KR101963045B1 - Controller of nonlinear zet engine using fuzzy adaptive unscented kalman filter - Google Patents

Abstract

The present invention relates to a control apparatus of a non-linear zet engine using a fuzzy adaptive unscented Kalman filter. The control apparatus of a non-linear zet engine using a fuzzy adaptive unscented Kalman filter according to the present invention comprises: a fuzzy controller controlling an input fuel quantity of a jet engine by using fuzzy inference with respect to a non-linear dynamic characteristic model of a jet engine; and a fuzzy adaptive unscented Kalman filter, wherein an unscented Kalman filter is used to assess an output measured value with respect to a state variable of the fuzzy controller and the non-linear dynamic characteristic model, and a fuzzy logic is adopted during the process of tuning the unscented Kalman filter in order to reduce a covariance error caused by a noise while allowing the filter to be adaptive to the optimum gain.

Description

TECHNICAL FIELD [0001] The present invention relates to a control device for a nonlinear jet engine employing a fuzzy adaptive non-directed Kalman filter,

The present invention relates to a control apparatus for a nonlinear jet engine to which a fuzzy adaptive non-directed Kalman filter is applied, and more particularly, to a control apparatus for a jet engine having a severe nonlinear dynamic characteristic, And more particularly to a control apparatus for a nonlinear jet engine to which a fuzzy adaptive non-directed Kalman filter is applied.

Turbojet engines with rapid thrust output characteristics over a wide operating range are critical to understanding nonlinear dynamics and operating noise and noise characteristics during operation and effectively controlling them.

In the meantime, researches have been made on the controller design technique of jet engines for aircraft that are robust against noise or disturbance characteristics using linear and nonlinear control methods. Most of them apply the general Kalman filter to the linear model, and there is almost no case where the nonlinear filter is applied to the nonlinear model. However, the application of the general Kalman filter in the nonlinear region has a clear limit, and it is difficult to apply the nonlinear filter to the dynamic characteristic code of the jet engine reflecting the nonlinearity, so that there are many restrictions on the practical application of the system. Therefore, it is urgent to design a nonlinear filter that is applied to a nonlinear controller that reflects nonlinear dynamic characteristics for effective operation of a real jet engine.

Representative examples of the nonlinear filter include an extended Kalman filter based on a local approach based on Gaussian noise, an unscented Kalman filter and an improved global approach And particle filter by Monte Carlo method are known and used in various fields such as navigation, guidance, monitoring / tracking, financial and stock market prediction.

The extended Kalman filter can not guarantee the stability of the filter because the error can be diverted due to the average and covariance distortion due to the local linearization when the nonlinearity is severe like the jet engine, and the sequential numerical analysis method The computerization of Jabobian for linearization is complicated, which is unsuitable for application to engine cycle analysis codes. In addition, a particle filter that reflects non-linear characteristics well can secure stable filter performance by increasing the number of collocation points, but it has a drawback in that it requires a long calculation time in each step (time step) . On the other hand, the non-directed Kalman filter minimizes the distortion of mean and covariance by using scaled unscented transformation that reflects nonlinear characteristics, so that the divergence problem due to local optimization caused by design point linearization can be solved considerably. Due to the ease of application that does not require Corbian, it is widely used in today's nonlinear filter designs.

However, the jet engine has a severe nonlinear characteristic, and the control is limited only by the conventional unoriented Kalman filter of the fixed gain type.

This patent grasps the limitations in the control design of a jet engine employing such a non-directional Kalman miller, and proposes a new designing method.

The paper is organized as follows. Han, D. J., "Non-linear Control of Turbojet Engine for High Maneuverability UAV," Journal of the Korean Society for Aeronautical and Space Sciences, 40 (5), May 2012, pp. 431-438.

SUMMARY OF THE INVENTION It is therefore an object of the present invention to provide a control method of a jet engine having nonlinear dynamic characteristics by applying fuzzy logic in a process of tuning an ungrained Kalman filter to actively adapt the filter performance according to a time step, The present invention provides a control apparatus for a nonlinear jet engine to which a fuzzy adaptive non-directed Kalman filter capable of improving performance is applied.

The problems to be solved by the present invention are not limited to the above-mentioned problems, and other matters not mentioned can be clearly understood by those skilled in the art from the following description.

The above object can be accomplished by a fuzzy controller for controlling an input fuel quantity of a jet engine using a fuzzy inference system for a nonlinear dynamic model of a jet engine according to the present invention; And a non-linear Kalman filter for estimating output measurements on the fuzzy controller and the state variable of the nonlinear dynamic behavior model, wherein the non-linear Kalman filter is tuned to adapt to the optimal gain while reducing covariance error by noise, The present invention can be achieved by a control apparatus of a nonlinear jet engine applying a fuzzy adaptive non-directed Kalman filter including a fuzzy adaptive non-directed Kalman filter to which logic is applied.

Here, the fuzzy adaptive non-directed Kalman filter is a covariance of the measurement noise in order to minimize the matching error (DOM _k ) between the covariance for innovation and the output covariance, which defines the difference between the measurement value and the evaluation value at step k of the discrete time The displayed R _{k =} R _{k -1} + R _k can be adjusted for each step (k).

Herein, the fuzzy logic may be applied to the fuzzy adaptive non-directed Kalman filter in the process of obtaining the parameter ΔR _k for the DOM _k with the optimal filter gain.

Here, the fuzzy controller may be formed by combining a PI type fuzzy controller and a differential controller.

According to the controller of the nonlinear jet engine to which the fuzzy adaptive irregular Kalman filter of the present invention as described above is applied, the control performance can be remarkably improved as compared with the case of using the conventional irregular Kalman filter.

FIG. 1 shows an example of a target jet engine to which a control device of a nonlinear jet engine applying the fuzzy-adaptive non-directed Kalman filter of the present invention is applied.
Fig. 2 shows characteristic curves of the compressor, combustor and turbine of Fig.
3 is a diagram showing a control flow of the fuzzy controller according to the present invention.
Fig. 4 shows an example of the membership function used in the fuzzy controller.
5 shows an overall control flow diagram of a jet engine control apparatus to which an anisotropic Kalman filter is applied for a fuzzy controller used for controlling a jet engine and an estimator for an output measurement value (thrust) relating to a state variable (engine speed) Respectively.
6 is a graph showing the control performance regarding the engine speed and the thrust when the control of the jet engine is performed using the purge controller having the non-directed Kalman filter.
7 is a control flowchart illustrating a tuning process of a fuzzy adaptive non-directed Kalman filter using fuzzy logic according to an embodiment of the present invention.
FIG. 8 shows an example of the membership function of the matching error DOMk and? R _k in the design process of the fuzzy adaptive non-directed Kalman filter according to an embodiment of the present invention.
9 is a graph showing the control performance regarding the engine speed and the thrust when the control of the jet engine is performed using the controller of the nonlinear jet engine to which the fuzzy adaptive non-directed Kalman filter according to the embodiment of the present invention is applied .

The details of the embodiments are included in the detailed description and the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS The advantages and features of the present invention, and the manner of achieving them, will be apparent from and elucidated with reference to the embodiments described hereinafter in conjunction with the accompanying drawings. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. To fully disclose the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims. Like reference numerals refer to like elements throughout the specification.

Hereinafter, the present invention will be described with reference to the drawings for explaining a control apparatus for a nonlinear jet engine to which a fuzzy adaptive non-directed Kalman filter is applied according to embodiments of the present invention.

First, a description will be made of a design of a fuzzy controller and an unirradiated Kalman filter for controlling a jet engine, prior to describing a control apparatus for a nonlinear jet engine applying a fuzzy adaptive irregular Kalman filter according to an embodiment of the present invention.

FIG. 1 shows an example of a target jet engine to which a control device of a nonlinear jet engine applying a fuzzy-adaptive non-directed Kalman filter according to the present invention is applied. FIG. 2 shows characteristic curves of a compressor, a combustor, Fig. 3 is a diagram showing a control flow of the fuzzy controller according to the present invention, Fig. 4 shows an example of the belonging function used in the fuzzy controller, Fig. 5 shows the fuzzy controller used for the control of the jet engine, FIG. 6 shows a general control flowchart of a jet engine control apparatus to which an unleaded Kalman filter is applied for estimating an output measurement value (thrust) with respect to a variable (engine revolution number). FIG. And the control performance regarding the engine speed and thrust when performing the control of the jet engine.

FIG. 1 shows an example of a target jet engine for performing control according to the present invention, which is a turbo jet engine (TRI 60-3) used for an actual unmanned aerial vehicle.

The dynamic characteristic model of the jet engine as shown in Fig. 1 can be obtained from the thermodynamic transient performance. This is based on the thermodynamic cycle analysis that derives the thermodynamic parameters on the characteristic curves of the compressor 10, the combustor 20, the turbine 30, etc., which are components of the jet engine, (Temperature, pressure, density, speed, etc.) for the operating parameters of the engine (engine speed, flight speed, altitude) and then apply the thermodynamic equilibrium conditions The unsteady thermal equilibrium equation of Equation 1 to Equation 3 is applied to the power, energy, flow rate, and the like for each component in the static performance analysis result for determining the thrust, fuel consumption rate,

Power balance between compressor (c) and turbine (t):

<수학식 1>

&Quot; (1) &quot;

Energy balance:

<수학식 2>

&Quot; (2) &quot;

Flow Equilibrium:

<수학식 3>

&Quot; (3) &quot;

I: input side, W: flow rate, P: (total) pressure, T: (total) temperature, I: rotor shaft inertia (t) N: engine speed (RPM), H: enthalpy, V: volume, U: internal energy)

The thermal equilibrium relation with respect to the input fuel quantity is expressed by the nonlinear dynamics equation according to discrete time k as follows.

<수학식 4>

&Quot; (4) &quot;

(Where, x: the state variables (engine speed, pressure, temperature), y: the output variables (thrust), u: Fuel input, w: noise process v; measurement noise, k: sample time)

A nonlinear controller suitable for the nonlinear dynamic model as described above will be designed. At this time, the controller design goal of the jet engine is to control the input fuel amount effectively to obtain a stable and rapid thrust characteristic within the surge region of the compressor 10 for the jet engine system having the non-linear characteristic as shown in Equation (4) The fuzzy control technique is applied to the design of the nonlinear controller as shown in FIG.

At this time, the fuzzy controller 100 to which the fuzzy control technique is applied may be configured by combining a PI type fuzzy controller and a general differential controller. More specifically, the PI type fuzzy controller with the engine speed proportional to the thrust can be used as a state variable, and a general differential controller for efficient controller design based on efficiency. In this case, in the fuzzy controller 100 using the PI type fuzzy inference system, in order to prevent the saturation of the control input due to the wind-up in the case of the integrator, The following type of incremental reasoning method can be used for resetting.

For the following fuzzy rule (i-th rule)

는 각각 전제부와 결론부의 소속함수들로서, 7개의 삼각형 퍼지화 변수(NB, NM, NS, ZO, PS, PM, PB)를 사용하였고, 입력(

)으로는 엔진 전수(RPM)(오차, 오차증분)가 되며 출력값 증분

는 연료량 증분이 된다. 이때 사용된 전제부 및 결론부 각각의 소속함수는 도 4에 도시된 함수일 수 있는데, 이에 한정되는 것은 아니다.

(NB, NM, NS, ZO, PS, PM, and PB) are used as the membership functions of the pre-

(RPM) (error, error increment), and the output value increment

Becomes the fuel amount increment. The membership functions of the preamble and the conclusion used at this time may be the functions shown in FIG. 4, but the present invention is not limited thereto.

)은 도출된 퍼지 출력값과 함께 오차증분

에 대한 일반적인 미분제어기를 결합한 다음과 같은 PID형 퍼지 제어기(100)를 통하여 구해질 수가 있다.Input fuel amount (

) &Lt; / RTI &gt; is the error increment along with the derived fuzzy output value

Can be obtained through the following PID type fuzzy controller 100 which combines a general differential controller for the PID type.

<수학식 5>

Equation (5)

는 각각 엔진 회전수(RPM)의 오차증분 및 오차의 퍼지추론값, 오차증분의 변화량을 표시하고,

는 각각 비례퍼지게인, 적분퍼지게인, 일반적인 미분게인으로서 각각 5.95, 0.1, 0.00035로 조정된다. here,

Respectively represent the error increment of the engine speed RPM and the fuzzy inference value of the error and the variation amount of the error increment,

Are adjusted to 5.95, 0.1, and 0.00035, respectively, as general differential gain, proportional spreading, integral spreading, respectively.

Hereinafter, the case where the non-directed Kalman filter is applied to the controller to which the above-described fuzzy controller 100 is applied will be described.

,

에 대해 평균

과 공분산

을 매개변수로 변환된 비선형변수

로 수학식 6과 같이 시그마점(sigma point)을 표시한 후,The covariance assuming each Gaussian noise acting on the process and output measurements

,

Average for

And covariance

Into nonparametric variables

, A sigma point is expressed as Equation (6)

<수학식 6>

&Quot; (6) &quot;

: 조정상수)(Where, L : number of state variables,

: Adjustment constant)

Converting the state variables and outputs to the following, respectively,

<수학식 7>

&Quot; (7) &quot;

<수학식 8>

&Quot; (8) &quot;

The mean and covariance for each are predicted as follows,

<수학식 9>

&Quot; (9) &quot;

<수학식 10>

&Quot; (10) &quot;

<수학식 11>

Equation (11)

<수학식 12>

&Quot; (12) &quot;

<수학식 13>

&Quot; (13) &quot;

는 각각 평균과 공분산의 가중치로서 적당한 값을 정한다.)(here,

Is a weight of the mean and covariance, respectively.

)을 이용하여 다음과 같이 실시간(k)으로 평균과 공분산을 보정(update)한 후,This is called filter gain

) To update the mean and covariance in real time (k) as follows,

<수학식 14>

&Quot; (14) &quot;

<수학식 15>

&Quot; (15) &quot;

The process of Equations (6) to (15) is repeated at the next time step.

 For reference, FIG. 5 is a graph showing the relationship between the fuzzy controller 100 used for the control of the target jet engine of FIG. 1 and an unirradiated Kalman filter for estimating output measurements (thrust) 1 shows a general control flow diagram of a jet engine controller.

FIG. 6 is a graph showing the relationship between the actual covariance (true w / o filter) and the non-covariant Kalman filter, when the noise covariance of the rotational speed and the thrust measurement is 1000 RPM and 100 N, respectively. 100) is compared with the engine speed, the state variable, and the output variable, thrust. It can be seen that the performance of the controller and the filter is rapidly deteriorated after the transient of the engine speed and the thrust. In the case of the engine speed, there is a large error in the tendency of the average value as well as the dispersion error in comparison with the actual value without the filter. Especially, it is deviated from the steady state value of 27,000 RPM, which shows that the distortion of the average value due to the smell diffusion is severely appeared. In the case of thrust, the dispersion error is somewhat reduced compared to the actual value, but the trend of the average value tends to be divergent compared to the steady state value, indicating the unstable filter performance in which the average value diverges due to the non-conversion.

It can be seen that the nonlinearity of the target jet engine represented by Equation (4) shows a very large tendency in comparison with the operating range in FIG. 6 (22,000 RPM -> 27,000 RPM). Thus, the performance degradation of the non-linear Kalman filter, which is a kind of nonlinear filter, is due to the severe non-linear characteristics of the target jet engine. In this case, due to the distortion error generated in the non- .

The most suitable nonlinear filter for a system with severe nonlinear characteristics such as the target jet engine is Bayesian type particle filter based on a measurement value represented by a probability density function (PDF). However, the use of the Bayesian filter optimized with the Gaussian type probability density function is extremely limited, and there is a fundamental limitation in the design of the controller and the filter using the Bessian filter because of the enormous computation time required for the Monte Carlo simulation at each time step. Same as. Accordingly, it is determined that a method of supplementing the conventional non-directed Kalman filter is most effective. According to the present invention, as described later, the adaptive filter gain adjustment method, which adapts the filter performance actively according to the time step, The non-directed Kalman filter is subjected to additional tuning of the filter gain.

Hereinafter, a control apparatus for a nonlinear jet engine to which a fuzzy adaptive non-directed Kalman filter according to an embodiment of the present invention is applied will be described with reference to FIGS. 7 to 9. FIG.

FIG. 7 is a control flowchart showing a tuning process of a fuzzy adaptive non-directed Kalman filter using fuzzy logic according to an embodiment of the present invention, and FIG. 8 is a flowchart illustrating a process of tuning a fuzzy adaptive non-directed Kalman filter according to an embodiment of the present invention. 9 shows an example of the membership function of the matching error DOMk and the deviation error function R _{k in} the process of the embodiment of the present invention. FIG. 5 is a graph showing the control performance regarding the engine speed and thrust when performing the control of FIG.

The controller of the nonlinear jet engine applying the fuzzy adaptive irregular Kalman filter according to an embodiment of the present invention may be configured to include the fuzzy controller 100 and the fuzzy adaptive irregular Kalman filter 200. [

The fuzzy controller 100 controls the input fuel amount of the jet engine using a fuzzy inference system for the nonlinear dynamic model of the jet engine obtained as described above. In the present invention, the fuzzy controller 100 may be configured by combining a PI type fuzzy controller and a general differential controller. Since the description of the fuzzy controller 100 has been described with reference to FIG. 3, detailed description thereof will be omitted .

The fuzzy adaptive non-directed Kalman filter 200 uses the above-described non-directed Kalman filter to evaluate the state variables of the fuzzy controller 100 and the nonlinear dynamic behavior model, and uses the non-directed Kalman filter to reduce the covariance error by folding, It is an unfiltered Kalman filter with additional fuzzy logic in the process of tuning the filter.

That is, in step k, an innovation, which defines the difference between the measured value and the evaluated value,

<수학식 16>

&Quot; (16) &quot;

Covariance to

<수학식 17>

&Quot; (17) &quot;

(Where M is the window length)

를 최소화하기 위해 측정잡음의 공분산으로 표시되는

을 이에 매 단계(k)마다 조정하여 적응해 가는 과정이다(도 7 참조). 이때, 최적 필터게인을 갖는

에 대한

을 구하는 방안에 있어 다음과 같은 퍼지논리를 적용할 수가 있다. And the output covariance (DOM: Degree of Matching)

Lt; RTI ID = 0.0 &gt; covariance &lt; / RTI &gt; of the measurement noise to minimize

(K) for each step (see FIG. 7). At this time,

For

The following fuzzy logic can be applied.

The fuzzy rules used in this paper are as follows. The fuzzy rules used are five triangular fuzzy variables (NM, NS, ZE, PS, PM) and (IL, I, M, D, DL)

각각의 소속함수의 일 예의 형상은 도 8과 같을 수가 있는데, 퍼지규칙 및 소속함수의 예는 이에 한정되는 것은 아니다. 이때,

는 목표점 부근으로 갈수록 면밀히 배치하고

는 더욱 조밀하게 분포시켜 튜닝의 정밀도가 확보될 수가 있다.

The shape of an example of each belonging function may be the same as that of FIG. 8, but examples of the fuzzy rule and the membership function are not limited thereto. At this time,

Is placed closer and closer to the target point

Can be distributed more densely and the accuracy of tuning can be ensured.

FIG. 7 illustrates a tuning process of a fuzzy adaptive unscented Kalman filter (FAUKF) according to an embodiment of the present invention.

Fig. 9 shows the engine speed and thrust performance of a control apparatus using a fuzzy adaptive non-directed Kalman filter according to the present invention. As shown in Fig. 6, it can be seen that the error of the average value, as well as the actual value and the dispersion error, are significantly reduced compared with the result of applying the conventional unoriented Kalman filter, and that the dispersion error is less stable than the actual value . In particular, the engine performance shows a stable filter performance with a reduced average error as well as variance error than the actual value, and the steady state trend after the transition shows a fairly stable state even in the thrust case.

The scope of the present invention is not limited to the above-described embodiments, but may be embodied in various forms of embodiments within the scope of the appended claims. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the appended claims.

10: Compressor
20: Combustor
30: Turbine
100: Fuzzy controller
200: Fuzzy adaptive irregular Kalman filter

Claims (4)

A fuzzy controller for controlling an input fuel quantity of the jet engine using a fuzzy inference system for a nonlinear dynamic model of the jet engine; And
Wherein the non-linear Kalman filter is used for the evaluation of the output measurement values of the fuzzy controller and the state variable of the nonlinear dynamic behavior model, and wherein in the process of tuning the non-Kalman filter to adapt to the optimum gain while reducing the covariance error by noise, And a fuzzy adaptive non-directed Kalman filter to which the fuzzy adaptive non-directed Kalman filter is applied,
The fuzzy adaptive irregular Kalman filter
Matching error between the covariance and the output covariance of the innovations, which defines the difference between the measured value and the evaluation value in step k the discrete time (DOM _k) of R _{k =} R _k-1 represented by the covariance of the measurement noise to minimize + A controller for a nonlinear jet engine applying a fuzzy adaptive non-directed Kalman filter for adjusting? R _k every step (k). delete The method according to claim 1,
Wherein the fuzzy adaptive non-directed Kalman filter is a fuzzy adaptive non-directed Kalman filter for applying the fuzzy logic in the process of obtaining ΔR _k for the DOM _k with an optimal filter gain. The method according to claim 1,
Wherein the fuzzy controller is a fuzzy adaptive non-directed Kalman filter formed by combining a PI type fuzzy controller and a differential controller.

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