The developments of proportional-double derivative-linear quadratic regulator controller for attitude and altitude motions of a quadcopter
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Date
2019-06
Authors
Mohamad Norherman Shauqie Mohamed Raihan
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Abstract
Unmanned Aerial Vehicle (UAV), in this case, a quadcopter, is a small-scale
UAV that has been widely used in the recent years due to its capability to perform a
various application either in the military or civilian application such as environment
monitoring, surveillance, and inspection. In order to guarantee a high performance of
the quadcopter in the various mission applications, it needs reliable hardware and
control systems. Therefore, it is important to developing an effective control algorithm
for the controller for the performance and application of the quadcopter. In this thesis,
studies of the attitude control and stabilization of the quadcopter through a simulation
in Matlab/Simulink software has been done. First, several controllers, Proportional
Integral-Derivative (PID), Proportional-Derivative (PD), Linear Quadratic Regulator
(LQR), Proportional-Linear Quadratic Regulator (P-LQR), and Proportional
Derivative-Linear Quadratic Regulator (PD-LQR) controller have been chosen to be
studied and analyzed. After that, from the analysis obtained another controller was
proposed to improve the performance of the quadcopter control. It is found that by
adding another Derivative gain in the PD-LQR control system, the performance can be
improved further. Thus, a Proportional-Double Derivative-Linear Quadratic Regulator
(PD2-LQR) controller has been designed and developed. The mathematical model of
the quadcopter using the Newton-Euler approach is applied to the controller system
illuminate the attitude and altitude motions of the quadcopter. The simulation results of
the proposed PD2-LQR controller have been compared with the PD, PID, LQR, P-LQR,
PD-LQR controller. The comparative study of the response plots reveals that the
proposed PD2-LQR controller significantly improves the performance of the control
system in almost all responses. In pitch motion, the PD2-LQR controller can improve
the rise time up to 82.9% in average compared to other controllers, settling time
improved by 86.58% in average, overshoot improved by 39.16% in average, steady
state error improved by 39.2% in average, and RMSE improved by 28.32% in average.
In roll motion, rise time improved by 63% in average, settling time improved by 65.5%
in average, overshoot improved by 57.7% in average, steady-state error improved by
32.82% in average, and RMSE improved by 29.4% in average. In yaw motion, rise
time improved by 41.8% in average, settling time improved by 41.5% in average,
overshoot improved by 34.3% in average, the improvement of steady-state error in yaw
motion is very small it can be approximately equal to zero, and RMSE improved by
19.4% in average. In altitude motion, rise time improved by 31.7% in average, settling
time improved by 52.7% in average, overshoot improved by 75.7% in average, and
RMSE improved by 10.2% in average. Therefore, the proposed PD2-LQR controller is
best-suited for the modelled quadcopter in all four motions, pitch, roll, yaw, and
altitude.