Abstract
A quadcopter control system is a fundamentally difficult and challenging problem because its dynamics modelling is highly nonlinear, especially after accounting for the complicated aerodynamic effects. Plus, its variables are highly interdependent and coupled in nature. There are six controllers studied and analysed in this work which are (1) Proportional–Integral–Derivative (PID), (2) Proportional-Derivative (PD), (3) Linear Quadratic Regulator (LQR), (4) Proportional-Linear Quadratic Regulator (P-LQR), (5) Proportional-Derivative-Linear Quadratic Regulator (PD-LQR) and lastly (6) the proposed controller named Proportional-Double Derivative-Linear Quadratic Regulator (PD2-LQR) controller. The altitude control and attitude stabilization of the quadcopter have been investigated using MATLAB/Simulink software. The mathematical model of the quadcopter using the Newton–Euler approach is applied to these controllers has illuminated the attitude (i.e. pitch, yaw, and roll) 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, and PD-LQR controllers. The findings elucidated that the proposed PD2-LQR controller significantly improves the performance of the control system in almost all responses. Hence, the proposed PD2-LQR controller can be applied as an alternative controller of all four motions in quadcopters.
Highlights
In recent years, the popularity of the small-scale Unmanned Aerial Vehicle (UAV) such as quadcopter has drastically increased due to its advantages and wide range of military and civilian applications
In order to see in better display, the P-Linear Quadratic Regulator (LQR) controller and the Proportional-Double Derivative-Linear Quadratic Regulator (PD2-LQR) are compared; the rise time of the PD2-LQR controller is improved by 58.3%, 79.3% improvement in settling time was achieved by the PD2LQR controller, percentage overshoot of the controller has improved by 88.3%, the minimization of the steadystate error is up to 97.0%, and the root mean square error (RMSE) reduce by 17.4%
In comparison between the Proportional-Derivative-Linear Quadratic Regulator (PD-LQR) and the PD2-LQR controller; the rise time of the PD2-LQR controller is improved by 68.7%, 71.4% improvement in settling time was achieved by the PD2-LQR controller, percentage overshoot of the controller has improved by 98.9%, the difference of the steady-state error between the PD-LQR controller and PD2-LQR controller is minimal the value can be negligible, and the RMSE reduce by 10.2%
Summary
The popularity of the small-scale Unmanned Aerial Vehicle (UAV) such as quadcopter has drastically increased due to its advantages and wide range of military and civilian applications. The simulation result shows that the system’s overshoot is less than 25% in roll, pitch, and yaw motion, respectively, and the controller produces a very fast settling time around 1.3 s Other than that, they perform an experimental study to test the controller’s robustness against external disturbances such as wind and collision. The simulation result shows that when K is lower, the state response time will become slower to reach zero, but the controller response becomes faster, and it will produce overshoot and steady-state error. Based on the simulation results, the developed hybrid PD2LQR controller is best-suited to control and stabilize the states of the quadcopter with a better dynamic performance in terms of rising time, settling time, percentage overshoot, steady-state error, and RMSE.
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