CN113110571B - Method for estimating flight attack angle based on dimension reduction state observer - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 18
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- 230000009466 transformation Effects 0.000 claims description 8
- 238000004422 calculation algorithm Methods 0.000 abstract description 2
- 229920001971 elastomer Polymers 0.000 description 2
- 239000000806 elastomer Substances 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- RZVHIXYEVGDQDX-UHFFFAOYSA-N 9,10-anthraquinone Chemical compound C1=CC=C2C(=O)C3=CC=CC=C3C(=O)C2=C1 RZVHIXYEVGDQDX-UHFFFAOYSA-N 0.000 description 1
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- G05D1/10—Simultaneous control of position or course in three dimensions
- G05D1/107—Simultaneous control of position or course in three dimensions specially adapted for missiles
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Abstract
The invention discloses a method for estimating a flight attack angle based on a dimensionality reduction state observer. Most tactical missiles are not provided with an attack angle sensor, and the attack angle is a basic input quantity of the design of a multi-loop control system of the tactical missiles. The invention provides a method for estimating a flight attack angle based on a dimension reduction state observer, which comprises dynamic modeling and the dimension reduction state observer, wherein the dynamic modeling constructs a bivalent state equation according to the real-time missile flight state, a first-order state observer is constructed on the basis, and the observer parameters are determined according to the bandwidth of the state observer, so that the flight attack angle can be estimated. The method is based on the dimensionality reduction state observer to estimate the flight attack angle of the missile, and therefore an algorithm capable of effectively obtaining the flight attack angle of the missile is provided.
Description
Technical Field
The method relates to a method for estimating the flight attack angle, which is suitable for estimating the flight attack angle of an airplane or a guided missile.
Background
When the flight control system can utilize flight angle of attack information, the control quality can be improved, and for the missile, an angle of attack sensor is not equipped in general, so that the angle of attack information cannot be accurately obtained based on the missile-borne sensor. It is therefore desirable to develop an estimation of the flight angle of attack based on known flight state quantities.
Disclosure of Invention
The technical problem of the invention is solved: the method overcomes the defects of the prior art, provides a method for estimating the flight attack angle based on the dimensionality reduction state observer, and solves the problem that the missile cannot accurately obtain the flight attack angle under the condition of not being provided with an attack angle sensor.
The technical solution of the invention is as follows: a method for estimating a flight attack angle based on a dimensionality reduction state observer comprises the following steps:
(1) And dynamic modeling: calculating a projectile dynamic coefficient according to the flying state, the aerodynamics and the structural parameters of the missile, and constructing a second-order linear differential state equation based on the projectile dynamic coefficient; the second-order linear differential state equation takes an attack angle and an angular speed as state quantities, a pitching rudder deflection as a control quantity and an angular speed as an output quantity;
(2) Constructing a dimension reduction state observer: constructing a nonsingular equivalent transformation matrix P, performing equivalent linear transformation on a state matrix and a control matrix in the second-order linear differential state equation obtained in the step (1), constructing a dimension reduction state observer, determining an observer characteristic root on the basis of determining the bandwidth of the observer, and calculating by using the characteristic root to obtain a feedback matrix; the method comprises the steps that a dimensionality reduction state observer is constructed by taking a pitching rudder deflection as a control quantity and an angular speed as an input quantity, and an estimator of the dimensionality reduction state observer is a function of an attack angle;
(3) Obtaining an estimator of the dimension reduction state observer based on the angular velocity and the pitching rudder deflection, and calculating an attack angle x according to the estimator of the dimension reduction state observer 1 Is estimated by 1 。
The second-order linear differential equation set established in the step (1) is as follows:
wherein x is a state quantity,
alpha is angle of attack, omega z Angular velocity, u control variable, u = δ z ，δ z Is the pitch rudder deflection, y is the output quantity, A is the state matrix,
b is a control matrix, and B is a control matrix,
c is an output matrix, C = [01 ]]。
The parameters of the state matrix A are obtained by calculation according to the real-time flight state, pneumatic parameters and structural parameters, and specifically comprise the following steps:
wherein P is thrust, Y α The lift increment caused by the increment of the attack angle, m is the projectile body mass, V is the flying speed,
moment induced for angle of attack increment, J z Is the moment of inertia of the projectile body around the side shaft,
the moment caused by one unit is added to the angular velocity of the projectile.
The parameters of the control matrix B are obtained by calculation according to the real-time flight state, the pneumatic parameters and the structural parameters, and specifically comprise the following steps:
wherein m is the mass of the elastomer, VIn order to obtain the flying speed of the aircraft,
for the lift increase caused by rudder deflection increase,
moment due to rudder deflection, J z Is the moment of inertia of the projectile body around the side shaft.
The dimension reduction state observer is as follows:
wherein,
and
are respectively a matrix
The block matrix in (1) is a one-dimensional matrix,
is a feedback matrix, is constant e.
In the step (2), the characteristic root of the observer is determined according to the bandwidth of the observer, and the constant e in the feedback array is determined according to the characteristic root of the observer.
The constant e is calculated by the following formula:
where s is the characteristic root of the observer.
The estimator of the dimensionality reduction state observer is as follows: w = z 1 Ey, extracting the estimators on the basis of the output of the reduced-dimension state observer: w = z 1 -ey wherein z 1 Of angle of attackAnd estimating, wherein w is the estimated quantity of the dimensionality reduction state observer, e is a constant in the feedback array, and y is the output quantity of a second-order state equation.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the invention, the angular speed output by the missile can be used as the input quantity of the observer, the pitching rudder deflection is used as the control input quantity of the observer to construct a dimension-reduced first-order state observer, the flight attack angle is estimated in real time, the flight attack angle can be used as the input of a control system, the traditional two-loop control system is transformed into a three-loop control system, and the control quality can be greatly improved.
(2) The method is simple and easy to understand, the calculated amount is small, and a more accurate estimated value can be obtained.
(3) The method has the advantages of simple algorithm, less calculation amount, no need of adding other hardware equipment, guaranteed resolving precision, use of the estimated attack angle output by the observer in control loop design and capability of improving control quality to a greater extent.
Drawings
FIG. 1 is a schematic block diagram of a dimension reduction state observer according to an embodiment of the present invention;
FIG. 2 (a) shows the estimated output of the observer according to the embodiment of the present invention;
fig. 2 (b) shows an estimation error of the dimension reduction state observer according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, the present invention provides a method for estimating a flight angle of attack based on a reduced-dimension state observer, the method comprising the steps of:
(1) And dynamic modeling: calculating a projectile dynamic coefficient according to the flying state, the aerodynamics and the structural parameters of the missile, and constructing a second-order linear differential state equation based on the projectile dynamic coefficient; the second-order linear differential state equation takes an attack angle and an angular speed as state quantities, a pitching rudder deflection as a control quantity, and an angular speed as an output quantity;
the second-order linear differential equation set established in the step is as follows:
wherein x is a state quantity,
alpha is angle of attack, omega z Is angular velocity, u is control quantity, u = δ z ，δ z Is the pitch rudder deflection, y is the output quantity, A is the state matrix,
b is a control matrix, and B is a control matrix,
c is an output matrix, C = [01 ]]。
The parameters of the state matrix A are obtained by calculation according to the real-time flight state, pneumatic parameters and structural parameters, and specifically comprise the following steps:
wherein P is thrust, Y α The lift increment caused by the increment of the attack angle, m is the projectile body mass, V is the flying speed,
moment induced for angle of attack increment, J z Is the moment of inertia of the projectile about the side shafts,
the moment caused by one unit is added to the angular velocity of the projectile.
The parameters of the control matrix B are obtained by calculation according to the real-time flight state, the pneumatic parameters and the structural parameters, and specifically comprise the following steps:
wherein m is the mass of the projectile body, V is the flying speed,
for the lift increment caused by the rudder deflection increment,
moment due to rudder deflection, J z Is the moment of inertia of the projectile body around the side shaft.
(2) Constructing a dimension reduction state observer: constructing a nonsingular equivalent transformation matrix P, performing equivalent linear transformation on a state matrix and a control matrix in the second-order linear differential state equation obtained in the step (1), constructing a dimension reduction state observer, determining an observer characteristic root on the basis of determining the bandwidth of the observer, and calculating by using the characteristic root to obtain a feedback matrix; the method comprises the steps that a dimensionality reduction state observer is constructed by taking a pitching rudder deflection as a control quantity and an angular speed as an input quantity, and an estimator of the dimensionality reduction state observer is a function of an attack angle;
the dimensionality reduction state observer is as follows:
wherein,
and
are respectively a matrix
The block matrix in (1) is a one-dimensional matrix,
is a feedback matrix, is a constant e.
In the step, the characteristic root of the observer is determined according to the bandwidth of the observer, and the constant e in the feedback array is determined according to the characteristic root of the observer.
The constant e is calculated by the following formula:
where s is the characteristic root of the observer.
(3) Obtaining an estimator of the dimension reduction state observer based on the angular velocity and the pitching rudder deflection, and calculating an attack angle x according to the estimator of the dimension reduction state observer 1 Is estimated by 1 。
The estimator of the dimensionality reduction state observer is as follows: w = z 1 Ey, extracting the estimators on the basis of the output of the reduced-dimension state observer: z is a radical of 1 = w + ey wherein, z 1 For the estimation of the attack angle, w is the estimation quantity of the dimensionality reduction state observer, e is a constant in the feedback array, and y is the output quantity of a second-order state equation.
Example (b):
a missile flying at height 5500 meters at 0.7464mach (speed Vel =237.345 m/s) with aerodynamic coefficient: pneumatic static stability
Pneumatic rudder effect
Pneumatic damping
Coefficient of lift caused by angle of attack
Lift coefficient caused by one-degree pitching rudder deflection
(pneumatic reference area Sref =0.1m 2 Reference length Lref =3.50 m); the structural quality characteristics of the elastomer are as follows: moment of inertia J z ＝500Kg/m 2 Mass m =700Kg.
(1) Establishing a model
According to the flight state, the structural parameters and the pneumatic parameters, the dynamic coefficient of the projectile body can be calculated and solved
a 24 ＝-19.70，a 25 ＝-57.75，a 34 ＝0.8438，a 35 ＝0.0905，a 22 ＝-1.10
The flight attack angle and the flight angular rate are state variables of the single body in the longitudinal short period, the influence of the flight speed and gravity on the longitudinal motion is ignored, and a state equation of the longitudinal short period mode is established
Let the output be angular rate omega z The above equation can be written in the form of a state space of the second order linear differential equation set in the above step (1)
Wherein
u＝Δδ z ，y＝Δω z ，
C＝[0 1]
The parameters of the state matrix A are obtained by calculation according to the real-time flight state, the pneumatic parameters and the structural parameters, and specifically comprise the following steps:
wherein P is thrust, Y α The lift increment caused by the increment of the attack angle, m is the projectile body mass, V is the flying speed,
moment due to angle of attack increment, J z Is the moment of inertia of the projectile body around the side shaft,
the moment caused by one unit is added to the angular velocity of the projectile.
The parameters of the control matrix B are obtained by calculation according to the real-time flight state, the pneumatic parameters and the structural parameters, and specifically comprise the following steps:
wherein m is the mass of the projectile body, V is the flying speed,
for the lift increase caused by rudder deflection increase,
moment due to rudder deflection, J z Is the moment of inertia of the projectile body around the side shaft.
(2) Design dimension reduction state observer
1) Constructing a non-singular equivalent transformation matrix P
2) Performing equivalent linear transformation on the original state quantity
Namely that
3) Constructing a dimension reduction state observer:
u and y are known quantities, w is an estimated quantity, and x is extracted on the basis of the obtained w 1 Is estimated by 1 。
4) Determining feedback arrays
Suppose a feedback matrix is
Then
Assuming that the observer has a characteristic root of-24, then
Solve to obtain e = -1.1755
5) Determining a state observer
According to the formula (1), a
The state observer outputs:
z 1 ＝w+ey＝w-1.1755y
(3) Simulation result
The simulation results are shown in FIGS. 2 (a) and 2 (b), where FIG. 2 (a) is the true angle of attack (x) 1 ) And the output angle of attack (z) of the reduced dimension state observer 1 ) Fig. 2 (b) shows the estimation error of the dimension reduction state observer, and therefore, a certain estimation error exists at the initial position based on the estimated flight angle of attack by the dimension reduction observer, but the estimation error quickly tends to a small value with time, and a satisfactory estimation effect can be obtained.
Claims (1)
1. A method for estimating a flight attack angle based on a dimensionality reduction state observer is characterized by comprising the following steps:
(1) And dynamic modeling: calculating a projectile dynamic coefficient according to the flying state, the aerodynamics and the structural parameters of the missile, and constructing a second-order linear differential state equation based on the projectile dynamic coefficient; the second-order linear differential state equation takes an attack angle and an angular speed as state quantities, a pitching rudder deflection as a control quantity and an angular speed as an output quantity;
the second-order linear differential state equation established in the step (1) is as follows:
wherein x is a state quantity,
alpha is angle of attack, omega z Is angular velocity, u is control quantity, u = δ z ，δ z Is the pitch rudder deflection, y is the output quantity, A is the state matrix,
b is a control matrix, and B is a control matrix,
c is an output matrix, C = [01 ]]；
The parameters of the state matrix A are obtained by calculation according to the real-time flight state, pneumatic parameters and structural parameters, and specifically comprise the following steps:
wherein P is thrust, Y α The lift increment caused by the increment of the attack angle, m is the projectile body mass, V is the flying speed,
moment induced for angle of attack increment, J z Is the moment of inertia of the projectile body around the side shaft,
adding a unit-induced moment to the projectile angular velocity;
the parameters of the control matrix B are obtained by calculation according to the real-time flight state, the pneumatic parameters and the structural parameters, and specifically comprise the following steps:
wherein m is the mass of the projectile body, V is the flying speed,
for the lift increase caused by rudder deflection increase,
moment due to rudder deflection, J z The moment of inertia of the projectile body around the side shaft;
(2) Constructing a dimension reduction state observer: constructing a nonsingular equivalent transformation matrix Q, performing equivalent linear transformation on a state matrix and a control matrix in the second-order linear differential state equation obtained in the step (1), constructing a dimension reduction state observer, determining an observer characteristic root on the basis of determining the bandwidth of the observer, and calculating by using the characteristic root to obtain a feedback matrix; the method comprises the steps that a dimensionality reduction state observer is constructed by taking a pitching rudder deflection as a control quantity and an angular speed as an input quantity, and an estimator of the dimensionality reduction state observer is a function of an attack angle;
the dimensionality reduction state observer is as follows:
wherein,
and
are respectively a matrix
The block matrix in (1) is a one-dimensional matrix,
is a feedback matrix, is a constant e;
determining a characteristic root of an observer according to the bandwidth of the observer, and determining a constant e in a feedback array according to the characteristic root of the observer, wherein the constant e is calculated by the following formula:
wherein s is a characteristic root of the observer;
(3) Obtaining an estimator of the dimension reduction state observer based on the angular velocity and the pitching rudder deflection, and calculating an attack angle x according to the estimator of the dimension reduction state observer 1 Is estimated by 1 ；
The estimator of the dimensionality reduction state observer is as follows: w = z 1 Ey, extracting the estimators on the basis of the output of the reduced-dimension state observer: w = z 1 -ey, wherein z 1 For estimation of the angle of attack, w is the estimator of the dimensionality reduction state observer, and e is a constant in the feedback array.
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| US11029706B2 (en) * | 2018-12-07 | 2021-06-08 | The Boeing Company | Flight control system for determining a fault based on error between a measured and an estimated angle of attack |
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| CN107168925A (en) * | 2017-06-21 | 2017-09-15 | 同济大学 | A kind of state of linear system and Unknown inputs method |
| CN107450588A (en) * | 2017-09-29 | 2017-12-08 | 北京航空航天大学 | A kind of strong disturbance rejection control method of Flexible Spacecraft control system |
| CN108363305A (en) * | 2018-03-14 | 2018-08-03 | 中国人民解放军国防科技大学 | Tactical missile robust overload autopilot design method based on active interference compensation |
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