CN112859606B - Turbofan engine transition state disturbance suppression method based on preset performance - Google Patents

Turbofan engine transition state disturbance suppression method based on preset performance Download PDF

Info

Publication number
CN112859606B
CN112859606B CN202110040824.1A CN202110040824A CN112859606B CN 112859606 B CN112859606 B CN 112859606B CN 202110040824 A CN202110040824 A CN 202110040824A CN 112859606 B CN112859606 B CN 112859606B
Authority
CN
China
Prior art keywords
turbofan engine
pressure rotor
state
performance
matrix
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110040824.1A
Other languages
Chinese (zh)
Other versions
CN112859606A (en
Inventor
曾建平
岳世壮
张家熹
朱平芳
余联郴
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xiamen University
Original Assignee
Xiamen University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xiamen University filed Critical Xiamen University
Priority to CN202110040824.1A priority Critical patent/CN112859606B/en
Publication of CN112859606A publication Critical patent/CN112859606A/en
Application granted granted Critical
Publication of CN112859606B publication Critical patent/CN112859606B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention discloses a turbofan engine transition state disturbance suppression method based on preset performance, which considers that the transition process of a turbofan engine needs to meet given performance indexes, and external disturbance has great influence on the stability of a system in practical application, and a controller may be disabled under severe conditions. In order to ensure that the transition state performance of the turbofan engine can still meet the given performance index under the action of external disturbance, the influence of the external disturbance on the system is regarded as the structural uncertainty of the system, an index conversion strategy is designed based on a preset performance method, the given performance index is constrained and converted into the design index of the controller, and finally the feasible controller is obtained by utilizing the square sum technology. The control method and the control system realize that the transition state control system of the turbofan engine normally operates and each performance index reaches the preset effect when external disturbance exists.

Description

Turbofan engine transition state disturbance suppression method based on preset performance
Technical Field
The invention relates to the technical field of aero-engine control, in particular to a turbofan engine transition state disturbance suppression method based on preset performance.
Background
Turbofan engines are the most central components of an aircraft, and their operating conditions directly determine the stability and safety of the entire aircraft. The performance of the turbofan engine in the transition state directly influences the performance of the airplane such as takeoff, acceleration, maneuvering flight and the like. Therefore, requirements for rapidity, stability and interference resistance of the transition state control of the aircraft engine are extremely high. The research on the steady-state controller of the turbofan engine is mature, the transition state control needs to span a plurality of different steady-state working areas, the system at each steady-state working point has strong nonlinearity, and the design difficulty of the controller is undoubtedly increased by considering the influence of external disturbance. How to ensure that the transition performance of the turbofan engine still meets the requirement under the condition of disturbance is a problem troubling aviation researchers. It is therefore necessary to study disturbance suppression in the transient control of turbofan engines.
The existing design method of the transition state controller mainly comprises an approximate determination method, a dynamic programming method and a power extraction method. The approximation determination is to approximate transient engine operating conditions using steady state equilibrium equations. The dynamic programming method is based on an engine dynamic calculation model, considers engine performance and aircraft design constraints, and generates a transition state control rule by optimizing a preset performance objective function. The optimal control problem of the accelerating process of the turbofan engine is solved by a Sequence Quadratic Programming (SQP) method. And the von linshuang and the like are combined with the strong global optimization capability of the particle swarm algorithm and the strong local search capability of the SQP, so that the transition state performance is further optimized. In order to reduce the time complexity of the SQP algorithm, Li and the like provide a hybrid optimization method combining the genetic algorithm and the SQP, and the instantaneity of the SQP method is improved. And yellow Ruyi and the like are introduced into a sparse least square support vector machine to train transition state parameter change data, and the obtained model is used as a feedforward and proportional-integral controller to form a closed-loop controller engine to perform transition state control.
In summary, although many scholars have proposed solutions to the problem of transient control of turbofan engines, the problem of disturbance suppression in transient control of turbofan engines has been rarely achieved, and a method for suppressing disturbance in transient control of engines is needed.
Disclosure of Invention
The invention aims to solve the problem of disturbance suppression in transition state control of a turbofan engine, and provides a method for suppressing disturbance in a transition state of the turbofan engine based on preset performance.
In order to solve the problems, the invention is realized by the following technical scheme:
the turbofan engine transition state disturbance suppression method based on the preset performance comprises the following steps:
step 1, designing a performance function rho of the rotating speed of the high-pressure rotor according to given performance indexes2(t) and let the performance function rho of the low pressure rotor speed of the turbofan engine1(t) Performance function ρ equal to the high pressure rotor speed2(t); wherein:
Figure BDA0002895782310000021
step 2, based on the performance function rho of the low-pressure rotor rotating speed in the step 11(t) and Performance function ρ of high pressure rotor speed2(t) constructing a preset performance parameter matrix R (x, t), wherein:
Figure BDA0002895782310000022
step 3, designing solvability conditions of the state feedback gain matrix K (x) based on the preset performance parameter matrix R (x, t) constructed in the step 3, namely:
Figure BDA0002895782310000023
step 4, solving solvability conditions of the state feedback gain matrix K (x) designed in the step 3 by utilizing an SOS technology to obtain solving process parameters of the first controller
Figure BDA0002895782310000024
And the second controller solvedThe process parameters L (x);
step 5, solving process parameters by using the first controller obtained in the step 4
Figure BDA0002895782310000025
And the second controller solving for the process parameter l (x) calculating a state feedback gain matrix k (x), wherein:
Figure BDA0002895782310000026
step 6, designing a state feedback controller based on preset performance based on the state feedback gain matrix k (x) obtained in step 5, that is:
u(t)＝K(x)x(t)-kRR(x,t)x(t)
and 7, controlling the turbofan engine based on the state feedback controller based on the preset performance designed in the step 6, namely:
Figure BDA0002895782310000027
in the above formula: rho1(t) is a performance function of the low pressure rotor speed, ρ2(t) is a performance function of the speed of the high-pressure rotor, x2(0) Is an initial value of the high-pressure rotor speed of the turbofan engine1Is a dynamic overshoot threshold value of the high-pressure rotor rotating speed when no disturbance exists,
Figure BDA0002895782310000028
for disturbances of the rotational speed of the high-pressure rotor, σ2For dynamic overshooting of the speed of rotation of the high-pressure rotor in the presence of disturbances, x2eSteady state value, rho, representing the high pressure rotor speed of a turbofan engine2∞≤x2eδ1，
Figure BDA0002895782310000029
δ1Is a steady state error threshold value of the rotating speed of the high-pressure rotor, a is a constant, T1Is a step response time constant;
r (x, t) is a preset performance parameter matrix,
Figure BDA0002895782310000031
is the state error of the low-pressure rotor rotating speed,
Figure BDA0002895782310000032
the state error of the high-pressure rotor rotating speed;
k (x) is a state feedback gain matrix,
Figure BDA0002895782310000033
the process parameters are solved for the first controller,
Figure BDA0002895782310000034
for a given positive polynomial, I is an appropriately dimensioned identity matrix, phiSOSSet of SOS polynomials, Ψ1As an intermediate parameter, E1Is a first adaptive constant matrix, λ2(x) For a given positive polynomial, A (x)2) Is a state matrix, B (x)2) For the input matrix, L (x) solves for the process parameter, k, for the second controllerRTo be adjustable factor, xhIs Ah(x2) State of (1), Ah(x2) Is A (x)2) H line of (1), x is the system state, F1Is a second multidimensional constant matrix, J is B (x)2) A row number set of all-zero middle rows;
x (t) is the system state, x (t) [. x ]1(t) x2(t)]T，x1(t) is the low pressure rotor speed, x, of the turbofan engine2(t) the high pressure rotor speed of the turbofan engine;
Figure BDA0002895782310000039
is the first derivative of the system state, Δ is the uncertainty matrix, u (t) is the system input to the turbofan engine, u (t) is [ u (t) ]1(t )u2(t)]T，u1(t) is the main fuel flow of the turbofan engine, u2(t) throat area of turbofan engine, z (t) system output, C (x)2) Is composed ofAnd outputting the matrix.
In step 1, the performance index of the given system includes:
high pressure rotor speed x for turbofan engine2(t) its control performance index should meet the requirement that the steady state error is not greater than its steady state error threshold delta1Dynamic overshoot not greater than its dynamic overshoot threshold σ1And the step response time is not greater than its step response time threshold T1Namely:
Figure BDA0002895782310000035
for the nozzle pressure ratio pi (t) of the turbofan engine, the control performance index of the turbofan engine meets the condition that the steady state error is not more than the steady state error threshold value delta (t)2Namely:
Figure BDA0002895782310000036
in the presence of disturbances of the high-pressure rotor speed of a turbofan engine, the dynamic overshoot of the high-pressure rotor speed is less than its dynamic overshoot threshold σ2And the suppression of the disturbance can be realized, namely:
Figure BDA0002895782310000037
wherein: x is the number of2(0) For high-pressure rotor speed x of turbofan engine2Initial value of (t), x2(∞) is high-pressure rotor speed x of turbofan engine2End value of (t), x2eSteady state value, x, representing the speed of the high pressure rotor of a turbofan engine2(tp) For high-pressure rotor speed x of turbofan engine2(t) at the overshoot instant tpThe value of (a) is,
Figure BDA0002895782310000038
step response time of the rotating speed of the high-pressure rotor; pi (∞) is the final value of the nozzle pressure ratio, pieSteady state of nozzle pressure ratioA value; x is the number of2ω(t) high pressure rotor speed x of turbofan engine due to disturbance2(t) amount of change, x2ω(tp) High-pressure rotor speed x of turbofan engine for disturbance2(t) at the overshoot instant tpThe amount of change in (c).
Compared with the prior art, the invention has the following characteristics:
1. designing a state feedback controller based on a preset performance method to enable the transition process of the closed-loop system to meet the requirements of given steady-state error, overshoot and adjusting time;
2. the performance index of the system is converted into the design index of the controller, and a feasible method for converting the performance index is provided, so that the given performance indexes of dynamic overshoot, steady-state error and step response time are converted into the design index of a robust controller, and the design of the controller is facilitated;
3. in a predetermined performance parameter matrix
Figure BDA0002895782310000041
An error transformation function is designed in the selection, so that the controller has a control function on the condition that the initial state error is within or outside a preset performance limit;
4. the influence of external disturbance on the system is regarded as the structural uncertainty of the system, and a robust controller is designed to enable the closed-loop system to have a good suppression effect on the disturbance in the transition process;
5. the robust controller is solved by using the SOS planning method, so that the solving complexity of the controller is effectively reduced;
6. in the transition process, the state and the output of the closed-loop system can be effectively and quickly tracked to the steady-state value, and the control effect is good.
Drawings
FIG. 1 is a flow chart of a turbofan engine transient disturbance suppression method based on preset performance.
FIG. 2 depicts an initial state error diagram for the system at time t, where (a) is for an initial state error greater than zero and (a) is for an initial state error less than zero.
FIG. 3 shows the errorTransformation function T1(x, t) is plotted against the change in state error.
FIG. 4 is an error transformation function T1(x, t) versus state time.
FIG. 5 is a state quantity x of a turbofan engine transitioning from a throttled state to an intermediate state under external disturbances2Error x of2errGraph over time.
FIG. 6 is a state quantity x of a turbofan engine transitioning from a throttled state to an intermediate state under external disturbances2The convergence graph of (a).
FIG. 7 is a graph of the convergence of the state quantity π during the transition of a turbofan engine from a throttled state to an intermediate state under external disturbances.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to specific examples.
Referring to fig. 1, a turbofan engine transition state disturbance suppression method based on preset performance includes the following steps:
step 1, designing a performance function rho of the rotating speed of the high-pressure rotor according to given performance indexes2(t) and let the performance function rho of the low pressure rotor speed of the turbofan engine1(t) Performance function ρ equal to the high pressure rotor speed2(t)。
High pressure rotor speed x for turbofan engine2(t) its control performance index should meet the requirement that the steady state error is not greater than its steady state error threshold delta1Dynamic overshoot not greater than its dynamic overshoot threshold σ1And the step response time is not greater than its step response time threshold T1Namely:
Figure BDA0002895782310000051
for the nozzle pressure ratio pi (t) of the turbofan engine, the control performance index of the turbofan engine meets the condition that the steady state error is not more than the steady state error threshold value delta (t)2Namely:
Figure BDA0002895782310000052
in the presence of disturbances of the high-pressure rotor speed of a turbofan engine, the dynamic overshoot of the high-pressure rotor speed is less than its dynamic overshoot threshold σ2And the suppression of the disturbance can be realized, namely:
Figure BDA0002895782310000053
wherein: x is the number of2(0) For high-pressure rotor speed x of turbofan engine2Initial value of (t), x2(∞) is high-pressure rotor speed x of turbofan engine2End value of (t), x2eSteady state value, x, representing the speed of the high pressure rotor of a turbofan engine2(tp) For high-pressure rotor speed x of turbofan engine2(t) at the overshoot instant tpThe value of (a) is,
Figure BDA0002895782310000054
step response time of the rotating speed of the high-pressure rotor; pi (∞) is the final value of the nozzle pressure ratio, pieIs the steady state value of the pressure ratio of the spray pipe; x is the number of2ω(t) high pressure rotor speed x of turbofan engine due to disturbance2(t) amount of change, x2ω(tp) High-pressure rotor speed x of turbofan engine for disturbance2(t) at the overshoot instant tpThe amount of change in (c).
At this time, a performance function rho of the high-pressure rotor rotating speed is designed2(t) is:
Figure BDA0002895782310000055
aiming at the problem of disturbance suppression of the turbofan engine, the characteristics of a preset performance method are combined, in the invention, only the performance index of the rotating speed of the high-pressure rotor is concerned, and rho is made1(t)＝ρ2(t) to reduce the complexity of the default performance parameters.
Step 2, based on the stepsPerformance function ρ of low pressure rotor speed of 11(t) and Performance function ρ of high pressure rotor speed2(t) constructing a preset performance parameter matrix R (x, t), wherein:
Figure BDA0002895782310000056
step 3, designing solvability conditions of the state feedback gain matrix K (x) based on the preset performance parameter matrix R (x, t) constructed in the step 3, namely:
Figure BDA0002895782310000057
step 4, solving solvability conditions of the state feedback gain matrix K (x) designed in the step 3 by utilizing an SOS technology to obtain solving process parameters of the first controller
Figure BDA0002895782310000061
And the second controller solving for a process parameter l (x);
step 5, solving process parameters by using the first controller obtained in the step 4
Figure BDA0002895782310000062
And the second controller solving for the process parameter l (x) calculating a state feedback gain matrix k (x), wherein:
Figure BDA0002895782310000063
step 6, designing a state feedback controller based on preset performance based on the state feedback gain matrix k (x) obtained in step 5, that is:
u(t)＝K(x)x(t)-kRR(x,t)x(t)
and 7, controlling the turbofan engine based on the state feedback controller based on the preset performance designed in the step 6, namely:
Figure BDA0002895782310000064
in the above formula: rho1(t) is a performance function of the low pressure rotor speed, ρ2(t) is a performance function of the speed of the high-pressure rotor, x2(0) Is an initial value of the high-pressure rotor speed of the turbofan engine1Is a dynamic overshoot threshold value of the high-pressure rotor rotating speed when no disturbance exists,
Figure BDA0002895782310000065
for disturbances of the rotational speed of the high-pressure rotor, σ2For dynamic overshooting of the speed of rotation of the high-pressure rotor in the presence of disturbances, x2eSteady state value, rho, representing the high pressure rotor speed of a turbofan engine2∞≤x2eδ1，
Figure BDA0002895782310000066
δ1Is a steady state error threshold value of the rotating speed of the high-pressure rotor, a is a constant, T1Is a step response time constant;
r (x, t) is a preset performance parameter matrix,
Figure BDA0002895782310000067
is the state error of the low-pressure rotor rotating speed,
Figure BDA0002895782310000068
the state error of the high-pressure rotor rotating speed;
k (x) is a state feedback gain matrix,
Figure BDA0002895782310000069
the process parameters are solved for the first controller,
Figure BDA00028957823100000610
for a given positive polynomial, I is an appropriately dimensioned identity matrix, phiSOSSet of SOS polynomials, Ψ1As an intermediate parameter, E1Is a first adaptive constant matrix, λ2(x) For a given positive polynomial, A (x)2) Is a state matrix, B (x)2) For the input matrix, L (x) solves for the process parameter, k, for the second controllerRTo be adjustable factor, xhIs Ah(x2) State of (1), Ah(x2) Is A (x)2) H line of (1), x is the system state, F1Is a second multidimensional constant matrix, J is B (x)2) A row number set of all-zero middle rows;
x (t) is the system state, x (t) [. x ]1(t )x2(t)]T，x1(t) is the low pressure rotor speed, x, of the turbofan engine2(t) the high pressure rotor speed of the turbofan engine;
Figure BDA00028957823100000611
is the first derivative of the system state, Δ is the uncertainty matrix, u (t) is the system input to the turbofan engine, u (t) is [ u (t) ]1(t) u2(t)]T，u1(t) is the main fuel flow of the turbofan engine, u2(t) throat area of turbofan engine, z (t) system output, C (x)2) Is an output matrix.
Considering that the turbofan engine needs to meet given performance indexes in the transition process, and external disturbance has a great influence on the stability of the system in practical application, the controller may be disabled in a severe case. In order to ensure that the transition state performance of the turbofan engine can still meet the given performance index under the action of external disturbance, the invention provides a method for suppressing the transition state disturbance of the turbofan engine based on preset performance. According to the method, the influence of external disturbance on a system is regarded as the uncertainty of the system structure, an index conversion strategy is designed based on a preset performance method, the given performance index constraint is converted into the design index of a robust controller, and finally the controller is solved by utilizing the sum of squares (SOS) technology, so that the disturbance suppression in the transition state control of the turbofan engine is realized.
The following takes a certain type of double-shaft turbofan engine with a small bypass ratio as a research object to discuss the control problem of the transition of a turbofan engine system from a throttling state to an intermediate state.
The polynomial nonlinear model of the engine on the ground is:
Figure BDA0002895782310000071
wherein the content of the first and second substances,
Figure BDA0002895782310000072
A11(x2)＝365.59x2 2-680.99x2+311.12，A12(x2)＝245.80x2 2-437.90x2+198.66，A21(x2)＝108.43x2 2-191.32x2+83.43，A22(x2)＝-273.44x2 2+484.57x2-214.94；
Figure BDA0002895782310000073
B11(x2)＝-7.28x2 2+132.69x2-5.63，B12(x2)＝-205.84x2 2+375.47x2-1708.3，B21(x2)＝7.18x2 2-13.51x2+6.58，B22(x2)＝587.60x2 2-1042.1x2+464.91；
Figure BDA0002895782310000074
C11(x2)＝0，C12(x2)＝1，C21(x2)＝-667.97x2 2+1220.0x2-551.46，C22(x2)＝623.34x2 2-1136.9x2+513.91。
(I): the effect of external disturbances on the system is considered as uncertainty on the system structure.
The form of the external disturbance is:
E1ω(t) (2)
where ω (t) is the external disturbance given, in this example,
Figure BDA0002895782310000075
x2e＝0.9437，x2(0)＝0.8632。E1is a constant matrix of appropriate dimensions.
Adding post-disturbance open-loop system
Figure BDA0002895782310000076
Become into
Figure BDA0002895782310000077
Order to
ω(t)＝ΔF1·x(t) (5)
Wherein, F1Is a constant matrix of appropriate dimensions, and Δ is an uncertainty matrix satisfying ΔTΔ ≦ I, which is an identity matrix of appropriate dimensions.
At this time, the external disturbance ω (t) is converted into the matrix A (x)2) Changing the middle coefficient, i.e. expanding the state space equation containing the disturbance omega (t), then rearranging and simplifying, merging the part of omega (t) into A (x)2) I.e. structural uncertainty of the system. Considering the external disturbance as an uncertainty of the controlled system, the open loop can be expressed as
Figure BDA0002895782310000081
Then a non-linear model of a certain operating point of the turbofan engine can be written as
Figure BDA0002895782310000082
Wherein, the system state x (t) ═ x1(t) x2(t)]TThe system input u (t) ═ u1(t) u2(t)]T。x1(t) is the low pressure rotor speed of the turbofan engine, x2(t) is the high pressure rotor speed of the turbofan engine. u. of1(t) is the main fuel flow of the turbofan engine, u2(t) is the throat area of the turbofan engine. ω (t) is the external disturbance input. Output variable z (t) of the system [. sup.x ]2(t) π(t)]TAnd pi (t) is the pressure ratio of the nozzle.
And (II) converting the performance index of the system into the design index of the controller.
For all allowed parameter uncertainties, the closed loop system meets the following criteria: 1) the closed loop system is asymptotically stable, and the state converges to a steady state value; 2) the transition process meets the performance index (8-10).
High pressure rotor speed x for turbofan engine2(t) the control performance index of which should satisfy the steady state error of not more than δ1Dynamic overshoot
Figure BDA0002895782310000083
Not more than sigma1Step response time
Figure BDA0002895782310000084
Not more than T1I.e. by
Figure BDA0002895782310000085
In this example, δ1＝0.1％，σ1＝1％，T1＝1s。
For the closed-loop control pressure ratio pi (t) of the spray pipe, the control performance index of the closed-loop control pressure ratio pi (t) of the spray pipe meets the condition that the steady-state error is not more than delta2I.e. by
Figure BDA0002895782310000086
In this example, δ2＝0.5％。
While disturbing the rotor speed at high pressure
Figure BDA0002895782310000087
In the presence of a dynamic overshoot of the high-pressure rotor speed of less than sigma2And can realize the disturbance
Figure BDA0002895782310000088
Is inhibited, i.e.
Figure BDA0002895782310000089
In this example, σ21% of the total weight. Wherein x2ω(t) is the external disturbance vs. state x2(t) influence of the reaction.
Wherein x is2(0),x2(∞) represents the closed-loop system state x2Initial and final values of (t), x2ω(t) represents the disturbance versus state quantity x2Influence of (a) x2eSteady state value, t, representing a state quantitypRepresenting the overshoot time, pi (∞) representing the final value of the closed loop system output, pieRepresenting the steady state value of the nozzle pressure ratio.
The transient disturbance suppression problem is that: for a system (7) with external disturbance omega (t), a state feedback controller based on preset performance is designed
Figure BDA0002895782310000091
Where K (x) is the state feedback gain array to be designed, kRIs a harmonic coefficient of the signal to be transmitted,
Figure BDA0002895782310000092
is a preset performance parameter matrix to be designed,
Figure BDA0002895782310000093
therefore, the performance index of the system is converted into the design index of the controller, and only a proper preset performance parameter matrix needs to be selected
Figure BDA0002895782310000094
The system can be brought to a preset performance index.
(III) presetting a performance parameter matrix
Figure BDA0002895782310000095
And (4) selecting.
Setting the state error as
Figure BDA0002895782310000096
For convergence, the performance parameter matrix is preset at any time
Figure BDA0002895782310000097
It should satisfy:
Figure BDA0002895782310000098
and the preset performance limit should satisfy:
Figure BDA0002895782310000099
wherein the content of the first and second substances,
Figure BDA00028957823100000910
indicating the maximum overshoot of the state error allowed by the transition,
Figure BDA00028957823100000911
(i ═ 1,2) is a performance function of exponential convergence. Wherein, γi＞0，ρi0Representing the initial error bound, pi∞Indicating the maximum state error allowed at steady state. The relationship between the state error represented by equation (13) and its upper and lower bounds is shown in fig. 2.
The given performance indicators (8-10) are converted into performance function parameter indicators as follows:
(1)ρiselection of (∞)
Get
Figure BDA00028957823100000912
Is provided with
Figure BDA00028957823100000913
Then when
Figure BDA00028957823100000914
When the temperature of the water is higher than the set temperature,
Figure BDA00028957823100000915
within the performance bounds, otherwise
Figure BDA00028957823100000916
Outside the performance limits.
From a predetermined property
Figure BDA00028957823100000917
Available | ρ |2(∞)|＝|x2(∞)-x2e|≤x2eδ1From a predetermined property
Figure BDA00028957823100000918
Obtaining | Pi (∞) -Pie|≤πeδ2The simplified model (7) can be obtained
z2(t)＝C21(x2(t))x1(t)+C22(x2(t))x2(t) (14)
Further get x1(t)、x2(t)、Z2(t) relationship among the three:
Figure BDA00028957823100000919
|ρ1(∞)|≤max x1(∞) (16)
Figure BDA0002895782310000101
solving an optimization problem: s.t | x2(∞)|≤x2eδ1
|Z2(∞)|≤πeδ2
Maxx can be obtained1(∞)
Wherein x is1eIs a steady state value of the low pressure rotor speed. Rho2∞Can be represented by
Figure BDA0002895782310000102
Simple transformation to obtain: rho2∞≤x2eδ1。
In this embodiment, ρ in the third step according to the technical solutioniThe method for selecting the (∞) can be as follows:
ρ1(∞)＝ρ2(∞)＝10-3
(2)ρi0,γiand (4) selecting.
Get
Figure BDA0002895782310000103
Is provided at tsWhen the following relationship holds, t is calledsTo adjust the time of day.
Figure BDA0002895782310000104
From the above formula, γ can be obtained2Should satisfy
Figure BDA0002895782310000105
a＞0,0≤δ1Less than or equal to 1. In the same way, can obtain pairs
Figure BDA0002895782310000106
Performance constraints.
In this embodiment, ρ in the third step according to the technical solutioni0,γiThe selection method can obtain: rho10＝0.08，ρ20＝0.075，γ1＝γ2＝1.73。
Given an error transformation function of
Figure BDA0002895782310000107
Will be provided with
Figure BDA0002895782310000108
Is substituted to obtain
Figure BDA0002895782310000109
To sum up, select
Figure BDA00028957823100001010
To satisfy a predetermined performance matrix of properties.
In the present embodiment, it is preferred that,
Figure BDA00028957823100001011
Figure BDA00028957823100001012
Figure BDA00028957823100001013
Figure BDA00028957823100001014
FIGS. 3 and 4 are at given times, respectively
Figure BDA00028957823100001015
First diagonal T1(x, T) curve of variation with State error and T for given State error1(x, t) curves over time. As can be seen from fig. 3 and 4: 1) the preset performance parameter matrix can ensure that the state error converges in the boundary, and can also make the state error converge in the boundary under the condition that the state error is out of the boundary. 2) The predetermined performance parameter matrix may still maintain a certain magnitude over time. The device has a restraining effect on an external disturbance controller occurring at any running time.
(IV) robust controller design
For the following system
Figure BDA0002895782310000111
Given a matrix R (x, t), a constant kRPositive scalar quantity
Figure BDA0002895782310000112
λ2(x) If symmetric matrices are present
Figure BDA0002895782310000113
The matrix l (x) is such that:
Figure BDA0002895782310000114
Figure BDA0002895782310000115
wherein the content of the first and second substances,
Figure BDA0002895782310000116
operator he (a) ═ a + aTRecord Ah(x) H line of A (x), J ═ h1,…hHIs the line number set of all zero lines in B (x). Definition of
Figure BDA0002895782310000117
The transition state disturbance control problem can be solved, and the corresponding controller gain is:
Figure BDA0002895782310000118
the following was demonstrated:
selecting a Lyapunov function as
Figure BDA0002895782310000119
As shown in formula (21), V (x) > 0.
The closed loop system is recorded as
Figure BDA00028957823100001110
Wherein the content of the first and second substances,
Figure BDA00028957823100001111
then
Figure BDA00028957823100001112
Due to DeltaTDelta ≦ I, further obtainable from the above formula
Figure BDA0002895782310000121
Namely, it is
Figure BDA0002895782310000122
Wherein
Figure BDA0002895782310000123
Order to
Figure BDA0002895782310000124
The above formula is equivalent to
Figure BDA0002895782310000125
By the formula (22)To obtain
Figure BDA00028957823100001210
According to the Lyapunov stability theory, the closed-loop system is asymptotically stable to all uncertain parameters under the action of the controller. Further, by combining the properties of the predetermined performance method, it can be known
Figure BDA0002895782310000126
Namely, it is
Figure BDA0002895782310000127
The system state converges to a steady state value.
After the syndrome is confirmed.
And (V) solving the gain of the controller by utilizing the SOS technology.
The solvability conditions of the robust controller translate into SOS planning problems. One possible solution for robust controllers can be obtained by stools based on MATLAB. The method comprises the following specific steps: 1) loading a model of the turbofan engine; 2) initializing SOS items and declaring variables; 3) defining variables in the form of an SOS matrix; 4) adding constraints of the formula (21) and the formula (22); 5) calling a SeDuMi solver; 6) obtaining a set of feasible solutions
Figure BDA0002895782310000128
And L (x); 7) according to
Figure BDA0002895782310000129
And obtaining a robust controller.
In this embodiment, λ in the fourth step is taken1＝λ2＝10-6，kR0.01. The robust controller solved with the SOS toolset was K ═ 1.4768, -8.8194; 0.1128,0.2726]。
FIG. 5 is a state quantity x of a turbofan engine transitioning from a throttled state to an intermediate state under external disturbances2Error x of2errCurve over time. FIG. 6 is a state quantity x of a turbofan engine transitioning from a throttled state to an intermediate state under external disturbances2The convergence curve of (1). FIG. 7 is a graph of turbofan engine transitioning from a throttled state to an intermediate state under external disturbancesConvergence curve of the state quantity pi. In conclusion, the turbofan engine transition state disturbance suppression method based on the preset performance is effective and feasible, well suppresses external disturbance borne by a turbofan engine system, has universality, and can be applied to transition state control rule optimization of other types of engines. According to the invention, when external disturbance exists, the transition state control system of the turbofan engine normally operates, and each performance index reaches the preset effect, so that disturbance suppression in transition state control of the turbofan engine is realized.
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be made by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.

Claims (2)

1. The turbofan engine transition state disturbance suppression method based on the preset performance is characterized by comprising the following steps of:
step 1, designing a performance function rho of the rotating speed of the high-pressure rotor according to given performance indexes2(t) and let the performance function rho of the low pressure rotor speed of the turbofan engine1(t) Performance function ρ equal to the high pressure rotor speed2(t); wherein:
Figure FDA0002895782300000011
step 2, based on the performance function rho of the low-pressure rotor rotating speed in the step 11(t) and Performance function ρ of high pressure rotor speed2(t) constructing a preset performance parameter matrix R (x, t), wherein:
Figure FDA0002895782300000012
step 3, designing solvability conditions of the state feedback gain matrix K (x) based on the preset performance parameter matrix R (x, t) constructed in the step 3, namely:
Figure FDA0002895782300000013
step 4, solving solvability conditions of the state feedback gain matrix K (x) designed in the step 3 by utilizing an SOS technology to obtain solving process parameters of the first controller
Figure FDA0002895782300000014
And the second controller solving for a process parameter l (x);
step 5, solving process parameters by using the first controller obtained in the step 4
Figure FDA0002895782300000015
And the second controller solving for the process parameter l (x) calculating a state feedback gain matrix k (x), wherein:
Figure FDA0002895782300000016
step 6, designing a state feedback controller based on preset performance based on the state feedback gain matrix k (x) obtained in step 5, that is:
u(t)＝K(x)x(t)-kRR(x,t)x(t)
and 7, controlling the turbofan engine based on the state feedback controller based on the preset performance designed in the step 6, namely:
Figure FDA0002895782300000017
in the above formula: rho1(t) is a performance function of the low pressure rotor speed, ρ2(t) is a performance function of the speed of the high-pressure rotor, x2(0) Is an initial value of the high-pressure rotor speed of the turbofan engine1When there is no disturbanceA dynamic overshoot threshold for the high pressure rotor speed,
Figure FDA00028957823000000210
for disturbances of the rotational speed of the high-pressure rotor, σ2For dynamic overshooting of the speed of rotation of the high-pressure rotor in the presence of disturbances, x2eSteady state value, rho, representing the high pressure rotor speed of a turbofan engine2∞≤x2eδ1，
Figure FDA0002895782300000021
δ1Is a steady state error threshold value of the rotating speed of the high-pressure rotor, a is a constant, T1Is a step response time constant;
r (x, t) is a preset performance parameter matrix,
Figure FDA0002895782300000022
is the state error of the low-pressure rotor rotating speed,
Figure FDA0002895782300000023
the state error of the high-pressure rotor rotating speed;
k (x) is a state feedback gain matrix,
Figure FDA0002895782300000024
the process parameters are solved for the first controller,
Figure FDA0002895782300000025
for a given positive polynomial, I is an appropriately dimensioned identity matrix, phiSOSSet of SOS polynomials, Ψ1As an intermediate parameter, E1Is a first adaptive constant matrix, λ2(x) For a given positive polynomial, A (x)2) Is a state matrix, B (x)2) For the input matrix, L (x) solves for the process parameter, k, for the second controllerRTo be adjustable factor, xhIs Ah(x2) State of (1), Ah(x2) Is A (x)2) H line of (1), x is the system state, F1Is a matrix of second dimension-appropriate constants,j is B (x)2) A row number set of all-zero middle rows;
x (t) is the system state, x (t) [. x ]1(t) x2(t)]T，x1(t) is the low pressure rotor speed, x, of the turbofan engine2(t) the high pressure rotor speed of the turbofan engine;
Figure FDA0002895782300000026
is the first derivative of the system state, Δ is the uncertainty matrix, u (t) is the system input to the turbofan engine, u (t) is [ u (t) ]1(t) u2(t)]T，u1(t) is the main fuel flow of the turbofan engine, u2(t) throat area of turbofan engine, z (t) system output, C (x)2) Is an output matrix.
2. The method for suppressing transient disturbance of turbofan engine based on preset performance as claimed in claim 1, wherein in step 1, the given performance index of the system comprises:
high pressure rotor speed x for turbofan engine2(t) its control performance index should meet the requirement that the steady state error is not greater than its steady state error threshold delta1Dynamic overshoot not greater than its dynamic overshoot threshold σ1And the step response time is not greater than its step response time threshold T1Namely:
Figure FDA0002895782300000027
for the nozzle pressure ratio pi (t) of the turbofan engine, the control performance index of the turbofan engine meets the condition that the steady state error is not more than the steady state error threshold value delta (t)2Namely:
Figure FDA0002895782300000028
high pressure in the presence of high pressure rotor speed disturbances of turbofan enginesDynamic overshoot of rotor speed less than its dynamic overshoot threshold sigma2And the suppression of the disturbance can be realized, namely:
Figure FDA0002895782300000029
wherein: x is the number of2(0) For high-pressure rotor speed x of turbofan engine2Initial value of (t), x2(∞) is high-pressure rotor speed x of turbofan engine2End value of (t), x2eSteady state value, x, representing the speed of the high pressure rotor of a turbofan engine2(tp) For high-pressure rotor speed x of turbofan engine2(t) at the overshoot instant tpThe value of (a) is,
Figure FDA0002895782300000031
step response time of the rotating speed of the high-pressure rotor; pi (∞) is the final value of the nozzle pressure ratio, pieIs the steady state value of the pressure ratio of the spray pipe; x is the number of2ω(t) high pressure rotor speed x of turbofan engine due to disturbance2(t) amount of change, x2ω(tp) High-pressure rotor speed x of turbofan engine for disturbance2(t) at the overshoot instant tpThe amount of change in (c).
CN202110040824.1A 2021-01-13 2021-01-13 Turbofan engine transition state disturbance suppression method based on preset performance Active CN112859606B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110040824.1A CN112859606B (en) 2021-01-13 2021-01-13 Turbofan engine transition state disturbance suppression method based on preset performance

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110040824.1A CN112859606B (en) 2021-01-13 2021-01-13 Turbofan engine transition state disturbance suppression method based on preset performance

Publications (2)

Publication Number Publication Date
CN112859606A CN112859606A (en) 2021-05-28
CN112859606B true CN112859606B (en) 2022-03-11

Family

ID=76003222

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110040824.1A Active CN112859606B (en) 2021-01-13 2021-01-13 Turbofan engine transition state disturbance suppression method based on preset performance

Country Status (1)

Country Link
CN (1) CN112859606B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115128966A (en) * 2022-04-11 2022-09-30 厦门大学 Design method and simulation method of turbofan engine full-envelope controller

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101230802A (en) * 2006-12-06 2008-07-30 通用电气公司 Variable coupling of high pressure rotor and low pressure rotor of turbofan engine
CN106681148A (en) * 2017-01-10 2017-05-17 南京航空航天大学 Design method of aeronautical engine integral tangent fuzzy self - adaptive sliding mode controller
CN107100741A (en) * 2017-05-08 2017-08-29 南京航空航天大学 A kind of method and its system for improving fanjet control system performance
CN109441644A (en) * 2018-12-11 2019-03-08 大连理工大学 A kind of fanjet stable state transition state multi-variant control method based on active disturbance rejection theory
CN111177930A (en) * 2019-12-31 2020-05-19 厦门大学 Aeroengine system identification modeling method based on mixed sequence
CN113075882A (en) * 2021-03-25 2021-07-06 浙江大学 Turbofan engine multivariable robust variable gain control method based on non-equilibrium state linearization

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101230802A (en) * 2006-12-06 2008-07-30 通用电气公司 Variable coupling of high pressure rotor and low pressure rotor of turbofan engine
CN106681148A (en) * 2017-01-10 2017-05-17 南京航空航天大学 Design method of aeronautical engine integral tangent fuzzy self - adaptive sliding mode controller
CN107100741A (en) * 2017-05-08 2017-08-29 南京航空航天大学 A kind of method and its system for improving fanjet control system performance
CN109441644A (en) * 2018-12-11 2019-03-08 大连理工大学 A kind of fanjet stable state transition state multi-variant control method based on active disturbance rejection theory
CN111177930A (en) * 2019-12-31 2020-05-19 厦门大学 Aeroengine system identification modeling method based on mixed sequence
CN113075882A (en) * 2021-03-25 2021-07-06 浙江大学 Turbofan engine multivariable robust variable gain control method based on non-equilibrium state linearization

Non-Patent Citations (8)

* Cited by examiner, † Cited by third party
Title
Estimate of the domain of attraction for polynomial systems using bisectional sum-of-squares optimization;Linhong Lu 等;《Proceedings of the 37th Chinese Control Conference》;20180727;全文 *
Observer-based control for nonlinear parameter-varying systems: A sum-of-squares approach;Pingfang Zhu 等;《ISA Transactions》;20201231;全文 *
基于多项式平方和规划的涡扇发动机切换控制;孙昊博 等;《航空发动机》;20181231;全文 *
涡扇发动机的一类大包线系统建模;凌彦聪 等;《南京航空航天大学学报》;20210831;全文 *
涡扇发动机线性变参数控制方法研究;孙昊博;《CNKI》;20180331;全文 *
涡扇发动机自适应加减速控制研究;王曦;《航空发动机》;20210430;全文 *
航空发动机过渡状态线性变参数控制研究;张弛;《CNKI》;20171231;全文 *
非线性变参数系统控制及其应用;付荣;《CNKI》;20181231;全文 *

Also Published As

Publication number Publication date
CN112859606A (en) 2021-05-28

Similar Documents

Publication Publication Date Title
US11454177B2 (en) Method of aero-engine on-line optimization and multivariable control based on model prediction
Bao et al. Switching control of thrust regulation and inlet buzz protection for ducted rocket
Richter Multiple sliding modes with override logic: Limit management in aircraft engine controls
CN112859606B (en) Turbofan engine transition state disturbance suppression method based on preset performance
Lv et al. Recent research progress on airbreathing aero-engine control algorithm
Qi et al. State-based switching control strategy with application to aeroengine safety protection
CN111731490B (en) Helicopter comprehensive control method and device with variable rotor rotation speed
CN112483261B (en) Method for resisting stress application disturbance of aircraft engine
Hu et al. System analysis and controller design for the electric pump of a deep-throttling rocket engine
CN114237029B (en) Turbofan engine acceleration process control method and device based on active switching logic
Kolmanovsky et al. Developments in constrained control using reference governors
Li et al. Sliding mode control of systems with delayed states and controls
CN111255574A (en) Autonomous control method for thrust recession under inlet distortion of aircraft engine
Lv et al. Fast nonsingular fixed-time fuzzy fault-tolerant control for HFVs with guaranteed time-varying flight state constraints
CN112594069A (en) Turboshaft engine anti-interference control method and device based on power demand prediction
Han et al. Robust approximate optimal control for air‐breathing hypersonic vehicle
CN115981156A (en) Aeroengine active limit protection control method under time-varying output constraint
CN114637210A (en) Multi-loop comprehensive control method and system for aircraft engine
Abdelbaky et al. Stable economic model-predictive control for TS fuzzy systems with persistent disturbances
Le Brun et al. Control laws design of a turboprop engine
Kumon et al. Robust attitude control of vectored thrust aerial vehicles
CN103823377A (en) Design method for longitudinal flight model cluster flutter-restraining composite root-locus compensation robust controller
Gangopadhyay et al. Multivariable pi tuning and application to engine idle speed control
CN114625001A (en) Aero-engine limit protection control method based on multi-mode instruction regulator
Zhang et al. Research on improved aero-engine Min-Max controller method based on coordination function

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant