Metering valve breakage fault processing method and system based on engine on-board model

Abstract

The present application relates to the technical field of aero-engine control, and specifically discloses a metering valve breakage fault processing method based on an engine on-board model, which comprises the following steps: obtaining an engine speed given value at a current time and an engine speed feedback value at the current time, and calculating a main fuel flow given value at the current time according to the difference between the two values, while inputting the engine speed feedback value at the current time into the engine on-board model to output a main fuel flow calculation value at the current time; calculating a control current at the current time according to the difference between the main fuel flow given value at the current time and the main fuel flow calculation value; and driving the main fuel metering valve to output fuel for the engine combustion according to the control current, so as to realize the control of the engine speed. The present application also discloses a metering valve breakage fault processing system based on an engine on-board model. The present application can realize the controllable engine speed when the main fuel metering valve sensor breakage fault occurs.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aero-engine control, and more particularly to a metering valve breakage fault processing method based on an engine on-board model and a metering valve breakage fault processing system based on an engine on-board model. BACKGROUND

[0002] In an aero-engine control system, the target requirement of the rotating speed is achieved by controlling the flow of the main fuel, thereby forming a main fuel rotating speed control loop. The actual supply amount of the main fuel is achieved by controlling the opening position of the main fuel metering valve through a main fuel servo loop, i.e. a current control value of the main fuel metering valve. Therefore, there are usually two loops in the main fuel control, an outer loop for calculating the main fuel given value and an inner loop for calculating the current control value of the main fuel metering valve. Whether the inner loop is controlled in place is confirmed by the feedback of the main fuel metering valve obtained by a sensor. In actual work, the main fuel metering valve sensor may break and the feedback value cannot be obtained. This fault will cause the inner loop to be uncontrollable, and further cause the rotating speed to be uncontrollable, thus an urgent need for a fault processing method.

[0003] In view of the main fuel control loop metering valve sensor breakage fault, a control scheme based on equivalent transformation is provided. The scheme solves the problem of engine rotating speed control in the fault, and realizes the observability of the control flow, so that the closed-loop calculation of the fuel quantity can still be open-loop limited in the fault. SUMMARY

[0004] In order to solve the problems in the prior art, the present application provides a metering valve breakage fault processing method and system based on an engine on-board model, which realizes controllable engine rotating speed and still observable control flow when the main fuel metering valve sensor breaks.

[0005] As a first aspect of the present application, a metering valve breakage fault processing method based on an engine on-board model is provided, comprising:

[0006] Step S1: obtaining an engine rotating speed given value at a current time, an engine rotating speed feedback value at the current time and an engine rotating speed feedback value at a previous time, and constructing an engine on-board model;

[0007] Step S2: calculating a main fuel flow given value at the current time according to the difference between the engine rotating speed given value at the current time and the engine rotating speed feedback value at the current time, and inputting the engine rotating speed feedback value at the current time and the engine rotating speed feedback value at the previous time into the engine on-board model to output a main fuel flow calculation value at the current time;

[0008] Step S3: calculating a control current at the current time according to a difference between a main fuel flow given value at the current time and a main fuel flow calculation value at the current time;

[0009] Step S4: driving the main fuel metering valve to output fuel for supplying the engine to combust according to the control current at the current time, so as to realize control on the engine speed.

[0010] Further, the inputting of the engine speed feedback value at the current time and the engine speed feedback value at the last time into the engine on-board model to output the main fuel flow calculation value at the current time further comprises:

[0011] a first-order LPV model 1 / Gs2 is constructed with the engine speed feedback value N as a scheduling variable, the first-order LPV model being an engine fuel-speed model, and the first-order LPV model being expressed in a continuous domain as:

[0012]

[0013] wherein Wf'(s) is the main fuel flow calculation value in the continuous domain; N(s) is the engine speed feedback value in the continuous domain; Ke and Te are respectively a gain and a time constant of the engine local linear model;

[0014] the first-order LPV model is discretized, i.e.:

[0015]

[0016] wherein Wf'(z) is the main fuel flow calculation value in the discrete domain; N(z) is the engine speed feedback value in the discrete domain;

[0017] further obtaining an expression as:

[0018]

[0019] wherein Wf'(k) is the main fuel flow calculation value at the kth sampling period; N(k) is the engine speed feedback value at the kth sampling period; N(k-1) is the engine speed feedback value at the (k-1)th sampling period; t is a sampling time;

[0020] Meanwhile, for the first-order LPV model, according to linear system principle, the following processing is performed:

[0021] N(k) = Ke·Wf Steady (k)

[0022] wherein Wf steady (k) is a steady-state fuel flow value of the engine at the kth sampling period;

[0023] Based on the above series of linear models, there are:

[0024]

[0025] According to the similar principle, the steady-state fuel flow value Wf steady , gain Ke and time constant Te are obtained according to the engine speed feedback value N, the inlet pressure P2 and the inlet temperature T2 within the envelope range. steady , Ke and Te are as follows:

[0026] [Wf steady ,Ke,Te]=f(N,P2,T2)

[0027] At this point, the construction of the engine on-board model is completed, that is, the steady-state fuel flow value Wf steady , gain Ke and time constant Te are obtained according to the engine speed feedback value N, the inlet pressure P2 and the inlet temperature T2, and then the main fuel flow calculation value wf' is calculated according to the steady-state fuel flow value Wf steady , gain Ke, time constant Te and engine speed feedback value N.

[0028] As a second aspect of the application, a metering valve breakage fault processing system based on an engine on-board model is provided, comprising:

[0029] An outer loop controller is configured to obtain an engine speed given value at a current time and an engine speed feedback value at the current time, and to calculate a main fuel flow given value at the current time according to the difference between the engine speed given value at the current time and the engine speed feedback value at the current time.

[0030] An inner loop controller is configured to obtain the main fuel flow given value at the current time, the engine speed feedback value at the current time and the engine speed feedback value at the previous time, and to construct an engine on-board model; and to input the engine speed feedback value at the current time and the engine speed feedback value at the previous time into the engine on-board model to output a main fuel flow calculation value at the current time; and to calculate a control current at the current time according to the difference between the main fuel flow given value at the current time and the main fuel flow calculation value at the current time; and to drive the main fuel metering valve to output fuel for the engine to burn according to the control current at the current time, so as to realize control of the engine speed.

[0031] Further, the inner loop controller is specifically configured to:

[0032] A first-order LPV model 1 / Gs2 with the engine speed feedback value N as the scheduling variable is constructed, and the first-order LPV model is an engine fuel-speed model, which is expressed in continuous domain as:

[0033]

[0034] wherein Wf'(s) is the continuous domain main fuel flow calculation value; N(s) is the continuous domain engine speed feedback value; Ke and Te are the gain and time constant of the engine local linear model respectively;

[0035] Discretize the first order LPV model, namely:

[0036]

[0037] wherein Wf'(z) is the discrete domain main fuel flow calculation value; N(z) is the discrete domain engine speed feedback value;

[0038] Further, the expression is:

[0039]

[0040] wherein Wf'(k) is the kth sampling period main fuel flow calculation value; N(k) is the kth sampling period engine speed feedback value; N(k-1) is the (k-1)th sampling period engine speed feedback value; t is the sampling time;

[0041] At the same time, for the first order LPV model, according to the linear system principle, the following processing is performed:

[0042] N(k) = Ke·Wf steady (k)

[0043] wherein Wf steady (k) is the steady state fuel flow value of the engine in the kth sampling period;

[0044] According to the above series of linear models, the following can be obtained:

[0045]

[0046] According to the similarity principle, within the envelope range, the steady state fuel flow value Wf steady , the gain Ke and the time constant Te are obtained according to the engine speed feedback value N, the inlet pressure P2 and the inlet temperature T2, so the function relationship is as follows:

[0047] [Wf steadyi Ke, Te] = f(N, P2, T2)

[0048] At this point, the construction of the engine on-board model is completed, that is, the steady state fuel flow value Wf steady , the gain Ke and the time constant Te are obtained according to the engine speed feedback value N, the inlet pressure P2 and the inlet temperature T2, and then the steady state fuel flow value Wfsteady , gain Ke, time constant Te and engine speed feedback value N to calculate the main fuel flow calculation value wf'.

[0049] The engine on-board model-based metering valve breakage fault processing method and system has the following advantages:

[0050] (1) The original controller and control parameters during non-fault are directly used during breakage fault, without the need for additional design of the controller or control parameters;

[0051] (2) The purpose of controllable speed is still achieved after the breakage of the inner ring main fuel metering valve sensor;

[0052] (3) After the breakage of the metering valve sensor, the main fuel flow for control is still observable, and the output quantity can be limited in open loop, such as fuel gas ratio. BRIEF DESCRIPTION OF DRAWINGS

[0053] The accompanying drawings are included to provide a further understanding of the present application, and constitute a part of the specification, and are used together with the following detailed description to explain the present application, but do not constitute a limitation of the present application.

[0054] Figure 1 The flowchart of the engine on-board model-based metering valve breakage fault processing method of the present application.

[0055] Figure 2 The structure diagram of the engine on-board model-based metering valve breakage fault processing system of the present application.

[0056] Figure 3 The engine speed control effect comparison diagram of the engine on-board model-based metering valve breakage fault processing method of the present application and the engine speed control effect when there is no breakage fault. DETAILED DESCRIPTION

[0057] To further illustrate the technical means and effects adopted by the present application to achieve the predetermined invention purposes, the engine on-board model-based metering valve breakage fault processing method and system according to the present application, its specific implementation, structure, features and effects are described in detail as follows in combination with the drawings and preferred embodiments. Obviously, the described embodiments are part of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0058] In the present embodiment, an engine on-board model-based metering valve breakage fault processing method is provided, as shown in Figure 1As shown, the metering valve disconnection fault processing method based on the engine on-board model comprises:

[0059] Step S1: obtaining an engine speed given value at a current time, an engine speed feedback value at the current time and an engine speed feedback value at a previous time, and constructing an engine on-board model;

[0060] Step S2: calculating a main fuel flow given value at the current time according to a difference between the engine speed given value at the current time and the engine speed feedback value at the current time, and inputting the engine speed feedback value at the current time and the engine speed feedback value at the previous time into the engine on-board model to output a main fuel flow calculation value at the current time;

[0061] Specifically, the inputting the engine speed feedback value at the current time and the engine speed feedback value at the previous time into the engine on-board model to output the main fuel flow calculation value at the current time further comprises:

[0062] constructing a first-order LPV model 1 / Gs2 with the engine speed feedback value N as a scheduling variable, the first-order LPV model being an engine fuel-speed model, which is expressed in a continuous domain as:

[0063]

[0064] wherein Wf'(s) is a main fuel flow calculation value in a continuous domain; N(s) is an engine speed feedback value in a continuous domain; Ke and Te are respectively a gain and a time constant of a local linear model of the engine;

[0065] discretizing the first-order LPV model, i.e.:

[0066]

[0067] wherein Wf'(z) is a main fuel flow calculation value in a discrete domain; N(z) is an engine speed feedback value in a discrete domain;

[0068] further obtaining an expression as:

[0069]

[0070] wherein Wf'(k) is a main fuel flow calculation value at a kth sampling period; N(k) is an engine speed feedback value at the kth sampling period; N(k-1) is an engine speed feedback value at a (k-1)th sampling period; t is a sampling time;

[0071] Meanwhile, for the first-order LPV model, according to linear system principle, the following processing is performed:

[0072] N(k) = Ke·Wf steady (k)

[0073] wherein Wf steady (k) is a steady-state fuel flow value of the engine in the kth sampling period;

[0074] In combination with the above series of linear models, we can have:

[0075]

[0076] According to the similar principle, within the envelope range, the steady-state fuel flow value Wf steady , the gain Ke and the time constant Te are obtained according to the engine speed feedback value N, the inlet pressure P2 and the inlet temperature T2, so that the function relationship is as follows when it is extended to nonlinearity:

[0077] [Wf stead , Ke, Te] = f(N, P2, T2)

[0078] At this point, the construction of the engine on-board model is completed, that is, the steady-state fuel flow value Wf steady , the gain Ke and the time constant Te are obtained according to the engine speed feedback value N, the inlet pressure P2 and the inlet temperature T2, and then the main fuel flow calculation value wf' is calculated according to the steady-state fuel flow value Wf steady , the gain Ke, the time constant Te and the engine speed feedback value N.

[0079] Step S3: calculating the control current at the current moment according to the difference between the main fuel flow given value at the current moment and the main fuel flow calculation value at the current moment;

[0080] Step S4: driving the main fuel metering valve to output fuel for supplying the engine for combustion according to the control current at the current moment, so as to realize the control of the engine speed.

[0081] The engine on-board model-based metering valve disconnection fault processing method provided by the application is suitable for engine main fuel control, and when the main fuel metering valve sensor disconnection fault occurs, the engine speed is controllable, and the control flow is still observable.

[0082] As another embodiment of the application, an engine on-board model-based metering valve disconnection fault processing system is provided, as shown in Figure 2 The engine on-board model-based metering valve disconnection fault processing system comprises:

[0083] an outer loop controller, configured to obtain an engine speed given value at a current moment and an engine speed feedback value at the current moment, and to calculate a main fuel flow given value at the current moment according to a difference between the engine speed given value at the current moment and the engine speed feedback value at the current moment;

[0084] an inner loop controller, configured to obtain the main fuel flow given value at the current moment, the engine speed feedback value at the current moment and an engine speed feedback value at a previous moment, and to construct an engine on-board model; and to input the engine speed feedback value at the current moment and the engine speed feedback value at the previous moment into the engine on-board model to output a main fuel flow calculation value at the current moment; and to calculate a control current at the current moment according to a difference between the main fuel flow given value at the current moment and the main fuel flow calculation value at the current moment; and to drive the main fuel metering valve to output fuel for the engine combustion according to the control current at the current moment, so as to realize control of the engine speed.

[0085] Specifically, the equivalent change principle is adopted to change Figure 2 the original double-loop control architecture into a new double-loop architecture, as shown in Figure 2 FIG. 1. The upper half of the figure is the original double-loop control architecture in a non-disconnection fault mode, and the lower half is the new double-loop control architecture in a main fuel metering valve sensor disconnection fault mode.

[0086] Mode 1) In the non-disconnection fault mode, the original double-loop control architecture is used for control: the outer loop controller calculates the main fuel flow given value WfDem according to a difference between the engine speed given value NDem and the speed feedback value N; then the inner loop controller calculates the control current I according to a difference between the main fuel flow given value WfDem and the main fuel flow actual value Wf (i.e. the sensor feedback value of the main fuel metering valve); after that, the inner loop controller drives the main fuel metering valve to move according to the control current I, and the sensor on the main fuel metering valve outputs the main fuel flow actual value Wf. The main fuel output by the main fuel metering valve changes the engine speed N after the fuel is combusted by the engine, and finally the engine speed feedback value N is equal to the speed given value NDem, so that the speed closed-loop control purpose is achieved.

[0087] Mode 2) In the disconnection fault mode, based on the equivalent change principle, the new double-loop control architecture is used for control: since the main fuel metering valve sensor is disconnected, the inner loop cannot obtain the output value Wf of the main fuel metering valve. Therefore, based on the equivalent change principle, the original double-loop control architecture is changed to Figure 2 the part shown in the dashed box in the upper half is changed to Figure 2The part shown in the dashed box in the lower half forms a new double-loop control architecture. In the new architecture, an engine on-board model 1 / GS2 is constructed, which takes the engine speed output N as input and the main fuel flow calculation value Wf' as output. The control process of the new architecture is as follows: the outer loop controller still calculates the main fuel flow given value WfDem according to the difference between the speed given value NDem and the engine speed feedback value N, while the inner loop controller obtains the main fuel flow model calculation value Wf' in the state according to the constructed engine on-board model, and then calculates the control current I according to the difference between the main fuel flow given value WfDem and the main fuel flow calculation value Wf', and the control current I drives the main fuel metering valve to output the actual fuel supply to the engine combustion, thereby changing the output speed N of the engine, and then taking the output N of the engine as the input of the on-board model to obtain the main fuel flow calculation value Wf'. In the case of no actual fuel feedback value Wf (i.e. the main fuel metering valve sensor is disconnected), the process realizes the engine target speed control, and at the same time, the control flow observation can be realized according to the output value Wf' of the 1 / GS2 model. Moreover, the original two controllers are directly used in the process, and no additional controller or control parameter needs to be designed.

[0088] From Figure 3 It can be seen that after the method of the present application is adopted, the control effect in the case of metering valve sensor disconnection fault is basically the same as that in the case of no fault.

[0089] It should be noted that the main fuel metering valve sensor disconnection fault flag word is established to switch the state: when the flag word is invalid (no disconnection fault), mode 1) control is selected; when the flag word is valid (disconnection fault), mode 2) control is selected.

[0090] Thus, the metering valve sensor disconnection fault handling based on the simplified model is completed.

[0091] Since the actual engine is nonlinear, it is obviously not suitable to adopt a single linear 1 / GS2 model. Therefore, in order to improve the model efficiency and simplify the logic structure, a linear variable parameter (LPV) model based on the principle of balanced manifold is adopted, which has extremely high accuracy in both steady state and dynamic state. The LPV model of the present scheme adopts the engine speed feedback value N as the scheduling variable, and approximates the engine fuel-speed (Wf-N) model to an inertia link in the local state. Accordingly, a first-order LPV model with N as the scheduling variable is established, and further the main fuel metering valve sensor disconnection fault handling control method based on the model is completed, and the control target in the fault condition is realized.

[0092] Specifically as follows:

[0093] A first order LPV model 1 / Gs2 is constructed with the engine speed feedback value N as the scheduling variable, which is an engine fuel-speed model expressed in continuous domain as:

[0094]

[0095] wherein Wf'(s) is the main fuel flow calculation value in continuous domain; N(s) is the engine speed feedback value in continuous domain; Ke and Te are the gain and time constant of the engine local linear model respectively;

[0096] The first order LPV model is discretized, i.e.:

[0097]

[0098] wherein Wf'(z) is the main fuel flow calculation value in discrete domain; N(z) is the engine speed feedback value in discrete domain;

[0099] Further, the expression is obtained as:

[0100]

[0101] wherein Wf'(k) is the main fuel flow calculation value in the kth sampling period; N(k) is the engine speed feedback value in the kth sampling period; N(k-1) is the engine speed feedback value in the (k-1)th sampling period; t is the sampling time;

[0102] Meanwhile, for the first order LPV model, according to the linear system principle, the following processing is performed:

[0103] N(k) = Ke · Wf steady (k)

[0104] wherein Wf steady (k) is the steady state fuel flow value of the engine in the kth sampling period;

[0105] In combination with the above series of linear models, the following can be obtained:

[0106]

[0107] In combination with the similarity principle, the steady state fuel flow value Wf steady , the gain Ke and the time constant Te are obtained according to the engine speed feedback value N, the inlet pressure P2 and the inlet temperature T2 within the envelope range, so that the function relationship is as follows when generalized to nonlinearity:

[0108] [Wf steaay , Ke, Te] = f(N, P2, T2)

[0109] Thus, the engine on-board model is completed, i.e. the steady-state fuel flow value wf is obtained according to the engine speed feedback value N, the inlet pressure P2 and the inlet temperature T2 steady , the gain Ke and the time constant Te, and then the main fuel flow calculation value wf' is calculated according to the steady-state fuel flow value wf steady , the gain Ke, the time constant Te and the engine speed feedback value N.

[0110] The above is only the preferred embodiment of the present application, and is not intended to limit the present application in any form. Although the present application has been disclosed above with the preferred embodiment, it is not intended to limit the present application. Any person skilled in the art can make some changes or modifications to the above disclosed technical content to obtain equivalent embodiments with equivalent changes, without departing from the technical solution of the present application. Any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present application, which does not depart from the technical solution of the present application, still belongs to the scope of the technical solution of the present application.

Claims

1. An engine on-board model based metering valve breakage fault handling method, characterized by, Comprising: Step S1: obtaining an engine speed given value at a current time, an engine speed feedback value at the current time and an engine speed feedback value at a previous time, and constructing an engine on-board model; Step S2: calculating a main fuel flow given value at the current time according to a difference between the engine speed given value at the current time and the engine speed feedback value at the current time, and inputting the engine speed feedback value at the current time and the engine speed feedback value at the previous time into the engine on-board model to output a main fuel flow calculation value at the current time; Step S3: calculating a control current at the current time according to a difference between the main fuel flow given value at the current time and the main fuel flow calculation value at the current time; Step S4: driving a main fuel metering valve to output fuel for engine combustion according to the control current at the current time, so as to realize control on the engine speed; Wherein, the inputting the engine speed feedback value at the current time and the engine speed feedback value at the previous time into the engine on-board model to output the main fuel flow calculation value at the current time further comprises: Constructing an engine speed feedback value N a first order LPV model 1 Gs 2, the first order LPV model being an engine fuel-speed model, the first order LPV model being expressed in continuous domain as: , wherein, Wf'(s) is a continuous domain main fuel flow calculated value; N(s) is a continuous domain engine speed feedback value; Ke and Te are respectively a gain and a time constant of the engine local linear model; The first order LPV model is discretized, i.e. , wherein, Wf'(z) Qdiscrete is the discrete domain main fuel flow calculated value; N(z) Ndiscrete is the discrete domain engine speed feedback value; Further, the expression is obtained as: , wherein, Wf'(k) is the main fuel flow calculated value for the kth sampling period; N(k) is the engine speed feedback value for the kth sampling period; N(k-1) is the engine speed feedback value for the k-1th sampling period; t is the sampling time; At the same time, for the first-order LPV model, according to the principle of linear system, the following processing is performed: , wherein, is the steady state fuel flow value for the engine in the kth sampling period; Based on the above series of linear models, we get: , Combining similar principles, within the envelope, according to the engine speed feedback value N , the inlet pressure P2 and the inlet temperature T2 , the steady-state fuel flow value , gain Ke and time constant Te are obtained, so the promotion to nonlinear has the following function relationship: , At this point, the construction of the engine on-board model is completed, i.e. the steady-state fuel flow value is obtained from the engine speed feedback value N , the inlet pressure P2 and the inlet temperature T2 、 gain Ke、 time constant Te , after which the main fuel flow calculation value is calculated from the steady-state fuel flow value 、 gain Ke、 time constant Te and the engine speed feedback value N wf' .​​ 2. An engine on-board model based metering valve line break fault handling system, characterized by, Comprising: An outer loop controller, configured to obtain an engine speed given value at a current time and an engine speed feedback value at the current time, and calculate a main fuel flow given value at the current time according to a difference between the engine speed given value at the current time and the engine speed feedback value at the current time; An inner loop controller, configured to obtain the main fuel flow given value at the current time, the engine speed feedback value at the current time and an engine speed feedback value at a previous time, and construct an engine on-board model; and input the engine speed feedback value at the current time and the engine speed feedback value at the previous time into the engine on-board model to output a main fuel flow calculation value at the current time; and calculate a control current at the current time according to a difference between the main fuel flow given value at the current time and the main fuel flow calculation value at the current time; and drive a main fuel metering valve to output fuel for engine combustion according to the control current at the current time, so as to realize control on the engine speed; Wherein, the inner loop controller is specifically configured to: Constructing an engine speed feedback value N a first order LPV model 1 Gs 2, the first order LPV model being an engine fuel-speed model, the first order LPV model being expressed in continuous domain as: , wherein, Wf'(s) is the continuous domain main fuel flow calculated value; N(s) is the continuous domain engine speed feedback value; Ke and Te are the gain and time constant, respectively, of the engine local linear model; The first order LPV model is discretized, i.e. , wherein, Wf'(z) Qdiscrete is the discrete domain main fuel flow calculated value; N(z) Ndiscrete is the discrete domain engine speed feedback value; Further, the expression is obtained as: , wherein, Wf'(k) is the main fuel flow calculated value for the kth sampling period; N(k) is the engine speed feedback value for the kth sampling period; N(k-1) is the engine speed feedback value for the k-1th sampling period; t is the sampling time; At the same time, for the first-order LPV model, according to the principle of linear system, the following processing is performed: , wherein, is the steady state fuel flow value for the engine in the kth sampling period; Based on the above series of linear models, we get: , Combining similar principles, within the envelope, according to the engine speed feedback value N , the inlet pressure P2 and the inlet temperature T2 , the steady-state fuel flow value , gain Ke and time constant Te are obtained, so the promotion to nonlinear has the following function relationship: , This completes the construction of the airborne engine model, based on the engine speed feedback value. N Import pressure P2 and inlet temperature T2 Obtain steady-state fuel flow rate 、 Gain Ke、 time constant Te Then, based on the steady-state fuel flow rate value 、 Gain Ke、 time constant Te and engine speed feedback value N Calculated value of main fuel flow wf' .

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