Aerospace and Electronic Systems Magazine July 2018 - 23
Shraim, Awada, and Youness
Several references treat this problem, as presented in [28],
[224], [225]. In the case of external disturbances, such as wind,
we can cite [219].
CASE STUDY AND COMPARATIVE STUDY
In this section, we propose a certain significant trajectory and we
test the efficiency of some of the controllers on it. The model used
for the simulation and comparison is that proposed in [40], and
model parameters used are those identified by Shamaa [215]. Control strategies are all developed and modeled in MATLAB. Concerning the parameters and gains of controllers, several studies
have been made for purpose of choosing optimal gains; we cite
for example [215] and [226]. The strategy is as follows for each
controller: first we define, based on the theoretical study, the permitted domain for the variation of gain in order to stabilize the
system. Then, we define several significant trajectories. Thirdly, an
iterative loop in which the gain varies in its domain of definition
and tracking error is calculated. And finally, we choose the optimal
value and fix it to the controller.
The Trajectory is proposed to be complex, containing ramp,
step, and helicoïdal motion. The desired trajectory on the X, Y, and
Z axis is shown in Figure 2.
We present four criterions of comparison:
a. Trajectory tracking precision criterion:
X displacement (Table 2)
Y displacement (Table 3)
Z displacement (Table 4)
b. Fine dynamic performance criterion:
Figure 2.
The desired trajectory on the X, Y, and Z axis.
Table 2.
Trajectory Tracking Precision on Data over x Position
PID
Feedback
Linearization
Classical
Spatial Modulation (SM)
Second Order
SM
Integral
Backstepping
Lyapunov
>2
0.4654
0.0757
0.0939
0.5539
0.0859
Overshoot (%)
6.9931
2.5967
2.0396
0.6214
4.6187
0.7865
RMS
2.7979
0.0928
0.0619
0.0152
0.1713
0.0197
1.7610
0.5793
1.1827
0.4749
1.0513
0.3730
>6.5
0.9169
1.5478
0.9535
1.9342
0.7277
Overshoot (%)
11.2942
2.0203
0.2333
2.2528
0
3.4284
RMS
1.8005
0.9108
0.9600
0.7998
0.9161
0.8936
3.7627
0.3641
0.1195
0.2868
0.4116
0.3160
Part 1
Settling Time
Part 2
Rise time
Settling Time
Part 3
RMS
JULY 2018
IEEE A&E SYSTEMS MAGAZINE
23
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