Advanced Mathematics and Numerical Modeling of IoT

Noise

0 12345678910

Time

Noise

6 5 4 3 2 1 0

−1

−2

−3

−4

(a) Disturbance of푥-axis

Desired

Current

012345678910

Time

Displacement

7 6 5 4 3 2 1 0

−1

(b) Position of quadrotor (푥-axis)

012345678910

Time

Angle

5 4 3 2 1 0

−1

−2

(c) Attitude of quadrotor (휑)

Figure 13: Tracking displacement with noise.

That is, the transform function refers to the error value
in the PID feedback control shown inFigure 6,andthe
feedback control system can minimize the error by adjusting
the process control outputs. Consider

푢(푡)=퐾푝푒(푡)+

1

푇푖

∫

푡

0

푒(휏)푑휏 + 푇푑

푑푒(푡)

푑푡

, (26)

where휏is a variable of integration and takes values from time
zero to the present time,푡.퐾푝,푇푖,and푇푑signify the gain, a
tuning parameter. Consider

휃=sin−1(

푢푥(푡)푚

푈 1

), (27)

−sin휃min≤

푢푥(푡)푚

푈 1

≤sin휃max. (28)

The appropriate angle can be calculated using ( 28 ). The
physical meaning of this expression is as follows (Figure 7,left
block).

(i) A large mass requires a large angle.

(ii) If the motor output is large, the desired angle is

reduced.

(iii) The larger the control signal, the more the angle tilts.

The displacement control layer enables the quadrotor
to move to the desired point while resisting disturbance.

Table 2: Control parameter values.

Parameters Value

푃term 푃 1.2

퐼term 퐼 0.1

퐷term 퐷 0.4

Invariably, it also makes it possible for the quadrotor to hover.

However, this control layer calculates only the angle for the

respective distance error. In other words, this layer is designed

to faithfully conduct an indigenous mission.

4. Implementation and Experimentation

We implemented our proposed control system in MATLAB

Simulink and conducted several simulations (Figure 7). The

experimental values obtained are listed in Tables 1 and 2.

Optimization is not within the scope of this paper.

As a result, approximate values were used. To verify our

proposed multilayered control system, only layers 1 and 2

were implemented in the first set of experiments.

InFigure 7,theleftblockistheattitudecontrollayerand

the right block is the physical layer. The remaining small

blocks are the input and output gates.

Figure 8shows the results of the first set of experiments.

As expected, in situations where there is a continuous

disturbance, the quadrotor is able to maintain its attitude.