CN106886151A - The design and dispatching method of constrained forecast controller under a kind of aero-engine multi-state - Google Patents

Abstract

The invention provides the design and dispatching method of constrained forecast controller under a kind of aero-engine multi-state, belong to the system control in Aerospace Propulsion Theory and Engineering and emulation field.Control system has two-layer, and ground floor is flight envelope dispatch layer, and scheduling parameter is flying height and Mach number, using the weights of fuzzy membership method distribution forecast controller, obtains the controlled quentity controlled variable under current flight conditions, multiple nominal operation states；The second layer is working condition dispatch layer, and scheduling parameter is rotating speed, and linear interpolation method is used to the controlled quentity controlled variable that ground floor is obtained, and determines the final controlled quentity controlled variable under current working.Carry out flight envelope and operating condition divides, determine many nominal operating modes；The control targe for expecting rotating speed is issued in input and output constraint according to aero-engine, corresponding constrained forecast controller under different operating modes is designed；The double-deck scheduling logic of design, coordinates the constrained forecast controller at above-mentioned multi-state, realizes the stable state control under non-nominal operating mode.

Description

Design and scheduling method of constraint prediction controller of aircraft engine under multiple working conditions

Technical Field

The invention provides a design and scheduling method of a constraint prediction controller under multiple working conditions of an aircraft engine, and belongs to the field of system control and simulation in the aviation aerospace propulsion theory and engineering.

Background

With the development of the technology of the aero-engine, the working conditions of the aero-engine are increasingly complex, and a control system of the aero-engine not only ensures that the engine is stably and quickly transited from one working state to another working state, but also prevents the engine from entering abnormal states such as over-rotation, over-temperature, stall/surge and the like. In order to improve the inherent conservatism of the traditional method for combining the linear PID controller with Min-Max switching, the prediction control technology can be applied to the design of an engine control system because the prediction control technology can directly process input and output constraints, the Min-Max switching can be omitted, and the structure of the original controller is simplified. However, considering the characteristics of many working conditions and wide flight conditions of an aircraft engine, it is difficult for a constrained predictive controller under a single working condition to ensure satisfactory effects under all conditions, and according to the existing documents, the following methods are generally used for designing a predictive controller meeting the control requirements of various working conditions of an engine: firstly, a prediction model is continuously corrected by a system identification method to be matched with the actual state of the aircraft engine, but some working conditions do not meet the identifiable conditions, so that the identification parameters are possibly deteriorated; secondly, designing a nominal constraint prediction controller under a certain flight condition, and converting parameters of other flight conditions to design point conditions by using the similarity principle of the aero-engine, but the conventional similarity criterion is not necessarily applicable to all types of engines; and thirdly, dividing the flight envelope and the working state of the aircraft engine, designing a nominal constraint predictive controller for each sub-area, and designing scheduling logics among a plurality of constraint predictive controllers, wherein the control effect of the method depends on the rationality of a scheduling scheme to a certain extent. So far, no patent discloses a scheduling scheme of a constraint predictive controller under multiple working conditions in a full flight envelope and multiple working states.

Disclosure of Invention

The invention provides a design and double-layer scheduling method of a constraint prediction controller under multiple working conditions of an aircraft engine, aiming at ensuring that the aircraft engine can reach an expected rotating speed under the whole flight envelope and full working state and simultaneously avoiding the problems of overtemperature, overtravel, stall, surge and the like.

The invention relates to a design and scheduling method of a constraint prediction controller under multiple working conditions of an aeroengine.A control system has a two-layer structure, wherein the first layer is a flight envelope scheduling layer, scheduling parameters are flight altitude and Mach number, and a weight of a nominal prediction controller is distributed by adopting a fuzzy membership method to obtain the control quantity under the current flight condition and multiple nominal working states; the second layer is a working state scheduling layer, the scheduling parameter is the rotating speed, and the final control quantity under the current working condition is determined by adopting a linear interpolation method for the control quantity obtained by the first layer.

A design and scheduling method of a constraint predictive controller under multiple working conditions of an aircraft engine comprises the following steps:

step 1, determining the nominal working condition of the aeroengine

The aeroengine has different flight altitudes H, Mach number Ma and rotating speed N_fFlying under working conditions, and corresponding to different engine linear dynamic models; selecting N in flight envelope₁A nominal point, selecting N under working condition₂A nominal point corresponds to N₁N₂Nominal operating conditions, in which the nominal point in the operating state is driven from the slow vehicle N_fTo a maximum state N_fThe method for determining the nominal point in the flight envelope line comprises the following steps:

according to the working principle of the aircraft engine, the output of the aircraft engine is only a function of the flight altitude H and the Mach number Ma, and the total temperature T of the inlet of the engine₁And total pressure P₁And is also a function of H and Ma, and the calculation formula is as follows:

when H is less than or equal to 11km

When H >11km

Thus, the linear dynamic model of the engine and T₁、P₁Directly related, the flying envelope is divided by the following formula (3),

wherein, T₁₀、P₁₀And T_1x、P_1xRespectively indicating the total inlet temperature and the total pressure of a nominal point and a point to be selected in the flight envelope, if the root mean square of the variation of the total temperature and the total pressure of the point to be selected and the nominal point is not more than the root mean square, considering that the linear dynamic model of the engine in the flight state to be selected does not change much compared with the model of the nominal point, classifying the linear dynamic model into the same subarea, wherein one subarea has one nominal point; the selection of the size directly influences the control effect of the system and the number of the nominal points, and is determined by adopting a trial and error method: for a certain value, randomly selecting a state point at the boundary position of the sub-region for simulation, if the effect is satisfactory, amplifying and continuing verification, otherwise, reducing and continuing verification;

step 2, design N₁N₂Constraint prediction controller under nominal working condition

Aiming at the control requirements of the aero-engine, improving a conventional linear constraint predictive control algorithm, and processing the tracking output quantity and the constraint output quantity in different modes;

taking an aircraft engine discrete state space model at a certain nominal working condition as a prediction model:

by an augmented stateForm, formula (4) is expressed as an extended state form:

due to interference, component degradation and non-linearity reasons, the states of a prediction model and the current engine are not identical, model mismatch exists, a feedback link is introduced for correction, and the actual output y of the engine at the current k moment is defined_p(k) And the output of the prediction modelHas an error ofPrediction model outputIncluding a trace output y_t(k) And limit the output y_l(k) Predicting the corrected outputExpressed as:

wherein the correction factor h_i,i＝1,2,...,n_ySelecting between 0 and 1, taking h₁1, the rest of h_i<1；

The control target of the aircraft engine is to adjust the rotating speed to reach the expected value under the input and output constraints, and ensure good dynamic quality, and the performance index formula (7):

wherein, y_r(k + j) is a desired reference trajectory for the engine to track output;andpredicted correction outputs respectively representing the engine tracking amount and the constraint amount;representing the variation value of the control quantity to be optimized, wherein the weight coefficient lambda is a positive definite matrix; n is_yAnd n_uRefers to a prediction time domain and a control time domain; constraint formula u_max、u_minAnd Δ u_max、Δu_minRespectively, the maximum and minimum constraints of the control quantity and the change rate thereof; y is_{l max}And y_{l min}A maximum and minimum constraint of the pointing quantity;

substituting the formulas (4) to (6) into the performance index formula (7) to form a quadratic programming problem with constraint conditions, calling a quadratic programming optimization function quadprog in Matlab at each sampling moment to solve, and acting a first quantity delta u (k) of a control sequence on a controlled object;

step 3, designing a double-layer scheduling method to coordinate N₁N₂Constrained predictive controller

The double-layer scheduling method comprises the following steps: the first layer is a flight envelope scheduling layer, the scheduling parameters are H and Ma, and a fuzzy membership method is adopted to allocate N₁The weight of each nominal prediction controller is used for obtaining the current flight condition N₂Control quantity under nominal working state; the second layer is a working state scheduling layer, and the scheduling parameter is N_fDetermining the final control quantity under the current working condition by adopting a linear interpolation method for the control quantity obtained by the first layer; the method comprises the following specific steps:

A. flight envelope scheduling layer

The first layer takes (H, Ma) as a scheduling parameter, and for a certain nominal working state, the current flight condition is defined as (H)_x，Ma_x) The measurable parameter (T) is obtained from the formula (1) or (2)_1x、P_1x) Nominal flight state 1,2, …, N₁Are respectively expressed asThe output of the corresponding constrained predictive controller isDefinition of

Wherein,respectively representing the current flight condition and N₁The closer the nominal flight state points are, the closer the state is indicated by the smaller value of the similarity;

if J₁Is 0, let the control quantity W at the current flight condition_fx＝W_f1，Similarly, if none of them is 0, then orderAt this time W_fxIs defined as:

in the flight envelope scheduling layer, the control quantity of the non-nominal flight condition is represented by the output of all nominal constraint prediction controllers, and the weight value occupied by each nominal controller gradually changes along with the change of the flight condition, so that the control quantity continuously changes;

B. working state scheduling layer

Second layer rotating at a speed N_fObtaining N under the current flight condition by a flight envelope scheduling layer as a scheduling parameter₂Control quantity under nominal working state; for the current operating state N_fxIn the presence of N_fk<N_fx<N_f(k+1)In which N is_fkAnd N_f(k+1)Represents and N_fxAdjacent kth and (k + 1) th nominal operating states;andthe control quantity under the k-th and the (k + 1) -th nominal working states under the current flight condition is represented, and the linear interpolation scheduling method adopted by the working state scheduling layer is as follows:

reasonably scheduling N through double-layer scheduling method₁N₂A constraint prediction controller under each nominal working condition obtains the control quantity u under the current flight condition and the working state_cmd。

The invention has the beneficial effects that:

(1) the scheduling method of the prediction controller under the multiple working conditions of the aircraft engine, provided by the invention, is characterized in that a flight envelope layer membership scheduling method and a working state layer linear interpolation scheduling method are fused, a plurality of constraint prediction controllers under different working conditions are scheduled, the limited protection control range of a single constraint prediction controller under a certain working condition is expanded, and the steady state control under the non-nominal working condition and the transition state control under the large-range change of the working state in the flight envelope are realized.

(2) The invention can directly consider the control quantity and the speed constraint of the aero-engine, the output constraints of temperature, surge margin and the like in the constraint prediction controller designed aiming at the nominal working condition, thereby omitting Min-Max switching logic in the traditional method, greatly simplifying the structure of the original controller and avoiding the problem of integral saturation caused by switching.

(3) The double-layer scheduling method provided by the invention has expansibility, and is not only suitable for various nominal prediction controllers, but also suitable for other types of controllers under multiple working conditions.

Drawings

FIG. 1 is a control region within a flight envelope.

FIG. 2 is a diagram of control area division and nominal point selection within a flight envelope.

Fig. 3 is a schematic diagram of a two-tier scheduling method.

FIG. 4 is a fuel flow response over a wide range of operating conditions of an aircraft engine.

FIG. 5 is a graph of the speed response over a wide range of operating conditions of an aircraft engine.

FIG. 6 is a temperature response over a wide range of operating conditions of an aircraft engine.

FIG. 7 is a surge margin response over a wide range of operating conditions of an aircraft engine.

FIG. 8 is a trace of a change in flight condition of an aircraft engine.

FIG. 9 is a speed response for a wide range of aircraft engine flight conditions.

FIG. 10 is the fuel flow response of the flight envelope schedule layer (sub-area schedule method).

FIG. 11 is the fuel flow response (membership degree scheduling method) of the flight envelope scheduling layer.

Fig. 12 is a fuel flow response of the operating condition scheduling layer (sub-area scheduling method).

Fig. 13 is a fuel flow response (membership degree scheduling method) of the operating condition scheduling layer.

Detailed Description

The following further describes a specific embodiment of the present invention with reference to the drawings and technical solutions.

The embodiment is a design and scheduling method of a constraint predictive controller under multiple working conditions of an aircraft engine. The specific detailed design steps are as follows:

step 1, firstly, dividing a flight envelope. According to the working principle of the aero-engine, for a certain control law, the output (such as the rotating speed of a high-low pressure rotor, the pressure drop ratio of a turbine and the like) of the aero-engine is only a function of the flight altitude H and the Mach number Ma, and the total temperature T of an inlet of the aero-engine is₁And total pressure P₁And is a function of the height and the Mach number, and the calculation formula is as follows:

when H is less than or equal to 11km

When H >11km

Thus, the linear model of the engine and T₁、P₁Directly related, the flight envelope is divided by the following equation (3):

wherein, T₁₀、P₁₀Nominal fly of fingerTotal inlet temperature and total pressure, T, of the running state_1x、P_1xIf the root mean square of the variation of the total temperature and the total pressure of the to-be-selected state in the flight envelope does not exceed the variation of the total temperature and the total pressure of the to-be-selected point, the linear dynamic model of the state point is considered to have small variation compared with the model of the nominal point, and can be classified into the same sub-region, and one sub-region has one nominal point. The selection of the size directly influences the control effect of the system and the number of the nominal points, and is determined by adopting a trial and error method: and (3) for a certain value, randomly selecting a state point (namely, a relatively severe condition in the sub-region) at the boundary position of the sub-region for simulation, if the effect is satisfactory, amplifying and continuing verification, and otherwise, reducing and continuing verification. Through the trial, the requirement of less than or equal to 0.2 is met for the double-shaft turbofan engine with large bypass ratio in the embodiment.

Different working conditions (height H, Mach number Ma, speed N)_f) Corresponding to different linear models of the engine, so that if N is selected in the flight envelope₁A nominal point, selecting N under working condition₂A nominal point, N is total₁N₂And (4) carrying out various working conditions. Assuming that only one control zone within the flight envelope is considered (fig. 1), three sub-zones can be divided by the above method and the nominal flight state point for each sub-zone is obtained, as shown in fig. 2. The example considers that the operating condition is 80% N_f～104％N_fIn the process of large transition state, three nominal points of the working state, namely 86 percent N, are selected at equal intervals_f，92％N_fAnd 98% N_fAnd considering three flight condition nominal points in the control area, wherein the number of the flight condition nominal points is 9.

And 2, respectively designing corresponding constraint predictive controllers for the 9 working conditions according to the control requirements of the engine, wherein the method is as follows. Taking an aircraft engine discrete state space model at a certain working condition as a prediction model:

by an augmented stateIn this case, equation (4) can be expressed as an augmented state form:

in actual engine control, due to reasons such as interference, component degradation and nonlinearity, a prediction model and a current engine state are not completely the same, namely model mismatch exists, and a feedback link needs to be introduced for correction. Defining the actual output y of the engine at the current k moment_p(k) And the output of the prediction model(including the trace output y_t(k) And limit the output y_l(k) An error ofPrediction corrected outputCan be expressed as:

wherein the correction factor h_i,i＝1,2,...,n_yChosen between 0 and 1, usually taken as h₁1, the rest of h_i<1。

The control aim of the aircraft engine is to adjust the rotating speed to reach a desired value under the input and output constraints, and to ensure good dynamic quality, namely small overshoot, fast response, less oscillation, stability and reliability. One performance index has the following form:

wherein, y_r(k + j) is a reference trajectory of j steps in the future from the current time, corresponding to an expected response trajectory of the engine tracking output quantity;anda prediction correction output representing the tracking amount and the limiting amount of j steps in the future from the current time respectively;representing the predicted input variable quantity of the step i in the future from the current moment, wherein the weight coefficient lambda of the predicted input variable quantity is a positive definite matrix; upper limit value n of summation sign_yAnd n_uRespectively representing a prediction time domain and a control time domain, and n in general_y≥n_u. U in constraint expression_maxAnd u_minRespectively, the maximum and minimum limits, Deltau, of the controlled variable_maxAnd Δ u_minThe maximum and minimum limits respectively represent the change rate of the control quantity, and are mainly used for representing the limitation that the actual output of the controller is limited by the limit position, the change rate and the like of the actuating mechanism; y is_{l max}And y_{l min}Respectively, the maximum and minimum constraints on the output.

Substituting the equations (4) - (6) into the performance index equation (7) can form a quadratic programming problem with constraint conditions, calling a quadratic programming optimization function quadprog in Matlab to solve at each sampling moment, and applying a first quantity delta u (k) of a control sequence to a controlled object.

Step 3, considering the flight conditions and 9 nominal working condition points (as shown in' in fig. 3) in the working state, designing a double-layer scheduling scheme on the basis of the 9 nominal constraint predictive controllers designed in the step 2, coordinating the constraint predictive controllers in the nominal working conditions, and sequentially passing through a flight envelope scheduling layer and a working state scheduling layer to realize the non-nominal working conditionSteady state and transition state control. FIG. 3 shows the operating conditions (H, Ma, N)_f) Three parameters are coordinates, which illustrate the double-layer scheduling method of the present invention: the control quantity of the non-nominal m working condition is related to 6 nominal constraint predictive controllers corresponding to 1,2, 3, 4, 5 and 6 similar working conditions, and the working condition m is determined through a flight envelope scheduling layer₁(determined by the 4, 5, 6 nominal controller) and m₂(determined by the 1,2, 3 nominal controller); then passes through the working state scheduling layer, and is composed of m₁And m₂And determining the final control value under the m working conditions.

A. Flight envelope scheduling layer

The first layer has (H, Ma) as a scheduling parameter. In the operating state 92% N in FIG. 3_fThe scheduling method employed within the flight envelope is illustrated for purposes of example. At 92% N_fIn the operating state, for the current flight conditions (H)_x，Ma_x) The measurable parameter (T) is obtained from the formula (2) or (3)_1x、P_1x) The parameters of the nominal flight states 1,2, 3 are respectively denoted by (T)₁₁、P₁₁)，(T₁₂、P₁₂)，(T₁₃、P₁₃) The output of the corresponding constrained predictive controller is W_f1，W_f2，W_f3. Definition of

Wherein, J₁，J₂，J₃Respectively representing the closeness degree of the current flight condition in the flight envelope to 3 nominal flight state points, and the smaller the value of the current flight condition, the closer the state is.

If J₁Is 0, let W_fx＝W_f1，J₂And J₃The same is true. If none of the three is 0, let Q₁＝1/J₁，Q₂＝1/J₂，Q₃＝1/J₃Then the current flight condition (H)_x，Ma_x) W to be solved_fxCan be expressed as:

if the point to be found is located in the sub-area covered by the nominal point 1, for W_f1Coefficient of (2)The closer to the state of nominal point 1, Q₁The larger the coefficient, the larger W_f1Plays a leading role, in line with reality. Assuming that the point to be solved almost coincides with the nominal point 1, J₁→0，Q₁→ infinity at this timeThen there is W_fx≈W_f1. The same conclusion can be reached when the point to be found is located in the sub-region of the nominal points 2, 3.

In the flight envelope scheduling layer, the control quantity of the non-nominal flight condition is represented by the output of all the nominal constraint prediction controllers, and the weight value occupied by each nominal controller gradually changes along with the change of the flight condition, so that the control quantity continuously changes.

B. Working state scheduling layer

Second layer rotating at a speed N_fAs a scheduling parameter. For the current operating state N_fxIn the presence of N_fk<N_fx<N_f(k+1)In which N is_fkAnd N_f(k+1)Represents and N_fxAdjacent kth and (k + 1) th nominal operating states. From the above flight envelope scheduling layer, theControl variables to the kth and k +1 th nominal operating states under the current flight conditionsAndthe linear interpolation scheduling method adopted by the layer comprises the following steps:

for this example, m is obtained from the first layer₁(H_x，Ma_x，86％N_f) And m₂(H_x，Ma_x，92％N_f) Obtaining the control quantity u under the final m working conditions by interpolation of the control quantity at the working conditions_cmd。

In order to further explain the effect of the double-layer scheduling method in the embodiment, the effectiveness of the method in the invention is verified through two sets of simulation experiments.

(1) Wide range of change of working state of aeroengine

FIGS. 4-7 show aircraft engines at altitude H11 km, Mach Ma 0.8 flight conditions, 80% N_f-104％N_f(4200r/min-5200r/min) control effect under the condition of wide range change of working state. As can be seen from FIG. 5, the constraint prediction controller based on the double-layer scheduling method can adjust the rotating speed to reach the expected value under the input and output constraints, the transition state process is almost free of overshoot, the adjusting time is short, and the dynamic performance is good. As shown in fig. 4, during acceleration and deceleration, the controlled variable rate constraint is first applied, and the controlled variable is increased or decreased by an amount of 0.03kg/s per control cycle until other limits are touched. As can be seen from FIGS. 6 and 7, the limited output turbine outlet temperature T is shown₄₅And surge margin smHPC are within their respective constraints throughout the process. The simulation example illustrates that the double-layer scheduling method can cope with the situation that the working state is changed in a large range.

(2) Aircraft engine flight conditions vary widely

FIGS. 8-13 show an aircraft engine operating at 90% N_fControl effect under large variation of flight conditions (H, Ma). To illustrate the advantages of the flight envelope level scheduling method of the present invention, this example compares the proposed membership scheduling method with a simpler direct sub-area scheduling method, where sub-area scheduling refers to the operation of a nominal predictive controller in a certain sub-area if the flight conditions are in that sub-area.

Fig. 8 is a flight condition variation trajectory, and as can be seen from a comparison of fig. 2, the flight trajectory spans two sub-regions. Firstly, obtaining the control quantity at the working conditions of m1 and m2 through a flight envelope dispatching layer of a first layer, and then obtaining the final control quantity W according to a linear interpolation method of a working state dispatching layer of a second layer_f. Taking "m 2" as an example, fig. 10 is a sub-area scheduling method, in which a nominal controller 1 or 2 determines a control quantity, and at about time 89s, the controller is switched due to the control right of the nominal predictive controller 1 and 2, so that the control quantity jumps and the rotational speed response is not smooth (shown in fig. 9); FIG. 11 is a membership scheduling method according to the present invention, in which three nominal predictive controllers 1,2, 3 jointly determine a control quantity, the control quantity can be continuously changed, and the dynamic effect of the rotation speed is better (shown in FIG. 9). FIG. 12 and FIG. 13 are fuel flow responses of the operating condition scheduling layer by a linear interpolation method, and FIG. 12 shows that the jump of the flight envelope scheduling layer control quantity directly affects the final control quantity W_fA jump also occurs.

The embodiment specifically simulates and analyzes the change of the control quantity of each layer in the double-layer scheduling method, and can know that the membership scheduling method of the flight packet layer and the linear interpolation scheduling method of the working state layer can coordinate to work, so that the control quantity continuously changes, and the control target is realized with a better dynamic effect.

Claims (1)

1. A design and scheduling method of a constraint predictive controller under multiple working conditions of an aircraft engine is characterized by comprising the following steps:

step 1, determining the nominal working condition of the aeroengine

The aeroengine has different flight altitudes H, Mach number Ma and rotating speed N_fFlying under working conditions, and corresponding to different engine linear dynamic models; selecting N in flight envelope₁A nominal point, selecting N under working condition₂A nominal point corresponds to N₁N₂Nominal working condition, in which the working condition is inNominal point slave slow vehicle N_fTo a maximum state N_fThe method for determining the nominal point in the flight envelope line comprises the following steps:

according to the working principle of the aircraft engine, the output of the aircraft engine is only a function of the flight altitude H and the Mach number Ma, and the total temperature T of the inlet of the engine₁And total pressure P₁And is also a function of H and Ma, and the calculation formula is as follows:

when H is less than or equal to 11km

$\left\{\begin{array}{c}{T}_1=(288.15-6.5\&times;H)\&times;(1+0.2\&times;{\mathrm{Ma}}^2)-273\\ P_1=1.03323\&times;{(1-\frac{H}{44.3})}^{5.2553}\&times;{(1+0.2\&times;{\mathrm{Ma}}^2)}^{3.5}\end{array}\right.---\left(1\right)$

When H >11km

$\left\{\begin{array}{c}{T}_1=216.6\&times;(1+0.2\&times;{\mathrm{Ma}}^2)-273\\ P_1=0.2314\&times;e^{\left(\frac{11-H}{6.318}\right)}\&times;{(1+0.2\&times;{\mathrm{Ma}}^2)}^{3.5}\end{array}\right.---\left(2\right)$

Thus, the linear dynamic model of the engine and T₁、P₁Directly related, the flying envelope is divided by the following formula (3),

$J=\sqrt{{\left(\frac{P_{1x}-P_{10}}{P_{10}}\right)}^2+{\left(\frac{T_{1x}-T_{10}}{T_{10}}\right)}^2}\&le;\mathrm{\&epsiv;}---\left(3\right)$

wherein, T₁₀、P₁₀And T_1x、P_1xRespectively indicating the total inlet temperature and the total pressure of a nominal point and a point to be selected in the flight envelope, if the root mean square of the variation of the total temperature and the total pressure of the point to be selected and the nominal point is not more than the root mean square, considering that the linear dynamic model of the engine in the flight state to be selected does not change much compared with the model of the nominal point, classifying the linear dynamic model into the same subarea, wherein one subarea has one nominal point; the selection of the size directly influences the control effect of the system and the number of the nominal points, and is determined by adopting a trial and error method: for a certain value, randomly selecting a state point at the boundary position of the sub-region for simulation, if the effect is satisfactory, amplifying and continuing verification, otherwise, reducing and continuing verification;

step 2, design N₁N₂Constraint prediction controller under nominal working condition

Aiming at the control requirements of the aero-engine, improving a conventional linear constraint predictive control algorithm, and processing the tracking output quantity and the constraint output quantity in different modes;

taking an aircraft engine discrete state space model at a certain nominal working condition as a prediction model:

$\left\{\begin{array}{c}\hat{x}(k+1)=A_d\hat{x}\left(k\right)+B_d\hat{u}\left(k\right)\\ \hat{y}\left(k\right)=C\hat{x}\left(k\right)+D\hat{u}\left(k\right)\end{array}\right.---\left(4\right)$

by an augmented stateForm, formula (4) is expressed as an extended state form:

$\left\{\begin{array}{c}\left[\begin{array}{c}\hat{x}(k+1)\\ \hat{u}\left(k\right)\end{array}\right]=\left[\begin{array}{cc}{A}_d& B_d\\ 0& I\end{array}\right]\left[\begin{array}{c}\hat{x}(k+1)\\ \hat{u}\left(k\right)\end{array}\right]+\left[\begin{array}{c}{B}_d\\ I\end{array}\right]\mathrm{\&Delta;}\hat{u}\left(k\right)\\ \hat{y}\left(k\right)=\left[\begin{array}{cc}C& D\end{array}\right]\left[\begin{array}{c}\hat{x}\left(k\right)\\ \hat{u}(k-1)\end{array}\right]+D\mathrm{\&Delta;}\hat{u}\left(k\right)\end{array}\right.---\left(5\right)$

due to interference, component degradation and non-linearity reasons, the prediction model and the current engine state are not identical, model mismatch exists, a feedback link is introduced for correction and determinationActual engine output y at current k moment_p(k) And the output of the prediction modelHas an error ofPrediction model outputIncluding a trace output y_t(k) And limit the output y_l(k) Predicting the corrected outputExpressed as:

$\left[\begin{array}{c}{\hat{y}}_{COR}(k+1)\\ {\hat{y}}_{COR}(k+2)\\ .\\ .\\ .\\ {\hat{y}}_{COR}(k+n_y)\end{array}\right]=\left[\begin{array}{c}\hat{y}(k+1)\\ \hat{y}(k+2)\\ .\\ .\\ .\\ \hat{y}(k+n_y)\end{array}\right]+\left[\begin{array}{c}{h}_1\\ h_2\\ .\\ .\\ .\\ h_{n_y}\end{array}\right]\&lsqb;y_p\left(k\right)-\hat{y}\left(k\right)\&rsqb;---\left(6\right)$

wherein the correction factor h_i,i＝1,2,...,n_ySelecting between 0 and 1, taking h₁1, the rest of h_i<1；

The control target of the aircraft engine is to adjust the rotating speed to reach the expected value under the input and output constraints, and ensure good dynamic quality, and the performance index formula (7):

$\begin{array}{c}\underset{\mathrm{\&Delta;}u}{\min }J=\underset{j=1}{\overset{j=n_y}{\mathrm{\&Sigma;}}}{\left({\hat{y}}_{tCOR}\right(k+j)-y_r(k+j\left)\right)}^2+\underset{i=0}{\overset{n_u-1}{\mathrm{\&Sigma;}}}\mathrm{\&lambda;}\mathrm{\&Delta;}\hat{u}{(k+i)}^T\mathrm{\&Delta;}\hat{u}(k+i)\\ \begin{array}{cc}s.t.& u_{\min }\&le;\hat{u}(k+i)\&le;u_{\max }\\ & {\mathrm{\&Delta;u}}_{\min }\&le;\mathrm{\&Delta;}\hat{u}(k+i)\&le;{\mathrm{\&Delta;u}}_{\max }\\ & y_{l\min }\&le;{\hat{y}}_{lCOR}(k+j)\&le;y_{l\max }\\ & i=0,1,\mathrm{...},n_u-1\\ & j=1,2,\mathrm{...},n_y\end{array}\end{array}---\left(7\right)$

wherein, y_r(k + j) is a desired reference trajectory for the engine to track output;andpredicted correction outputs respectively representing the engine tracking amount and the constraint amount;representing the variation value of the control quantity to be optimized, wherein the weight coefficient lambda is a positive definite matrix; n is_yAnd n_uRefers to a prediction time domain and a control time domain; constraint formula u_max、u_minAnd Δ u_max、Δu_minRespectively, the maximum and minimum constraints of the control quantity and the change rate thereof; y is_lmaxAnd y_lminA maximum and minimum constraint of the pointing quantity;

substituting the formulas (4) to (6) into the performance index formula (7) to form a quadratic programming problem with constraint conditions, calling a quadratic programming optimization function quadprog in Matlab at each sampling moment to solve, and acting a first quantity delta u (k) of a control sequence on a controlled object;

step 3, designing a double-layer scheduling method to coordinate N₁N₂Constrained predictive controller

The double-layer scheduling method comprises the following steps: the first layer is a flight envelope scheduling layer, the scheduling parameters are H and Ma, and a fuzzy membership method is adopted to allocate N₁The weight of each nominal prediction controller is used for obtaining the current flight condition N₂Control quantity under nominal working state; the second layer is a working state scheduling layer, and the scheduling parameter is N_fDetermining the final control quantity under the current working condition by adopting a linear interpolation method for the control quantity obtained by the first layer; the method comprises the following specific steps:

A. flight envelope scheduling layer

The first layer takes (H, Ma) as a scheduling parameter, and for a certain nominal working state, the current flight condition is defined as (H)_x，Ma_x) The measurable parameter (T) is obtained from the formula (1) or (2)_1x、P_1x) Nominal flight state 1,2, …, N₁Are respectively expressed asThe output of the corresponding constrained predictive controller isDefinition of

$\begin{array}{c}{J}_1=\sqrt{{\left(\frac{P_{1x}-P_{11}}{P_{11}}\right)}^2+{\left(\frac{T_{1x}-T_{11}}{T_{11}}\right)}^2}\\ J_2=\sqrt{{\left(\frac{P_{1x}-P_{12}}{P_{12}}\right)}^2+{\left(\frac{T_{1x}-T_{12}}{T_{12}}\right)}^2}\\ .\\ .\\ .\\ J_3=\sqrt{{\left(\frac{P_{1x}-P_{1N_1}}{P_{1N_1}}\right)}^2+{\left(\frac{T_{1x}-T_{1N_1}}{T_{1N_1}}\right)}^2}\end{array}---\left(8\right)$

Wherein,respectively representing the current flight condition and N₁The closer the nominal flight state points are, the closer the state is indicated by the smaller value of the similarity;

if J₁Is 0, let the control quantity at the current flight conditionSimilarly, if none of them is 0, then orderAt this time W_fxIs defined as:

$W_{fx}=\frac{Q_1}{Q_1+Q_2+\mathrm{...}+Q_{N_1}}{W}_{f1}+\frac{Q_2}{Q_1+Q_2+\mathrm{...}+Q_{N_1}}{W}_{f2}+\mathrm{...}+\frac{Q_{N_1}}{Q_1+Q_2+\mathrm{...}+Q_{N_1}}{W}_{{\mathrm{fN}}_1}---\left(9\right)$

in the flight envelope scheduling layer, the control quantity of the non-nominal flight condition is represented by the output of all nominal constraint prediction controllers, and the weight value occupied by each nominal controller gradually changes along with the change of the flight condition, so that the control quantity continuously changes;

B. working state scheduling layer

Second layer rotating at a speed N_fObtaining N under the current flight condition by a flight envelope scheduling layer as a scheduling parameter₂Control quantity under nominal working state; for the current operating state N_fxIn the presence of N_fk<N_fx<N_f(k+1)In which N is_fkAnd N_f(k+1)Represents and N_fxAdjacent kth and (k + 1) th nominal operating states;andthe control quantity under the k-th and the (k + 1) -th nominal working states under the current flight condition is represented, and the linear interpolation scheduling method adopted by the working state scheduling layer is as follows:

$u_{cmd}=W_{fk\_H_x,{\mathrm{Ma}}_x}+\frac{N_f-N_{fk}}{N_{f(k+1)}-N_{fk}}\&times;(W_{f(k+1)\_H_x,{\mathrm{Ma}}_x}-W_{fk\_H_x,{\mathrm{Ma}}_x})---\left(10\right)$

reasonably scheduling N through double-layer scheduling method₁N₂A constraint prediction controller under each nominal working condition obtains the control quantity u under the current flight condition and the working state_cmd。