CN110985216B - Intelligent multivariable control method for aero-engine with online correction - Google Patents

Intelligent multivariable control method for aero-engine with online correction Download PDF

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CN110985216B
CN110985216B CN201911132301.9A CN201911132301A CN110985216B CN 110985216 B CN110985216 B CN 110985216B CN 201911132301 A CN201911132301 A CN 201911132301A CN 110985216 B CN110985216 B CN 110985216B
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CN110985216A (en
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鲁峰
闫召洪
黄金泉
仇小杰
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • 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
    • 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
    • F05D2270/00—Control
    • F05D2270/70—Type of control algorithm
    • F05D2270/709—Type of control algorithm with neural networks

Abstract

The invention discloses an intelligent multivariable control method for an aeroengine with online correction, which comprises the following steps: establishing an NARMA-L2 model of an engine speed and pressure ratio control system by adopting a neural network group; and (3) designing a controller online correction module based on an NARMA-L2 linear compensation strategy and a gradient descent algorithm by combining an NARMA-L2 model to obtain the intelligent multivariable controller of the aero-engine with self-adaptive capacity within a certain working condition range in an envelope. The invention solves the problems that the traditional neural network prediction model based establishment and the online solution of the control law are difficult, and the control quality is reduced when the controller is expanded and applied in the envelope, is suitable for the multivariable control of the engine speed and the pressure ratio at different working points in a certain flight envelope, and has positive promotion effects on eliminating the steady-state error of an engine control system, and improving the application range and the control quality in the controller envelope.

Description

Intelligent multivariable control method for aero-engine with online correction
Technical Field
The invention belongs to the technical field of multi-variable control of aero-engines, and particularly relates to an intelligent multi-variable control method for an aero-engine with online correction.
Background
With the rapid development of modern aviation technology, aircraft require aero-engines with higher performance and higher reliability. An aircraft engine is a complex thermodynamic system with strong uncertainties and time-varying properties that make the design of the controller difficult. Classical control theory and modern control theory rely on accurate mathematical models since the subject of the study is mainly a linear time invariant system, which leads to great difficulties in the application of such strongly non-linear, time variant and complex control systems in aircraft engines. Researchers have therefore attempted to replace complex systems with simple approximation models and judge their value in terms of their ease of analysis, ease of handling, and likelihood of application in practical problems. Although one recognizes from the outset that practical dynamic systems are nonlinear, linearization within a small neighborhood of equilibrium states is mathematically tractable. In particular the superposition principle, makes the calculation in a linear manner sufficiently simple. Most importantly, the linearized model of most nonlinear systems can obtain satisfactory precision in a normal use range, and therefore, the nonlinear system is widely applied.
The intelligent control method is a control theory based on an artificial intelligence algorithm close to a human thinking mode, and the neural network method is an important branch of the intelligent control theory. In recent years, rapid advances in technology have led to systems that are often required to operate in regions of state space that are not sufficiently linearized. To solve this problem, neural networks are widely used due to their good approximation and generalization capabilities. A Nonlinear autoregressive Moving Average with Feedback Linearization (NARMA-L2) controller is an effective artificial neural network controller architecture. Under certain conditions, the input-output relationship of the nonlinear system can be identified by a NARMA-L2 model, and the control law can be obtained by simple mathematical transformation. The model was first introduced by Narendra and Mukhopadhyay and is now widely used in many non-linear systems.
The NARMA-L2 model is a neural network approximation model that has modeling errors and training errors. In order to improve the applicability of the controller in the flight envelope, the invention provides an intelligent multivariable control method for an aircraft engine with online correction. The method utilizes a gradient descent algorithm to carry out online correction on neural network parameters in the NARMA-L2 model, so that the neural network parameters have self-adaptive characteristics, and simultaneously provides a NARMA-L2 linear compensation strategy, thereby further improving the control quality of the controller in an envelope range.
Disclosure of Invention
Aiming at the technical problems, the invention provides an intelligent multivariable control method for an aero-engine with online correction, which solves the problems that the traditional neural network prediction model-based establishment and online solution of a control law are difficult, and the control quality is reduced due to the fact that a controller is expanded and applied in an envelope.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
an intelligent multivariable control method for an aircraft engine with online correction is characterized by comprising the following steps:
step A), constructing a NARMA-L2 model of the intelligent multivariable control system of the aircraft engine by adopting a neural network group according to the relationship between the main fuel quantity and the rotating speed of a high-pressure rotor of an engine model and the area of a throat of a tail nozzle and the pressure ratio of the whole aircraft engine;
and step B) combining with an NARMA-L2 model, designing a controller online correction module based on an NARMA-L2 linear compensation strategy and a gradient descent algorithm, and obtaining the intelligent multivariable controller of the aero-engine with self-adaptive capacity within a certain working condition range in an envelope.
Further, in the step A), according to the relation between the main fuel quantity and the high-pressure rotor rotating speed of the engine model and the relation between the area of the throat of the tail nozzle and the overall pressure ratio, the NARMA-L2 model of the intelligent multivariable control system of the aero-engine is constructed by adopting a neural network group, and the specific steps are as follows:
Step A1), selecting the main fuel quantity of the engine as the input quantity u1[k]High pressure rotor speed as output y1[k](ii) a Selecting the area of the throat of the engine tail nozzle as an input quantity u2[k]The total pressure ratio is used as the output quantity y2[k]And constructing a double-loop NARMA-L2 model according to the selected input and output quantities as follows:
y1[k]＝f1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])+g1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])u1[k]
y2[k]＝f2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])+g2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])u2[k]
wherein f is1(·)、g1(·)、f2(·)、g2Can be connected by four feedforward neural networks f1、g1、f2And g2Obtaining an approximation;
step A2), f is performed1、g1、f2And g2And (4) randomly initializing four neural network structures, and performing off-line training on the neural networks by using a gradient descent method according to the training samples to obtain a NARMA-L2 model of the intelligent multivariable control system of the trained aircraft engine.
Further, the specific steps of designing a controller online correction module based on an NARMA-L2 linear compensation strategy and a gradient descent algorithm by combining the NARMA-L2 model in the step B) to obtain the intelligent multivariable controller of the aero-engine with self-adaptive capability within a certain working condition range in an envelope are as follows:
step B1), constructing a structure diagram of an aircraft engine intelligent multivariable control system of a neural network, wherein the structure diagram comprises an NARMA-L2 model, a rotating speed controller, a pressure ratio controller, an engine model and an online correction module;
and B2), designing an online correction module based on a gradient descent algorithm and a NARMA-L2 linear compensation strategy to obtain the intelligent multivariable controller of the aero-engine.
Further, the step B2) is to design an online correction module based on a gradient descent algorithm and a NARMA-L2 linear compensation strategy, and the specific steps of obtaining the intelligent multivariable controller of the aircraft engine are as follows:
step B2.1), respectively solving the initial control laws of the rotating speed and the pressure ratio according to the NARMA-L2 model obtained by training in the step A2) as follows:
Figure BDA0002278662110000031
Figure BDA0002278662110000032
wherein, y1 *[k]And y2 *[k]Respectively outputting expected rotation speed of a high-pressure rotor of the engine and the overall pressure ratio; f. of1(k)、g1(k)、f2(k) And g2(k) The expression of (a) is:
f1(k)＝f1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])
g1(k)＝g1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])
f2(k)＝f2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])
g2(k)＝g2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])
step B2.2), based on the error between the desired output and the actual output, the u is compensated for by using the NARMA-L2 linear compensation strategy1[k]And u2[k]Compensating and modifying the neural network f according to a gradient descent algorithm1、g1、f2And g2The topology parameter of (2).
Further, in the step B2.2), the pair u is linearly compensated by using a NARMA-L2 linear compensation strategy according to the error between the expected output and the actual output1[k]And u2[k]Compensating and modifying the neural network f according to a gradient descent algorithm1、g1、f2And g2The topology parameters are as follows:
step B2.2.1), judging whether the current time is the initial time, if so, not compensating; if the current time is not the initial time, calculating a compensation value delta u [ k ] of the initial control quantity at the current time according to the actual input u [ k-1] and the actual output y [ k-1] of the engine at the previous time and the outputs f (k-1) and g (k-1) of the neural network in the NARMA-L2 model, wherein the specific formula is as follows:
Figure BDA0002278662110000041
Figure BDA0002278662110000042
Wherein alpha is compensation gain and is determined by a multi-trial method;
step B2.2.2), obtaining the control quantity u according to the initial control law at the current momentoriginal[k]Compensation value delta u k with control quantity]And calculating to obtain the actual control quantity u [ k ]]The concrete formula is as follows:
u1[k]＝u1_original[k]+Δu1[k]
u2[k]＝u2_original[k]+Δu2[k]
step B2.2.3) applying the control quantity to the aircraft engine to obtain the actual output y [ k ] at the current moment]Using the error e between the desired output and the actual outputC[k]For the neural network group f1、g1、f2And g2The topological parameters are corrected on line, and the specific formula is as follows:
W(k+1)＝W(k)+βΔW(k)
V(k+1)＝V(k)+βΔV(k)
wherein, W and V are weight and threshold of the neural network group respectively; beta is the learning rate, the adjustment speed of the parameters is influenced by the size of the learning rate, and the learning rate is determined by a multi-trial method; Δ w (k) and Δ v (k) are jacobian matrices, representing the increments of the weights and thresholds, respectively. The update of each element in the topology vector at time k is as follows:
wi(k+1)＝wi(k)-βΔwi(k)
vi(k+1)＝vi(k)-βΔvi(k)
Figure BDA0002278662110000043
Figure BDA0002278662110000044
wherein, T ═ y (k), y (k-1), y (k-2),. ·, y (k-n), u (k-1), u (k-2), …, u (k-n) }; w is ai、viThe ith elements representing W and V, respectively; g0Denotes g1Or g2；Δwi、ΔviRespectively, the i-th elements of Δ w (k) and Δ v (k).
And obtaining the rotating speed and pressure ratio controller at the k +1 moment according to the updated NARMA-L2 model. To this end, the intelligent multivariable controller design ends.
Has the advantages that: the invention solves the problems that the traditional neural network prediction model based establishment and the online solution of the control law are difficult, and the controller is expanded and applied in the envelope to cause the control quality to be reduced, is suitable for multivariable control of the engine speed and the pressure ratio of different working points in a certain flight envelope, and has positive promotion effects on eliminating the steady-state error of an engine control system, and improving the application range and the control quality in the controller envelope.
Drawings
FIG. 1 is a block diagram of the neural network-based intelligent multivariable control of an aircraft engine according to the present invention.
FIG. 2 is a fuel quantity input data sample set distribution plot.
FIG. 3 is a plot of a sample set of high pressure rotor speed output data.
FIG. 4 is a sample set distribution plot of jet nozzle throat area input data.
Fig. 5 is a plot of the whole press ratio output data sample set.
FIG. 6 is a schematic representation of H, Ma as a function of time.
Fig. 7 is a schematic diagram of the change in fuel amount.
FIG. 8 is a schematic representation of the change in area of the jet nozzle throat.
FIG. 9 is a schematic of the high pressure rotor speed versus command signal tracking.
FIG. 10 is a schematic diagram of a press ratio versus command signal trace.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
The invention discloses an intelligent multivariable control method for an aeroengine with online correction, which is characterized by comprising the following steps of:
step A), constructing a NARMA-L2 model of the intelligent multivariable control system of the aircraft engine by adopting a neural network group according to the relationship between the main fuel quantity and the rotating speed of a high-pressure rotor of an engine model and the area of a throat of a tail nozzle and the pressure ratio of the whole aircraft engine;
and step B) combining with an NARMA-L2 model, designing a controller online correction module based on an NARMA-L2 linear compensation strategy and a gradient descent algorithm, and obtaining the intelligent multivariable controller of the aero-engine with self-adaptive capacity within a certain working condition range in an envelope.
Step A1), selecting the main fuel quantity of the engine as an input quantity u1[k]High pressure rotor speed as output y1[k](ii) a Selecting the area of the throat of the engine tail nozzle as an input quantity u2[k]The total pressure ratio is taken as the output y2[k]And constructing a double-loop NARMA-L2 model according to the selected input and output quantities as follows:
y1[k]＝f1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])+g1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])u1[k]
y2[k]＝f2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])+g2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])u2[k]
wherein f is1(·)、g1(·)、f2(·)、g2Can be connected by four feedforward neural networks f1、g1、f2And g2Obtaining an approximation;
step A2), f is performed1、g1、f2And g2And (4) randomly initializing four neural network structures, and performing off-line training on the neural networks by using a gradient descent method according to the training samples to obtain a NARMA-L2 model of the intelligent multivariable control system of the trained aircraft engine.
Step B1), constructing a structure diagram of the neural network aeroengine intelligent multivariable control system, wherein the structure diagram comprises an NARMA-L2 model, a rotating speed control formula, a pressure ratio control formula, an engine model and an online correction module;
and B2), designing an online correction module based on a gradient descent algorithm and a NARMA-L2 linear compensation strategy to obtain the intelligent multivariable controller of the aero-engine.
Further, the step B2) is to design an online correction module based on a gradient descent algorithm and a NARMA-L2 linear compensation strategy, and the specific steps of obtaining the intelligent multivariable controller of the aircraft engine are as follows:
Step B2.1), respectively obtaining the initial control laws of the rotating speed and the pressure ratio according to the NARMA-L2 model obtained by the training of the step A2):
Figure BDA0002278662110000061
Figure BDA0002278662110000062
wherein, y1 *[k]And y2 *[k]Respectively outputting expected rotation speed of a high-pressure rotor of the engine and the overall pressure ratio; f. of1(k)、g1(k)、f2(k) And g2(k) The expression of (a) is:
f1(k)＝f1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])
g1(k)＝g1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])
f2(k)＝f2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])
g2(k)＝g2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])
step B2.2), based on the error between the desired output and the actual output, the u is compensated for by using the NARMA-L2 linear compensation strategy1[k]And u2[k]Compensating and modifying the neural network f according to a gradient descent algorithm1、g1、f2And g2The topology parameter of (2).
Step B2.2.1), judging whether the current time is the initial time, if so, not compensating; if the current time is not the initial time, calculating a compensation value delta u [ k ] of the initial control quantity at the current time according to the actual input u [ k-1] and the actual output y [ k-1] of the engine at the previous time and the neural network outputs f (k-1) and g (k-1) in the NARMA-L2 model, wherein the specific formula is as follows:
Figure BDA0002278662110000071
Figure BDA0002278662110000072
wherein alpha is the compensation gain and is determined by a multi-trial method;
step B2.2.2), obtaining the control quantity u according to the initial control law at the current timeoriginal[k]Compensation value delta u k with control quantity]And calculating to obtain the actual control quantity u [ k ]]The concrete formula is as follows:
u1[k]＝u1_original[k]+Δu1[k]
u2[k]＝u2_original[k]+Δu2[k]
step B2.2.3) applying the control quantity to the aircraft engine to obtain the actual output y [ k ] at the current moment ]Using the error e between the desired output and the actual outputC[k]For the neural network group f1、g1、f2And g2The topological parameters are corrected on line, and the specific formula is as follows:
W(k+1)＝W(k)+βΔW(k)
V(k+1)＝V(k)+βΔV(k)
wherein, W and V are weight and threshold of the neural network group respectively; beta is the learning rate, the adjustment speed of the parameters is influenced by the size of the learning rate, and the learning rate is determined by a multi-trial method; Δ W (k) and Δ V (k) are Jacobian matrices. The update of each element in the topology vector at time k is as follows:
wi(k+1)＝wi(k)-βΔwi(k)
vi(k+1)＝vi(k)-βΔvi(k)
Figure BDA0002278662110000073
Figure BDA0002278662110000074
wherein, T ═ y (k), y (k-1), y (k-2),.., y (k-n), u (k-1), u (k-2), …, u (k-n) }.
And obtaining the rotating speed and pressure ratio controller at the k +1 moment according to the updated NARMA-L2 model. To this end, the intelligent multivariable controller design ends.
In order to verify the effectiveness of the neural network-based intelligent multivariable control method for the aircraft engine, digital simulation of the takeoff, acceleration and deceleration processes of the engine in a certain envelope is carried out in an MATLAB environment.
The invention adopts a nonlinear part model of a certain type double-rotor turbofan engine with small bypass ratio as a controlled object. The model is constructed by an object-oriented programming method, comprises important parts of an aircraft engine such as an air inlet channel, a fan, an air compressor, a combustion chamber, a turbine, a tail nozzle and the like, and is easy to call in an MATLAB environment.
Before carrying out simulation verification on the performance of the controller, first, two sets of NARMA-L2 models are respectively identified by utilizing a neural network. Each model comprises two neural networks which are single hidden layers, and the number of the neurons of the input layer, the hidden layers and the output layer is 6, 10 and 1 respectively. Before training, an aircraft engine model is used for generating a main fuel quantity-high-pressure rotor rotating speed data set containing 20000 groups of training samples under the flight conditions of H & lt0 & gt and Ma & lt0 & gt, and 20000 groups of tail pipe fuel quantity-total machine pressure ratio data sets are generated by the same method. The ranges of the individual parameters in the data set are shown in fig. 2-5, and the NARMA-L2 model of the neural network set was trained based on the generated training data.
In order to verify the applicability of the method provided by the invention in the flight envelope, the engine running track is selected in the full envelope range, as shown in fig. 6, when the engine is in a state, and the change of the control quantity and the rotating speed-pressure ratio tracking simulation result are shown in fig. 7-10.
The simulation result shows that the engine rotating speed and the pressure ratio command signal change along with the change of the flight condition, and the intelligent multivariable control method provided by the invention has good applicability in the envelope, so that the rotating speed of the high-pressure rotor of the engine and the pressure ratio of the whole engine can track the command signal, and the dynamic response is good. Simulation results show that the intelligent multivariable control method for the aero-engine with online correction has good control quality in a flight envelope.
The invention designs an intelligent multivariable control method for an aircraft engine with online correction, which solves the problems that the traditional neural network prediction model based establishment and online solution of a control law are difficult, the controller is expanded and applied in a covered line, and the control quality is reduced, is suitable for multivariable control of the engine speed and the pressure ratio of different working points in a certain flight covered line, and has positive promotion effects on eliminating steady-state errors of an engine control system, and improving the application range and the control quality in the covered line of the controller.
It should be noted that the above mentioned embodiments are only specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any changes and substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (2)

1. An intelligent multivariable control method for an aircraft engine with online correction is characterized by comprising the following steps:
step A), constructing a NARMA-L2 model of the intelligent multivariable control system of the aircraft engine by adopting a neural network group according to the relationship between the main fuel quantity and the rotating speed of a high-pressure rotor of an engine model and the area of a throat of a tail nozzle and the pressure ratio of the whole aircraft engine;
Step B), combining an NARMA-L2 model, designing a controller online correction module based on an NARMA-L2 linear compensation strategy and a gradient descent algorithm, and obtaining an aeroengine intelligent multivariable controller with self-adaptive capacity within a certain working condition range in an envelope;
in the step A), according to the relation between the main fuel quantity and the rotating speed of a high-pressure rotor of an engine model and the relation between the area of a throat of a tail nozzle and the pressure ratio of the whole aircraft, a neural network group is adopted to construct a NARMA-L2 model of the intelligent multivariable control system of the aircraft engine, and the specific steps are as follows:
step A1), selecting the main fuel quantity of the engine as the input quantity u1[k]High pressure rotor speed as output y1[k]K represents time; selecting the area of the throat of the engine tail nozzle as an input quantity u2[k]The total pressure ratio is taken as the output y2[k]And constructing a dual-loop NARMA-L2 model according to the selected input and output quantities as follows:
y1[k]＝f1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])+g1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])u1[k]
y2[k]＝f2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])+g2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])u2[k]
wherein f is1(·)、g1(·)、f2(·)、g2Through four feedforward neural networks f1、g1、f2And g2Obtaining an approximation;
step A2), f is performed1、g1、f2And g2Four feedforward neural network structures are initialized randomly, and a gradient descent method is used for a neural network group f according to training samples1、g1、f2And g2Performing off-line training to obtain a NARMA-L2 model of the trained aircraft engine intelligent multivariable control system;
The step B) is combined with an NARMA-L2 model, a controller online correction module based on an NARMA-L2 linear compensation strategy and a gradient descent algorithm is designed, and the specific steps of obtaining the intelligent multivariable controller of the aircraft engine with self-adaptive capacity in a certain working condition range in an envelope are as follows:
step B1), constructing a structure diagram of an aircraft engine intelligent multivariable control system of a neural network, wherein the structure diagram comprises an NARMA-L2 model, a rotating speed controller, a pressure ratio controller, an engine model and an online correction module;
step B2), designing an online correction module based on a gradient descent algorithm and a NARMA-L2 linear compensation strategy to obtain an intelligent multivariable controller of the aero-engine;
the step B2) is designed into an online correction module based on a gradient descent algorithm and a NARMA-L2 linear compensation strategy, and the specific steps of obtaining the intelligent multivariable controller of the aero-engine are as follows:
step B2.1), respectively obtaining the initial control laws of the rotating speed and the pressure ratio according to the NARMA-L2 model obtained by the training of the step A2):
Figure FDA0003594157050000021
Figure FDA0003594157050000022
wherein, y1 *[k]And y2 *[k]Respectively outputting expected rotation speed of a high-pressure rotor of the engine and the overall pressure ratio; f. of1(k)、g1(k)、f2(k) And g2(k) The expression of (a) is:
f1(k)＝f1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])
g1(k)＝g1(y1[k-1],y1[k-2],...,y1[k-n+1],u1[k-1],...,u1[k-n+1])
f2(k)＝f2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])
g2(k)＝g2(y2[k-1],y2[k-2],...,y2[k-n+1],u2[k-1],...,u2[k-n+1])
step B2.2), based on the error between the desired output and the actual output, the u is compensated for by using the NARMA-L2 linear compensation strategy 1[k]And u2[k]Compensating and correcting the neural network f according to a gradient descent algorithm1、g1、f2And g2The topology parameter of (2).
2. The intelligent multivariable control method for the aero-engine with online correction as claimed in claim 1, wherein: said step B2.2) of using a NARMA-L2 linear compensation strategy for u depending on the error between the desired output and the actual output1[k]And u2[k]Compensating and modifying the neural network f according to a gradient descent algorithm1、g1、f2And g2The topology parameters are as follows:
step B2.2.1), judging whether the current time is the initial time, if so, not compensating; if the current time is not the initial time, calculating a compensation value delta u [ k ] of the initial control quantity at the current time according to the actual input u [ k-1] and the actual output y [ k-1] of the engine at the previous time and the neural network outputs f (k-1) and g (k-1) in the NARMA-L2 model, wherein the specific formula is as follows:
Figure FDA0003594157050000023
Figure FDA0003594157050000024
wherein alpha is the compensation gain and is determined by a multi-trial method;
step B2.2.2), obtaining the control quantity u according to the initial control law at the current timeoriginal[k]Compensation value delta u k with control quantity]And calculating to obtain the actual control quantity u [ k ]]The concrete formula is as follows:
u1[k]＝u1_original[k]+Δu1[k]
u2[k]＝u2_original[k]+Δu2[k]
step B2.2.3) applying the actual control quantity to the aircraft engine to obtain the actual output y [ k ] at the current moment ]Using the error e between the desired output and the actual outputC[k]For neural network group f1、g1、f2And g2The topological parameters are corrected on line, and the specific formula is as follows:
W(k+1)＝W(k)+βΔW(k)
V(k+1)＝V(k)+βΔV(k)
wherein, W and V are the weight and the threshold of the neural network group respectively; beta is a learning rate, and the adjustment speed of the parameters influenced by the beta is determined by a multi-time trial method; Δ w (k) and Δ v (k) are jacobian matrices, representing the increments of the weights and thresholds, respectively; the update of each element in the topology vector at time k is as follows:
wi(k+1)＝wi(k)-βΔwi(k)
vi(k+1)＝vi(k)-βΔvi(k)
Figure FDA0003594157050000031
Figure FDA0003594157050000032
wherein, T ═ y (k), y (k-1), y (k-2),. ·, y (k-n), u (k-1), u (k-2), …, u (k-n) }; w is ai、viThe ith elements representing W and V, respectively; g0Denotes g1Or g2；Δwi、ΔviThe i-th elements respectively representing Δ w (k) and Δ v (k);
obtaining a rotating speed and pressure ratio controller at the k +1 moment according to the updated NARMA-L2 model; to this end, the intelligent multivariable controller design ends.
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