  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.
