CN114115325B - Online closed-loop guidance method for gliding missile based on hp-RPM algorithm - Google Patents
Online closed-loop guidance method for gliding missile based on hp-RPM algorithm Download PDFInfo
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Abstract
The invention belongs to the field of projectile guidance, and particularly relates to an hp-RPM algorithm-based online closed-loop guidance method for a gliding projectile. The method comprises the following steps: (1): calculating a multi-constraint optimal control law with the current ballistic parameters as initial conditions by adopting an hp-RPM algorithm; (2): the measuring system takes the end moment of each hp-RPM program operation as a sampling point, and the sampling period is equal to the hp-RPM algorithm calculation time in the current period; (3): the projectile attitude adjustment is realized by controlling the rudder deflection angle so as to inhibit the uncertain interference in the actual flying process and realize the fixed point striking target of the projectile. The method is used for inhibiting the influence of uncertain factors such as environmental interference, model errors and the like possibly occurring in the flight process of the gliding projectile on various parameters of the trajectory, so that the projectile realizes the preset terminal combat index, and simultaneously meets various constraints in the flight process.
Description
Technical Field
The invention belongs to the field of projectile guidance, and particularly relates to an hp-RPM algorithm-based online closed-loop guidance method for a gliding projectile.
Background
The gliding guided projectile is an unmanned flying device guided by a navigation guidance system to control the gliding guided projectile to fly to a specified target, and the trajectory optimization is to design a control mechanism which can enable the projectile to reach tactical indexes under a specific constraint condition. The constraint condition generally means that a plurality of ballistic parameters of the projectile in a certain stage of the flight process meet requirements, and tactical indexes generally comprise the range, precision, speed, posture when the projectile strikes a target and the like of the projectile. In the actual flight process of the projectile, the actual trajectory of the projectile deviates from the pre-calculated scheme trajectory due to the existence of calculation errors, model errors and external interference. When the projectile flies to the position near the top of the trajectory, the sliding control section starts, the duck rudder is popped out, meanwhile, the guidance control system detects the deviation of the actual trajectory of the projectile and the trajectory of a preset scheme, generates a guidance control instruction, and controls the deflection mode of the rudder, so that the flying trajectory of the projectile is changed, the projectile flies along the trajectory of the scheme, and the preset striking effect is realized.
The numerical solution of the trajectory optimization problem is mainly divided into an indirect method and a direct method. The indirect method converts the solution of the optimal control problem into the solution of a Hamilton multi-point boundary value problem, thereby obtaining the optimal control law and being widely applied to the early track optimization problem. Because two point edge values of the indirect method are difficult to solve when the indirect method is used for processing a complex optimal control problem and are limited in practical engineering application, the direct method which is simple in structure and rapid in convergence becomes a research hotspot of the current trajectory optimization problem. Pseudo-spectral method (PM) is a common direct numerical solution for solving Nonlinear optimal control problem, and a group of orthogonal bases are used to approach state variables and control variables at discrete points to convert the optimal control problem in continuous time into a Nonlinear Programming problem (NLP) for solving.
The hp self-adaptive pseudo-spectrum method automatically adjusts the grid refining mode and the number of times of interpolating polynomial according to a certain error criterion, and compared with an h-type pseudo-spectrum method only changing grid division and a p-type pseudo-spectrum method only adjusting polynomial order, the hp self-adaptive pseudo-spectrum method can obtain a solution with higher precision with less calculation cost, and is suitable for the optimization problem of rapid change of state variables and control variables curvature.
The core of the projectile reentry guidance problem is that a feasible reentry flight reference trajectory is quickly generated on line according to the current state of the projectile, and then a control method with strong robustness is designed to track the reference trajectory so as to overcome the effects of model errors, calculation errors and external interference in the flight process. With the requirements of complex combat indexes, the improvement of computing power and the improvement of a numerical optimization algorithm, the re-entry guidance algorithm is developing along a real-time online and self-adaptive direction. The feedback control of the existing nonlinear dynamic model real-time optimization needs to linearize a nonlinear system along an optimal track to provide closed-loop feedback control, which can limit some performances of the system to a certain extent, such as reducing a maximum safe reachable area and the like.
Disclosure of Invention
The invention aims to provide a closed-loop guidance method based on an hp-RPM algorithm, which is used for inhibiting parameter errors and external interference in a pill reentry process.
The technical solution for realizing the purpose of the invention is as follows: an hp-RPM algorithm-based online closed-loop guidance method for a gliding missile comprises the following steps:
step (1): calculating a multi-constraint optimal control law with the current ballistic parameters as initial conditions by adopting an hp-RPM algorithm;
step (2): the measuring system takes the end moment of each hp-RPM program operation as a sampling point, and the sampling period is equal to the hp-RPM algorithm calculation time in the current period;
and (3): the projectile attitude adjustment is realized by controlling the rudder deflection angle so as to inhibit the uncertain interference in the actual flying process and realize the fixed point striking target of the projectile.
Further, the step (1) specifically comprises:
step (1-1): initializing ballistic parameters: determining state variables, control variables, end point constraints, path constraints and performance indexes, and establishing a kinetic equation of the projectile with the specific type in the glide section;
step (1-2): initializing grid iteration parameters: setting the initial grid number K and the kth grid interpolation value polynomial degree N k And grid iteration tolerance ε d ；
Step (1-3): time domain transformation: the problem of multi-constraint guidance of the gliding missile can be regarded as an optimal control problem, and the definition domain is the missile flight time [ t ] 0 ,t f ]The time domain transformation is the domain [ t ] of the original optimal control problem 0 ,t f ]Mapping to [ -1,1]The space is used for calculating LGR discrete points, lagrange polynomial interpolation is used on the LGR discrete points, and state variables, control variables and differential equations are discretized, so that the optimal control problem in a continuous time domain is converted into a discrete nonlinear optimization problem to be solved;
step (1-4): refining and splitting the grid by using an hp self-adaptive method, and calculating the calculation accuracy under the current grid;
step (1-5): judging whether the iteration termination condition is met, if not, returning to the step (1-3), iterating until the required calculation precision is reached, and turning to the next step;
step (1-6): and updating the optimal control law in the current state.
Further, the step (2) is specifically as follows:
step (2-1): let t be 0 For the initial time, x is determined 0 ＝x(t 0 ) For initial state variable, open-loop optimal control law u is calculated off-line by adopting hp-RPM method 0 ；
Step (2-2): let t be 1 For the 1 st sampling instant of the measurement system, at time t 0 ,t 1 ]Interior, use the control law u 0 Directing the projectile to fly and recording t 1 The measured value of each state variable at the moment is x 1 ＝x(t 1 ) (ii) a With x 1 As a new initial state variable, updating the control law u of the residual trajectory by using the hp-RPM method 1 Assuming that the hp-RPM method program is operated for a time Δ t 1 If the next system sampling time is t 2 ＝t 1 +△t 1 Let i =2;
step (2-3): let t be i For the ith sampling instant of the measurement system, at time t i-1 ,t i ](i =2,3, \ 8230;), in which control law u is used i-1 Controlling the projectile to fly and recording t i Each state variable of the time projectile is x i ＝x(t i ) (ii) a With x i As a new initial state, the control law u of the residual trajectory is updated by using the hp-RPM method i Let the hp-RPM routine run for Δ t i The next sampling time of the measurement system is t i+1 ＝t i +△t i Let i = i +1.
Further, the step (3) is specifically as follows: in each guidance period, the optimal guidance law calculated in the previous period is utilized to control the rudder wing to deflect, so that the shot can overcome errors.
Compared with the prior art, the invention has the remarkable advantages that:
the method utilizes the hp-RPM algorithm, designs a closed-loop online optimal control law generation strategy with free sampling frequency based on the actual situation that the gliding projectile deviates from the scheme trajectory due to model errors and environmental interference in the flight process, has simple principle, is easy to realize, and can realize quick and accurate guidance control and accurate target hitting while ensuring the operational performance of the projectile.
Drawings
FIG. 1 is a flowchart of the hp-RPM algorithm of the present invention.
Fig. 2 is a flow chart of the closed loop control strategy of the present invention.
Figure 3 is a graph comparing ballistic trajectories for closed-loop control and open-loop control of an embodiment of the present invention.
FIG. 4 is a speed comparison graph of closed loop control versus open loop control for an embodiment of the present invention.
Figure 5 is a graph comparing ballistic inclination angle for closed loop control and open loop control of an embodiment of the present invention.
FIG. 6 is a graph comparing normal overload for closed loop control and open loop control of an embodiment of the present invention.
Detailed Description
The following detailed description of the embodiments of the present invention will be made with reference to the accompanying drawings and the working principle.
As shown in the figures 1 and 2, the method combines the hp-RPM algorithm and the closed-loop control strategy, and can effectively inhibit model errors and external interference in the process of reentry of the projectile into the flight. The example of the method is to design the trajectory of a landing angle constraint scheme of a certain type of guided missile glider, and relevant parameters of the guided missile are as follows: mass m =50.31kg, reference area S =1.327 × 10 -2 m 2 The closed loop control procedure of the present invention is described next with reference to examples.
As shown in FIG. 1, the method for solving the optimal control law by using the hp-RPM algorithm in the embodiment of the invention comprises the following steps:
step 1: various ballistic parameters are initialized. Determining state variables as a speed v, a trajectory inclination angle theta, a horizontal distance x, a flying height y and an attack angle alpha; the control variable being the rate of change of rudder deflection angle
The initial state is as follows: initial velocity v 0 =400m/s, launch coordinates (x) 0 ,y 0 ) = (0km, 20km), trajectory inclination angle theta 0 Angle of attack α =0rad 0 =0rad, process constraint is rudder deflectionRate of change of angle
Rudder deflection angle | δ z Less than or equal to 15 degrees, and normal overload n y The angle of attack | alpha | is less than or equal to 2 degrees and less than or equal to 15 degrees; the performance index is min J = t f Representing a scheme trajectory with the shortest flight time and requiring solution to meet various constraint conditions; terminal constraint is fall angle theta f = 85 °, end point moment projectile velocity v f Not less than 120m/s, and the coordinate of the terminal point moment is (x) 0 ,y 0 )＝(60km,0km)。
The system of equations for gliding missile kinematics in the longitudinal plane is used as follows:
in the formula: (x, y) is the position coordinates of the projectile in the longitudinal plane; v is the projectile flight speed; theta is the inclined angle of the ballistic path; s is the reference area of the projectile; ρ is the air density; g is the acceleration of gravity; m is mass; alpha is an attack angle; delta z Is the rudder deflection angle;
in order to manipulate the torque,
for longitudinal static moment, C x 、C y Respectively is a total elastic resistance coefficient and a total elastic lift coefficient, and the calculation method is as follows:
in the formula: c x0 The missile wing assembly has zero lift resistance coefficient; c y0 Coefficient of lift of the missile-wing assembly at zero angle of attack, for axisymmetric missile, C y0 ＝0；k 1 The induced drag coefficient of the missile wing assembly;
is the derivative of the combined lift coefficient of the missile wing.
Step 2: initializing grid iteration parameters and setting a grid refinement tolerance to epsilon d ＝1×10 -4 The initial grid number K =10, the grid initial polynomial interpolation degree is N k ＝3。
And step 3: time domain transformation, converting the definition domain of original optimal control problem [ t ] 0 ,t f ]Mapping to [ -1,1 [ ]]Space, the formula is:
wherein, [ t ] k-1 ,t k ]K =1,2, \8230;, K denotes the domain defining the original OCP problem [ t 0 ,t f ]And dividing the grid into K-th sub-intervals after the K grid sub-intervals. Let x (k) (t) and u (k) (t) denotes the kth sub-interval [ t ] respectively k-1 ,t k ]State variables and control variables within.
And 4, step 4: calculating LGR discrete points by using a Newton iteration method, and recording interpolation points obtained by nth iteration in kth grid subinterval as
Selecting a Chebyshev-Gauss-Radau node with a specific expression as an iteration initial value, as shown in formula (5), and then
The recurrence formula is:
and 5: the state variables, control variables and differential equations are discretized at discrete points. Converting the optimal control problem into a discrete nonlinear optimization problem to be solved, wherein the discrete equation system is as follows:
wherein, the first and the second end of the pipe are connected with each other,
a Radau differential approximation matrix for the kth subinterval representing the differential value of the Lagrange interpolation basis function at the LGR node;
and
respectively represent X (k) And U (k) In that
The value of the point;
and
for the interpolation basis function, the expression is:
step 6: refining and splitting the grid by using an hp self-adaptive method, and defining approximate error estimates of a dynamic constraint equation and a process constraint equation on error sampling points as
And
the expression is as follows:
in the formula: error sampling point
Is time domain [ -1,1]The midpoints of adjacent discrete points within the array,
representing error sample points in the kth grid
The state variable derivative of (d);
can be obtained by Lagrange interpolation and respectively represent error sampling points in the kth grid
Taking values of the state variable and the control variable, and defining the maximum value of the error in the kth grid as:
and 7: epsilon d For a user-defined grid iteration error, if
Then, it means that the interpolation precision of the kth grid subinterval does not meet the requirement, and the grid needs to be refined continuously or the order of interpolation polynomial needs to be increased. Let r max Greater than 1 is the user-defined tolerance relative curvature, if r (k) ≥r max It is indicated that the curvature of the segment is greatly changed, the grid needs to be further refined, more subintervals are divided, and the kth grid is further divided into n k The calculation method of the smaller grid interval is as follows:
if r (k) <r max If the curvature change in the kth grid subinterval is not obvious, in order to control the accuracy within the allowable range, the order of the interpolation polynomial needs to be increased, and the increased order is:
after the operation in the step 7 is executed, the step 5 is returned to, and the iteration is carried out until all grids exist
Step 8 is performed.
And step 8: and updating the optimal control law in the current state.
In the real-time feedback control algorithm, the hp-RPM algorithm is used for each calculation of the optimal control law, a measurement system obtains actual ballistic parameters at the initial moment of the current guidance period and generates a control rule of the next guidance period on line as an initial value, the length of the current guidance period is determined by the calculation efficiency of the hp-RPM algorithm and the running speed of a computer, and the feedback calculation process is shown in figure 2.
Examples
In the embodiment, the projectile is assumed to have fluctuation of +/-10% in the lift coefficient and the drag coefficient due to model errors, and meanwhile, the projectile is interfered by gusts of 0-50 m/s when flying to 50-100 s. The simulation experiment is carried out by respectively adopting open-loop control and a closed-loop guidance mode in the invention, the hardware environment comprises a Core i7 processor, a 16.0GB RAM, a 64-bit win10 operating system in a software environment and MatlabR2018a software, the experimental result is shown in figures 3-6, and the feedback process after combining the examples is as follows:
step 1: let t 0 =0 as initial time, determine x 0 ＝x(t 0 ) Selecting initial iteration grid number and polynomial times of hp-RPM algorithm for initial state variable, and calculating open-loop optimal control law u off line 0 。
Step 2: let t 1 For the 1 st sampling instant of the measurement system, at time t 0 ,t 1 ]Internal and external control law u 0 Flying with finger-guided missile and recording t 1 The measured value of each state variable at the moment is x 1 ＝x(t 1 ). With x 1 Updating the control law u of the residual trajectory by using the hp-RPM algorithm as a new initial state variable 1 Suppose the optimization program runs for time Δ t 1 The next sampling time of the measurement system is t 2 ＝t 1 +△t 1 Let i =2.
And 3, step 3: let t i For the ith sampling instant of the measurement system, at time t i-1 ,t i ](i =2,3, \ 8230;), in which control law u is used i-1 Controlling the projectile to fly and recording t i Each state variable of the time projectile is x i ＝x(t i ). With x i As a new initial state, updating the control law u of the residual trajectory by using the hp-RPM method i Suppose the optimization program runs for time Δ t i If the next system sampling time is t i+1 ＝t i +△t i Let i = i +1.
And 4, step 4: judging whether the shot hits a certain target on the ground or not, and if not, returning to the step (3); otherwise, the loop exits.
The application effect of the invention in the embodiment is shown in fig. 3-6, and it can be known from the experimental results that, compared with the gust effect, the impact of + -10% of the fluctuation of the aerodynamic parameter on each parameter of the ballistic trajectory is not large. If open-loop control is adopted, when the projectile flies to 50-100 s, the flying speed obviously deviates from the reference trajectory due to the influence of gusts, meanwhile, the inclination angle of the trajectory is obviously reduced, and if the optimal control law u of off-line design is adopted 0 When the method is applied to a control system, the projectile can hit the ground ahead of time and cannot hit the target accurately. The distance between the shot terminal moment and the target in the horizontal direction under the open-loop control is 1.554km, the falling angle is-30.28 degrees, and the terminal constraint cannot be met. When the closed-loop guidance mode mentioned in the text is adopted, the shot is located at 60001.03m in the horizontal direction when hitting the ground, and is 1.03m away from a target, so that the general battle requirements are met. The actual drop angle of the terminal of the ballistic trajectory under the open-loop control system is-84.46 degrees, the flight time of the projectile is 208.12s, the difference between the actual drop angle and the glide time of the reference ballistic trajectory is not large compared with the-85 degree drop angle and the 202.19s glide time, and the preset operational index of rapid large-drop-angle accurate striking can be basically realized.
The embodiment shows that the online guidance strategy based on the hp-RPM method can effectively inhibit random interference generated by model errors and external disturbance in the re-entering process of the projectile, ensures the operational performance of the projectile, and has the characteristics of rapidity, accuracy and large-range error regulation. In addition, the control period of the system is equal to the optimal calculation time of the hp-RPM program in the period, so that the faster the running speed of the computer is, the better the error inhibition effect is, and the accuracy requirement can be met by a general military computer.
Claims (1)
1. An hp-RPM algorithm-based online closed-loop guidance method for a gliding missile is characterized by comprising the following steps:
step (1): calculating a multi-constraint optimal control law with the current ballistic parameters as initial conditions by adopting an hp-RPM algorithm;
step (2): the measuring system takes the end moment of each hp-RPM program operation as a sampling point, and the sampling period is equal to the hp-RPM algorithm calculation time in the current period;
and (3): the attitude of the projectile is adjusted by controlling the rudder deflection angle so as to inhibit uncertain interference in the actual flight process and realize the fixed point hitting target of the projectile;
the step (1) is specifically as follows:
step (1-1): initializing ballistic parameters: determining state variables, control variables, end point constraints, path constraints and performance indexes, and establishing a kinetic equation of the projectile with the specific type in the glide section;
step (1-2): initializing grid iteration parameters: setting the initial grid number K and the kth grid interpolation value polynomial degree N k And grid iteration tolerance ε d ；
Step (1-3): time domain transformation: the problem of multi-constraint guidance of the gliding missile can be regarded as an optimal control problem, and the definition domain is the missile flight time [ t ] 0 ,t f ]The time domain transformation is the definition domain [ t ] of the original optimal control problem 0 ,t f ]Mapping to [ -1,1 [ ]]The space is used for calculating LGR discrete points, lagrange polynomial interpolation is used on the LGR discrete points, and state variables, control variables and differential equations are discretized, so that the optimal control problem in a continuous time domain is converted into a discrete nonlinear optimization problem to be solved;
step (1-4): refining and splitting the grids by using an hp self-adaptive method, and calculating the calculation precision under the current grid;
step (1-5): judging whether the iteration termination condition is met or not, if not, returning to the step (1-3), iterating until the required calculation precision is achieved, and turning to the next step;
step (1-6): updating the optimal control law in the current state;
the step (2) is specifically as follows:
step (2-1): let t be 0 For the initial time, x is determined 0 ＝x(t 0 ) For initial state variable, open-loop optimal control law u is calculated off-line by adopting hp-RPM method 0 ；
Step (2-2): let t be 1 For the 1 st sampling instant of the measurement system, at time t 0 ,t 1 ]Interior, use the control law u 0 Directing the projectile to fly and recording t 1 The measured value of each state variable at the moment is x 1 ＝x(t 1 ) (ii) a With x 1 As a new initial state variable, updating the control law u of the residual trajectory by using the hp-RPM method 1 Assuming that the hp-RPM method program is operated for a time Δ t 1 The next sampling time of the measurement system is t 2 ＝t 1 +△t 1 Let i =2;
step (2-3): let t i For the ith sampling instant of the measurement system, at time t i-1 ,t i ](i =2,3, \8230;), in which the control law u is used i-1 Controlling the projectile to fly and recording t i Each state variable of the time projectile is x i ＝x(t i ) (ii) a With x i As a new initial state, the control law u of the residual trajectory is updated by using the hp-RPM method i Assuming that the hp-RPM method program is operated for a time Δ t i The next sampling time of the measurement system is t i+1 ＝t i +△t i Let i = i +1;
the step (3) is specifically as follows: in each guidance period, the optimal guidance law obtained by calculation in the previous period is utilized to control the rudder wing to deflect, so that the shot can overcome errors.
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