Design and Stability Analysis of a Fractional Order State Feedback Controller for Trajectory Tracking of a Differential Drive Robot

Abstract

In this paper, a new structure of a Fractional Order State Feedback Controller (FOSFC) is designed to solve the problem of trajectory tracking of a Differential Drive Robot (DDR), which is a nonlinear Multi-Input Multi-Output (MIMO) system. One of the main features of this paper is that it considers both the kinematic and dynamic models of the robot. For comparison purposes, a conventional Integer Order State Feedback Controller (IOSFC) is designed for the same system. The parameters of both controllers are tuned (using the fmincon Matlab function) to minimize the Integral of Time multiplied by Squared Error (ITSE) performance index when the DDR tracks a circular reference trajectory. The FOSFC gives a better value for this performance index than that of the IOSFC, which means that the FOSFC enhances the performance of the system with respect to this performance index. While the stability of the closed loop system is verified using Lyapunovs direct method for the IOSFC, a new approach is presented in this paper to analyze the stability of the closed loop system for the designed FOSFC. Simulation results demonstrate that the FOSFC outperforms the IOSFC for two other performance indices, namely, the Integral of Absolute Error (IAE) and the Integral of Squared Error (ISE).