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

Abstract

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).