WO2022037157A1 - 基于神经网络的narma-l2多变量控制方法 - Google Patents

基于神经网络的narma-l2多变量控制方法 Download PDF

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WO2022037157A1
WO2022037157A1 PCT/CN2021/095598 CN2021095598W WO2022037157A1 WO 2022037157 A1 WO2022037157 A1 WO 2022037157A1 CN 2021095598 W CN2021095598 W CN 2021095598W WO 2022037157 A1 WO2022037157 A1 WO 2022037157A1
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narma
neural network
output
engine
control
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黄金泉
唐杰
鲁峰
仇小杰
高亚辉
秦海勤
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南京航空航天大学
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G05B13/027—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks only
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02C—GAS-TURBINE PLANTS; AIR INTAKES FOR JET-PROPULSION PLANTS; CONTROLLING FUEL SUPPLY IN AIR-BREATHING JET-PROPULSION PLANTS
    • F02C9/00—Controlling gas-turbine plants; Controlling fuel supply in air- breathing jet-propulsion plants
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/084—Backpropagation, e.g. using gradient descent
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/09—Supervised learning
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2260/00—Function
    • F05D2260/80—Diagnostics
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2260/00—Function
    • F05D2260/81—Modelling or simulation

Definitions

  • the invention belongs to the field of aero-engine simulation and control, in particular to a NARMA-L2 multivariable control method based on a neural network.
  • the performance of the early aero-engines is not high, generally only a control amount of fuel flow can keep the engine speed unchanged.
  • the variables that need to be controlled are gradually increasing.
  • the afterburner fuel supply in order to ensure that the turbine drop pressure ratio remains unchanged, the afterburner fuel supply must also be used as a control amount.
  • the development of aero-engine control system from single-variable control system to multi-variable control system is inevitable.
  • NARMA-L2 control method is mainly aimed at single-variable control.
  • a multi-variable control system is often composed of decentralized loops, which is essentially just a combination of multiple single-variable control systems. This combined control method does not consider the influence of coupling, which has a certain impact on the control accuracy of the system.
  • the technical problem to be solved by the present invention is to deduce the NARMA-L2 equation design control law of the multi-input multi-output system, and design the turbofan engine high-pressure speed and pressure ratio dual-variable controller for the defects of the background technology, which are used to solve the distributed loop control system.
  • the coupling problem caused by the simulation shows that the controller has good stable and dynamic performance.
  • a NARMA-L2 multivariate control method based on neural network comprising the following steps:
  • Step A deduce the NARMA-L2 equation and the multivariate control law of the multi-input multi-output nonlinear discrete system
  • step A the concrete steps of step A) are as follows:
  • Step A1) according to the state space description of multi-input multi-output nonlinear discrete system, obtain the NARMA equation of multi-input multi-output system by recursion;
  • Step A2) according to the NARMA equation of the multi-input multi-output system, carry out multivariate Taylor expansion near the equilibrium point, and ignore the Taylor high-order remainder above the quadratic term, obtain the NARMA-L2 equation of the multi-input multi-output system;
  • Step A3) the NARMA-L2 equation of the dual-input dual-output system is operated to obtain the dual-variable control law of the system;
  • step B) the concrete steps are as follows:
  • Step B1) taking the design of the dual-variable controller of a certain type of turbofan engine as an example, the six nonlinear functions in the dual-variable control law are identified offline through six neural networks, and the network model adopts the BP-NN network topology, with The input and output data of the past time is used as the input of the neural network, and the mapping result of the nonlinear function is used as the output of the neural network to complete the training;
  • the NARMA-L2 bivariate controller for turbofan engine based on neural network includes neural network module and online optimization module.
  • the neural network module is used for approximating the nonlinear function in the control law according to the past input and output information of the system.
  • the online optimization module is used for online correction of controller parameters. After the dual-variable controller obtains the command of the controlled quantity at each moment, it calculates the corresponding control quantity of the command according to the control law and inputs it into the engine, and then the engine outputs the real controlled quantity, and compares the controlled quantity command with the actual output Combined with the quadratic performance index, the neural network approximating the nonlinear function is corrected online to achieve the trajectory tracking of the engine within the full flight envelope.
  • the present invention adopts the above technical scheme, and has the following technical effects:
  • the NARMA-L2 multi-variable control method proposed by the present invention can form a single-loop multi-variable closed-loop control system, eliminate the coupling problem of multi-variables, and improve the control quality;
  • the NARMA-L2 bivariate controller based on the neural network proposed by the present invention can stably track any command within the full flight envelope, has good stable dynamic performance, and shortens the response time of the controller, which verifies the control method effectiveness.
  • Fig. 1 is the structure diagram of offline identification of NARMA-L2 neural network
  • Fig. 3 is the structure diagram of NARMA-L2 double-variable closed-loop control
  • Fig. 8 is a graph showing the change of altitude and Mach number during take-off, climb, descent, and acceleration and deceleration of the aircraft;
  • Fig. 9 is the output speed tracking response diagram of the aircraft taking off, climbing, descending and acceleration and deceleration
  • the idea of the invention is to firstly obtain the NARMA equation of the multi-input and multi-output system by recursion for the multi-input multi-output nonlinear discrete system, and perform multivariate Taylor expansion at the equilibrium point to obtain the NARMA-L2 equation of the system.
  • the control law can be obtained by derivation.
  • a dual-variable controller is designed based on neural network approximation to the nonlinear function in the control law.
  • the controller eliminates the influence of coupling, has better tracking effect and improved accuracy.
  • the control method is simple in structure, easy to design the control law, and has good stability and dynamic performance.
  • the specific embodiment of the present invention takes the design of a high-pressure rotational speed and pressure ratio dual-variable controller of a certain turbofan engine as an example, and the NARMA-L2 multivariable control method includes the following steps:
  • Step A deduce the NARMA-L2 equation and the multivariate control law of the multi-input multi-output nonlinear discrete system
  • step A is as follows:
  • Step A1) the state space of the multi-input multi-output nonlinear discrete system is described as:
  • ⁇ ( ⁇ ) and ⁇ ( ⁇ ) are smooth functions.
  • F( ⁇ ), ⁇ ( ⁇ ) and ⁇ ( ⁇ ) are smooth functions.
  • y 1 [k+1] F(y 1 [k-n+1],y 1 [k-n+2],...,y 1 [k],u[k-n+1],u [k-n+2],...,u[k])
  • y 2 [k+1] G(y 2 [k-n+1],y 2 [k-n+2],...,y 2 [k],u[k-n+1],u [k-n+2],...,u[k])
  • y m [k+1] H(y m [k-n+1],y m [k-n+2],...,y m [k],u[k-n+1],u [k-n+2],...,u[k])
  • Step A2) but the NARMA model is actually an accurate mathematical expression of the nonlinear system in the equilibrium state, but it is not applicable to the actual system due to the excessive computational complexity, so the NARMA model needs to be approximately simplified.
  • M 1 (y 1 [k-n+1],y 1 [k-n+2],...,y 1 [k],u[k-n+1],u[k-n+2], ...,u[k-1])
  • M 2 (y 2 [k-n+1],y 2 [k-n+2],...,y 2 [k],u[k-n+1],u[k-n+2], ...,u[k-1])
  • M m (y m [k-n+1],y m [k-n+2],...,y m [k],u[k-n+1],u[k-n+2], ...,u[k-1])
  • Step A3) the multi-input and multi-output NARMA-L2 equation is transformed into a matrix form to obtain:
  • F 0 F
  • G 0 G
  • Step B1) take the fuel flow of the turbofan engine and the critical cross-sectional area of the tail nozzle as the control variables, and take the high-pressure rotational speed and the engine pressure ratio as the controlled variables to design a dual-variable controller.
  • the control law is:
  • the nonlinear functions F 0 , F 1 , F 2 , G 0 , G 1 , and G 2 can be fitted by a neural network respectively.
  • the six nonlinear functions in the bivariate control law are identified offline through six neural networks, and the network model adopts the BP-NN network topology.
  • the engine model is used to generate a large number of input and output data of ground points, which are used as the input of each neural network, and the model output of the NARMA-L2 equation is calculated through the output of each neural network, and the error is back propagated to train each neural network.
  • the internet The internet.
  • ym 1 and ym 2 represent the model output calculated according to the NARMA-L2 equation, respectively, and y 1 and y 2 represent the actual high-pressure rotational speed and pressure ratio of the engine, respectively.
  • the offline identification structure of the NARMA-L2 model is shown in Figure 1.
  • the identification error curve of NARMA-L2 model is shown in Figure 2. With the increase of training times, the neural network identification is basically completed, and the theoretical output value calculated by the NARMA-L2 equation is basically consistent with the actual output value.
  • Step B2 according to the NARMA-L2 bivariate control law, the output of the nonlinear function identified by the neural network is formed into a corresponding matrix, and a closed-loop control structure of the high-pressure speed and pressure ratio of the engine is built, and the control quantity is solved online, and according to the actual output and command output.
  • r 1 and r 2 represent the high-pressure rotational speed and pressure ratio command of the engine, respectively, and y 1 and y 2 represent the actual high-pressure rotational speed and pressure ratio of the engine, respectively.
  • Step B3) after the dual-variable controller is designed, a dual-variable closed-loop control system of the turbofan engine is established, and the tracking performance is verified at the design point, the non-design point and the full flight envelope.
  • the high-pressure speed and pressure ratio can basically track the changes of the command stably, and the response of the system is fast, which can well meet the needs of dual-variable control, has good control quality, and can adapt to the engine. of various working conditions.

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Abstract

一种基于神经网络的NARMA-L2多变量控制方法，包括：推导非线性离散系统的NARMA-L2多变量控制律；利用神经网络离线辨识控制律中的非线性函数；利用该控制律设计控制器，设计某型涡扇发动机闭环控制系统，并在此基础上加入神经网络的误差在线更新以修正控制器参数，对控制系统的跟踪性能进行研究。该方法利用神经网络结合推导出的NARMA-L2多变量控制律，以发动机高压转速和压比的误差二次型性能指标最小为目标，设计双变量控制器，计算发动机控制量，对燃油流量及尾喷管临界界面面积进行控制，结构简单，控制律易推导，对于设计控制器工作量的降低以及多变量控制律的设计具有一定的积极促进作用。

Description

基于神经网络的NARMA-L2多变量控制方法 技术领域
本发明属于航空发动机仿真与控制领域，具体涉及一种基于神经网络的NARMA-L2多变量控制方法。
背景技术
早期的航空发动机的性能不高，一般仅需燃油流量一个控制量即可以保持发动机的转速不变。但随着航空发动机性能要求的提高，为了满足发动机的控制要求，所需要控制的变量也逐渐增多。如对于加力涡喷发动机，为了保证涡轮落压比保持不变，必须将加力供油量也作为控制量。航空发动机的控制系统从单变量控制系统向多变量控制系统的发展已是必然。
航空发动机的高精度实时模型建模存在着局限性，过于精确的描述在实际控制器的运用中并不合适，人们常用平衡状态小邻域内的线性化模型来设计控制器。这种方法满足叠加原理，计算方式简单，并且一般在正常使用的范围内均能获得令人满意的精度。而NARMA-L2模型由于其可以精确描述非线性系统的输入输出关系，并且结构简单，易于计算控制律而在发动机控制领域得到了一定的应用。
但目前常用的NARMA-L2控制方法主要针对于单变量控制，在多变量控制中常用分散回路组成多变量控制系统，实质上只是多个单变量控制系统的组合。这种组合控制方式没有考虑耦合带来的影响，对系统的控制精度造成了一定的影响。
发明内容
本发明所要解决的技术问题是针对背景技术的缺陷，推导多输入多输出系统的NARMA-L2方程设计控制律，设计涡扇发动机高压转速、压比双变量控制器，用于解决分散回路控制系统带来的耦合问题，仿真表明该控制器具有良好的稳动态性能。
本发明为解决上述技术问题采用以下技术方案：
一种基于神经网络的NARMA-L2多变量控制方法，包括以下步骤：
步骤A)，推导多输入多输出非线性离散系统的NARMA-L2方程及多变量控制律；
步骤B)，设计某涡扇发动机高压转速及压比双变量控制器并在设计点、非设计点及全飞行包线进行性能验证。
作为本发明一种基于神经网络的NARMA-L2多变量控制方法进一步的优化方案，步骤A)的具体步骤如下：
步骤A1)，根据多输入多输出非线性离散系统的状态空间描述，通过递推得到多输入多 输出系统的NARMA方程；
步骤A2)，根据多输入多输出系统的NARMA方程，在平衡点附近进行多元泰勒展开，并忽略二次项以上的泰勒高阶余项，得到多输入多输出系统的NARMA-L2方程；
步骤A3)，对双输入双输出系统的NARMA-L2方程进行运算，得到系统的双变量控制律；
作为本发明一种基于神经网络的NARMA-L2多变量控制方法进一步的优化方案，步骤B)具体步骤如下：
步骤B1)，以某型涡扇发动机的双变量控制器设计为例，通过六个神经网络离线辨识双变量控制律中的六个非线性函数，该网络模型采用BP-NN网络拓扑结构，以过去时刻的输入输出数据作为神经网络的输入，以非线性函数的映射结果作为神经网络的输出完成训练；
步骤B2)，根据控制律将神经网络已辨识的非线性函数输出组成对应矩阵，并建立发动机高压转速及压比闭环控制器，在线求解控制量，并且根据实际输出与指令输出的误差建立二次型性能指标，对神经网络参数进行在线优化；
步骤B3)，双变量控制器设计后，建立涡扇发动机的双变量闭环控制系统，对设计点和非设计点以及全飞行包线内进行跟踪性能的验证。
基于神经网络的涡扇发动机NARMA-L2双变量控制器，包括神经网络模块和在线优化模块。
所述神经网络模块用于根据系统过去的输入输出信息逼近控制律中的非线性函数。
所述在线优化模块用于在线修正控制器参数。双变量控制器得到每一时刻的被控量指令后，根据控制律计算出该指令所对应的控制量并输入到发动机中，然后发动机输出真实的被控量，将被控量指令与实际输出结合二次型性能指标，对逼近非线性函数的神经网络进行在线修正，以达到发动机在全飞行包线内的轨迹跟踪。
本发明采用以上技术方案与现有技术相比，具有以下技术效果：
(1)本发明提出的NARMA-L2多变量控制方法，能够组成单回路多变量闭环控制系统，消除多变量的耦合问题，提高控制品质；
(2)本发明提出的基于神经网络的NARMA-L2双变量控制器，在全飞行包线内可以稳定跟踪任意指令，具有良好的稳动态性能，且控制器响应时间缩短，验证了该控制方法的有效性。
附图说明
图1是NARMA-L2神经网络离线辨识结构图；
图2是神经网络离线辨识误差曲线图；
图3是NARMA-L2双变量闭环控制结构图；
图4是设计点H＝0m，Ma＝0时输出转速跟踪响应图；
图5是设计点H＝0m，Ma＝0时输出压比跟踪响应图；
图6是非设计点H＝4000m，Ma＝0.8时输出转速跟踪响应图；
图7是非设计点H＝4000m，Ma＝0.8时输出压比跟踪响应图；
图8是飞机起飞、爬升、下降以及加减速过程高度、马赫数变化图；
图9是飞机起飞、爬升、下降以及加减速过程输出转速跟踪响应图；
图10是飞机起飞、爬升、下降以及加减速过程输出压比跟踪响应图。
具体实施方式
下面结合附图对本发明的技术方案做进一步的详细说明。
本发明的思路是首先针对多输入多输出非线性离散系统，通过递推得到多输入多输出系统的NARMA方程，并在平衡点进行多元泰勒展开得到系统的NARMA-L2方程，该方程经过简单的推导就可以得到控制律。针对涡扇发动机多变量控制等要求，以涡扇发动机部件级模型为基础，通过推导出的NARMA-L2多变量控制律，基于神经网络逼近控制律中的非线性函数来设计双变量控制器。相比于分散回路双变量控制系统，该控制器消除了耦合带来的影响，跟踪效果更好，精度得到了一定的提高。相比于其他多变量控制方法，该控制方法结构简单，控制律易于设计，并且稳动态性能良好。
本发明的具体实施方式以某型涡扇发动机的高压转速及压比双变量控制器设计为例，该NARMA-L2多变量控制方法包括以下步骤：
步骤A)，推导多输入多输出非线性离散系统的NARMA-L2方程及多变量控制律；
步骤B)，设计NARMA-L2双变量控制器并在设计点、非设计点及全飞行包线进行性能验证。
其中步骤A)的详细步骤如下：
步骤A1)，多输入多输出非线性离散系统的状态空间描述为：
x[k+1]＝f(x[k],u[k])
y 1[k]＝h 1(x[k])
y 2[k]＝h 2(x[k])
…
y m[k]＝h m(x[k])
式中，输入u[k]＝[u 1[k] u 2[k] … u m[k]]∈R m，状态向量x[k]∈R n，输出 y 1[k]∈R,y 2[k]∈R,…,y m[k]∈R，函数f(·),h 1(·),…,h m(·)∈C ∞，并且原点为平衡状态，k为时刻。
实际应用中，由于通常只获得了输入和输出信号，因此需要建立系统的输入输出描述。通过递推得到：
y 1[k]＝h 1(x[k])＝Ψ 1(x[k])
y 1[k+1]＝h 1(x[k+1])＝h 1(f(x[k],u[k]))＝Ψ 2(x[k],u[k])
y 1[k+2]＝h 1(x[k+2])＝h 1(f(x[k+1],u[k+1]))
＝h 1(f(f(x[k]),u[k]),u[k+1]))＝Ψ 3(x[k],u[k],u[k+1])
…
Figure PCTCN2021095598-appb-000001
定义：
Y 1n[k]＝[y 1[k],y 1[k+1],…,y 1[k+n-1]]＝Ψ(x[k],u n-1[k])
u n-1[k]＝[u[k],u[k+1],…,u[k+n-2]]
则可以推出：
Ψ(x[k],u n-1[k])＝Y 1n[k]
假如
Figure PCTCN2021095598-appb-000002
非奇异，由于隐函数存在定理，可以推出状态向量x[k]可以由Y 1n[k]和u n-1[k]来表示。
同时还有：
Figure PCTCN2021095598-appb-000003
式中，Φ(·)和Ω(·)为平滑函数。
根据y 1[k+n]＝h 1(x[k+n])得到：
y 1[k+n]＝h 1(x[k+n])
＝h 1(Ω(y 1[k],y 1[k+1],...,y 1[k+n-1],u[k],u[k+1],...,u[k+n-1]))
＝F(y 1[k],y 1[k+1],...,y 1[k+n-1],u[k],u[k+1],...,u[k+n-1])
式中，F(·)、Φ(·)和Ω(·)为平滑函数。
同理可得：
y 2[k+n]＝h 2(x[k+n])
＝h 2(ψ(y 2[k],y 2[k+1],...,y 2[k+n-1],u[k],u[k+1],...,u[k+n-1]))
＝G(y 2[k],y 2[k+1],...,y 2[k+n-1],u[k],u[k+1],...,u[k+n-1])
y m[k+n]＝h m(x[k+n])
＝h m(Ρ(y m[k],y m[k+1],...,y m[k+n-1],u[k],u[k+1],...,u[k+n-1]))
＝H(y m[k],y m[k+1],...,y m[k+n-1],u[k],u[k+1],...,u[k+n-1])
式中，ψ(·)、G(·)、Ρ(·)和H(·)为平滑函数。
因此递推得到多输入多输出系统的NARMA方程为：
y 1[k+1]＝F(y 1[k-n+1],y 1[k-n+2],...,y 1[k],u[k-n+1],u[k-n+2],...,u[k])
y 2[k+1]＝G(y 2[k-n+1],y 2[k-n+2],...,y 2[k],u[k-n+1],u[k-n+2],...,u[k])
…
y m[k+1]＝H(y m[k-n+1],y m[k-n+2],...,y m[k],u[k-n+1],u[k-n+2],...,u[k])
式中，输入u[k]＝[u 1[k] u 2[k] … u m[k]]∈R m，输出y 1[k]∈R,y 2[k]∈R,…,y m[k]∈R，函数F(·),G(·),H(·)∈C ∞，k为时刻。
步骤A2)，但NARMA模型实际上是非线性系统在平衡状态的精确数学表达，但由于计算量过大而并不适用于实际系统，因此需要对NARMA模型进行近似简化。
令：
M 1＝(y 1[k-n+1],y 1[k-n+2],…,y 1[k],u[k-n+1],u[k-n+2],…,u[k-1])
M 2＝(y 2[k-n+1],y 2[k-n+2],…,y 2[k],u[k-n+1],u[k-n+2],…,u[k-1])
…
M m＝(y m[k-n+1],y m[k-n+2],…,y m[k],u[k-n+1],u[k-n+2],…,u[k-1])
通过对NARMA方程在平衡点附近进行多元泰勒展开，并忽略泰勒高阶余项，得到系统的NARMA-L2方程为：
Figure PCTCN2021095598-appb-000004
Figure PCTCN2021095598-appb-000005
步骤A3)，将多输入多输出的NARMA-L2方程化为矩阵形式得到：
Figure PCTCN2021095598-appb-000006
式中，F 0＝F，
Figure PCTCN2021095598-appb-000007
G 0＝G，
Figure PCTCN2021095598-appb-000008
H 0＝H，
Figure PCTCN2021095598-appb-000009
分别代表非线性函数，其输入参数是(y 1[k-n+1],y 1[k-n+2],...,y 1[k],u[k-1],...,u[k-n+1])。
因此，根据矩阵运算，得到多变量控制律为：
Figure PCTCN2021095598-appb-000010
步骤B)的详细步骤如下：
步骤B1)，以涡扇发动机的燃油流量和尾喷管临界截面面积作为控制变量，取高压转速和发动机压比作为被控变量设计双变量控制器。对于双变量控制系统，其控制律为：
Figure PCTCN2021095598-appb-000011
式中，非线性函数F 0、F 1、F 2、G 0、G 1、G 2分别可用一个神经网络来进行拟合。通过六个神经网络离线辨识双变量控制律中的六个非线性函数，网络模型采用BP-NN网络拓扑结构。
三个逼近非线性函数F 0、F 1、F 2的神经网络均以M 1＝(y 1[k-n+1],y 1[k-n+2],…,y 1[k],u[k-n+1],u[k-n+2],…,u[k-1])作为输入，输出分别为F 0(y 1[k-n+1],y 1[k-n+2],…,y 1[k],u[k-n+1],u[k-n+2],…,u[k-1],u[k])、F 1(y 1[k-n+1],y 1[k-n+2],…,y 1[k],u[k-n+1],u[k-n+2],…,u[k-1],u[k])、F 2(y 1[k-n+1],y 1[k-n+2],…,y 1[k],u[k-n+1],u[k-n+2],…,u[k-1],u[k])的近似值。对应于该涡扇发动机，由于其一般辨识为二阶系统，因此取n＝3，神经网络输入神经元为9，隐含层神经元为25，输出层神经元为1，隐含层激活函数为tanh函数。
三个逼近非线性函数G 0、G 1、G 2的神经网络均以M 2＝(y 2[k-n+1],y 2[k-n+2],…,y 2[k],u[k-n+1],u[k-n+2],…,u[k-1])作为输入，输出分别为G 0(y 2[k-n+1],y 2[k-n+2],…,y 2[k],u[k-n+1],u[k-n+2],…,u[k-1],u[k])、G 1(y 2[k-n+1],y 2[k-n+2],…,y 2[k],u[k-n+1],u[k-n+2],…,u[k-1],u[k])、G 2＝(y 2[k-n+1],y 2[k-n+2],…,y 2[k],u[k-n+1],u[k-n+2],…,u[k-1],u[k])的近似值。同样取n＝3，神经网络输入神经元为9，隐含层神经元为25，输出层神经元为1，隐含层激活函数为tanh函数。
利用发动机模型产生大量的地面点输入输出数据，以之作为各神经网络的输入，并通过各神经网络的输出计算出NARMA-L2方程的模型输出，并对误差进行反向传播，从而训练各神经网络。
其性能指标为：
Figure PCTCN2021095598-appb-000012
e 1＝y 1[k]-ym 1[k]
e 2＝y 2[k]-ym 2[k]
式中，ym 1、ym 2分别代表根据NARMA-L2方程计算出的模型输出，y 1、y 2分别代表发动机的实际高压转速和压比。
NARMA-L2模型离线辨识结构如图1所示，图中加粗变量均为矩阵， u[k]＝[u 1[k] u 2[k]] T,y[k]＝[y 1[k] y 2[k]] T,ym[k]＝[ym 1[k] ym 2[k]] T,e＝[e 1 e 2] T。NARMA-L2模型辨识误差曲线图如图2所示，随着训练次数的增加，神经网络辨识基本完成，经NARMA-L2方程计算得到的理论输出值与实际输出值基本保持一致。
步骤B2)，根据NARMA-L2双变量控制律将神经网络已辨识的非线性函数输出组成对应矩阵，并搭建发动机高压转速及压比闭环控制结构，在线求解控制量，并且根据实际输出与指令输出的误差建立二次型性能指标，使用反向传播算法对神经网络参数进行在线优化。
其性能指标为：
Figure PCTCN2021095598-appb-000013
e c1＝y 1[k]-r 1[k]
e c2＝y 2[k]-r 2[k]
式中，r 1、r 2分别代表发动机的高压转速、压比指令，y 1、y 2分别代表发动机的实际高压转速和压比。
搭建的控制结构如图3所示，图中加粗变量均为矩阵，u[k]＝[u 1[k] u 2[k]] T,y[k]＝[y 1[k] y 2[k]] T,r[k]＝[r 1[k] r 2[k]] T,e c＝[e c1 e c2] T。
步骤B3)，双变量控制器设计后，建立涡扇发动机的双变量闭环控制系统，对设计点和非设计点以及全飞行包线内进行跟踪性能的验证。
设计点H＝0m，Ma＝0状态下的仿真结果如图4、5所示。由图可知，在该状态下的高压转速及压比能够稳定跟踪指令阶跃信号，不存在稳态误差，并且高压转速的超调量为6.32％，调节时间小于2s，压比的超调量为5.53％，调节时间小于1.4s，具有良好的稳动态性能。
非设计点H＝4000m，Ma＝0.8状态下的仿真结果如图6、7所示。由图可知，此状态下的高压转速及压比能够稳定跟踪指令信号的变化，基本不存在稳态误差，并且高压转速的超调量为7.95％，调节时间小于2.5s，压比的超调量为6.34％，调节时间小于2s，具有良好的动态特性。
飞机起飞、爬升、下降以及加减速过程的高度、马赫数变化如图8所示，高压转速和压比的输出跟踪效果如图9、10所示。由图可知，在各种过程中高压转速及压比基本都能够稳定跟踪指令的变化，并且系统的响应较快，能够很好的满足双变量控制的需求，具有良好的控制品质，可以适应发动机的各种工况变化。
需要指出的是，以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到的变化和替 换，都应涵盖在本发明的保护范围内。因此，本发明的保护范围应以所述权利要求的保护范围为准。

Claims (7)

  1. 一种基于神经网络的NARMA-L2多变量控制方法，其特征在于，包括以下步骤：
    步骤A)，推导多输入多输出非线性离散系统的NARMA-L2方程及多变量控制律；
    步骤B)，利用神经网络离线辨识多变量控制律中的非线性函数；利用已辨识的神经网络设计双变量控制器，建立涡扇发动机的双变量闭环控制系统，并对控制器的稳动态性能进行验证。
  2. 根据权利要求1所述的一种基于神经网络的NARMA-L2多变量控制方法，其特征在于，步骤A)的具体步骤如下：
    步骤A1)，根据非线性离散系统的状态空间描述，将其推广到多输入多输出系统，通过递推得到多输入多输出系统的NARMA方程；
    步骤A2)，利用多输入多输出系统的NARMA方程，在其平衡点进行多元泰勒展开，并忽略泰勒高阶余项，得到非线性系统的多输入多输出NARMA-L2方程；
    步骤A3)，利用非线性系统的多输入多输出NARMA-L2方程，进行矩阵运算，推导得到多输入多输出系统的多变量控制律。
  3. 如权利要求1所述的一种基于神经网络的NARMA-L2多变量控制方法，其特征在于，步骤B)的具体步骤如下：
    步骤B1)，首先选取发动机的燃油流量及尾喷管临界截面面积为控制变量，选取高压转速及发动机压比作为被控变量，利用发动机模型产生输入及输出数据，并通过神经网络离线辨识控制律中的非线性函数；
    步骤B2)，根据控制律将神经网络已辨识的非线性函数输出组成对应矩阵，并建立发动机高压转速及压比闭环控制器，在线求解控制量，并且根据实际输出与指令输出的误差建立二次型性能指标，对神经网络参数进行在线优化；
    步骤B3)，双变量控制器设计后，对设计点和非设计点以及全飞行包线内进行跟踪性能的验证。
  4. 如权利要求2所述的一种基于神经网络的NARMA-L2多变量控制方法，其特征在于，步骤A1)中多输入多输出非线性离散系统的状态空间描述为：
    x[k+1]＝f(x[k],u[k])
    y 1[k]＝h 1(x[k])
    y 2[k]＝h 2(x[k])
    …
    y m[k]＝h m(x[k])
    式中，u[k]＝[u 1[k] u 2[k] … u m[k]]∈R m为系统的控制量输入， y 1[k]∈R,y 2[k]∈R,…,y m[k]∈R为系统的被控制量输出，m代表选取的控制量与被控制量的个数，状态向量x[k]∈R n，n代表状态量的维度，函数f(·),h 1(·),…,h m(·)∈C ∞，并且原点为平衡状态，k为时刻；
    多输入多输出系统的NARMA方程为：
    y 1[k+1]＝F(y 1[k-n+1],y 1[k-n+2],...,y 1[k],u[k-n+1],u[k-n+2],...,u[k])
    y 2[k+1]＝G(y 2[k-n+1],y 2[k-n+2],...,y 2[k],u[k-n+1],u[k-n+2],...,u[k])
    …
    y m[k+1]＝H(y m[k-n+1],y m[k-n+2],...,y m[k],u[k-n+1],u[k-n+2],...,u[k])
    式中，输入u[k]＝[u 1[k] u 2[k] … u m[k]]∈R m，输出y 1[k]∈R,y 2[k]∈R,…,y m[k]∈R，函数F(·),G(·),H(·)∈C ∞，k为时刻。
  5. 如权利要求4所述的一种基于神经网络的NARMA-L2多变量控制方法，其特征在于，步骤A2)中多输入多输出系统的NARMA-L2方程为：
    Figure PCTCN2021095598-appb-100001
    式中，
    Figure PCTCN2021095598-appb-100002
  6. 如权利要求5所述的一种基于神经网络的NARMA-L2多变量控制方法，其特征在于，步骤A3)中系统的多变量控制律为：
    Figure PCTCN2021095598-appb-100003
    式中，F 0＝F，
    Figure PCTCN2021095598-appb-100004
    G 0＝G，
    Figure PCTCN2021095598-appb-100005
    H 0＝H，
    Figure PCTCN2021095598-appb-100006
  7. 如权利要求5所述的一种基于神经网络的NARMA-L2多变量控制方法，其特征在于，步骤B2)中建立的二次型性能指标函数为：
    Figure PCTCN2021095598-appb-100007
    e c1＝y 1[k]-r 1[k]
    e c2＝y 2[k]-r 2[k]
    式中，r 1、r 2分别代表发动机的高压转速、压比指令，y 1、y 2分别代表发动机的实际高压转速和压比；
    所述双变量控制器得到每一时刻的被控量指令后，根据控制律计算出该指令所对应的控制量并输入到发动机中，然后发动机输出真实的被控量，将被控量指令与实际输出结合二次型性能指标，对逼近非线性函数的神经网络进行在线修正，以达到发动机在全飞行包线内的自适应控制。
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CN113741195B (zh) * 2021-09-14 2023-09-08 厦门大学 一种航空发动机非线性控制方法及系统
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CN116400597B (zh) * 2023-04-07 2023-10-24 盐城工学院 一种二阶神经网络的同步控制方法
CN117919546B (zh) * 2024-01-26 2024-10-01 广东食品药品职业学院 基于神经网络反馈线性化闭环胰岛素输注控制方法及系统

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105184416A (zh) * 2015-09-23 2015-12-23 上海大学 基于粒子群优化反向传播神经网络的脉动风速预测方法
US20180300737A1 (en) * 2017-04-17 2018-10-18 Nexosis, Inc. Methods and apparatus for self-adaptive time series forecasting engine
CN109162813A (zh) * 2018-10-09 2019-01-08 南京航空航天大学 一种基于迭代学习修正的航空发动机智能转速控制方法
CN110513199A (zh) * 2019-07-23 2019-11-29 南京航空航天大学 一种航空发动机推力衰退缓解的神经网络控制方法
CN110985216A (zh) * 2019-11-19 2020-04-10 南京航空航天大学 一种含在线修正的航空发动机智能多变量控制方法
CN112286047A (zh) * 2020-09-28 2021-01-29 南京航空航天大学 基于神经网络的narma-l2多变量控制方法

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8068731B2 (en) * 2009-04-07 2011-11-29 Chunghwa Telecom Co., Ltd. Dynamic bandwidth allocation method of Ethernet passive optical network
CN104951836A (zh) * 2014-03-25 2015-09-30 上海市玻森数据科技有限公司 基于神经网络技术的发帖预测系统

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105184416A (zh) * 2015-09-23 2015-12-23 上海大学 基于粒子群优化反向传播神经网络的脉动风速预测方法
US20180300737A1 (en) * 2017-04-17 2018-10-18 Nexosis, Inc. Methods and apparatus for self-adaptive time series forecasting engine
CN109162813A (zh) * 2018-10-09 2019-01-08 南京航空航天大学 一种基于迭代学习修正的航空发动机智能转速控制方法
CN110513199A (zh) * 2019-07-23 2019-11-29 南京航空航天大学 一种航空发动机推力衰退缓解的神经网络控制方法
CN110985216A (zh) * 2019-11-19 2020-04-10 南京航空航天大学 一种含在线修正的航空发动机智能多变量控制方法
CN112286047A (zh) * 2020-09-28 2021-01-29 南京航空航天大学 基于神经网络的narma-l2多变量控制方法

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
WANG, LEI ET AL.: "Multi-Step Predictive Control for Aero-Engine Distributed Control System Based on RVM Regression Error Compensation", JOURNAL OF AEROSPACE POWER, vol. 28, no. 6, 30 June 2013 (2013-06-30), pages 1420 - 1428, XP055902006, ISSN: 1000-8055 *

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