Proportional Linear Quadratic Regulator Research Articles

An effective proportional-double derivative-linear quadratic regulator controller for quadcopter attitude and altitude control

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.

Proportional Double Derivative Linear Quadratic Regulator Controller Using Improvised Grey Wolf Optimization Technique to Control Quadcopter

A hybrid proportional double derivative and linear quadratic regulator (PD2-LQR) controller is designed for altitude (z) and attitude (roll, pitch, and yaw) control of a quadrotor vehicle. The derivation of a mathematical model of the quadrotor is formulated based on the Newton–Euler approach. An appropriate controller’s parameter must be obtained to obtain a superior control performance. Therefore, we exploit the advantages of the nature-inspired optimization algorithm called Grey Wolf Optimizer (GWO) to search for those optimal values. Hence, an improved version of GWO called IGWO is proposed and used instead of the original one. A comparative study with the conventional controllers, namely proportional derivative (PD), proportional integral derivative (PID), linear quadratic regulator (LQR), proportional linear quadratic regulator (P-LQR), proportional derivative and linear quadratic regulator (PD-LQR), PD2-LQR, and original GWO-based PD2-LQR, was undertaken to show the effectiveness of the proposed approach. An investigation of 20 different quadcopter models using the proposed hybrid controller is presented. Simulation results prove that the IGWO-based PD2-LQR controller can better track the desired reference input with shorter rise time and settling time, lower percentage overshoot, and minimal steady-state error and root mean square error (RMSE).