Aerospace and Electronic Systems Magazine July 2018 - 19

Shraim, Awada, and Youness
of the sliding surface. This advantage gives more freedom in the
design of the controller and allows changing the system model
by introducing virtual disruptions to satisfy certain conditions
or requirements.
In [64], [67], [91], authors enhanced controllers by using a sliding mode observer. The observer helps to estimate the velocity in
order to overcome measurement limitations. It imposes robustness
properties on the overall closed loop system. These authors discovered that the proposed controller is unable to reject disturbances.
Although these papers show the performance of sliding mode controller, they decouple the system without conserving its nonholonomic nature. In [92], researchers used a sliding-mode controller
to stabilize the system and maintain the roll, pitch, and yaw angles
to zero. Although the controller worked well in stabilizing the system for the roll and pitch angles, the shattering effect remained
present for yaw control.
They judge this controller to give average results; however, in
their proposed model they neglected gyroscopic and some aerodynamic effects while using small angles. Reference [93] presents a
full control scheme for quadrotors using SMC, without considering weather disturbances. It ensures attitude and position stabilization with trajectory tracking.
However, the results show some shattering effects, and thus
this controller cannot work for a long time because of actuator constraints. Both [43] and [77] present the application of sliding mode
on Starmac; with integral sliding mode, the quadrotor is capable of
outdoor flight. This method proves a significant enhancement and
provides stable attitude on the system with bounded disturbance
forces, in comparison to linear control design techniques implemented on the aircraft.

Backstepping
Backstepping is a control approach based on Lyapunov criteria.
It allows formal obtainment of a control that stabilizes a nonlinear system. Indeed, backstepping is well-suited for the cascade structure of quadrotor dynamics. The design process of the
controller is simple if done correctly. Several researchers have
tested backstepping to design an attitude controller. A backstepping controller demonstrates the ability to control angles of orientation with relatively few large disturbances. The helicopter
is stabilized quickly, despite hard initial conditions; it shows
good results compared to other controllers. Also, the usage of
an integral backstepping controller has eliminated steady state
errors. With this technique, the OS4 can perform autonomous
hovering with control of altitude, as well as autonomous takeoff
and landing [40]. Other studies have used a cascade approach for
position and attitude in order to control the quadrotor; they illustrate the robust behavior of the backstepping and sliding mode
controllers with regard to the stabilization and set point tracking
of the complete UAV model. The feedback controller performed
poorly compared to the backstepping and sliding mode controller [94]. In [64], the authors applied a backstepping controller
to the quadrotor. At the same time, they used a speed observer
and disturbance estimator, which relied on sliding mode control. The controller completed its tasks of trajectory tracking
JULY 2018

and disturbance rejection, as well as compensated for parameter
uncertainties and modeling errors. Finally, in [95], researchers
tested backstepping on a linearized nonlinear model to solve the
problem of quadrotor stability. The results show that the backstepping method is able to control and stabilize the quadrotor.
For practical purposes, however, saturation limits need to be imposed to prevent instability [95].

Feedback Linearization
The main idea of the state feedback linearization is to algebraically transform (completely or partly) nonlinear dynamic
systems to linear, so that linear control techniques become applicable. The basic idea of simplification is to choose a nonusual state representation, or to change the frame for dynamic
coordinates of the system. In [28], the PID attitude controller is
able to successfully reject small disturbances, steady state larger disturbances, and some model error. Feedback linearization
was used to compensate blade flapping and total thrust variation in translational flight while performing aggressive maneuvers, where PID fails. This type of disturbance is associated
with high speeds and maneuvers like stall turn. Feedback linearization was also associated to other controllers to control the
movement of the quadrotor. The motion was separated in steps.
Exact feedback linearization cannot ensure stability in all cases;
it introduces zero dynamics, which results in the drift of the helicopter in the x-y plane [96]. Other researchers have associated
feedback linearization with the h-infinity controller. The author
linearized the inner loop of control under Sobolev norm, then
transformed the nonlinear system into its tangent linearized system around an operating point. Then, an H-infinity in the outer
loop was applied. This showed good results for altitude control,
and average results for translational displacement [67].

Neural Network and Fuzzy Logic
Neural networks create a nonlinear mapping from inputs to
outputs that can make an image of the quadrotor dynamics and
create a controller. This mapping remarkably improves the robustness of the controller. In [97], the authors have chosen the
Cerebellar Model Articulation Controller. The control strategy
for the flight modes and hovering is implemented in two loops.
The outer loop is responsible for the generation of instructions
for roll and pitch, as well as speed. This method is compared
with adaptive techniques such as dead band and e-modification;
the simulation shows a significant improvement in desired attitude achievement, as well as in drift reduction of weight.
The authors of [98] present a hierarchical neuro-controller for
quadrotor control. For stabilization purposes, an adaptive neural
network was applied in the presence of sinusoidal disturbances
[99]. The proposed strategy shows a reduction in tracking errors,
and no weights drift were achieved.
Fuzzy logic allows taking into account the qualitative
knowledge of designers in the control systems. This method is
complementary to conventional control. Its ability to formalize
and simulate the expertise of a designer gives a simple answer
to difficult model processes; it considers seamless exceptions

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Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine July 2018