A Comparative Study Between a Classical and Optimal Controller for a Quadrotor

TL;DR

This paper compares classical PID and optimal LQR controllers for a linearized quadrotor model through simulation, highlighting differences in robustness and response under identical conditions.

Contribution

It provides a simulation-based comparison of PID and LQR controllers for quadrotors, including derivation of a linear model and implementation in Simulink.

Findings

LQR shows greater robustness than PID.

Both controllers achieve satisfactory responses.

Simulation results highlight differences in control performance.

Abstract

This paper presents a simulation-based comparison between the two controllers, Proportional Integral Derivative (PID), a classical controller and Linear Quadratic Regulator (LQR), an optimal controller, for a linearized quadrotor model. To simplify an otherwise complicated dynamic model of a quadrotor, we derive a linear mathematical model using Newtonian and Euler's laws and applying basic principles of physics. This derivation gives the equations that govern the motion of a quadrotor, both concerning the body frame and the inertial frame. A state-space model is developed, which is then used to simulate the control algorithms for the quadrotor. Apart from the classic PID control algorithm, LQR is an optimal control regulator, and it is more robust for a quadrotor. Both the controllers are simulated in Simulink under the same initial conditions and show a satisfactory response.