CN115128966A - Design method and simulation method of turbofan engine full-envelope controller - Google Patents
Design method and simulation method of turbofan engine full-envelope controller Download PDFInfo
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Abstract
The application provides a design method of a turbofan engine full-envelope controller, which comprises the following steps: s1, establishing an NPV model of the turbofan engine, wherein the NPV model comprises external disturbance, and converting the NPV model into an uncertain model according to the external disturbance; s2, designing a robust controller of a large envelope curve S3 based on the uncertain model, and designing a preset performance parameter matrix in the robust controller of the large envelope curve according to the performance index requirement of a turbofan engine closed-loop system; s4, solving a state feedback gain matrix in the robust controller of the large envelope curve by utilizing an SOS technology, thereby solving the robust controller of the large envelope curve; s5, designing a PI controller of the turbofan engine in a throttling state, and combining the PI controller and the large-envelope linear robust controller into the full-envelope controller by using a switching module. The full-envelope controller can better adapt to the non-linear model of the turbofan engine, so that the full-envelope controller has better control stability.
Description
Technical Field
The application relates to the technical field of aero-engine control, in particular to a design method and a simulation method of a turbofan engine full-envelope controller.
Background
Turbofan engines are widely applied to the fields of national defense and civil use at present due to the advantages of large thrust, high propulsion efficiency and the like. However, as the flight parameters and internal parameters of the turbofan engine can be changed in a large range and the mechanical structure of the engine is complex, the aerodynamic thermodynamic behavior of the turbofan engine system is complex, and the turbofan engine system has significant nonlinearity, time variation, strong coupling and uncertainty, which brings great challenges to the design of the full-envelope controller of the turbofan engine.
In an active turbofan engine control system, a gain scheduling scheme is mostly adopted for designing a full-envelope controller. And the gain is adjusted on line through the controller to adapt to the nonlinearity and parameter change characteristics of the system. However, the simple gain scheduling lacks the theoretical tightness, and the effectiveness of the control effect depends on a large number of foundation and control flight simulation experiments. And the parameters of the controller are changed in an open loop mode, and when the scheduling variables change rapidly and the nonlinear characteristics of the controlled object are difficult to capture, the stability of the system is difficult to guarantee. With the development and improvement of nonlinear system modeling methods, linear parameter-varying (LPV) models for nonlinear system control have come into force. However, the LPV model is only a first-order approximation of the original system at the corresponding operating point, and cannot reflect the complete dynamics of the system. Nonlinear parameter-varying (NPV) models can describe time-varying and nonlinear dynamics of a controlled object. On one hand, the model makes up the deficiency of LPV in describing the nonlinear characteristic of the controlled object, and on the other hand, by taking the realization that Prajna represents a nonlinear system as a state-dependent linear system, the nonlinear time-varying problem can be processed by means of a mature tool. On the basis, a performance analysis method and a control design theory of the nonlinear time-varying system are established, and the problems related to control of the turbofan engine can be effectively solved.
Based on the background, the design method and the simulation method of the turbofan engine full-envelope controller are provided, aiming at the problem of controlling the turbofan engine full-envelope in a stable state and a transition state, the full-envelope robust nonlinear controller is designed based on a full-digital simulation platform of the turbofan engine, and the closed-loop system is guaranteed to meet the expected performance index under the full-envelope flight condition and has good robustness.
Disclosure of Invention
In order to solve the technical problem that the control stability of the turbofan engine full-wrap controller in the prior art is poor, the application provides a design method and a simulation method of the turbofan engine full-wrap controller.
According to a first aspect of the present application, a method for designing a turbofan engine full envelope is provided, comprising the steps of:
s1, establishing an NPV model of the turbofan engine, wherein the NPV model comprises external disturbance, and converting the NPV model into an uncertain model according to the external disturbance;
s2, designing a robust controller of the large covered wire based on the uncertain model;
s3, designing a preset performance parameter matrix in the large envelope robust controller according to the performance index requirement of the turbofan engine closed-loop system;
s4, solving a state feedback gain matrix in the robust controller of the large envelope curve by utilizing an SOS technology, thereby solving the robust controller of the large envelope curve;
s5, designing a PI controller of the turbofan engine in a throttling state, and combining the PI controller and the large package wire robust controller into the full package wire controller by using a switching module, so that the PI controller is used by the turbofan engine in the throttling state, and the large package wire robust controller is switched to be used by the switching module in other states.
According to the technical scheme, aiming at the problems of control over the full-envelope steady state and the transition state of the turbofan engine, the full-envelope controller is combined by designing the large-envelope robust controller and the PI controller, the turbofan engine control system adopts a PI-PP (proportional-Integral and proportional-Performance) mixed control strategy, namely the PI controller is used by the turbofan engine in a throttling state, the large-envelope robust controller is used by the other flight states, and the Performance index of the control system is converted into the design index of the controller based on a preset Performance method, so that the controller is better adapted to the engine nonlinear model, and the control stability is better.
Preferably, the NPV model including the external disturbance specifically includes:
wherein x ∈ R n Is the system state, u ∈ R n Is a control input, rho (t) is ∈ R s Is a time-varying parameter vector, A (-), B (-), and C (-,) are polynomial matrices about x and ρ (t), ω (t) is an external perturbation, E 1 Is a constant matrix of suitable dimensions;
the uncertain model is specifically as follows:
wherein, Δ F 1 x (t) is the transformed external disturbance, Δ is the uncertainty matrix, satisfies Δ T △≤I， F 1 I is a constant matrix and an identity matrix of suitable dimensions, respectively, satisfying F 1 T F 1 ≥0。
Preferably, the expression of the robust controller for the large envelope line is specifically as follows:
wherein,
is the state feedback gain matrix, k, to be designed R Is the adjustable coefficient of the linear motion vector,
is to be provided withAnd designing a preset performance parameter matrix.
Through the technical scheme, as can be seen from the formula, only a proper preset performance parameter matrix is selected
The turbofan engine closed loop system can meet the problem of a given performance index.
Preferably, the performance index requirements of the turbofan engine are specifically: the high-pressure rotor rotating speed control steady-state error, the dynamic overshoot, the step response time, the spray pipe closed-loop control pressure ratio steady-state error and the rotating speed dynamic overshoot under the high-pressure rotor rotating speed disturbance of the turbofan engine closed-loop system are all within a preset threshold value;
the design process of the preset performance parameter matrix specifically comprises the following steps: based on the preset performance parameter matrix to be designed, performing difference operation on a value of a system state at any moment and a preset expected value to obtain a state error, introducing a performance function, defining an error transformation function, and designing to obtain the preset performance parameter matrix, wherein an expression of the preset performance parameter matrix specifically comprises:
wherein the continuous function T is defined as an error transformation function T i (x,t)，
For the state error, rho, of the turbofan engine closed-loop system i (t) is the introduced performance function.
Through the technical scheme, the preset performance parameter matrix is constructed by introducing the performance function and defining the error transformation function.
Preferably, the solving process of the state feedback gain matrix specifically includes:
designing solvability conditions of the state feedback gain matrix to be designed, wherein an expression specifically comprises the following steps:
wherein,
and
is given a positive number,. phi SOS For the set of SOS polynomials to be,
solving solvability conditions of the state feedback gain matrix to be designed by utilizing an SOS technology to obtain the state feedback gain matrix, wherein an expression of the state feedback gain matrix is specifically as follows:
according to the technical scheme, the SOS technology is utilized to solve and obtain the state feedback gain matrix according to the constructed preset performance parameter matrix.
Preferably, the control law expression of the PI controller is specifically:
wherein, K p And T i Is constant, e (t) is the systematic error.
Preferably, the control law expression of the full-envelope controller is specifically:
wherein, PLA is throttle lever angle, and V is the constant.
According to the technical scheme, the large-envelope-line NPV model of the turbofan engine has no characteristic of a low working state, and the large-envelope-line robust controller designed based on the NPV model has poor control effect below a throttling state, so that the turbofan engine adopts the PI controller in the throttling state, the PI controller is a classical control algorithm, a control deviation is formed according to a given value and an actual output value, and the proportion and integral of the deviation are linearly combined to form a control quantity to control a controlled object.
According to a second aspect of the present application, a simulation method for a turbofan engine full-envelope controller is provided, which simulates the full-envelope controller in the above design method, and includes the following steps:
a) building the full-envelope controller on a full-digital simulation platform;
b) optimizing the full-envelope controller by adopting a gain parameter adjusting method;
c) performing full-digital simulation on the optimized full-envelope controller;
wherein, the step b) specifically comprises the following steps:
b1) determining a plurality of typical working points according to the flight altitude and the Mach number of the turbofan engine, and selecting the parameters in the full wrap controller by adopting a grid search method under different typical working points and different working states so as to optimize the dynamic performance of the turbofan engine closed loop system, thereby realizing the tuning of the parameters;
b2) and combining and setting the parameters by adopting a linear interpolation method, so that the turbofan engine closed-loop system meets the performance index requirements at all working points, and is synthesized into the variable-gain full-envelope controller.
By the technical scheme, aiming at the strong nonlinear characteristics of the turbofan engine nonlinear component model, parameters of the controller at different working points are adjusted by a gain parameter adjusting method, so that the controller is better adapted to the engine nonlinear model, and the control effect is further improved.
Preferentially, the control law expression of the full-envelope controller to be optimized in the step b) is specifically as follows:
wherein, K u ，K 1 ，K R ，K p ，T i Is a parameter to be set.
Through the technical scheme, the parameters of the full-envelope controller are set by a gain parameter adjusting method under different typical working points, so that the designed full-envelope controller has better robustness on unmodeled dynamics on the basis that the performance of the turbofan engine closed-loop system meets the given control effect.
Preferably, the method further comprises the following steps: and performing steady-state experiments and dynamic experiments on the full-envelope controller on a ring platform and a semi-physical platform in a hardware mode.
Through the technical scheme, the hardware-in-loop simulation system has the real I/O interface, the controller hardware equipment and the virtual controlled object model, and is a control algorithm test and verification means with higher confidence. The semi-physical simulation has a real oil circuit system, can carry out synthesis and experimental verification on a controller, a hydraulic mechanical system and related sensors, and has higher vividness compared with hardware-in-the-loop simulation.
The application provides a design method and a simulation method of a turbofan engine full-envelope controller, aiming at the problem of turbofan engine full-envelope steady-state and transition-state control, the full-envelope robust nonlinear controller is designed based on a turbofan engine full-digital simulation platform, and the closed-loop system is guaranteed to meet expected performance indexes under the full-envelope flight condition and has good robustness. The turbofan engine control system adopts a PI-PP hybrid control strategy, namely a PI controller is used in a throttling state, and a large envelope linear robust controller is used in the rest flight states. The control system converts the performance index of the system into the design index of the controller based on a preset performance method, and adjusts the parameters of the controller at different typical working points by using a gain parameter adjusting method, so that the controller is better adapted to the nonlinear model of the engine. Simulation experiments are carried out on a full-digital simulation platform, a Hardware-in-the-Loop (HIL) platform and a semi-physical platform by the designed full-wrap controller, and simulation results show that the designed controller can ensure that the system has global stability in a full-wrap range, meet given performance indexes and has good robustness.
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The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments and together with the description serve to explain the principles of the application. Other embodiments and many of the intended advantages of embodiments will be readily appreciated as they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale relative to each other. Like reference numerals designate corresponding similar parts.
FIG. 1 is a flow chart of a design method of a turbofan engine full-envelope controller according to an embodiment of the application;
FIG. 2 is a block diagram of a turbofan engine control system according to an embodiment of the present application;
FIG. 3 is a flow chart of a simulation method of a turbofan engine full-envelope controller according to an embodiment of the application;
FIG. 4 is a schematic diagram illustrating a main structural division of an all-digital simulation platform according to an embodiment of the present application;
FIG. 5 is a block diagram of a full-envelope controller for primary fuel quantity according to one embodiment of the present application;
FIG. 6 is a block diagram of a full-envelope controller of throat area according to a specific embodiment of the present application;
FIG. 7 is a graph of a given PLA variation with a turbofan engine in a throttled state according to one embodiment of the present application;
FIG. 8 is a diagram of a given PLA variation in a turbofan engine in an intermediate state according to a particular embodiment of the present application;
FIG. 9 is a graph of a given PLA variation when the turbofan engine is in an energized state according to one embodiment of the present application;
FIG. 10 is a graph of turbofan engine in-envelope fly height, Mach number, and throttle lever angle versus time in accordance with an embodiment of the present application;
FIG. 11 is a graph illustrating a variation in the speed of a high pressure rotor obtained from a flight trajectory simulation experiment according to an embodiment of the present application;
FIG. 12 is a graph illustrating engine pressure ratio changes from flight trajectory simulation experiments in accordance with an exemplary embodiment of the present application;
FIG. 13 is a plot of high pressure rotor speed versus operating point (0, 0) throttle for a single-condition simulation experiment in accordance with an exemplary embodiment of the present application;
FIG. 14 is a plot of high pressure rotor speed at an intermediate operating point (0, 0) during a single-condition simulation experiment in accordance with an exemplary embodiment of the present application;
FIG. 15 is a plot of the speed of the high pressure rotor as simulated at the operating point (0, 0) with force applied during a single-condition simulation experiment in accordance with an exemplary embodiment of the present application;
FIG. 16 is a graph of engine pressure ratio curves simulated at an intermediate operating point (0, 0) for a single-condition simulation experiment according to an embodiment of the present application;
FIG. 17 is a graph of engine pressure ratio curves simulated at operating point (0, 0) force application for a single-condition simulation experiment according to an embodiment of the present application.
Detailed Description
Features and exemplary embodiments of various aspects of the present application will be described in detail below, and in order to make objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail below with reference to the accompanying drawings and the embodiments. It should be understood that the specific embodiments described herein are merely illustrative of and not restrictive on the broad application. It will be apparent to one skilled in the art that the present application may be practiced without some of these specific details. The following description of the embodiments is merely intended to provide a better understanding of the present application by illustrating examples thereof.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. The term "comprising", without further limitation, means that the element so defined is not excluded from the list of additional identical elements in a process, method, article, or apparatus that comprises the element.
According to a first aspect of the application, a design method of a turbofan engine full-envelope controller is provided.
The design method of the turbofan engine full-envelope controller is described below by taking a certain type of low bypass ratio double-shaft turbofan engine as a research object.
Fig. 1 shows a flowchart of a design method of a turbofan engine full-envelope controller according to an embodiment of the application, and as shown in fig. 1, the design method includes the following steps:
s1, establishing an NPV model of the turbofan engine, wherein the NPV model comprises external disturbance, and converting the NPV model into an uncertain model according to the external disturbance.
In a specific embodiment, consider an NPV model of a turbofan engine in the form of the following state variables:
wherein x ∈ R n Is the system state, u ∈ R n Is a control input, rho (t) is ∈ R s Is a time-varying parameter vector, A (-), B (-), and C (-), are polynomial matrices for x and ρ (t), n L At low rotor speed, n H At high rotor speed, W f A main amount of fuel, A 8 The area of the throat. a is ij ，b ij And c ij (i, j ═ 1, 2) the detailed expression is as follows:
a 11 ＝-0.01452H 3 +0.1052H 2 +0.7103H-3424.0n H 3 -10270.0n H 2 n Href +10010.0n H 2 -10270.0n H n Href 2 +20010.0n H n Href -9708.0n H -3424.0n Href 3 +10010.0n Href 2 -9708.0n Href -4.357Ma+3123.0
a 12 ＝2.038Ma-0.8023H+200.5W fref +42500.0A 8ref -9708.0n Lref -5998.0n Href -413.6W fref n Href -88810.0A 8ref n Href +20010.0n Lref n Href +0.007449H 2 +0.006477H 3 +212.1W fref n Href 2 +46220.0A 8ref n Href 2 -10270.0n Lref n Href 2 +n H 2 (70.71W fref +15410.0A 8ref -3424.0n Lref -4646.0n Href +3241.0)-1162.0n H 3 -1.0n H (206.8W fref +44410.0A 8ref -10010.0n Lref -9724.0n Href -212.1W fref n Href -46220.0A 8ref n Href +10270.0n Lref n Href +6969.0n Href 2 +2999.0) +9724.0n Href 2 -4646.0n Href 3 +924.8
a 21 ＝-0.01538H 3 +0.1659H 2 -0.5276H-817.5n H 3 -2452.0n H 2 n Href +2347.0n H 2 -2452.0n H n Href 2 +4695.0n H n Href -2239.0n H -817.5n Href 3 +2347.0n Href 2 -2239.0n Href +1.359Ma+708.5
a 22 ＝1.121H-2.098Ma-204.3W fref -11090.0A 8ref -2239.0n Lref +10980.0n Href +430.8W fref n Href +23540.0W fref n Href +4695.0n Lref n Href -1.0nH 2 (75.66W fref +4148.0A 8ref +817.5n Lref -8143.0n Href +5802.0)-0.3035H 2 +0.0255H 3 -227.0W fref n Href 2 -12440.0A 8ref n Href 2 -2452.0n Lref n Href 2 +n H (215.4W fref +11770.0A 8ref +2347.0n Lref -17400.0n Href -227.0W fref n Href -12440.0A 8ref n Href -2452.0n Lref n Href +12210.0n Href 2 +5489.0)+2036.0n H 3 -17400.0n Href 2 +8143.0n Href 3 -1726.0
b 11 ＝0.0002945H 3 -0.00616H 2 +0.01127H+70.71n H 3 +212.1n H 2 n Href -206.8n H 2 +212.1n H n Href 2 -413.6n H n Href +200.5n H +70.71n Href 3 -206.8n Href 2 +200.5n Href +0.1605Ma-64.06
b 12 ＝0.01606H 3 -0.2997H 2 +0.6669H+15410.0n H 3 +46220.0n H 2 n Href -44410.0n H 2 +46220.0n H n Href 2 -88810.0n H n Href +42500.0n H +15410.0n Href 3 -44410.0n Href 2 +42500.0n Href +5.999Ma-13510.0
b 21 ＝-0.0003558H 3 +0.003819H 2 -0.005397H-75.66n H 3 -227.0n H 2 n Href +215.4n H 2 -227.0n H n Href 2 +430.8n H n Href -204.3n H -75.66n Href 3 +215.4n Href 2 -204.3n Href -0.01056Ma+64.74
b 22 ＝-0.03469H 3 +0.4663H 2 -2.014H-4148.0n H 3 -12440.0n H 2 n Href +11770.0n H 2 -12440.0n H n Href 2 +23540.0n H n Href -11090.0n H -4148.0n Href 3 +11770.0n Href 2 -11090.0n Href +2.938Ma+3470.0
c 21 ＝0.01922H 3 -0.1625H 2 +0.155H+5873.0n H 3 +17620.0n H 2 n Href -17030.0n H 2 +17620.0n H n Href 2 -34060.0n H n Href +16390.0n H +5873.0n Href 3 -17030.0n Href 2 +16390.0n Href -0.03688Ma-5236.0
c 22 ＝16390.0n Lref -0.04604Ma-0.1191H-31400.0n Href -34060.0n Lref n Href +n H 2 (5873.0n Lref -22530.0n Href +16320.0)+0.1541H 2 -0.0185H 3 +17620.0n Lref n Href 2 -5633.0n H 3 +48960.0n Href 2 -22530.0n Href 3 -1.0n H (17030.0n Lref -48960.0n Href -17620.0n Lref n Href +33800.0n Href 2 +15700.0)+5011.0
wherein n is Href Indicating a desired value, n, of the speed of the high-pressure rotor Lref Indicating desired value, W, of low-pressure rotor speed fref Is the desired value of the main fuel quantity, A 8ref The expected value of the throat area is shown, H the altitude of flight and Ma the mach number.
Introducing external disturbance on the basis of the NPV model, and establishing the NPV model containing the external disturbance:
where ω (t) is an external disturbance, in this embodiment, ω (t) is 0.1 (n) Href -n H (0))sint， n Href ＝0.9437，n H (0)＝0.8632。E 1 Is a constant matrix of suitable dimensions.
Let ω (t) be Δ F 1 x (t). Delta is an uncertainty matrix satisfying Delta T △≤I。F 1 I is a constant matrix and an identity matrix of suitable dimensions, respectively, satisfying F 1 T F 1 Is more than or equal to 0. Thus, the external disturbance ω (t) translates into uncertainty of the system structure. Then, the NPV model containing the external perturbation is transformed into an uncertain model as follows:
with continued reference to fig. 1, after step S1,
and S2, designing a robust controller of the large envelope wire based on the uncertain model.
In a specific embodiment, for the uncertain model, a robust controller of the large envelope line based on a preset performance method is designed, and the shape is as follows:
wherein,
is the state feedback gain matrix, k, to be designed R Is the adjustable coefficient of the linear motion vector,
is a preset performance parameter matrix to be designed.
With continued reference to fig. 1, after step S2,
s3, designing a preset performance parameter matrix in the large package linear robust controller according to the performance index requirement of the turbofan engine closed-loop system.
In a specific embodiment, the performance presetting method is to design a large envelope linear robust controller by enabling a turbofan engine closed-loop system to meet the preset performance index requirement. The preset performance method is to make the system meet the expected performance index by limiting the maximum overshoot of the dynamic response of the system, the convergence speed and the steady-state error of the system. As can be seen from the expression of the large envelope linear robust controller, only the proper preset performance parameter matrix is selected
The closed loop system can be made to meet the problem of a given performance index.
In this embodiment, the performance index that the turbofan engine closed loop system should satisfy is: high-pressure rotor speed control steady-state error of turbofan engine is not more than delta 1 Small dynamic overshootAt sigma 1 Step response time
Not more than T 1 . The steady state error of the closed-loop control pressure ratio of the spray pipe is not more than delta 2 . At high rotor speed disturbances
The dynamic overshoot of the rotation speed is not more than sigma 2 Namely:
wherein n is H (0),n H In which n represents the initial and final values of the speed of the high-pressure rotor Href Indicating desired value, t, of high-pressure rotor speed p Representing the overshoot time, [ pi ] (∞) representing the final value of the nozzle pressure ratio, [ pi ] ref Indicating the desired value of the nozzle pressure ratio, delta 1 、σ 1 、T 1 、δ 2 And σ 2 Which are the preset thresholds of the performance indexes in this embodiment. In this embodiment, take δ 1 ＝0.1％，σ 1 ＝1％，T 1 ＝4s，δ 2 ＝0.5％，σ 2 ＝1％。
The design process of the preset performance parameter matrix specifically comprises the following steps: and based on a preset performance parameter matrix to be designed, carrying out difference operation on a value of the system state at any moment and a preset expected value to obtain a state error, introducing a performance function, defining an error transformation function, and designing to obtain the preset performance parameter matrix. The design process is as follows:
error of set state
Setting transient and steady state performance of the state error by introducing a performance function so as to meet the following inequality constraints:
where ρ is i (t) is the introduced performance function, t ∈ [0, ∞);
the performance function for a given exponential convergence is as follows:
wherein, γ i ＞0，ρ i (0) Representing the initial error bound, p i (∞) represents the maximum state error allowed at steady state.
Designing a performance function of the high-pressure rotor rotating speed according to given performance indexes:
and let the performance function rho of the low-pressure rotor speed 1 (t)＝ρ 2 (t) of (d). Where ρ is 2 (∞)≤n Href δ 1 ，
α is a constant, T 1 Is a step response time constant.
In this embodiment, take ω H ＝max{0.1(n Href -n H (0))sint}＝0.00805，α＝1，
According to the calculation, the following results are obtained:
ρ 1 (0)＝ρ 2 (0)＝0.08，γ 1 ＝γ 2 ＝1.73，ρ 1 (∞)＝ρ 2 (∞)＝10 -3
as a result of this, it is possible to,
ρ i (t)＝0.079e -1.73t +0.001
defining the continuous function T as an error transformation function if the following condition is satisfied:
1)
2)
then, the given error transformation function is:
wherein, T i (x, t) is an error transformation function,
is the state error of the turbofan engine closed loop system.
Then, the preset performance parameter matrix is:
in the present embodiment, it is preferred that,
with continued reference to fig. 1, after step S3,
and S4, solving a state feedback gain matrix in the robust controller of the large envelope curve by utilizing the SOS technology so as to solve the robust controller of the large envelope curve.
In a specific embodiment, the solvability condition of the state feedback gain matrix to be designed is designed, and the expression specifically is as follows:
wherein,
and
is given a positive number,. phi SOS For the set of SOS polynomials to be,
Solving state feedback matrix by SOS technology
The state feedback gain matrix obtained by the solvability condition of (a) is:
in this embodiment, take ε 1 ＝ε 2 ＝ε 3 ＝10 -6 ，k R 0.01. The robust controller for the large envelope curve obtained by solving by using the SOS tool kit in Matlab is as follows: k ═ K 11 ,k 12 ；k 21 ,k 22 ]Wherein
k 11 ＝0.07907n L 2 +1.124*10 -10 n L n H -1.631*10 -8 n L +0.000403n H 2 -17.55n H -10.21
k 12 ＝-0.3095n L 2 -4.398*10 -10 n L n H +6.369*10 -8 n L -0.001578n H 2 +115.4n H -44.61
k 21 ＝-0.0007736n L 2 -1.099*10 -12 n L n H +1.593*10 -10 n L -3.943*10 -6 n H 2 -0.04534n H +0.2149
k 22 ＝0.00412n L 2 +5.855*10 -12 n L n H -8.538*10 -10 n L +2.1*10 -5 n H 2 -0.5422n H +0.7073
with continued reference to fig. 1, after step S4,
s5, designing a PI controller of the turbofan engine in a throttling state, and combining the PI controller and the large-envelope-line robust controller into a full-envelope-line controller by using a switching module, so that the PI controller is used by the turbofan engine in the throttling state, and the large-envelope-line robust controller is switched to be used by the switching module in other states.
In a specific embodiment, the large envelope line robust controller designed based on the NPV model has poor control effect below the throttling state because the large envelope line NPV model of the turbofan engine has no characteristic of the low working state. Therefore, the throttle state is followed by a conventional PI controller. The PI control is a classical control algorithm, which forms a control deviation according to a given value and an actual output value, and linearly combines the proportion and the integral of the deviation to form a control quantity to control a controlled object. The control law expression of the PI controller is as follows:
wherein, K p And T i Is constant, e (t) is the systematic error. In this example, take K p ＝150，T i ＝1。
The designed large-envelope line robust controller and the PI controller are combined through a switching module, and in this embodiment, the switching module is specifically a switch. Therefore, a PI-PP hybrid control strategy is adopted, namely the turbofan engine is controlled by a traditional PI controller when the throttling state is lower than the throttling state, and a large-envelope robust controller is adopted when the throttling state is higher than the throttling state, so that the control effect of the turbofan engine closed-loop system under the full-envelope flight condition is finally ensured. The control law of the combined full-envelope controller is as follows:
wherein, PLA is the throttle lever angle, V is a constant, K R ，K p ，T i Is a parameter to be set. In this embodiment, V is 41.
Fig. 2 is a block diagram illustrating a control system of a turbofan engine according to an embodiment of the present application, as shown in fig. 2, the present application is implemented according to the following principle:
aiming at the problem of controlling the full-envelope steady state and the transition state of the turbofan engine, a large-envelope robust controller and a PI controller are designed, and a change-over switch is utilized to combine a full-envelope controller. The turbofan engine control system converts the performance index of the system into the design index of the full-envelope controller based on a preset performance method, so that the full-envelope controller is better adapted to the nonlinear model of the engine, and better control stability is achieved. The turbofan engine control system adopts a PI-PP hybrid control strategy, namely a PI controller is used in the turbofan engine in a throttling state, and large-envelope robust controllers are used in other flight states, so that the control effect of the turbofan engine closed-loop system under the full-envelope flight condition is finally ensured.
According to a second aspect of the present application, a simulation method of a turbofan engine full-envelope controller is provided, which is used for simulating a software portion and a hardware portion of the full-envelope controller.
Fig. 3 shows a flowchart of a simulation method of a turbofan engine full-envelope controller according to an embodiment of the present application, and as shown in fig. 3, the simulation method includes the following steps:
a) and constructing a full-envelope controller on a full-digital simulation platform.
In a specific embodiment, the all-digital simulation platform may employ Matlab or Simulink. In this embodiment, the all-digital simulation platform specifically uses Simulink, which can implement rapid modeling and simulation, and the encapsulated component-level real-time model generates a C code by using an automatic code generation function of the Simulink, and the generated code can be used for hardware-in-the-loop and semi-physical simulation verification.
Fig. 4 shows a schematic diagram of main structural division of an all-digital simulation platform according to an embodiment of the present application, and as shown in fig. 4, the all-digital simulation platform of a turbofan engine is an all-digital simulation performed on a real-time model of a turbofan engine component level, and mainly includes five modules, namely, a flight control command signal, a controller, an actuator, an engine, and an observation signal. The flight control instruction signal module can set the flight height (H), the Mach number (Ma) and the throttle lever angle (PLA) of the airplane so as to adjust the working state of the airplane; the controller is an implementation part of an engine control algorithm and ensures that the engine runs stably under a given working state.
Aiming at controlling the input main fuel quantity and the throat area, a corresponding PI control module is provided in the full digital simulation platform, and the closed-loop control below the throttling state is realized. On the basis, the large envelope linear robust controller designed in the first aspect of the application is substituted into a component-level model of the full-digital simulation platform for control, and stable operation of the turbofan engine system in a large envelope linear range is guaranteed. And then, switching different controllers by switching a switch, namely using a PI controller below a throttling state and using a robust controller of a large envelope line above the throttling state to form a full envelope line controller, so that the control effect of the closed-loop system under the full envelope line flight condition is ensured. FIG. 5 shows a block diagram of a full-envelope controller for primary fuel quantity according to an embodiment of the present application, and FIG. 6 shows a block diagram of a full-envelope controller for throat area according to an embodiment of the present application.
With continued reference to fig. 3, after step a),
b) and optimizing the full-envelope controller by adopting a gain parameter adjusting method.
Specifically, the step b) specifically comprises the following steps:
b1) determining a plurality of typical working points according to the flight altitude and the Mach number of the turbofan engine, and selecting parameters which enable the dynamic performance of a closed loop system of the turbofan engine to be optimal by adopting a grid search method for the parameters in the full wrap controller under different typical working points and different working states to realize parameter setting;
b2) and combining and setting parameters by adopting a linear interpolation method, so that the turbofan engine closed-loop system meets the performance index requirements at all working points, and is synthesized into the variable gain full-envelope controller.
In a specific embodiment, in order to further improve the control effect of the full-envelope controller, the full-envelope controller is adjusted and set under different typical working points based on a gain parameter adjusting methodAnd the parameters of the controller ensure that the designed full-envelope controller has better robustness to unmodeled dynamics on the basis that the performance of the closed-loop system meets the given control effect. Adding an adjustable parameter K u 、K 1 Then, the control law of the full-envelope controller to be optimized is:
wherein, K u And K 1 And the same parameter is to be set.
In a specific embodiment, five exemplary operating points are selected according to the altitude H and the mach number Ma, i.e., (0, 0), (8, 1.2), (3, 0.3), (6, 0.6) and (4, 0.8). Respectively carrying out grid search on the controller parameters of three working states of throttling, intermediate and stress application at five typical working points, selecting the parameter with the optimal dynamic performance, and taking the optimization index function variable as the rotating speed n of the high-pressure rotor of the engine H And a pressure ratio of π, and defining deviation e nH And e π The normalized deviation of (a), i.e.:
wherein e is * nH (t) is the normalized deviation of the high-pressure rotor speed, e * π (t) is the normalized deviation of the pressure ratio deviation amount, n H (0)、n Href Respectively representing an initial value and an expected value of the rotating speed of the high-pressure rotor of the closed-loop system; pi (0), pi ref Respectively representing the initial and expected values of the pressure ratio.
Then, normalized ITAE index quantities are defined for the high-pressure rotor speed and the pressure ratio, respectively:
the objective function is then normalized to the form:
wherein, w 1 ，w 2 The weight coefficients corresponding to the index components are dimensionless. The weight coefficient of the index component is: w is a 1 ＝1，w 2 ＝1。
Thus, the controller parameter optimization problem translates into solving the optimization
And (5) problems are solved. According to the target function normalization form, the parameter setting can be realized by utilizing a grid search method. In parameter setting of robust controller for large envelope line, K u The search range of (1, 0), the search step length is 0.1; k 1 The search range of (1) is (0, 0.1), and the search step length is 0.01; k R The search range of (1) is (-0.1, 0), and the search step size is 0.01. In parameter setting of PI controller, K P The search range of (1) is (0, 200); t is i The search range of (1) is (0, 10), the search step size is 0.1, and the search results are shown in table 1 and table 2.
TABLE 1 parameter table of robust controller for large envelope line
TABLE 2 PI controller parameter Table
After the parameters are set, the linear interpolation method is adopted to combine the set parameter values, so that the turbofan engine closed-loop system meets the performance index requirements at all working points, and the variable gain full-envelope controller is synthesized.
With continued reference to fig. 3, after step b),
c) and performing full-digital simulation on the optimized full-envelope controller.
d) And (3) performing steady-state experiments and dynamic experiments on the ring platform and the semi-physical platform by the full-envelope controller in a hardware mode.
The hardware-in-loop simulation system is provided with a real I/O interface, controller hardware equipment and a virtual controlled object model, and is a control algorithm test and verification means with high confidence. The semi-physical simulation has a real oil circuit system, can carry out synthesis and test verification on a controller, a hydraulic mechanical system and related sensors, and has higher vividness compared with hardware-in-the-loop simulation. Therefore, hardware-in-loop simulation and semi-physical simulation tests become the most important tests in the development of the engine control system, and newly developed control systems can be installed to carry out bench test runs after the hardware-in-loop simulation and semi-physical simulation tests.
In a specific embodiment, a flight track and 5 typical working points are selected randomly in a flight envelope of a certain type of small bypass ratio double-shaft turbofan engine, a designed full envelope controller is tested on a full digital simulation platform in a software mode, and the designed full envelope controller is tested on a Hardware-in-the-Loop (HIL) platform and a semi-physical platform in a Hardware mode. The wide-range step of the throttle lever is carried out at five working points of (0, 0), (8, 1.2), (3, 0.3), (6, 0.6) and (4, 0.8), and the control effect is observed according to a dynamic response curve, so that the performance of the designed full-envelope controller is checked.
Full-digital simulation experiment:
the all-digital simulation experiment comprises any flight path simulation experiment and single working condition simulation experiment. The single-working-condition simulation experiment comprises a steady-state simulation experiment and a dynamic simulation experiment for five points of (0, 0), (8, 1.2), (3, 0.3), (6, 0.6) and (4, 0.8). The steady-state simulation test mainly verifies the performance of the controller when the throttle lever is in a small step and a stress application state in a throttling state, an intermediate state and a small amplitude (+/-5 degrees) step of the throttle lever. The dynamic (or transition state) simulation test mainly verifies the performance of the full-envelope controller when the throttle lever rapidly and greatly steps when the slow vehicle enters throttling, the slow vehicle enters the middle, the slow vehicle enters full stress, the throttling enters the slow vehicle, the middle enters the slow vehicle and the full stress enters the slow vehicle.
FIG. 7 shows a given PLA variation graph when the turbofan engine is in the throttling state according to an embodiment of the present application, FIG. 8 shows a given PLA variation graph when the turbofan engine is in the middle state according to an embodiment of the present application, FIG. 9 shows a given PLA variation graph when the turbofan engine is in the stressing state according to an embodiment of the present application, as shown in FIGS. 7-9, 0-20 seconds and 80-100 seconds of the throttling state are dynamic simulation experiments, 20-80 seconds are steady state simulation experiments, 0-20 seconds and 100-120 seconds of the middle and stressing states are dynamic simulation experiments, and 20-100 seconds are steady state simulation experiments.
(1) Simulation experiment of any flight path in envelope:
FIG. 10 is a graph of the change in flying height, Mach number, and throttle lever angle over time within the envelope of a turbofan engine according to one embodiment of the present application, as shown in FIG. 10, wherein the flight trajectory includes the processes of rollout, takeoff, climb, cruise, acceleration, climb, acceleration, and the like. Fig. 11 shows a high-pressure rotor rotation speed variation curve obtained by a flight trajectory simulation experiment according to an embodiment of the present application, and fig. 12 shows an engine pressure ratio variation curve obtained by a flight trajectory simulation experiment according to an embodiment of the present application, as shown in fig. 11 and 12, it can be seen from simulation results that, along with changes in flight conditions, the rotation speed and pressure ratio of the high-pressure rotor of the engine can track a control target given by a control plan, and the dynamic response is good, and the full-envelope controller shows good robustness and stability, and can meet the requirements of control of the turbofan engine within the envelope.
(2) Single-working-condition simulation experiment:
the performance index requirement of the full-digital simulation test is as follows: within 4 seconds of the adjusting time of the high-pressure rotor rotating speed control, the steady-state error is not more than 0.1 percent, and the overshoot is not more than 1 percent; the steady state error of the low-pressure rotor is not more than 0.1%. The steady state error of the engine pressure ratio is not more than 0.5%.
The steady state test results for each operating point are shown in table 3.
TABLE 3 Steady-State test results table
The results of the PLA raising process in the dynamic experiments are shown in table 4.
TABLE 4 dynamic experiment (PLA rising process) results table
The results of the PLA lowering process are shown in table 5.
TABLE 5 dynamic test (PLA dropping process) results table
Where NA represents the corresponding recalcitrance. And (4) selecting a simulation result graph of the (0, 0) point for displaying.
Fig. 13 shows a high-pressure rotor speed variation curve simulated by a single-working-condition simulation experiment according to an embodiment of the present application in a throttling state at an operating point (0, 0), fig. 14 shows a high-pressure rotor speed variation curve simulated by a single-working-condition simulation experiment according to an embodiment of the present application in an intermediate state at an operating point (0, 0), and fig. 15 shows a high-pressure rotor speed variation curve simulated by a single-working-condition simulation experiment according to an embodiment of the present application in a forced state at an operating point (0, 0); fig. 16 shows a simulated engine pressure ratio variation curve of a single-operating-point simulation experiment in an intermediate state of an operating point (0, 0), and fig. 17 shows a simulated engine pressure ratio variation curve of a single-operating-point simulation experiment in an applied force state of an operating point (0, 0).
According to the experimental result recording table, in the steady-state control experiment, the control effect of each working point meets the requirement of the performance index; in a dynamic control experiment, except that the adjusting time of the rotating speed of the high-pressure rotor in a partial state exceeds 4 seconds, other performances meet the index requirements. The reason for the large adjustment time is that when the reference state is changed greatly, it cannot be changed greatly due to physical limitations imposed by the amount of fuel.
According to the simulation result, the steady-state error of the rotating speed of the high-pressure rotor is not more than 0.1 percent, and the overshoot is not more than 1 percent; the rotating speed can quickly and stably keep up with the instruction of the system, and the error convergence is quick. The steady state error of the engine pressure ratio is not more than 0.5%, and the engine pressure ratio is open loop control in a slow vehicle state or a state below, so that the reference value is not tracked. The full-digital simulation result shows that: the large-envelope controller of the turbofan engine can ensure the stability of the system in the full envelope range, meets the requirements of multiple performance indexes, has good dynamic characteristics, has good control effect and has certain robustness and stability.
Hardware-in-the-loop (HIL) simulation and semi-physical simulation experiments:
hardware-in-loop simulation and semi-physical simulation experiments not only complete steady-state experiments and dynamic experiments of five working points in all-digital simulation experiments, but also perform deviation experiments on three working points (0, 0), (3, 0.3) and (8, 1.2), namely the rotational inertia of a high rotor and a low rotor deviates by 10% in the whole process. The dynamic and steady state experimental results of five single-working-condition experimental points and three deflection single-working-condition experimental points obtained by hardware-in-loop simulation experiments are shown in tables 6, 7 and 8 respectively. The results of the semi-physically derived transient and steady state testing of the five single-regime test points and the three pull-off single-regime test points are shown in tables 9, 10 and 11, respectively.
TABLE 6 HIL dynamic experiment (PLA ascending process) results recording table
TABLE 7 HIL dynamic experiment (PLA dropping procedure) results recording table
TABLE 8 HIL Steady-State test results
TABLE 9 semi-physical dynamic experiment (PLA ascending process) results recording table
TABLE 10 results of semi-physical dynamic experiments (PLA dropping process) are reported in Table
TABLE 11 semi-physical Steady-State test results recording Table
According to the experimental result recording table, in the dynamic test, the steady-state errors and the overshoot of the five single-working-condition experimental points and the three deviation single-working-condition experimental points all meet the requirements of performance indexes. In addition, the partial pressure ratio was too large for adjustment time and overshoot. The reason for the timeout of the regulation time is that when the rotation speed of the high-pressure rotor is largely changed, the rotation speed cannot be largely changed due to the limitation of the amount of fuel. In a steady-state test, the adjusting time, the steady-state error and the overshoot of the high-pressure rotor at five single-working-condition experimental points and three deflection single-working-condition experimental points all meet the requirements of performance indexes.
In summary, the full-envelope controller can meet the design requirement of the control system, and can theoretically ensure the global stability of the system, so that the control system has good performance in the whole envelope range. Experimental results show that under the condition that the rotating speed of the engine changes in a large range, the full-envelope controller can enable the system to keep stable in the full-envelope range, meets the given requirement of multiple performance indexes, and has good dynamic performance and robustness.
The application provides a design method and a simulation method of a turbofan engine full-envelope controller, and provides a PI-PP hybrid control strategy in order to solve the problem that a controller designed by a turbofan engine NPV model is poor in control effect under a throttling state in a full-digital simulation stage. The control effect of the turbofan engine closed-loop system under the full-envelope flight condition is finally ensured through a full-envelope controller switching strategy of given design. Aiming at the strong nonlinear characteristics of the turbofan engine nonlinear component model, the full-envelope controller is optimized by adopting a gain parameter adjusting method, so that the full-envelope controller is better adapted to the engine nonlinear model, and the control effect is further improved. In hardware-in-the-loop simulation and semi-physical simulation experiments, the full-envelope controller built based on the strategies can ensure that the system has global stability in the full-envelope range, can ensure that the transition (dynamic) process can fully meet the given multi-performance index requirement on the basis of meeting the steady-state performance, and has good robustness.
In the embodiments of the present application, it should be understood that the disclosed technical contents may be implemented in other ways. The above-described embodiments of the apparatus/system/method are merely illustrative, and for example, the division of the units may be a logical division, and in actual implementation, there may be another division, for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, units or modules, and may be in an electrical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application, or portions or all or portions of the technical solutions that contribute to the prior art, may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic disk, or an optical disk, and various media capable of storing program codes.
It is apparent that various modifications and variations can be made to the embodiments of the present application by those skilled in the art without departing from the spirit and scope of the application. In this way, if these modifications and changes are within the scope of the claims of the present application and their equivalents, the present application is also intended to cover these modifications and changes. The word "comprising" does not exclude the presence of other elements or steps than those listed in a claim. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims shall not be construed as limiting the scope.
Claims (10)
1. A design method of a turbofan engine full-envelope controller is characterized by comprising the following steps:
s1, establishing an NPV model of the turbofan engine, wherein the NPV model comprises external disturbance, and converting the NPV model into an uncertain model according to the external disturbance;
s2, designing a robust controller of the large covered wire based on the uncertain model;
s3, designing a preset performance parameter matrix in the large envelope robust controller according to the performance index requirement of the turbofan engine closed-loop system;
s4, solving a state feedback gain matrix in the robust controller of the large envelope curve by utilizing an SOS technology, thereby solving the robust controller of the large envelope curve;
s5, designing a PI controller of the turbofan engine in a throttling state, and combining the PI controller and the large package wire robust controller into the full package wire controller by using a switching module, so that the PI controller is used by the turbofan engine in the throttling state, and the large package wire robust controller is switched to be used by the switching module in other states.
2. The design method according to claim 1, wherein the NPV model including the external disturbance is specifically:
wherein x ∈ R n Is the system state, u ∈ R n Is a control input, rho (t) is ∈ R s Is a time-varying parameter vector, A (-), B (-), and C (-,) are polynomial matrices about x and ρ (t), ω (t) is an external perturbation, E 1 Is a constant matrix of suitable dimensions;
the uncertain model is specifically as follows:
wherein, Δ F 1 x (t) is transformed external disturbance, Δ is uncertainty matrix, satisfies Δ T △≤I，F 1 I is a constant matrix and an identity matrix of suitable dimensions, respectively, satisfying F 1 T F 1 ≥0。
3. The design method as claimed in claim 2, wherein the expression of the robust controller for large envelope is as follows:
wherein,
is the state feedback gain matrix, k, to be designed R Is the adjustable coefficient of the linear motion vector,
is a preset performance parameter matrix to be designed.
4. A design method according to claim 3, wherein the performance index requirements of the turbofan engine closed loop system are specified as: the high-pressure rotor rotating speed control steady-state error, the dynamic overshoot, the step response time, the spray pipe closed-loop control pressure ratio steady-state error and the rotating speed dynamic overshoot under the high-pressure rotor rotating speed disturbance of the turbofan engine are all within a preset threshold value;
the design process of the preset performance parameter matrix specifically comprises the following steps: based on the preset performance parameter matrix to be designed, performing difference operation on a value of a system state at any moment and a preset expected value to obtain a state error, introducing a performance function, defining an error transformation function, and designing to obtain the preset performance parameter matrix, wherein an expression of the preset performance parameter matrix specifically comprises:
wherein the continuous function T is defined as an error transformation function T i (x,t)，
For the state error, rho, of the turbofan engine closed-loop system i (t) is the introduced performance function.
5. The design method according to claim 4, wherein the solving of the state feedback gain matrix specifically comprises:
designing solvability conditions of the state feedback gain matrix to be designed, wherein an expression specifically comprises the following steps:
wherein,
and
is given a positive number,. phi SOS For the set of SOS polynomials to be,
solving solvability conditions of the state feedback gain matrix to be designed by utilizing an SOS technology to obtain the state feedback gain matrix, wherein an expression of the state feedback gain matrix is specifically as follows:
6. the design method according to claim 3, wherein the control law expression of the PI controller is specifically:
wherein, K p And T i Is constant, e (t) is the systematic error.
7. The design method according to claim 6, wherein the control law expression of the full-envelope controller is specifically:
wherein, PLA is throttle lever angle, and V is the constant.
8. A simulation method of a turbofan engine full-envelope controller, which simulates the full-envelope controller in the design method according to any one of claims 1 to 7, comprising the steps of:
a) building the full-envelope controller on a full-digital simulation platform;
b) optimizing the full-envelope controller by adopting a gain parameter adjusting method;
c) performing full-digital simulation on the optimized full-envelope controller;
wherein, the step b) specifically comprises the following steps:
b1) determining a plurality of typical working points according to the flight altitude and the Mach number of the turbofan engine, and selecting the parameters in the full wrap controller by adopting a grid search method under different typical working points and different working states so as to optimize the dynamic performance of the turbofan engine closed loop system, thereby realizing the tuning of the parameters;
b2) and combining and setting the parameters by adopting a linear interpolation method, so that the turbofan engine closed-loop system meets the performance index requirements at all working points and is synthesized into a variable gain full-wrap controller.
9. The simulation method according to claim 8, wherein the control law expression of the full-envelope controller to be optimized in step b) is specifically:
wherein, K u ，K 1 ，K R ，K p ，T i Is a parameter to be set.
10. The simulation method of claim 8, further comprising: and performing steady-state experiments and dynamic experiments on the full-envelope controller on a ring platform and a semi-physical platform in a hardware mode.
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