parameter matrix specifically comprises:
Figure RE-RE-FDA0003753661360000024
Figure RE-RE-FDA0003753661360000025
wherein the continuous function T is defined as an error transformation function T i (x,t),
Figure RE-RE-FDA0003753661360000026
For the state error, rho, of the turbofan engine closed-loop system i (t) is the introduced performance function.
5. The design method according to claim 4, wherein the solving of the state feedback gain matrix specifically comprises:
designing solvability conditions of the state feedback gain matrix to be designed, wherein an expression specifically comprises the following steps:
Figure RE-RE-FDA0003753661360000027
Figure RE-RE-FDA0003753661360000028
Figure RE-RE-FDA0003753661360000031
wherein,
Figure RE-RE-FDA0003753661360000032
and
Figure RE-RE-FDA0003753661360000033
is given a positive number,. phi SOS For the set of SOS polynomials to be,
Figure RE-RE-FDA0003753661360000034
Figure RE-RE-FDA0003753661360000035
is an n x n dimensional symmetric polynomial matrix,
Figure RE-RE-FDA0003753661360000036
is an m x n dimensional polynomial matrix, k R Is a constant;
solving solvability conditions of the state feedback gain matrix to be designed by utilizing an SOS technology to obtain the state feedback gain matrix, wherein an expression of the state feedback gain matrix is specifically as follows:
Figure RE-RE-FDA0003753661360000037
6. the design method according to claim 3, wherein the control law expression of the PI controller is specifically:
Figure RE-RE-FDA0003753661360000038
wherein, K p And T i Is constant, e (t) is the systematic error.
7. The design method according to claim 6, wherein the control law expression of the full-envelope controller is specifically:
Figure RE-RE-FDA0003753661360000039
wherein, PLA is throttle lever angle, and V is the constant.
8. A simulation method of a turbofan engine full-envelope controller, which simulates the full-envelope controller in the design method according to any one of claims 1 to 7, comprising the steps of:
a) building the full-envelope controller on a full-digital simulation platform;
b) optimizing the full-envelope controller by adopting a gain parameter adjusting method;
c) performing full-digital simulation on the optimized full-envelope controller;
wherein, the step b) specifically comprises the following steps:
b1) determining a plurality of typical working points according to the flight altitude and the Mach number of the turbofan engine, and selecting the parameters in the full wrap controller by adopting a grid search method under different typical working points and different working states so as to optimize the dynamic performance of the turbofan engine closed loop system, thereby realizing the tuning of the parameters;
b2) and combining and setting the parameters by adopting a linear interpolation method, so that the turbofan engine closed-loop system meets the performance index requirements at all working points and is synthesized into a variable gain full-wrap controller.
9. The simulation method according to claim 8, wherein the control law expression of the full-envelope controller to be optimized in step b) is specifically:
Figure RE-RE-FDA0003753661360000041
wherein, K u ,K 1 ,K R ,K p ,T i Is a parameter to be set.
10. The simulation method of claim 8, further comprising: and performing steady-state experiments and dynamic experiments on the full-envelope controller on a ring platform and a semi-physical platform in a hardware mode.
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