CN114489125A - High-precision approach optimal deceleration control method for gliding aircraft - Google Patents
High-precision approach optimal deceleration control method for gliding aircraft Download PDFInfo
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Abstract
The invention discloses a high-precision approach optimal deceleration control method for a gliding aircraft, wherein the actual input conditions of the method are the current flight time, position vector and speed vector of the gliding aircraft provided by an inertial navigation device, and the initial flight track parameter and terminal deviation value are obtained by numerical integration by utilizing aircraft parameters and an initial instruction sequence; then, solving a state sensitivity matrix sequence through flight trajectory parameters, thereby quickly obtaining an instruction feedback matrix according to an inverse recursive format; and according to the updating amount of the basis function, the terminal deviation amount is obtained through the numerical value again, the steps are repeated for multiple times of quick iteration to obtain a new instruction sequence meeting the terminal deviation, a new instruction angle is calculated according to the target point parameter and the reference instruction, an instruction updating closed-loop format can be formed, and the solving process has important characteristics of rapidity and reliability, so that the aim of high-precision speed reduction control can be efficiently fulfilled.
Description
Technical Field
The invention belongs to the technical field of flight control, and particularly relates to an optimal deceleration control method.
Background
The main research idea of the existing glide vehicle deceleration control method in China is that a motor deceleration guidance form is formed by combining an original guidance instruction and a deceleration motor instruction. For the gliding aircraft, the energy of the gliding aircraft is monotonously reduced due to no external power assistance, the gliding aircraft can meet the high-precision speed control capability only through aerodynamic control, and the requirement on a guidance method is high. The existing methods mainly focus on the following points: firstly, a reverse booster is additionally arranged, and the speed is quickly reduced by utilizing reverse thrust; secondly, a track planning strategy is utilized, and the aim of deceleration control is fulfilled by increasing the flying distance; and thirdly, controlling the longitudinal axis of the aircraft to rotate around a speed vector at an allowed maximum attack angle, and decelerating by using aerodynamic force. However, these methods have different speed control accuracy and have limitations, and thus a deceleration control method with high accuracy and wide applicability cannot be formed.
The existing gliding aircraft deceleration control has the defects. Hardware equipment is increased and the complexity of the system is increased due to the additional arrangement of the reverse booster; the precise relationship between the flight distance and the flight speed in the trajectory planning method is difficult to obtain, so that the control precision is low; the maximum angle of attack rotation will cause a large positional deviation and it will be difficult to meet the intended task.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a high-precision approach optimal deceleration control method for a gliding aircraft, wherein the actual input conditions of the method are the current flight time, position vector and speed vector of the gliding aircraft provided by an inertial navigation device, and an initial flight track parameter and a terminal deviation value are obtained through numerical integration by utilizing aircraft parameters and an initial instruction sequence; then, solving a state sensitivity matrix sequence through flight trajectory parameters, thereby quickly obtaining an instruction feedback matrix according to an inverse recursive format; and according to the updating amount of the basis function, the terminal deviation amount is obtained through the numerical value again, the steps are repeated for multiple times of quick iteration to obtain a new instruction sequence meeting the terminal deviation, a new instruction angle is calculated according to the target point parameter and the reference instruction, an instruction updating closed-loop format can be formed, and the solving process has important characteristics of rapidity and reliability, so that the aim of high-precision speed reduction control can be efficiently fulfilled.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: constructing a discrete dynamics model of the gliding aircraft;
step 1-1: a dynamics model of a gliding aircraft belongs to a nonlinear time-varying differential equation system, a nonlinear discrete system is established, and a state equation and an output equation of the system are respectively expressed as formulas (1) and (2):
Xn+1＝Fn(Xn，Un) (1)
Yn＝Hn(Xn) (2)
wherein the state vector, the control vector and the output vector of the discrete system are respectively
And
Xnrepresenting the current state vector, UnRepresenting the current control vector, YnRepresenting a current output vector, wherein a time domain discrete node N is 1,2,3, …, N-1, N, and N is the number of nodes corresponding to a system terminal moment; fn(.) represents the state at the time of the next discrete point, Hn(.) represents an output equation, and p, q and s represent the dimensions of a state direction, a control quantity and an output quantity respectively;
step 1-2: defining an output vector Y of terminal momentsNAnd an ideal output vector
The difference between:
step 1-3: the discrete system state equation of the gliding aircraft dynamics model is obtained by applying the Euler integral rule according to the formula (1) as follows:
Xn+1＝Fn(Xn，Un)＝Xn+Δt·fn(Xn，Un) (3)
where Δ t is a discrete interval, fn(Xn，Un) Is the derivative of the discrete state vector; selecting the state vector as a position vector r ═ x y z]TAnd velocity vector v ═ vx vy vz]TNamely: x ═ rT vT]TThe specific state equation of the discrete system is obtained as follows:
in the formula, rnRepresenting the current position vector, vnRepresenting the current velocity vector, anRepresenting a current acceleration vector;
step 2: establishing a state sensitivity matrix analysis form of the gliding aircraft;
step 2-1: establishing a sensitivity matrix of the state vector at the next moment to the current state vector;
from equation (3), the state vector X of the next discrete pointn+1For the current state vector XnThe partial derivatives of (a) are:
the specific state vector is taken into:
wherein a is the applied velocity of the gliding aircraft;
step 2-2: establishing a sensitivity matrix of the state vector at the next moment to the current control vector;
from equation (3), the state vector X of the next discrete pointn+1For the current control vector UnThe partial derivatives of (a) are:
the specific state quantity and the control quantity are carried into the following conditions:
wherein, aAeroIt is indicative of the acceleration of the aerodynamic force,
pitch angle is indicated, yaw angle is indicated by psi;
step 2-3: establishing a sensitivity matrix of a terminal output vector to a terminal state vector;
defining the terminal output vector as speed V, speed inclination angle theta, speed deflection angle sigma and arrow lower point height hlocalLateral position z and transverse position x, the sensitivity matrix of the terminal output vector to the terminal state vector is:
wherein the variable with subscript N represents the last discrete point parameter;
and step 3: a high-precision approach optimal deceleration control method for the gliding aircraft;
step 3-1: in the dynamic iteration process, the deviation amount of two adjacent tracks generated by updating the control vector sequence at the same discrete node always meets the small deviation linearization condition, and then the output vector Y at the terminal momentNAnd an ideal output vector
Difference of delta YNThe approximate expression is:
through derivation, the output error vector expression is obtained as follows:
wherein the sensitivity coefficient matrix BnThe calculation is as follows:
step 3-2: fitting the flight command angle with a basis function, where cijIs the jth weight coefficient component, phi, of the ith control vectorj(t) is the jth basis function, then at discrete point tnThe method comprises the following steps:
let Cj＝[c1j c2j]，
Then:
in the formula (I), the compound is shown in the specification,
represents the nth control quantity of the current iteration,
j-th basis function coefficient representing the current iteration, l represents the current iteration, U (t)n) Represents tnControl amount of time, NpRepresenting the highest term degree of the basis function;
step 3-3: considering the condition of small deviation linearization, the quadratic objective function of the minimized control correction quantity is established as follows:
wherein R isjA positive definite weight matrix on the jth order basis function;
step 3-4: obtaining an expression updated by a control vector according to a Lagrange multiplier method in an optimization theory:
wherein the content of the first and second substances,
representing an output deviation amount of the current iteration;
thus, the iterated instructions are:
and finishing the high-precision approaching optimal deceleration control of the gliding aircraft.
The invention has the following beneficial effects:
1. the invention obtains the required analytic form solutions of all the matrixes through vector derivation for the solution of the sensitivity matrix, verifies the accuracy of the analytic form solutions, and the verification result shows that the relative deviation of the proposed analytic solution and the real solution is 10-8The magnitude, namely the relative deviation is only one billionth, the resolution precision of the visible analysis is very high, and the accuracy of the flight instruction resolution is ensured.
2. In the practical application process, the flight instantaneity has higher requirement on the solving efficiency, so the invention counts the iteration times in the practical flight verification process, and the iteration times are within 5 times under the extreme deviation condition and the Monte Carlo target shooting condition, thereby ensuring the rapidity of instruction solving.
Drawings
Fig. 1 is a flowchart of a high-precision approach optimization deceleration control method according to the present invention.
FIG. 2 is a flow chart of the calculation of the high accuracy near optimal deceleration control of the present invention.
Fig. 3 is a relative deviation curve obtained by analyzing the partial derivatives of the atmospheric parameters with respect to the altitude according to the embodiment of the present invention, wherein (a) the relative deviation of the partial derivatives of the atmospheric density with respect to the altitude, and (b) the relative deviation of the partial derivatives of the sound velocity with respect to the altitude.
Fig. 4 is a relative deviation curve obtained by analytic solution of euler angle versus speed partial derivative according to an embodiment of the present invention, wherein (a) the relative deviation of the partial derivative of speed inclination angle versus speed x component, and (b) the relative deviation of the partial derivative of side slip angle versus speed z component.
Fig. 5 is a graph illustrating a relative deviation curve obtained by analyzing and solving the output partial derivatives in the flight process according to an embodiment of the present invention, wherein (a) the relative deviation of the true proximal angle to the z-component partial derivative of the velocity, and (b) the relative deviation of the proximal amplitude angle to the y-component partial derivative of the velocity.
Fig. 6 is a time-dependent variation curve of closed-loop iteration times of the guidance method in the flight process according to the embodiment of the invention, wherein (a) is the iteration times under the condition of four limit pull biases, and (b) is the iteration times under the condition of monte carlo targeting.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
In order to solve the problem of high-precision deceleration control of the gliding aircraft, the deceleration control precision of the gliding aircraft is improved on the basis of not losing position precision and not increasing hardware equipment to reduce system complexity, analysis recursion is carried out according to trajectory error propagation, a Lagrange multiplier is introduced, and a first-order optimal condition is utilized.
As shown in fig. 1, a high-precision approach optimal deceleration control method for a gliding aircraft comprises the following steps:
step 1: constructing a discrete dynamics model of the gliding aircraft;
step 1-1: the dynamics model of the gliding aircraft belongs to a nonlinear time-varying differential equation system, so that a general nonlinear discrete system can be established, and the state equation and the output equation of the system are respectively expressed as the following formulas (1) and (2):
Xn+1＝Fn(Xn，Un) (1)
Yn＝Hn(Xn) (2)
wherein the state vector, the control vector and the output vector of the discrete system are respectively
And
Xnrepresenting the current state vector, UnRepresenting the current control vector, YnRepresenting a current output vector, wherein a time domain discrete node N is 1,2,3, …, N-1, N, and N is the number of nodes corresponding to a system terminal moment;
step 1-2: by solving a sequence of suitable discrete manipulated variables U for discrete equationsnMake the terminal state vector XNThe desired output equation constraint is satisfied, namely:
therefore, to meet the terminal output equation constraints, an output vector Y for the terminal time is definedNAnd an ideal output vector
The difference between:
step 1-3: the discrete system state equation of the gliding aircraft dynamics model is obtained by applying the Euler integral rule according to the formula (1) as follows:
Xn+1＝Fn(Xn，Un)＝Xn+Δt·fn(Xn，Un) (3)
where Δ t is a discrete interval, fn(Xn，Un) Is the derivative of the discrete state vector; selecting the state vector as a position vector r ═ x y z]TAnd velocity vector v ═ vx vy vz]TNamely: x ═ rT vT]TThe specific state equation of the discrete system is obtained as follows:
in the formula, rnRepresenting the current position vector, vnRepresenting a current velocity vector;
through discretization of a dynamics model of the gliding aircraft, a continuous optimization problem can be converted into a discrete optimization problem which is convenient to solve, a foundation can be provided for derivation of a sensitivity matrix of a subsequent state and derivation of a high-precision deceleration control method, and the sensitivity matrix in an instruction solving process is analyzed and analyzed firstly.
Step 2: establishing a state sensitivity matrix analysis form of the gliding aircraft;
step 2-1: establishing a sensitivity matrix of the state vector at the next moment to the current state vector;
from equation (3), the state vector X of the next discrete pointn+1For the current state vector XnThe partial derivatives of (a) are:
the specific state vector is taken into:
wherein a is the applied velocity of the gliding aircraft;
step 2-2: establishing a sensitivity matrix of the state vector at the next moment to the current control vector;
from equation (3), the state vector X of the next discrete pointn+1For the current control vector UnThe partial derivatives of (a) are:
the specific state quantity and the control quantity are carried into the following conditions:
step 2-3: establishing a sensitivity matrix of a terminal output vector to a terminal state vector;
in order to realize high-precision speed reduction control, a terminal output vector is defined as a speed V, a speed inclination angle theta, a speed deflection angle sigma and an arrow lower point height hlocalLateral position z and transverse position x, the sensitivity matrix of the terminal output vector to the terminal state vector is:
wherein the variable with subscript N represents the last discrete point parameter; the solution of the state sensitivity matrix provides technical support for a subsequent high-precision deceleration control method, and the derivation of the high-precision deceleration control method can be completed on the basis of the discretization dynamic model and the state sensitivity matrix, and the detailed analysis is carried out below.
And step 3: a high-precision approach optimal deceleration control method for the gliding aircraft;
step 3-1: in the dynamic iteration process, the deviation amount of two adjacent tracks generated by updating the control vector sequence at the same discrete node is always small, so that the small deviation linearization condition is met (the Taylor expansion expression is only reserved to a first-order term and ignores the rest term), and then the output vector Y at the terminal moment isNAnd an ideal output vector
Difference of delta YNThe approximate expression is:
through derivation, the output error vector expression is obtained as follows:
wherein the sensitivity coefficient matrix BnThe calculation is as follows:
step 3-2: fitting the flight command angle with a basis function, where cijIs the jth weight coefficient component, phi, of the ith control vectorj(t) is the jth basis function, then at discrete point tnThe method comprises the following steps:
let Cj＝[c1j c2j]，
Then:
step 3-3: considering the condition of small deviation linearization, the quadratic objective function of the minimized control correction quantity is established as follows:
wherein R isjA positive definite weight matrix on the jth order basis function; a standard static optimization problem is formed by a performance index function and equality constraint.
Step 3-4: obtaining an expression updated by a control vector according to a Lagrange multiplier method in an optimization theory:
thus, the iterated instructions are:
from equation (16), it can be derived: the basis function coefficients can be obtained by fast calculation of a control equation, so that a control instruction at each discrete node is obtained, and a sensitivity coefficient matrix in the control equation is a constant coefficient matrix in each iteration period, so that the reliability of solving a high-dimensional matrix equation and certain iteration convergence are realized. On the other hand, the weight matrix directly influences the calculation of the control quantity, and the method can have the capability of processing the flight process constraint by designing a proper weight matrix updating condition. Therefore, theoretical derivation of the high-precision near optimal deceleration control method of the gliding aircraft is completed.
The specific embodiment is as follows:
the optimal deceleration control method for the approach of the gliding aircraft is based on the current flight time t provided by the navigation device0Position vector r0Velocity vector v0Using pre-bound aircraft parameters and an initial command sequence U0Calculating a guidance instruction meeting the terminal speed constraint in real time; the calculation flow of the near-optimal high-precision deceleration control is shown in fig. 2:
the detailed calculation steps are as follows:
(1) determining the current time t0To terminal time tfBallistic parameter sequence Psave＝[t，r，v，m，U]: according to the current flight time t0Position vector r0Velocity vector v0To in order toAnd pre-bound glider parameters and initial instruction sequence U0Performing numerical integration according to the following formula to obtain a ballistic parameter P in the flight processsave. Where a is the aerodynamic acceleration to which the gliding aircraft is subjected, rfAnd vfThe position vector and the velocity vector at the moment of the flight terminal are provided, and U is an instruction sequence in the flight process;
Psave＝[t，r，v，m，U]
(2) determining a terminal output parameter Y of a gliding aircraftN＝[Vf θf σf hf zf xf]: obtaining a terminal state parameter r according to numerical integration in the step (1)fAnd vfThe output parameter Y of the aircraft terminal can be calculated according to the following formulaN. Wherein v isf(i) I is the i-th component of the velocity vector, rf(i) I is 1, 3 is the ith component of the position vector, RearthIs the radius of the earth;
Vf＝|vf|
θf＝arctan(vf(2)/vf(1))
σf＝-arcsin(vf(3)/Vf)
hf＝|rf|-Rearth
zf＝rf(3)
xf＝rf(1)
(3) determining a terminal output deviation of a gliding aircraft
Normalizing according to pre-bound aircraft terminal outputValue of
And (2) calculating to obtain the aircraft terminal parameter YNThe deviation of the terminal output of the gliding aircraft can be obtained according to the following formula
Wherein the subscript f represents the terminal flight time tfThe subscript std represents the terminal output nominal value;
(4) determining a matrix of sensitivities of the acceleration a at discrete nodes to state quantities r and v
Obtaining a sensitivity matrix of the acceleration at the discrete node to the state quantity according to the following formula, wherein alpha, beta, theta and sigma are respectively an attack angle, a sideslip angle, a speed inclination angle and a speed deflection angle, sos is the local sound velocity, Ma is the Mach number, rho is the local atmospheric density, V is the speed magnitude, m is the mass of the gliding aircraft, and S is the mass of the gliding aircraftrefIs the reference area of the gliding aircraft, C is the aerodynamic coefficient vector under the selected coordinate system,
and
the solution can be performed according to a specific atmospheric parameter table,
interpolation calculation can be carried out according to the pneumatic table;
θ＝arctan(vy/vx)σ＝-arcsin(vz/|v|)
(5) determining a sensitivity matrix of acceleration a at discrete nodes to a control quantity U
According to the influence relation of the guidance command on the aerodynamic acceleration, a sensitivity matrix of the acceleration at the discrete node to the control quantity can be obtained by the following formula, wherein,
psi is the pitch angle and yaw angle respectively,
interpolation calculation can be carried out according to the pneumatic table;
(6) determining state sensitivity matrices at discrete nodes
And a sensitivity matrix of the output parameter at the last discrete node to the state quantity
Obtaining the ballistic trajectory parameter P of the gliding aircraft in the flying process according to the step (1)saveObtaining the ballistic parameters at each discrete node through linear interpolation, and deriving the ballistic parameters through the correlation of the steps (4) and (5), and obtaining the ballistic parameters according to the following formula
And
where Δ t is a discrete interval, O3×3Is a 3 rd order zero matrix, Ii×iI is 3, and 6 is an i-order unit matrix;
(7) determining update values for basis function coefficients in an iterative process
And a new instruction U (t) at each discrete noden): the terminal deviation value obtained according to the step (3)
And (3) an analytic relational expression between the trajectory parameters and the trajectory parameters obtained in the step (6), a static optimization problem can be obtained by introducing a Lagrange multiplier, and a basis function coefficient updating value can be obtained according to the first-order requirement of optimality and the following formula so as to obtain a new instruction at each discrete node, wherein RjFor a positive weight matrix, N is the number of discrete nodes, NpIs the highest order term of the basis function, phijFor the (j) th basis function,
is the jth basis function coefficient of the iterative instruction;
φ0(t)＝1 φ1(t)＝t
φj+1(t)＝2tφj(t)-φj-1(t)
(8) determining an iteration jump-out condition and judging whether a closed loop iteration process is terminated: firstly, judging the current iteration number IterNumAnd maximum iteration number IterNummaxIf Iter, if IterNum≥IterNummaxIf so, ending iteration, jumping out of a loop and outputting a guidance instruction sequence U; otherwise, judging the terminal deviation dYNAnd a preset upper limit epsilon of precisionmaxIn relation to (II) dYN‖<εmaxThen, the terminal deviation dY is determinedNAnd a preset lower precision bound epsilonminIn relation to (II) dYN‖<εminIf so, ending the iteration, jumping out of the loop and outputting a guidance instruction sequence U; otherwise, judging the current iteration number IterNumWith minimum iteration number IterNumminIf Iter, if IterNum≥IterNumminThen, the current speed deviation value dV [ l +1 ] is determined]Deviation from last iteration speed by dV [ l ]]In the case of dV [ l +1 ]]≥dV[l]If so, ending the iteration, jumping out of the loop and outputting a guidance instruction sequence U, otherwise, continuing the iteration; if IterNum<IterNumminThen the iteration continues.
(9) Determining a flight command U (t) for a current time of flightnow): and (4) according to the command sequence output in the step (8) and the current time, obtaining the flight command angle of the current time by linear interpolation according to the following formula. Wherein interp1 is a one-dimensional interpolation function, and T is an instruction sequenceU corresponding to a time series.
U(tnow)＝interp1(T，U，tnow)
The implementation example of the invention is as follows:
(1) partial derivative matrix analysis solving accuracy verification
As shown in fig. 3 (a) and (b), when the partial derivative of the atmospheric density to the height and the partial derivative of the sound velocity to the height in the atmospheric parameter are solved, the relative deviation between the analytic solution and the actual value is only 10-7Magnitude, so analytic solution is very accurate; as shown in fig. 4 (a) and (b), the relative deviation of the partial derivative of the sideslip angle with respect to the x component of the velocity and the partial derivative of the sideslip angle with respect to the z component of the velocity in the euler angle from the actual value is about 10-6As shown in fig. 5 (a) and (b), the relative deviation between the actual value and the partial derivative of the true proximal angle with respect to the z component of the velocity and the partial derivative of the proximal amplitude angle with respect to the y component of the velocity, which are obtained by the analytical method, is 10 throughout the flight-7And the magnitude ensures the accuracy of the deceleration control method when the deceleration control method is applied.
(2) Closed loop iteration number analysis in simulation process
In the actual application process, the flight instantaneity has higher requirement on the solving efficiency, so the iteration times in the actual flight verification process are counted. As shown in fig. 6 (a) and (b), (a) is the number of iterations in the case of four extreme bias, and (b) is the number of iterations under the monte carlo targeting condition, it can be seen that the number of iterations in the simulation process is within 5, which ensures the rapidity of instruction solving.
Verification analysis is carried out according to some necessary technical means in the invention process, for solving the sensitivity matrix, required analytic form solutions of all the matrixes are obtained through vector derivation, the accuracy of the analytic form solutions is verified, and the verification result shows that (see table 1), the relative deviation between the proposed analytic solution and the real solution is 10-8The magnitude, namely the relative deviation is only one billionth, the resolution precision of the visible analysis is very high, and the accuracy of the flight instruction resolution is ensured.
TABLE 1 Euler Angle vs Euler angle sensitivity matrix analytic solution and true solution relative deviation table
| Sideslip angle | Angle of attack | Roll angle of velocity | |
| Pitch angle | -1.639738e-08 | 3.830313e-09 | 6.834792e-08 |
| Yaw angle | 2.743678-08 | 5.114941e-08 | -5.151366e-09 |
| Roll angle | 1.748765e-08 | -2.995515e-08 | -1.187136e-08 |
| Angle of inclination of velocity | -1.639738e-08 | 3.830313e-09 | 1.773239e-08 |
| Angle of speed declination | -1.575573e-08 | -5.528642e-08 | 1.690188e-08 |
| Angle of attack | ---- | 0 | 3.194074 |
| Sideslip angle | |||
| 0 | 2.703334e-08 | 4.260183e-09 |
In the practical application process, the flight instantaneity has higher requirement on the solving efficiency, so that the iteration times in the practical flight verification process are counted, the iteration times are within 5 times under the extreme deviation condition and the Monte Carlo target shooting condition, and the rapidity of instruction solving is ensured.
Claims (1)
1. A high-precision approach optimal deceleration control method for a gliding aircraft is characterized by comprising the following steps:
step 1: constructing a discrete dynamics model of the gliding aircraft;
step 1-1: a dynamics model of a gliding aircraft belongs to a nonlinear time-varying differential equation system, a nonlinear discrete system is established, and a state equation and an output equation of the system are respectively expressed as formulas (1) and (2):
Xn+1＝Fn(Xn,Un) (1)
Yn＝Hn(Xn) (2)
wherein the state vector, the control vector and the output vector of the discrete system are respectively
And
Xnrepresenting the current state vector, UnRepresenting the current control vector, YnRepresenting a current output vector, wherein a time domain discrete node N is 1,2,3, …, N-1, N, and N is the number of nodes corresponding to a system terminal moment; fn(.) represents the state at the time of the next discrete point, Hn(.) represents an output equation, and p, q and s represent the dimensions of a state direction, a control quantity and an output quantity respectively;
step 1-2: defining an output vector Y of terminal momentsNAnd an ideal output vector
The difference between:
step 1-3: the discrete system state equation of the gliding aircraft dynamics model is obtained by applying the Euler integral rule according to the formula (1) as follows:
Xn+1＝Fn(Xn,Un)＝Xn+Δt·fn(Xn,Un) (3)
where Δ t is a discrete interval, fn(Xn,Un) Is the derivative of the discrete state vector; selecting the state vector as a position vector r ═ x y z]TAnd velocity vector v ═ vx vy vz]TNamely: x ═ rT vT]TThe specific state equation of the discrete system is obtained as follows:
in the formula, rnRepresenting the current position vector, vnRepresenting the current velocity vector, anRepresenting a current acceleration vector;
step 2: establishing a state sensitivity matrix analysis form of the gliding aircraft;
step 2-1: establishing a sensitivity matrix of the state vector at the next moment to the current state vector;
from equation (3), the state vector X of the next discrete pointn+1For the current state vector XnThe partial derivatives of (a) are:
bringing the specific state vector into:
wherein a is the applied velocity of the gliding aircraft;
step 2-2: establishing a sensitivity matrix of the state vector at the next moment to the current control vector;
from equation (3), the state vector X of the next discrete pointn+1For the current control vector UnThe partial derivatives of (a) are:
the specific state quantity and the control quantity are carried into the following conditions:
wherein, aAeroIt is indicative of the acceleration of the aerodynamic force,
pitch angle is indicated, yaw angle is indicated by psi;
step 2-3: establishing a sensitivity matrix of a terminal output vector to a terminal state vector;
defining the terminal output vector as speed V, speed inclination angle theta, speed deflection angle sigma and arrow lower point height hlocalLateral position z and transverse position x, the sensitivity matrix of the terminal output vector to the terminal state vector is:
wherein the variable with subscript N represents the last discrete point parameter;
and step 3: a high-precision approach optimal deceleration control method for the gliding aircraft;
step 3-1: in the dynamic iteration process, the deviation amount of two adjacent tracks generated by updating the control vector sequence at the same discrete node always meets the small deviation linearization condition, and then the output vector Y at the terminal momentNAnd an ideal output vector
Difference of delta YNThe approximate expression is:
through derivation, the output error vector expression is obtained as follows:
wherein the sensitivity coefficient matrix BnThe calculation is as follows:
step 3-2: fitting the flight command angle with a basis function, where cijIs the jth weight coefficient component, phi, of the ith control vectorj(t) is the jth basis function, then at discrete point tnThe method comprises the following steps:
let Cj＝[c1j c2j]，
Then:
in the formula (I), the compound is shown in the specification,
represents the nth control quantity of the current iteration,
j-th basis function coefficient representing the current iteration, l represents the current iteration, U (t)n) Represents tnControl amount of time, NpRepresenting the highest term degree of the basis function;
step 3-3: considering the condition of small deviation linearization, the quadratic objective function of the minimized control correction quantity is established as follows:
wherein R isjA positive definite weight matrix on the jth order basis function;
step 3-4: obtaining an expression updated by a control vector according to a Lagrange multiplier method in an optimization theory:
wherein the content of the first and second substances,
representing an output deviation amount of the current iteration;
thus, the iterated instructions are:
and finishing the high-precision approaching optimal deceleration control of the gliding aircraft.
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