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

**Authors:** Prathamesh Saraf, Manan Gupta, Alivelu Manga Parimi  
**arXiv:** [2009.13175](https://arxiv.org/abs/2009.13175)  
**Date:** 2020-09-28  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2009.13175v1/

## Key points

- The paper presents a comparative study between two controllers for a linearized quadrotor model: PID and LQR.
- The authors derive a linear mathematical model using Newtonian and Euler's laws to simplify the dynamic model of a quadrotor.
- A state-space model is developed from these equations which is then used to simulate the control algorithms for the quadrotor.
- The authors compare the performance of PID and LQR controllers under identical initial conditions using Simulink simulations.
- LQR proves to be more robust for a quadrotor than PID, highlighting that it is an optimal control regulator that can provide better performance than classical controllers like PID.
- Optimal control regulators like LQR can offer better performance than classical controllers in certain scenarios.
- The approach of deriving a simplified mathematical model using fundamental principles of physics can also be useful for researchers working on similar problems in robotics and control systems engineering.

## Summary

In this paper, Prathamesh Saraf, Manan Gupta, and Alivelu Manga Parimi present a comparative study between two controllers for a linearized quadrotor model: the Proportional Integral Derivative (PID), a classical controller, and the Linear Quadratic Regulator (LQR), an optimal controller. The authors derive a linear mathematical model using Newtonian and Euler's laws to simplify the otherwise complicated dynamic model of a quadrotor. This derivation provides equations that govern the motion of a quadrotor in both the body frame and inertial frame. A state-space model is developed from these equations which is then used to simulate the control algorithms for the quadrotor. The authors compare the performance of PID and LQR controllers under identical initial conditions using Simulink simulations. While both controllers show satisfactory responses, LQR proves to be more robust for a quadrotor. The study highlights that LQR is an optimal control regulator that can provide better performance than classical controllers like PID. Overall, this paper presents valuable insights into controlling quadrotors using different types of controllers. The results suggest that optimal control regulators like LQR can offer better performance than classical controllers in certain scenarios. The authors' approach of deriving a simplified mathematical model using fundamental principles of physics can also be useful for researchers working on similar problems in robotics and control systems engineering.