CN113075882A - Turbofan engine multivariable robust variable gain control method based on non-equilibrium state linearization - Google Patents

Turbofan engine multivariable robust variable gain control method based on non-equilibrium state linearization Download PDF

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CN113075882A
CN113075882A CN202110321498.1A CN202110321498A CN113075882A CN 113075882 A CN113075882 A CN 113075882A CN 202110321498 A CN202110321498 A CN 202110321498A CN 113075882 A CN113075882 A CN 113075882A
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turbofan engine
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崔涛
唐一峰
季廷炜
郑耀
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Zhejiang University ZJU
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Abstract

The invention discloses a variable gain control method of multivariable robustness of a turbofan engine based on non-equilibrium state linearization, which is a variable gain control method for solving the problem of strong nonlinearity in the acceleration and deceleration process of the turbofan engine, and comprises the following steps: establishing a turbofan engine input and output model for non-equilibrium state linearization; establishing a turbofan engine polynomial linear variable parameter model containing noise information; and establishing a multivariable robust variable gain controller. The invention provides a design method of a multivariable acceleration and deceleration variable gain controller on the basis of an aircraft engine non-equilibrium state linearization method, which can not only overcome the problems of inaccurate linear model and the like in the acceleration and deceleration process of a turbofan engine, but also give consideration to the tracking capability of a plurality of target instructions and the inhibition capability of uncertain factors such as interference and the like.

Description

Turbofan engine multivariable robust variable gain control method based on non-equilibrium state linearization
Technical Field
The invention belongs to the technical field of aeroengine control, and particularly relates to a turbofan engine multivariable robust variable gain control method based on non-equilibrium state linearization.
Background
With the improvement of the maneuverability requirement of the airplane, particularly the maneuverability of the military airplane requiring rapid acceleration and deceleration and other dynamic severe changes, the aircraft engine is often far away from a balanced state.
When an airplane flies, the surrounding environment (cloud, fog and the like) can have unpredictable changes and is regarded as noise or disturbance, and the engine is required to still stably operate under the condition of the disturbance.
Under the transition states of rapid acceleration and deceleration and the like, the turbofan engine deviates from the equilibrium state and enters the non-equilibrium state, the dynamic characteristic of the engine changes violently, the precision of a linear model developed based on the traditional equilibrium state is obviously reduced, and the performance of a multi-variable controller of the turbofan engine designed by the linear model is also reduced. Multivariable controllers are one of the major directions in the future development of aircraft engine control, because the coupling of multiple variables to multiple outputs is also a difficult problem. The multivariable controller with good performance can help the pilot to take multiple instructions into account and complete a flight task with higher difficulty.
In addition, the aircraft engine control system guarantees smooth completion of the maneuvering action of the aircraft, so that the control system is required to have good dynamic instruction tracking capability and good disturbance suppression capability.
Therefore, aiming at the requirements of modeling the linear model of the aircraft engine and designing the controller, a multivariable acceleration and deceleration control method is needed to be invented, the problem of insufficient accuracy of the linear model in the transition states such as acceleration and deceleration is solved, and the controlled system is ensured to have good acceleration and deceleration dynamic instruction tracking performance and good disturbance suppression performance.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a turbofan engine multivariable robust variable gain control method based on non-equilibrium state linearization, which linearizes a system near a non-equilibrium point set, designs a multivariable robust variable gain controller by means of a linear model, and simultaneously ensures the dynamic instruction tracking capability and disturbance suppression robust performance of a turbofan engine.
In order to achieve the purpose, the invention adopts the technical scheme that:
the turbo-fan engine multivariable robust variable gain control method based on the non-equilibrium state linearization comprises the following steps:
step 1) establishing a turbofan engine input and output model for non-equilibrium state linearization;
step 2) establishing a turbofan engine linear variable parameter model containing disturbance information;
and 3) establishing a multivariable robust variable gain controller.
Further, the specific steps of establishing the turbofan engine input/output model for the non-equilibrium state linearization in the step 1) are as follows:
step 1.1) establishing a turbofan engine component level model according to the aerodynamic and thermodynamic characteristics and typical component characteristic data of the turbofan engine, wherein the main components comprise a fan, a gas compressor, a combustion chamber, a turbine, a tail nozzle and the like;
step 1.2) establishing a turbofan engine dynamic model;
and 1.3) canceling the integral relation of the rotating speed derivative in the turbofan engine dynamic model to the rotating speed to obtain an input and output model of the turbofan engine, wherein the input is the rotating speed, the fuel flow, the thick channel area of a tail nozzle and the like, and the output is the corresponding rotating speed derivative and measurement output.
Further, the specific steps of establishing the turbofan engine linear variable parameter model containing the disturbance information in the step 2) are as follows:
step 2.1) determining an unbalanced point set of the turbofan engine, and selecting the unbalanced point set of the turbofan engine, wherein the unbalanced point is formed by rho ═ n1，n2，wf，A8]Is represented by n1And n2Respectively high pressure rotor speed and low pressure rotor speed, wfFor main combustion chamber supply, A8Is the area of the throat of the tail nozzle. The unbalanced point set is composed of a set phi ═ rho | gi(ρ) ≧ 0, i ═ 1,2, … …, l } where gi(ρ) is the polynomial form, l is the number of constraints;
step 2.2) selecting a plurality of unbalanced points in the unbalanced point set in sequence as input, and inputting by using the turbofan engineThe output model calculates the rotating speed derivative of the corresponding point
Figure BDA0002993047010000021
And measuring the output vector y to obtain a data set of all unbalanced states of the turbofan engine
Figure BDA0002993047010000022
Step 2.3) derivative of the rotational speed at the non-equilibrium point
Figure BDA0002993047010000023
And the measurement output y are fitted to polynomial functions, respectively
Figure BDA0002993047010000024
y＝[p1(p) p2(ρ)]TWherein p is1(*)p2() is the sign of the function, f (, h) is also;
step 2.4) separately fitting polynomial functions
Figure BDA0002993047010000031
Partial derivatives of the respective variables are calculated to obtain a system matrix A in a polynomial forms(ρ)，Bs(ρ)，Cs(ρ)，Ds(ρ)；
Wherein the content of the first and second substances,
Figure BDA0002993047010000032
step 2.5) establishing a turbofan engine linear variable parameter state model:
Figure BDA0002993047010000033
wherein
Figure BDA0002993047010000034
Figure BDA0002993047010000035
Wherein y is1、y2Is a measurement output, which can be any output that is desired to be focused on;
Figure BDA0002993047010000036
for the reference point of the unbalanced state, scheduled by rho, where w is disturbance or noise, B1，D1Is a noise matrix, usually a constant matrix, whose values are related to the noise/disturbance magnitude.
Further, the specific steps of establishing the multivariable robust variable gain controller in the step 3) are as follows:
step 3.1) establishing a reference instruction rsTurbofan engine augmentation system of (1):
Figure BDA0002993047010000037
Figure BDA0002993047010000038
Figure BDA0002993047010000039
wherein Q and R are secondary performance indexes, reflect the noise suppression capability, have different engine performances, and are valued according to actual engines or experience, wherein Q and R are secondary performance indexes
Figure BDA00029930470100000310
Figure BDA00029930470100000311
rsIs the target instruction, z is the evaluation output;
step 3.2) solving the SOS (sum-of-squares) matrix Si(p) and a positive definite symmetry matrix Y, such that
Figure BDA00029930470100000312
Is a SOS matrix and satisfies
Figure BDA00029930470100000313
And
Figure BDA00029930470100000314
wherein
Figure BDA0002993047010000041
Step 3.3) solving the robust variable gain controller u (rho) ═ K (rho) x, wherein
Figure BDA0002993047010000042
Figure BDA0002993047010000043
Further, γ as described in step 3.2)∞The value range is [1.02.0 ]],γ2The value range is [ 0.12.0 ]]。γ∞And gamma2The smaller the noise suppression effect, the better, but the too small γ∞And gamma2The proper controller cannot be solved. For the characteristics of the engine object, gamma∞The value range is [1.02.0 ]],γ2The value range is [ 0.12.0 ]]。
Has the advantages that:
the invention provides a variable-gain control method for multivariable robustness of a turbofan engine based on non-equilibrium state linearization, and compared with the prior art, the technical scheme adopted by the invention has the following technical effects:
the engine linear model developed by the invention is based on the non-equilibrium state, simultaneously considers the dynamic instruction tracking problem and the noise suppression problem to construct a linear variable parameter model, and uses multivariable
Figure BDA0002993047010000044
The robust variable gain control method designs the controller, so that the controller changes a plurality of parameter variables in real time under the condition of different dynamic changes corresponding to a plurality of different control instructions, has good tracking performance on the plurality of instructions and has the advantages of good tracking performanceThe noise suppression capability is suitable for a turbofan engine control system.
Drawings
FIG. 1 is a block diagram of an engine control system employing a multivariable robust variable gain controller illustrating a control flow in accordance with the present invention.
FIG. 2 is a schematic diagram of an established turbofan engine dynamic model.
FIG. 3 is a schematic diagram of a turbofan engine input-output model established for non-equilibrium state linearization.
Detailed Description
The present invention will be further described with reference to the accompanying drawings.
The invention discloses a variable gain control method of multivariable robustness of a turbofan engine based on non-equilibrium state linearization, which is a variable gain control method for solving the problem of strong nonlinearity in the acceleration and deceleration process of the turbofan engine, and comprises the following steps: establishing a turbofan engine input and output model for non-equilibrium state linearization; establishing a turbofan engine polynomial linear variable parameter model containing noise information; and establishing a multivariable robust variable gain controller. On the basis of a turbofan engine non-equilibrium state linearization method, a design method of a multivariable robust variable gain controller is provided, the problems of inaccuracy of a linear model and the like in the dynamic severe change process of the turbofan engine are solved, and meanwhile the tracking capability of a plurality of target instructions and the inhibition capability of uncertain factors such as noise and the like can be considered.
The turbo-fan engine multivariable robust variable gain control method based on the non-equilibrium state linearization comprises the following steps:
step 1) establishing a turbofan engine input and output model for non-equilibrium state linearization;
step 1.1) establishing a turbofan engine component level model according to the aerodynamic and thermodynamic characteristics and typical component characteristic data of the turbofan engine, wherein the main components comprise a fan, a gas compressor, a combustion chamber, a turbine, a tail nozzle and the like;
step 1.2) establishing a turbofan engine dynamic model, as shown in FIG. 2;
and 1.3) canceling the integral relation of the rotating speed derivative to the rotating speed in the dynamic model of the turbofan engine to obtain an input and output model of the turbofan engine, wherein the input is the rotating speed, the fuel flow, the throat area of a tail nozzle and the like, and the output is the corresponding rotating speed derivative and measurement output as shown in figure 3.
Step 2) establishing a turbofan engine linear variable parameter model containing disturbance information;
step 2.1) selecting a set of non-equilibrium points of the turbofan engine, wherein the non-equilibrium points are defined by rho ═ n1，n2，wf，A8]Is represented by n1And n2High pressure rotor speed and low pressure rotor speed, w, respectivelyfFor main combustion chamber supply, A8Is the area of the throat of the tail nozzle. The unbalanced point set is composed of a set phi ═ rho | gi(ρ) ≧ 0, i ═ 1,2, … …, l } where gi(ρ) is the polynomial form, l is the number of constraints;
step 2.2) selecting a plurality of non-equilibrium points in the non-equilibrium point set in sequence as input, and calculating the rotating speed derivative of the corresponding point by using the input and output model of the turbofan engine
Figure BDA0002993047010000051
And measuring the output vector y to obtain a data set of all unbalanced states of the turbofan engine
Figure BDA0002993047010000052
Step 2.3) derivative of the rotational speed at the non-equilibrium point
Figure BDA0002993047010000053
And the measurement output y are fitted to polynomial functions, respectively
Figure BDA0002993047010000054
y＝[p1(ρ) p2(p)]T；
Step 2.4) separately fitting polynomial functions
Figure BDA0002993047010000055
Partial derivatives of the respective variables are calculated to obtain a system matrix A in a polynomial forms(ρ)，Bs(ρ)，Cs(ρ)，Ds(ρ)；
Wherein the content of the first and second substances,
Figure BDA0002993047010000056
step 2.5) establishing a turbofan engine linear variable parameter state model:
Figure BDA0002993047010000061
Figure BDA0002993047010000062
Figure BDA0002993047010000063
wherein
Figure BDA0002993047010000064
For the reference point of the unbalanced state, scheduled by rho, where w is disturbance or noise, B1，D1Is a noise matrix.
And 3) establishing a multivariable robust variable gain controller.
Step 3.1) establishing a reference instruction rsTurbofan engine augmentation system of (1):
Figure BDA0002993047010000065
Figure BDA0002993047010000066
Figure BDA0002993047010000067
wherein Q, R are derived from the actual engine, wherein
Figure BDA0002993047010000068
Figure BDA0002993047010000069
rsIs the target instruction and z is the evaluation output.
Step 3.2) selecting a performance index gamma∞And gamma2Solving for the SOS (sum-of-squares) matrix S using the sedumi toolkit of MATLABi(p) and a positive definite symmetry matrix Y, such that
Figure BDA00029930470100000610
Is a SOS matrix and satisfies
Figure BDA00029930470100000611
And
Figure BDA00029930470100000612
wherein
Figure BDA00029930470100000613
Step 3.3) robust variable gain controller u (ρ) ═ K (ρ) x, where
Figure BDA00029930470100000614
In order to verify the effectiveness of the method, aiming at the same engine, a controller based on the method and a controller based on a balance point linearization model are respectively designed and simulated. Both of these simulated operating conditions were standard atmospheric conditions at a height H of 0 km and a mach number Ma of 0. Simulation results show that the tracking performance of the controller based on the method is superior to that of the controller based on the balance point linearization model, a plurality of target instructions are quickly tracked without overshoot, and the controller has disturbance suppression capability; the controller based on the balance point linearization model has overshoot, and the tracking performance is inferior to the method.
The engine linear model developed by the invention is based on the non-equilibrium state, so the engine linear model can still have very accurate approximation in the process of rapid acceleration and deceleration. The invention considers the dynamic instruction tracking problem and the noise suppression problem at the same timeSubject, use
Figure BDA0002993047010000071
The robust variable gain control method designs the controller, so that the controller changes parameters in real time under different dynamic change conditions corresponding to different control instructions, has good tracking performance on different instructions, has noise suppression capability and is suitable for a turbofan engine control system.
The above description is only a preferred method of implementing the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications can be made without departing from the principles of the invention and these modifications are to be considered within the scope of the invention.

Claims (5)

1. The turbo-fan engine multivariable robust variable gain control method based on the non-equilibrium state linearization is characterized in that: the method comprises the following steps:
step 1) establishing a turbofan engine input and output model for non-equilibrium state linearization;
step 2) establishing a turbofan engine linear variable parameter model containing disturbance information;
and 3) establishing a multivariable robust variable gain controller and solving.
2. The non-equilibrium linearized turbofan engine multivariable robust variable gain control method of claim 1 wherein: the specific steps of establishing the turbofan engine input and output model for the non-equilibrium state linearization in the step 1) are as follows:
step 1.1) establishing a turbofan engine component level model according to the aerodynamic and thermodynamic characteristics and typical component characteristic data of the turbofan engine, wherein the main components comprise a fan, a gas compressor, a combustion chamber, a turbine and a tail nozzle;
step 1.2) establishing a turbofan engine dynamic model;
and 1.3) canceling the integral relation of the rotating speed derivative in the turbofan engine dynamic model to the rotating speed to obtain an input and output model of the turbofan engine, wherein the input is the rotating speed, the fuel flow and the thick channel area of the tail nozzle, and the output is the corresponding rotating speed derivative and measurement output.
3. The non-equilibrium linearized turbofan engine multivariable robust variable gain control method of claim 1 wherein: the specific steps of establishing the turbofan engine linear variable parameter model containing the disturbance information in the step 2) are as follows:
step 2.1) selecting a set of non-equilibrium points of the turbofan engine, wherein the non-equilibrium points are defined by rho ═ n1,n2,wf,A8]Is represented by n1And n2High pressure rotor speed and low pressure rotor speed, w, respectivelyfFor main combustion chamber supply, A8Is the area of the throat of the tail nozzle; the unbalanced point set is composed of a set phi ═ rho | gi(ρ) ≧ 0, i ═ 1,2, … …, l } where gi(ρ) is the polynomial form, l is the number of constraints;
step 2.2) selecting a plurality of non-equilibrium points in the non-equilibrium point set in sequence as input, and calculating the rotating speed derivative of the corresponding point by using the input and output model of the turbofan engine
Figure FDA0002993047000000011
And measuring the output vector y to obtain a data set of all unbalanced states of the turbofan engine
Figure FDA0002993047000000012
Step 2.3) derivative of the rotational speed at the non-equilibrium point
Figure FDA0002993047000000013
And the measurement output y are fitted to polynomial functions, respectively
Figure FDA0002993047000000014
y＝[p1(ρ) p2(ρ)]T；
Step 2.4) separately fitting polynomial functions
Figure FDA0002993047000000015
Partial derivatives of the respective variables are calculated to obtain a system matrix A in a polynomial forms(ρ),Bs(ρ),Cs(ρ),Ds(ρ)；
Wherein the content of the first and second substances,
Figure FDA0002993047000000021
Figure FDA0002993047000000022
step 2.5) establishing a turbofan engine linear variable parameter state model:
Figure FDA0002993047000000023
wherein
Figure FDA0002993047000000024
Figure FDA0002993047000000025
Wherein
Figure FDA0002993047000000026
Figure FDA0002993047000000027
For the reference point of the imbalance state, by scheduling, where w is disturbance or noise, B1,D1Is a noise matrix.
4. The non-equilibrium linearized turbofan engine multivariable robust variable gain control method of claim 1 wherein: the specific steps of establishing the multivariable robust variable gain controller in the step 3) are as follows:
step 3.1) establishing a reference instruction rsTurbofan engine augmentation system of (1):
Figure FDA0002993047000000028
wherein the content of the first and second substances,
Figure FDA0002993047000000029
Figure FDA00029930470000000210
wherein Q, R are derived from the actual engine, wherein
Figure FDA00029930470000000211
e＝ys-rs，rsIs the target instruction and z is the evaluation output.
Step 3.2) solving the SOS (sum-of-squares) matrix Si() And positively determining the symmetric matrix Y such that
Figure FDA00029930470000000212
Is a SOS matrix and satisfies
Figure FDA00029930470000000213
And
Figure FDA00029930470000000214
wherein
Figure FDA0002993047000000031
Step 3.3) solving the robust variable gain controller u (rho) ═ K (rho) x, wherein
Figure FDA0002993047000000032
5. The non-equilibrium linearized turbofan engine multivariable robust variable gain control method of claim 4 wherein: in said step 3.2)∞The value range is [1.02.0 ]],γ2The value range is [ 2 ]0.1 2.0]。
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