Aerospace and Electronic Systems Magazine January 2018 - 53

Aminzadeh, Roudbari, and Atashgah
Table 1.

Specification and RMS Value of Noise in Each Simulated Sensor's Measurements
Sensor
GPS

Measurements

Range

RMS Value of Noise

North and East GPS velocity (m/s)

0.05-5.0

0.5

Vertical GPS velocity (m/s)

0.05-5.0

0.7

GPS horizontal position (m)

0.1-10.0

0.5

Barometer

Altitude (m)

0.1-10.0

2

Compass

Magnetometer measurements
(gauss)

IMU

Rate gyro (rad/s)
Accelerometer (m/s )

0.05

0.001-0.05

0.015

0.05-1

2

high, then the filter will place less weighting on the measurements.
On the other hand, if we set this parameter too small, then the filter will constantly react to noise in the measurements, which can
cause the vehicle fall in a hazard. For instance, a too small RMS
value of noise in North and East GPS velocity measurements will
cause the filter roll and pitch angles to be noisy. Moreover, too
small noise parameter for vertical GPS velocity measurements will
cause the copter to jiggle up and down. Setting the RMS value of
noise in GPS horizontal position measurements too small can also
cause continual and rapid small attitude and position changes in
copters during loiter flight mode. According to Table 1, the RMS
value of noise in the altitude measurements is set to 2m while if
we set this parameter too small, then the filter will continually get
involved to the noise in the barometer measurements, which will
cause the copter jiggle up and down during altitude hold mode.
However, increasing the RMS value of noise in magnetometer
measurements reduces the weighting on these measurements; this
would make the filter yaw less affected by magnetometers errors
and more affected by Z gyro drift. Furthermore, a high RMS value
of noise in gyro and accelerometer measurements makes the filter
trust to these data less and to the other values more. These noise
parameters control the increase in estimated error due to gyro and
accelerometer measurements errors, except bias.

CONTROL SYSTEM
Dynamic model of the motion of a quadcopter is derived to use in the
development of the control system. The most common control system
is proportional-integral-derivative (PID) controller due to its simplicity and robustness [17]. The APM firmware uses PID controller
in which angular orientation of the quadcopter will be controlled by
APM_Control library, which includes roll, pitch, and yaw angles controllers. Parameters used in APM_Control library are listed in Table 2.
As can be seen in Figure 3, the roll controller calculates the demanded roll rate through multiplying the time constant parameter
by the difference between measured and demanded values of the
roll angle. A limiter will be applied to the roll rate in order to be
subtracted from the demanded roll rate for a specific flight mode
and then the derivative term of the PID controller will be applied
JANUARY 2018

0.01-0.5

Kind of Noise
Additive White
Gaussian Noise

0.25

Table 2.

Parameters Defined in Roll, Pitch, and Yaw
Controllers of APM Firmware
Parameter

Description

TCONST

Time constant parameter with default
value of 0.5

D

Derivative gain for damping oscillations
in roll and pitch with default value of
0.02

P

Proportional gain with default value of
0.4

I

Integral gain with default value of 0.04

RMAX

The most demanded roll rate

RMAX_
UP/
RMAX_
DN

The most demanded pitch rate for nose
up or nose down situation

RLL

Roll and yaw compensator gain with
default value of 1

INT

Integral gain of sideslip angle with
default value of 1

SLIP

Sideslip angle gain with default value
of 0

DAMP

Derivative gain for damping oscillations
in yaw with default value of 0

to the difference between them as well as the integral term. Proportional term will also be applied to the limited roll rate. Finally,
the total effect of these three terms of the designed PID controller
of APM firmware will be multiplied by a scale factor, which yields
the demanded roll angle in the whole flight duration.
To achieve the demanded pitch angle, the pitch controller calculates pitch rate through multiplying the time constant parameter
by the difference between the measured and demanded values of

IEEE A&E SYSTEMS MAGAZINE

53



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