Citation: Giernacki, W.; St˛epie´n, S.;
Chodnicki, M.; Wróblewska, A.
Hybrid Quasi-Optimal PID-SDRE
Quadrotor Control. Energies 2022, 15,
4312. https://doi.org/10.3390/
en15124312
Academic Editor: Adel Merabet
Received: 12 May 2022
Accepted: 10 June 2022
Published: 13 June 2022
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Article
Hybrid Quasi-Optimal PID-SDRE Quadrotor Control
Wojciech Giernacki
1,
* , Sławomir St˛epie ´n
2
, Marcin Chodnicki
3
and Agnieszka Wróblewska
4
1
Institute of Robotics and Machine Intelligence, Faculty of Automatic Control, Robotics and
Electrical Engineering, Poznan University of Technology, Piotrowo 3a, 60-965 Poznan, Poland
2
Institute of Automatic Control and Robotics, Faculty of Automatic Control, Robotics and
Electrical Engineering, Poznan University of Technology, Piotrowo 3a, 60-965 Poznan, Poland;
slawomir.stepien@put.poznan.pl
3
Aircraft Composite Structures Division, Air Force Institute of Technology, 6 Ksiecia Boleslawa St.,
01-494 Warsaw, Poland; marcin.chodnicki@itwl.pl
4
Institute of Heat Energy, Faculty of Environmental and Power Engineering, Poznan University of Technology,
Piotrowo 5, 61-138 Poznan, Poland; agnieszka.wroblewska@put.poznan.pl
* Correspondence: wojciech.giernacki@put.poznan.pl; Tel.: +48-61-665-2377
Abstract:
In the paper, a new cascade control system for an autonomous flight of an unmanned aerial
vehicle (UAV) based on Proportional–Integral–Derivative (PID) and finite-time State-Dependent
Riccati Equation (SDRE) control is proposed. The PID and SDRE controllers are used in a hybrid
control system for precise control and stabilization, which is necessary to increase the drone’s flight
stability and maneuver precision. The hybrid PID-SDRE control system proposed for the quadrotor
model is quasi-optimal, since the suboptimal control algorithm for the UAV stabilization is used.
The combination of the advantages of PID and SDRE control gives a significant improvement in the
quality of control while maintaining the simplicity of the control system. Furthermore, the use of the
suboptimal control technique provides the UAV attitude tracking in finite time. These remarks are
drawn from a series of simulation tests conducted for the drone model.
Keywords:
state-dependent riccati equation technique; SDRE control; PID control; attitude control;
UAV; quadrotor
1. Introduction
In recent years, there has been a strong trend in the development of control and
estimation techniques for unmanned aerial vehicles (UAVs) [
1
]. This is mainly due to their
wide availability, which, in combination with photo- and video-recording devices, greatly
extends the scope of their applicability. To operate safely and precisely in an environment
close to humans [
2
], drones need appropriate hardware and sensory tools as well as efficient
control algorithms.
Currently, a cascade closed-loop control system is widely used [
3
]. The speed and
precision of control is there based on the outer and inner loops for adjusting the orientation
and position of the drone in 3D space. It usually uses well-known, simple, fixed-value
controllers in the P, PD or PID structure. For an underactuated plant such as a drone, using
four inputs expressing the expected/reference position of the drone and its orientation
around the
Z
axis (yaw angle) in the observer (Earth) coordinate system, already roughly
selected controller gains allow for a stable, controllable, autonomous flight, which in terms
of image recording from a camera equipped with a stabilizer is more than enough.
The situation is quite different in the cases that require greater precision. Here, more
advanced solutions are sought to ensure fast stabilization in flights with variable mass [
4
],
mobile manipulation [
5
], or military missions [
6
]. Often in military tasks, the vector
correlated with the front of the drone marks the target, and it is necessary not only to
move the drone from point to point but also to orientate and stabilize it in the 3D space
by tracking predefined angles that express the orientation of the drone (roll, pitch, yaw
Energies 2022, 15, 4312. https://doi.org/10.3390/en15124312 https://www.mdpi.com/journal/energies
