JP5760772B2 - Flying object guidance control device - Google Patents

Description

  The present invention relates to a flying object guidance control apparatus for associating a flying object with a target.

Conventionally, a proportional navigation law has been frequently used when guiding a flying object (for example, pages 11 to 30 of Non-Patent Document 1).
Here, the proportional navigation law is a guidance law based on an acceleration command proportional to the rate of change of the visual line angle detected by the seeker and the relative approach speed estimated by the relative motion calculation.

  In addition, an optimal guidance law has been proposed in order to minimize the input cost with the aim of null distance reduction using a mathematical model in advance (for example, pages 143 to 162 of Non-Patent Document 1). .

Further, online optimal control has been performed in a system with a large time constant such as plant control (for example, Patent Document 1).
However, conventionally, online optimal control has not been used for a system with a small time constant such as a flying object and a large influence of noise due to the problem of calculation speed. This is because the next control cycle comes before the optimization calculation converges, and it is difficult to exhibit sufficient control performance.

JP 2008-199825 A

“Tactical and Strategic Missile Guidance Fourth Edition”, Paul Zarchan, ISBN: 1-56347-497-2

  In recent years, due to the development of stealth technology for aircraft and the like, which are target objects for flying objects, the target RCS (Radar Cross Section) has become smaller. As a result, the detection and tracking performance of the flying object's seeker deteriorates, and the distance at which the target can be detected with high precision (called lock-on range) is shortened. As a result, the terminal induction time for associating the flying object with the target is reduced. There was a problem that the probability of meeting with the target would be reduced by shortening.

  The present invention has been made to solve such a problem, and in order to accurately associate the flying object with the target even in a short terminal induction time, by performing a numerical simulation of the flying object and the movement of the target sequentially. An object of the present invention is to provide a guidance control technology that enables guidance in a short time by predicting with high accuracy and compensating for the influence of delay elements and nonlinear elements of a control system.

A flying object guidance control device according to the present invention includes a target motion calculation device that predicts a target motion, a guided bullet motion calculation device that predicts the motion of a guided bullet, and a constraint that calculates a constraint condition to be satisfied by the guided bullet. A condition calculation device, an evaluation function calculation device that calculates an evaluation function that serves as an index for optimization calculation, an evaluation value of a constraint condition output from the constraint condition calculation device for each sampling time that is a control period, and the evaluation Using the value of the evaluation function output from the function calculation device, the time derivative of the optimization parameter is calculated by a single convergence operation, and the optimization parameter is calculated by integrating the time derivative of the optimization parameter. An optimum guidance control device for controlling the movement of the guidance bullet .

  According to the present invention, optimization calculation can be performed online even when the terminal guidance distance is short, and as a result, the relative motion between the target and the flying object can be predicted with high accuracy. Further, since the delay element and nonlinear element of the control system can be compensated, the flying object can be associated with the target with higher probability than the conventional guidance law.

In the flying body guidance control apparatus of Embodiment 1, it is a figure which shows the structure of the guidance apparatus mounted in the flying body. In the flying object guidance control apparatus of Embodiment 2, it is a figure which shows the structure of the guidance apparatus mounted in the flying object.

Embodiment 1 FIG.
FIG. 1 is a diagram showing a configuration of a flying object guidance control apparatus according to the first embodiment. The flying object guidance device includes a target motion calculation device 1, a guided bullet motion calculation device 2, a constraint condition calculation device 3, an evaluation function calculation device 4, and an optimization calculation device 5.
The target motion calculation device 1 is a device that predicts a target position / velocity / turning acceleration from a given current state quantity to a finite future and outputs the target position / velocity / turning acceleration. .
The guided bullet motion calculation device 2 predicts the position / velocity / turning acceleration of the guided bullet up to a finite future using the given state quantity of the current guided bullet and the optimization parameters obtained from the optimization calculation device 5. Is a device that outputs the state quantity change rate of the guided bullet.
The constraint condition calculation device 3 is a device that calculates a constraint condition to be satisfied by the state amount of the guided bullet obtained by the guided bullet motion calculation device 2 and the rate of change thereof, and calculates and outputs the value.
The evaluation function calculation device 4 is a guided bullet that is calculated based on the target position / velocity / turning acceleration obtained by the target motion calculation device 1 and the induced bullet state quantity change rate obtained by the guided bullet motion calculation device 2. It is a device that calculates and outputs an evaluation function value derived from a predetermined equation from position, velocity, and turning acceleration.
The optimum guidance calculation device 5 uses the constraint condition values and the evaluation function values output from the constraint condition calculation device 3 and the evaluation function calculation device 4, respectively, to turn the guided bullets so as to minimize the given evaluation function. Perform optimization calculation on-line with the command.

The target motion calculation unit 1 performs target motion prediction by the following processing.
Current time is t0, target position at time t0 is (xt (0), yt (0)), speed is vt (0), speed azimuth etat (0), turning acceleration is at (0), sampling time Is T, the target state quantity {xt (i), yt (i), etat (i)} (i = 0 ,,, N at the time t '= t0 + kT (k = 0: N) ) Can be expressed by the following equation. Here, it is assumed that the target speed vt is constant. In the following formula, * represents multiplication and ^ represents power. ^ T represents the transpose of the matrix.

The guided bullet motion calculation unit 2 calculates the state quantity change rate of the guided bullet by the following processing.
Sampling the ammunition position at time t0 (xm (0), ym (0)), velocity vm (0), velocity azimuth etam (0), turning acceleration am (0), sampling If the time is T and the input optimization parameter is U, the rate of change of the induced bullet state quantity at time t '(i) = t0 + iT (i = 1,2, ..., N) {dxm (i) /dt,dym(i)/dt,dvm(i)/dt,detam(i)/dt,dam(i)/dt}(i=1,2,...N) Can do.

In the above formula, the variable i satisfies (i = 0,... N).
Here, the coefficients p_cla (0), p_cla (1), p_cla (2), p_cd0 (0), p_cd0 (1), p_cd0 (2), p_cdre (0), p_cdre (1), p_cdre (2) are determined in advance. The aerodynamic coefficient of the guided bullet. Also, p_ft (0), p_ft (1), and p_ft (2) are predetermined thrust coefficients of the guided bullet. P_m (0), p_m (1), and p_m (2) are the mass coefficients of the guided bullets determined in advance. Tau_ap is the induction time constant of the induction bullet.

The constraint condition calculation device 3 calculates the constraint condition of the guided bullet movement by the following processing.
Rate of change of the induced bullet state quantity calculated by the guided bullet motion calculation device 2 {dxm (i) / dt, dym (i) / dt, dvm (i) / dt, detam (i) / dt, dam (i) Based on / dt} (i = 0, 1,..., N) and the optimization parameter U given from the optimization calculation device 5, the guided bullet constraint condition matrices f and g are calculated by the following formulas.

The evaluation function calculation device 4 calculates an evaluation function used in the optimization calculation by the following processing.
The predicted state quantities {xt (i), yt (i), etat (i)} (i = 0, 1,..., N) calculated by the target motion calculator 1 and the guided bullet motion calculator 2 and Change rate of induced bullet state quantity {dxm (i) / dt, dym (i) / dt, dvm (i) / dt, detam (i) / dt, dam (i) / dt} (i = 0 ,,, From N), the elements phi (N) and L (i) of the evaluation function value are calculated by the following formula. Here, the evaluation function has an integral value of the guided bullet turning acceleration and the square of the LOS angle change rate at time t ′ = t0 + NT as elements.

The optimization calculation device 5 determines the optimization parameter U by the following processing.
The optimization parameter U is calculated using the constraint condition values f and g and the evaluation function values phi (N) and L (i) calculated by the constraint condition calculation device 3 and the evaluation function calculation device 4. The optimization parameter U is calculated by the following formula.

Where amax is the upper limit of the optimization parameter, lambda is the co-state, and mu is the Lagrange multiplier for the constraint. Hu represents partial differentiation of variable H by variable u, Hx represents partial differentiation of variable H by variable x, and Fu represents partial differentiation of variable F by variable u. ^ T represents matrix and vector transpose.
Note that F obtained above is a value in the state quantity X, and is written as F | X. Here, a slight disturbance h * dX / dt is added to the state quantity X, F is calculated again, and the value is described as F | X + h * dX / dt.
From the above, the time derivative of the optimization parameter U satisfies the following equation.

Solve this equation for dU / dt and integrate as follows:

The leading element U (1) of the obtained optimization parameter U is output as a turning acceleration command value for the guided bullet.

  In the conventional optimization calculation method, since the optimization parameter U is obtained by iterative calculation, the calculation load is high. However, in this embodiment, the optimization parameter U can be obtained without performing iterative calculation. For this reason, it is applicable to a system with a low calculation load and a relatively small time constant such as a flying object.

As described above, in the flying object guidance control apparatus of the present embodiment, the motion equation of the target and the guided bullet is taken into account when calculating the turning acceleration command value, It is possible to predict with high accuracy by performing numerical simulation sequentially.
Furthermore, it is possible to compensate for the influence of delay elements and nonlinear elements of the control system.

Embodiment 2. FIG.
FIG. 2 is a diagram showing the configuration of the flying object guidance control apparatus according to the second embodiment. The flying object guidance control apparatus according to the present embodiment includes a conventional guidance law calculation unit 6, an optimum guidance law calculation unit 7, and a gain 8.
In FIG. 2, a conventional guidance law calculation unit 6 performs the above-described proportional navigation law calculation. The optimum guidance law calculation unit 7 performs a series of calculations shown in the first embodiment. The gain 8 adjusts the gain according to the optimization calculation convergence calculated by the optimum guidance law calculation unit 7.
The optimization calculation convergence is composed of the norm of Hu (i) in the calculation of the first embodiment. When this norm is small, the optimization calculation converges well, but when this norm is large, the optimization calculation does not converge, so the conventional guidance law output is used.
The conventional guidance law output is a_png, the optimum guidance law output is a_ong, and the gain is s.
At this time, the final output a is defined as follows.

Here, gain s is defined as follows.

Here, exp is an exponential function with the Napier number as the base, and | Hu | indicates the 2-norm of Hu.

When the gain s is set as described above, when the optimization calculation is not converged (Hu >> 1), s is almost 0, and conversely (Hu≈0), s is almost 1 . By this action, the conventional guidance law and the optimum guidance law can be switched smoothly.

  1 target motion calculation device, 2 guided bullet motion calculation device, 3 constraint condition calculation device, 4 evaluation function calculation device, 5 optimization calculation device, 6 conventional guidance law, 7 optimal guidance law, 8 gain.

Claims (2)

A target motion calculator that predicts the target motion;
A guided bullet motion calculation device for predicting the motion of a guided bullet;
A constraint condition calculation device for calculating a constraint condition to be satisfied by the guided bullet;
An evaluation function calculation device for calculating an evaluation function as an index of optimization calculation;
Optimized by a single convergence operation using the evaluation value of the constraint condition output from the constraint condition calculation device and the value of the evaluation function output from the evaluation function calculation device at each sampling time that is a control cycle Calculating the time derivative of the parameter, calculating the optimization parameter by integrating the time derivative of the optimization parameter, and controlling the movement of the guided bullet ; and
A flying object guidance control apparatus comprising: Further, a proportional guidance control device that performs proportional navigation law calculation, and a commander that outputs an acceleration command value that adds the weighted outputs of the proportional guidance control device and the optimal guidance control device when the optimization calculation is not converged The flying object guidance control apparatus according to claim 1, further comprising a unit.

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