3. Control and Simulation

Using the physical values for the flyer, the coupled pitch and ξ_X translational dynamical equations can be computed. The error range of the parameters maps the roots of the plant into a space on the complex plane.

These can be solved for a single transfer function H = Θ/δω between pitch angle, θ, and the input change in rotor speeds, δω:

H = [5]

Where

c₁ =

c₂ = ρARω₀

c₃ =

We approximate the flapping angle as a linear function of ˙x and ˙θ:

a_1s = c₁x˙ + c₃ ˙θ

Using the previously given parameters and errors, the poles and zeros of the system are given in Figure 2.1. The rotor height above the CoG is the largest contributor to error, producing more than 80 per cent of the error of each pole calculation. Thus, accurate knowledge of the rotor height is important to determining the dynamic model.

Figure 3.1 Unstable system

Figure 3.2 Unstable systems(diagrams)

Below shows Unstable system (for this purpose in the negative feedback was added accelerometer and two integrals transforming acceleration in movement):

When: =0.8, _T=0,2,

Some transfer function of the accelerometer. He was put into a negative feedback for stability of the system. Double integral to translate measurement shot accelerometer in the movement are also present there [7].

Figure 3.3 Stable system

The rotor speed noise is modelled by an output disturbance to the rotor speed, d, characterized as white noise, w, passed through a coloured filter, F.

F =

Pitch angle is integrated to x position. Using equations 35 and 40, the transfer function, X, is:

X =

Figure 3.4 Matched coefficients (PID controller)

Figure 3.5 Stable systems (diagrams)

Figure 3.6 BEFORE noise filtering

Figure 3.7 AFTER noise filtering

*Link to original: https://drive.google.com/drive/u/1/my-drive

4. Programming code for Arduino

Here are the main fragments of out controller code. We've tried to compile the whole program , and found out that it works!

4.1 Фn example of our code

5. 3d-model Quadcopter

Expectation model is made in the Compass 3D:

Figure 5.1 Model 1

Figure 5.2 Model 2

Figure 5.3 Model 3

Figure 5.4 Model 4

*Link to original: https://drive.google.com/drive/u/1/my-drive

Real model:

6. Project plan

Figure 6.1: Gantt chart

*Link to original: https://drive.google.com/drive/u/1/my-drive

6.1. Project plan

The risks that we have encountered in the course of of our work:

• Do not timely delivery of parts to the site «ebay», which resulted in a shift of the deadline;

• When the test run were damaged some of the details, which entailed additional expenses by time;

But in the course of work, most of which was given to eliminate or reduce them to a negligible impact.