CN113297679B - Propellant mass flow observation method of variable thrust rocket engine - Google Patents

Propellant mass flow observation method of variable thrust rocket engine Download PDF

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CN113297679B
CN113297679B CN202110681485.5A CN202110681485A CN113297679B CN 113297679 B CN113297679 B CN 113297679B CN 202110681485 A CN202110681485 A CN 202110681485A CN 113297679 B CN113297679 B CN 113297679B
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胡润生
吴建军
程玉强
杨述明
刘育玮
崔孟瑜
戚元杰
邓凌志
石业辉
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Abstract

The invention discloses a propellant mass flow observation method of a variable thrust rocket engine, which comprises the following steps: s1, obtaining a state space expression of the electric pump system according to the kinetic equation of the motor and the pump; s2, discretizing a state space expression of the electric pump system; s3, designing a Kalman filter through a program according to the discretization relational expression of the electric pump system; and S4, bringing the Kalman filter into the whole system pipeline, observing the mass flow of the liquid oxygen path and the methane path, judging whether the set filtering effect is achieved, if so, completing the design, otherwise, repeating the step S3 and adjusting the noise covariance and the initial prediction error covariance matrix in the Kalman filter design process until the set filtering effect is achieved. The method can effectively weaken the error of the environmental noise on the mass flow measurement, and can obtain a real and reliable mass flow value of the propellant.

Description

Propellant mass flow observation method of variable thrust rocket engine
Technical Field
The invention relates to the technical field of aerospace technology and control, in particular to a propellant mass flow observation method of a variable thrust rocket engine.
Background
With the development of the aerospace field, many countries are beginning to focus on the research of advanced technologies such as aircraft repeatable recovery or planet surface soft landing. In order to realize soft landing, the depth variable thrust liquid rocket engine is an indispensable power device, and particularly for the surface soft landing of an atmospherical-free planet, the variable thrust liquid rocket engine is the only power device for realizing the soft landing.
For a single liquid rocket engine, thrust can be achieved by changing the type of propellant, the flow rate of the propellant, the outlet area of the nozzle and the throat of the nozzle. But due to the limitations of physical structure and heat flow, it is difficult to change the propellant type, nozzle throat and outlet area. Adjusting mass flow is the simplest way to adjust engine thrust. With the development of motor and battery technologies, the electric pump liquid rocket engine has the characteristics of low cost, high reliability, simple adjustment, easy realization of depth-to-thrust and the like, and is more and more valued.
For variable thrust liquid rocket engines, the accuracy of propellant mass flow observation determines the accuracy of thrust adjustment. The mass flow of the propellant is effectively observed and controlled, and the method has great significance for realizing the task of soft landing on the surface of the planet. However, in the case of a complex mechanical structure such as a rocket engine, strong noises such as the booming of the engine and various mechanical vibrations are accompanied during operation. Therefore, in order to accurately observe the mass flow of the propellant in the working process of the variable thrust rocket engine, a corresponding method for observing the mass flow of the propellant of the variable thrust rocket engine needs to be designed.
Disclosure of Invention
The invention aims to provide a propellant mass flow observation method of a variable thrust rocket engine, which overcomes the defects in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a propellant mass flow observation method of a variable thrust rocket engine comprises the following steps:
s1, obtaining a state space expression of the electric pump system according to the kinetic equation of the motor and the pump;
s2, discretizing a state space expression of the electric pump system;
s3, designing a Kalman filter through a program according to the discretization relational expression of the electric pump system;
and S4, bringing the Kalman filter into the whole system pipeline, observing the mass flow of the liquid oxygen path and the methane path, judging whether the set filtering effect is achieved, if so, completing the design, otherwise, repeating the step S3 and adjusting the noise covariance and the initial prediction error covariance matrix in the Kalman filter design process until the set filtering effect is achieved.
Further, the state space expression of the motor-driven pump system can be expressed as:
Figure BDA0003122933350000021
Figure BDA0003122933350000022
denotes the derivative of X, X ═ X1x2x3]T，x1，x2And x3As state variables
Further, the kinetic equation of the motor and pump is:
Figure BDA0003122933350000023
wherein, UmIs the motor voltage, RmIs the motor coil resistance, imIs the motor current, LmIs the motor inductance, t is the time, emIs the motor back electromotive force, ω is the motor rotational angular velocity, CeIs the motor back electromotive force and torque coefficient, Ce0Is the motor back electromotive force and the torque coefficient constant, ωRIs a reference rotational angular velocityThe degree of the magnetic field is measured,
Figure BDA0003122933350000024
is the mass flow rate of the fuel or oxidant,
Figure BDA0003122933350000025
is a reference value for the mass flow of fuel or oxidant, ImIs the moment of inertia of the motor, fmIs the friction coefficient of the motor, T is the load moment driving the pump, IF is the fluid inertia of the electric pump, TRElectric pump reference torque, theta is electric pump characteristic angle, N is electric pump specific speed, WH and WT are theta and Nsρ is the average density of the fluid entering and exiting the pump, g is the acceleration of gravity, a1And a2Is a constant coefficient;
three state variables x1，x2And x3Are respectively imω and
Figure BDA0003122933350000026
the input quantity U and the output quantity y of the system are U respectivelymAnd
Figure BDA0003122933350000027
wherein:
Figure BDA0003122933350000028
further, in the step S2, a four-step lattice stoke method is adopted to discretize the system state space expression, so as to obtain:
Figure BDA0003122933350000031
Figure BDA0003122933350000032
yk+1＝h(Xk+1，uk+1)＝xk+1，3；
where Δ t is the discretized time step, f1、f2、f3And f4Can be represented as:
f1＝f(Xk，uk)；
Figure BDA0003122933350000033
Figure BDA0003122933350000034
f4＝f(Xk+Δtf3，uk)。
further, the step S3 specifically includes the following steps,
s31, giving the mean value of the initial state at time step k
Figure BDA0003122933350000035
And an initial prediction error covariance matrix Pk|k；
Figure BDA0003122933350000036
Figure BDA0003122933350000037
S32, calculating the sigma point of the time step k:
Figure BDA0003122933350000038
Figure BDA0003122933350000039
Figure BDA00031229333500000311
wherein n is a state variable XkThe dimension(s) of (a) is,
Figure BDA00031229333500000310
is a matrix (n + lambda) Pk|kCholesky decomposes the ith column vector, and λ may be expressed as λ ═ α2(n+k)-n；
S33, calculation through a nonlinear model
Figure BDA0003122933350000041
Obtaining a new predicted mean value of the state variables
Figure BDA0003122933350000042
And the prediction covariance matrix Pk+1|k；
Figure BDA0003122933350000043
Figure BDA0003122933350000044
Wherein Q iskIs a process noise matrix, weights
Figure BDA0003122933350000045
And
Figure BDA0003122933350000046
are respectively defined as:
Figure BDA0003122933350000047
Figure BDA0003122933350000048
s34, sigma requires root in the step of updating measurementDigging machine
Figure BDA0003122933350000049
And Pk+1|kRecalculation
Figure BDA00031229333500000410
Figure BDA00031229333500000411
Figure BDA00031229333500000412
By means of the new sigma point
Figure BDA00031229333500000413
The mean value of the predicted values of the measurement results is as follows:
Figure BDA00031229333500000414
measuring the covariance matrix Pyy，k+1|kAnd a cross-covariance matrix P of state variables and measurementsxy，k+1|kExpressed as:
Figure BDA0003122933350000051
Figure BDA0003122933350000052
s35, calculating Kalman gain K of the kth time stepk+1Mean value of state variables
Figure BDA0003122933350000053
Sum covariance matrix Pk+1|k+1；
Kk+1＝Pxy，k+1|k(Pyy，k+1|k)-1
Figure BDA0003122933350000054
Pk+1|k+1＝Pk+1|k-Kk+1Pyy，k+1|kKk+1 T。
Further, the kalman filter is an unscented kalman filter.
Compared with the prior art, the invention has the advantages that: the invention can effectively weaken the error of the environmental noise on the mass flow measurement, can obtain the real and reliable propellant mass flow value, can provide more accurate state or output feedback for the design of the controller on one hand, and also provides certain technical support for realizing the fault detection and diagnosis of the variable thrust process and eliminating the sensor and the environmental interference on the other hand.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the propellant mass flow observation method of the variable thrust rocket engine of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the scope of the present invention will be more clearly and clearly defined.
Referring to fig. 1, the embodiment discloses a propellant mass flow observation method for a variable thrust rocket engine, which adopts an approximately linear control strategy to control a nonlinear system, and mainly comprises the following steps:
and step S1, obtaining a state space expression of the electric pump system according to the kinetic equation of the motor and the pump.
In this embodiment, the motor dynamic equation mainly includes three partial voltage balance equations, an electromagnetic torque equation, and a motor torque balance equation.
The voltage balance equation of the armature coil of the direct current motor is as follows:
Figure BDA0003122933350000061
wherein U ismIs the motor voltage, RmIs the coil resistance imIs a current, LmIs the inductance, t is the time, emIs the back electromotive force and can be expressed as:
em＝Ceω (2)
where ω is the angular speed of rotation of the motor, CeIs the motor back emf and torque coefficient, which can be expressed as:
Ce＝Ce0im (3)
wherein C ise0Is the motor back emf and torque coefficient constant.
The electromagnetic torque equation of the motor is
M＝imCe (4)
Where M is the output torque of the motor.
The torque balance equation of the motor is as follows:
Figure BDA0003122933350000062
wherein, ImIs the moment of inertia of the motor, fmIs the coefficient of friction of the motor and T is the load torque driving the pump.
The following is the pump kinetic equation, first defining two dimensionless parameters, as follows:
Figure BDA0003122933350000063
wherein v is the dimensionless volume flow rate, Q is the volume flow rate, QRIs a reference volumetric flow rate; alpha is the dimensionless speed, N is the pump speed, NRIs the reference rotational speed.
The fluid inertia IF, reference torque T is given nextRCharacteristic angle theta and specific rotation speed NsDefinition of (1):
Figure BDA0003122933350000064
Figure BDA0003122933350000065
Figure BDA0003122933350000066
Figure BDA0003122933350000071
where ρ isRFor reference density, LRFor pump reference flow path length, ARReference flow passage cross-sectional area, HRFor reference pump head, ηRFor reference efficiency, ρ is the average density of the fluid entering and exiting the pump, and g is the acceleration due to gravity.
The pump head and pump torque can be expressed as:
H＝HRWH(a2+ν2) (11)
T＝TRWT(α2+v2) (12)
wherein WH and WT are θ and NsThe function of (2) can be obtained by table lookup interpolation. For the same electric pump, NsIs a fixed value, therefore WH and WT are univariate functions of θ, which can be fitted experimentally, andreference may be made to the work in published literature.
Further, a dynamic equation of the volume flow rate of the centrifugal pump can be obtained:
Figure BDA0003122933350000072
from the volume flow rate, a mass flow expression can be obtained:
Figure BDA0003122933350000073
from the relationship between rotational speed and angular velocity and the relationship between mass and density, equation (6) can be written as follows:
Figure BDA0003122933350000074
wherein
Figure BDA0003122933350000075
Which represents the mass flow of fuel or oxidant,
Figure BDA0003122933350000076
is a reference value for the mass flow of fuel or oxidant, w is the angular rotation velocity, and wR is the reference angular rotation velocity.
In equation (13), there is a pump boost pressure, and the pump boost pressure is related to the mass flow rate by fitting data:
Figure BDA0003122933350000077
wherein a is1And a2Are constant coefficients, i.e., two coefficients within the relationship between pump boost and mass flow.
Combining equations (1) - (16), the system of kinetic equations can be obtained as:
Figure BDA0003122933350000078
three state variables x defining a system1，x2And x3Are respectively imω and
Figure BDA0003122933350000081
the input quantity U and the output quantity y of the system are U respectivelymAnd
Figure BDA0003122933350000082
the state space expression for the system can be expressed as:
Figure BDA0003122933350000083
wherein:
Figure BDA0003122933350000084
h(X，u)＝x3 (20)
and step S2, discretizing a state space expression of the motor-driven pump system.
In this embodiment, a four-order longge stoke method is adopted to discretize the system state space expression, so as to obtain:
Figure BDA0003122933350000085
Figure BDA0003122933350000086
yk+1＝h(Xk+1，uk+1)＝xk+1，3 (23)
where Δ t is the discretized time step, f1、f2、f3And f4Can be represented as:
f1＝f(Xk，uk) (24)
Figure BDA0003122933350000087
Figure BDA0003122933350000088
f4＝f(Xk+Δtf3，uk) (27)
step S3, designing a kalman filter by a program according to the discretized relational expression of the electric pump system, specifically including the following steps.
Step S31, giving the mean value of the initial state at time step k
Figure BDA0003122933350000089
And an initial prediction error covariance matrix Pk|k：
Figure BDA00031229333500000810
Figure BDA00031229333500000811
Step S32, calculating a sigma point at time step k, i.e. a sigma point or a standard deviation point:
Figure BDA0003122933350000091
Figure BDA0003122933350000092
Figure BDA0003122933350000093
wherein n is a state variable XkThe dimension(s) of (a) is,
Figure BDA0003122933350000094
is a matrix (n + lambda) Pk|kCholesky decomposes the ith column vector, and λ may be expressed as λ ═ α2(n + k) -n, typically, 0 ≦ α ≦ 1 and κ ≧ 0, thereby ensuring that the covariance matrix is semi-positive, typically, κ ≦ 0 or n + k ≦ 3.
Step S33, time updating, and obtaining through nonlinear model calculation:
Figure BDA0003122933350000095
further, a new predicted mean value of the state variables can be obtained
Figure BDA0003122933350000096
And the prediction covariance matrix Pk+1|k；
Figure BDA0003122933350000097
Figure BDA0003122933350000098
Wherein Q iskIs a process noise matrix, weights
Figure BDA0003122933350000099
And
Figure BDA00031229333500000910
are respectively defined as:
Figure BDA00031229333500000911
Figure BDA00031229333500000912
in the case of gaussian noise, β is typically set to 2.
Step S34, in the step of updating measurement, the sigma point is required to be based on
Figure BDA00031229333500000913
And Pk+1|kRecalculating:
Figure BDA0003122933350000101
Figure BDA0003122933350000102
Figure BDA0003122933350000103
by means of the new sigma point it is possible to obtain:
Figure BDA0003122933350000104
the mean value of the predicted values of the measurement results is as follows:
Figure BDA0003122933350000105
measuring the covariance matrix Pyy，k+1|kAnd a cross-covariance matrix P of state variables and measurementsxy，k+1|kExpressed as:
Figure BDA0003122933350000106
Figure BDA0003122933350000107
step S35, calculating parameters, and calculating Kalman gain K of the kth time stepk+1Mean value of state variables
Figure BDA0003122933350000108
Sum covariance matrix Pk+1|k+1：
Kk+1＝Pxy，k+1|k(Pyy，k+1|k)-1 (45)
Figure BDA0003122933350000109
Pk+1|k+1＝Pk+1|k-Kk+1Pyy，k+1|kKk+1 T (47)
And S4, bringing the Kalman filter into the whole system pipeline, observing the mass flow of the liquid oxygen path and the methane path, judging whether the set filtering effect is achieved, if so, completing the design, otherwise, repeating the step S3 and adjusting the noise covariance and the initial prediction error covariance matrix in the Kalman filter design process until the set filtering effect is achieved.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, various changes or modifications may be made by the patentees within the scope of the appended claims, and within the scope of the invention, as long as they do not exceed the scope of the invention described in the claims.

Claims (6)

1. A propellant mass flow observation method of a variable thrust rocket engine is characterized by comprising the following steps:
s1, obtaining a state space expression of the electric pump system according to the kinetic equation of the motor and the pump;
s2, discretizing a state space expression of the electric pump system;
s3, designing a Kalman filter through a program according to the discretization relational expression of the electric pump system;
and S4, bringing the Kalman filter into the whole system pipeline, observing the mass flow of the liquid oxygen path and the methane path, judging whether the set filtering effect is achieved, if so, completing the design, otherwise, repeating the step S3 and adjusting the noise covariance and the initial prediction error covariance matrix in the Kalman filter design process until the set filtering effect is achieved.
2. The method of observing mass flow of propellant in a variable thrust rocket engine according to claim 1, wherein: the state space expression for the electric pump system can be expressed as:
Figure FDA0003496416650000011
Figure FDA0003496416650000012
denotes the derivative of X, X ═ X1 x2 x3]T，x1，x2And x3Is a state variable.
3. The method of observing mass flow of propellant in a variable thrust rocket engine according to claim 2, wherein: the kinetic equation of the motor and the pump is as follows:
Figure FDA0003496416650000013
wherein, UmIs the motor voltage, RmIs the motor coil resistance, imIs the motor current, LmIs the motor inductance, t is the time, ω is the motor rotational angular velocity, Ce0Is the motor back electromotive force and the torque coefficient constant, ωRIs a reference to the angular speed of rotation,
Figure FDA0003496416650000014
is the mass flow rate of the fuel or oxidant,
Figure FDA0003496416650000018
is a reference value for the mass flow of fuel or oxidant, JmIs the moment of inertia of the motor, fmIs the friction coefficient of the motor, T is the load moment driving the pump, IF is the fluid inertia of the electric pump, TRElectric pump reference torque, theta is the electric pump characteristic angle, NsIs the specific speed of the electric pump, WH and WT are theta and Nsρ is the average density of the fluid entering and exiting the pump, g is the acceleration of gravity, a1And a2Is a constant coefficient;
three state variables x1，x2And x3Are respectively imω and
Figure FDA0003496416650000016
the input quantity U and the output quantity y of the system are U respectivelymAnd
Figure FDA0003496416650000017
wherein:
Figure FDA0003496416650000021
h(X，u)＝x3。
4. the method of observing mass flow of propellant in a variable thrust rocket engine according to claim 1, wherein: in the step S2, a four-step lattice stoke method is adopted to discretize the system state space expression, so as to obtain:
Figure FDA0003496416650000022
Figure FDA0003496416650000023
yk+1＝h(Xk+1，uk+1)＝xk+1，3；
where Δ t is the discretized time step, f1、f2、f3And f4Can be represented as:
f1＝f(Xk，uk)；
Figure FDA0003496416650000024
Figure FDA0003496416650000025
f4＝f(Xk+Δtf3，uk)。
5. the method of observing mass flow of propellant in a variable thrust rocket engine according to claim 1, wherein: the step S3 specifically includes the following steps,
s31, giving the mean value of the initial state at time step k
Figure FDA0003496416650000026
And an initial prediction error covariance matrix Pk|k；
Figure FDA0003496416650000027
Figure FDA0003496416650000028
S32, calculating the sigma point of the time step k:
Figure FDA0003496416650000029
Figure FDA0003496416650000031
Figure FDA0003496416650000032
wherein n is a state variable XkThe dimension(s) of (a) is,
Figure FDA0003496416650000033
is a matrix (n + lambda) Pk|kCholesky decomposes the ith column vector, and λ may be expressed as λ ═ α2(n+κ)-n；
S33, calculation through a nonlinear model
Figure FDA0003496416650000034
Obtaining a new predicted mean value of the state variables
Figure FDA0003496416650000035
And the prediction covariance matrix Pk+1|k；
Figure FDA0003496416650000036
Figure FDA0003496416650000037
Wherein Q iskIs a process noise matrix, weights
Figure FDA0003496416650000038
And
Figure FDA0003496416650000039
are respectively defined as:
Figure FDA00034964166500000310
Figure FDA00034964166500000311
s34, in the step of updating measurement, the sigma point is required to be based on
Figure FDA00034964166500000312
And Pk+1|kRecalculation
Figure FDA0003496416650000041
Figure FDA0003496416650000042
Figure FDA0003496416650000043
By means of the new sigma point
Figure FDA0003496416650000044
The mean value of the predicted values of the measurement results is as follows:
Figure FDA0003496416650000045
measuring the covariance matrix Pyy，k+1|kAnd a cross-covariance matrix P of state variables and measurementsxy，k+1|kExpressed as:
Figure FDA0003496416650000046
Figure FDA0003496416650000047
s35, calculating Kalman gain K of the kth time stepk+1Mean value of state variables
Figure FDA0003496416650000048
Sum covariance matrix Pk+1|k+1；
Kk+1＝Pxy，k+1|k(Pyy，k+1|k)-1
Figure FDA0003496416650000049
Pk+1|k+1＝Pk+1|k-Kk+1Pyy，k+1|kKk+1 T。
6. The method of observing mass flow of propellant in a variable thrust rocket engine according to claim 1, wherein: the Kalman filter is an unscented Kalman filter.
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