Figure 4.Equation of motion for uniformly accelerated motion
The time of falling 
of the body to Earth is found from the condition y = 0:
Figure 5.Time of falling of a body at uniformly accelerated motion
As we have already explained, the force acting on the body in free fall is described by the equation F = mg, where m is the mass of the incident body, and g is the acceleration of the free fall.
In order to overcome the effect of this force, it is necessary to create an air flow with a speed equal to or exceeding the velocity of the fall of the ball.
Since speed is the first derivative of coordinates with respect to time, the stabilization of the system will depend on time, i.e. the equation will be the second power of the time derivative t.
W(t)=ms2(t)
The coefficient m was experimentally chosen. It must be positive.
Figure 5.2Model of operation of the system without control
The figure shows that the system is unstable and the graph exponentially changes with time. So under an uncontrolled flow of air, the ball flies away - the system is unstable.
Thus, it is necessary to use a controller to manage the fan speed, to stabilize the ball in a certain range. Since fluctuations due to external factors will be, but are minimal. It depends on the fan: with what minimum step it can change the speed.
To stabilize the system, let us imagine that the ball is held on a spring with a damping coefficient -k. The transfer function will look like:
Wk (t) = - ks (t).
The minus sign means stretching the imaginary spring and holding it in tension, to raise the ball to a certain height.
To stabilize the system, you can use the PD regulator or Arduino, which is necessary to generate a control signal in order to obtain the necessary accuracy and quality of the transient process. The purpose of the PID controller is to maintain a given value of x0 of some value of x by changing another value of u.
Figure 5.1Model of operation of the system with using of PID regulation
The coefficients are also chosen experimentally, so the regulator can stabilize the system under different conditions, i.e. making it robust. This leads to the fact that instead of the ball it will be possible to use other bodies, with less streamlined shape and with a different center of gravity.
The system consists of:
1) Plastic pipe (arbitrary or printed on a 3D printer)
2) Fan of appropriate power
3) Ball (in perspective any other body) with suitable weight and dimensions
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4) Ultrasonic sensor and controller (Arduino)
General scheme of the system is represented at the Figures 5.3.-5.5.
At an initial stage, a ventilator is activated having its initial power - P0.Using a special sensor, the distance from the upper edge of the pipe to the soaring ball is measured in specified intervals of time.With the help of controller, which is specially set up the ventilator's power is changing so that to fix the item at a certain height.
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