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20 14 mathematical modeling contest a how to do Chang' e III?
In the case of high-speed flight, the key to ensure an accurate soft landing in the predetermined area of the moon is Chang 'e III.

The problem is the design of landing trajectory and control strategy.

Because there is no atmosphere on the moon, Chang 'e III can't rely on parachutes.

On land, only the variable thrust engine can complete the soft landing such as mid-course correction, braking in recent months, power drop and hovering section.

Mission. This article is in

Under the basic requirements of landing orbit design, the optimal control model is established to meet the needs of Chang 'e-3 in various stages.

In the state where the key points are located, three problems are divided according to the principle of minimum oil consumption during soft landing.

Analysis and exploration.

For this problem

1

In this paper, Chang 'e III is taken as the particle, and the length of the semi-focal length is calculated according to the ellipse formula.

appropriate

Used for all two-body problems

Kepler's third law model, which calculates the corresponding speeds of near and far moon points, near and far moon points.

The speed of the moon point is

1.69204 km/s

, the far moon speed is

1.61390km/s

, and then cross the square of the given landing site.

Push out the direction corresponding to Chang 'e III.

For this problem

2

Aiming at the optimization problem of precise fixed-point soft landing of lunar probe, a parameterized control method is studied.

Methods to control problems. First, the constraint transformation technique is used to approximate the small equality constraints, and then if ten constraints are used,

The piecewise constant is used to approximate the optimal solution, and then according to the reinforcement technique, through the transformation on the time axis, the continuity of each parameter is

Time is transformed into a new set of parameters, so the optimal control problem is transformed into a series of parameter optimization problems. Final application

The classical parameter optimization method can get the approximate solution of the optimal control function. Repeat the optimization by increasing the number of parameters.

The parametric solution of the approximate continuous optimal solution is obtained.

At the same time, the selection of braking starting point is considered in the optimization process.

The influence of. use

matlab

The landing trajectory curve is drawn by software, and the results show that the design method is simple and effective.

Yes The optimal initial point coordinates are obtained as follows

X

=837

.

7 1 km

Y

= 1423.9 km

Z

=586.26 km

For this problem

three

According to the dynamic equation of lunar probe's orbit around the moon, the orbit error of lunar probe's orbit around the moon is obtained

Based on the iterative equation, the orbit error caused by the error source of the initial orbit error is analyzed by covariance analysis method.

Combined with a specific example, the orbit error caused by the initial orbit position and velocity error of the detector is given

Time course and orbit terminal error. The calculation results show that the launch of Chang 'e-3 satellite must be carried out many times.

Midway orbit correction.