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

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  • Control Theory and Applications
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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).

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Authors and Affiliations

  1. College of Engineering, University of Baghdad, Baghdad, Iraq

    Omar Waleed Abdulwahhab & Nizar Hadi Abbas

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  1. Omar Waleed Abdulwahhab
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  2. Nizar Hadi Abbas
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Corresponding author

Correspondence to Omar Waleed Abdulwahhab.

Additional information

Recommended by Associate Editor Shihua Li under the direction of Editor Fuchun Sun.

Omar Waleed Abdulwahhab was born in Baghdad, 1975. He received his B.Sc. and M.Sc. degrees in computer engineering from University of Baghdad, Baghdad, Iraq, in 1998 and 2002, respectively. From 2008 to 2012, he served as a lecturer in Computer Engineering Department, College of Engineering, University of Baghdad. He is presently an assistant professor. His research interests include control theory, fractional order systems, optimization, and soft computing.

Nizar Hadi Abbas was born in Baghdad, 1975. He received his B.Sc. degree in electrical engineering from University of Baghdad, Baghdad, Iraq in 2000, an M.Sc. degree in control and computer engineering in 2002 from University of Baghdad, and a Ph.D. degree in advanced control in 2011 from Osmania University, Hyderabad, India. He is presently an assistant professor. His research interests include control theory, fractional order systems, and optimization.

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Abdulwahhab, O.W., Abbas, N.H. Design and Stability Analysis of a Fractional Order State Feedback Controller for Trajectory Tracking of a Differential Drive Robot. Int. J. Control Autom. Syst. 16, 2790–2800 (2018). https://doi.org/10.1007/s12555-017-0234-8

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  • DOI: https://doi.org/10.1007/s12555-017-0234-8

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