Fractional Order Control Methodology for the SelfBalance Robot

Dipak M Adhyaru,Sandip A Mehta

doi:10.35940/ijeat.a1956.049420

Abstract

In this research paper the control algorithms like LQR and PID has been proposed for the integer and fractional order system. In this research paper the modeling of the selfbalance robot system has been carried out in integer domain and fractional domain. This research paper presents the simulation analysis of control algorithms for two wheel self-balancing robot using Linear Quadratic Regulator, Proportional-IntegralDerivative and Fractional order Proportional-Integral-Derivative control algorithm. These all control algorithm are applied on the integer order system and the fractional order system and comparative analysis has been done. The comparison between integer order PID against the fractional order PID is also been made for the self-balance robot. It has been demonstrated through simulation that fractional order controller gives better response as compared to integer order controller. Further it has been found out that fractional order controller gives better results when applied to fractional order system compared to its integer order counterpart.

Highlights

This section is divided into two parts where in the first part LQR algorithm is applied to integer order system and it is applied to fractional order system
Where yellow line is for the PID control response and pink line is for the FOPID control response, from this response one can observe that FOPID have less oscillation, faster stability and less peak overshoot compare to PID control algorithm
For the novelty purpose, modeling of the self-balance robot is been carried out in fractional domain using the assumption of commensurate order fractional order system

Summary

INTRODUCTION

In last two decades the fractional order calculus gain the momentum and proves many advantages in scientific fields It starts with system modelling, identification and automatic control. From all these literature review one can say that the fractional order PID control is applied in almost every engineering field. Fractional PID gives faster response compared to the integer order PID[9–11], for nonlinear and unstable systems, fractional PID controller tuning is difficult, and control algorithms like LQR (Linear Quadratic Regulator)/ LQG(Linear Quadratic Gaussian) is used. The integer order LQR along with fractional order filters are used for the control purposes. In this work author has proposed the state feedback control which is equivalent to the integer order LQR formulation and Riccati equation formulation. For the simulation purpose some of codes available in [17] and in [18]

SYSTEM MODELLING

CONVERTING INTEGER ORDER TO FRACTIONAL ORDER

RESULTS

Results for LQR control on fractional order system

Applying PID and FOPID control algorithm on integer and fractional order system

CONCLUSION