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A robust fractional order fuzzy P + fuzzy I + fuzzy D controller for nonlinear and uncertain system

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Abstract

In this paper, a robust fractional order fuzzy P + fuzzy I + fuzzy D (FOFP + FOFI + FOFD) controller is presented for a nonlinear and uncertain 2-link planar rigid manipulator. It is a nonlinear fuzzy controller with variable gains that makes it selfadjustable or adaptive in nature. The fractional order operators further make it more robust by providing additional degrees of freedom to the design engineer. The integer order counterpart, fuzzy P + fuzzy I + fuzzy D (FP + FI + FD) controller, for a comparative study, was realized by taking the integer value for the fractional order operators in FOFP + FOFI + FOFD controller. The performances of both the fuzzy controllers are evaluated for reference trajectory tracking and disturbance rejection with and without model uncertainty and measurement noise. Genetic algorithm was used to optimize the parameters of controller under study for minimum integral of absolute error. Simulation results demonstrated that FOFP + FOFI + FOFD controller show much better performance as compared to its counterpart FP + FI + FD controller in servo as well as the regulatory problem and in model uncertainty and noisy environment FOFP + FOFI + FOFD controller demonstrated more robust behavior as compared to the FP + FI + FD controller. For the developed controller bounded-input and bounded-output stability conditions are also developed using Small Gain Theorem.

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Acknowledgements

The authors would like to thank their institute for providing excellent experimental facilities in the Advanced Process Control Lab (APCL) and Virtual Instrumentation and Control Technology (VICT), Centre for research.

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Authors and Affiliations

  1. Division of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology (NSIT), University of Delhi, New Delhi, 110078, India

    Vineet Kumar, K. P. S. Rana, Jitendra Kumar, Puneet Mishra & Sreejith S. Nair

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  1. Vineet Kumar
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  2. K. P. S. Rana
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  3. Jitendra Kumar
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  5. Sreejith S. Nair
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Correspondence to Vineet Kumar.

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Recommended by Associate Editor Jyh-Horng Chou

Vineet Kumar received the M. Sc. degree in physics with electronics from Govind Ballabh Pant University of Agriculture & Technology, India, M.Tech. degree in instrumentation from Regional Engineering College, Kurukshetra, India and Ph.D. degree from Delhi University, India. He has served industry from 1996 to 2000. Since July 2000, he has been associated with the Netaji Subhas Institute of Technology (NSIT), Delhi University, India. Currently, he holds the post of associate professor in the Instrumentation and Control Engineering Division, NSIT, India.

His research interests include process dynamics and control, intelligent control techniques and their applications, digital signal processing, and robotics.

K. P. S. Rana received the M. Sc. degree in physics (electronics major) from Meerut University, India in 1989 and M.Tech. degree in instrumentation from Indian Institute of Technology (IIT) India in 1991 and Ph. D. degree in “intelligent methods for complex vibration measurement and control” from Guru Gobind Singh Indraprastha University, India in 2011. He has served Indian Space Research Organization (ISRO) from 1993–2002 as Scientist “SD” in Sensors Division at Bangalore, India. Since August 2000, he has been with Netaji Subhas Institute of Technology (NSIT), Delhi University, India at the Department of Instrumentation and Control Engineering where he has served as assistant professor from August 2000 to December 2005, and since January 2006 he has been serving as associate professor.

His research and teaching interests include PC based measurement, real time systems, intelligent instrumentation and control, sensor linearization, digital signal processing.

Jitendra Kumar received the B.Tech. degree in electronics and instrumentation engineering from West Bengal University of Technology, India and M.Tech. degree in process control from Netaji Subhas Institute of Technology, Delhi University, India in year 2010 and 2013 respectively. He served as a lecturer at GLA University, Mathura, India. Currently, he is a Ph.D. candidate and also serving as a teaching-cum-research-fellow in the Division of Instrumentation and Control Engineering at Netaji Subhas Institute of Technology, Delhi University, India.

His research interests include the areas of conventional adaptive control, intelligent adaptive control, and different optimization techniques.

Puneet Mishra received the B. Tech. degree in electronics and instrumentation engineering from Uttar Pradesh Technical University, India and the M. Sc. degree in control and instrumentation engineering from Delhi College of Engineering, Delhi University, India in year 2009 and 2011 respectively. He was an assistant professor at GLA University, India. Currently, he is a Ph. D. candidate and also serving at the Division of Instrumentation and Control Engineering at Netaji Subhas Institute of Technology, India as a teaching-cum-research-fellow.

His research interests include intelligent adaptive control, fractional order modeling and control, and bio-inspired optimization techniques.

Sreejith S Nair received the B.Tech. degree in electronics and communication from Cochin University, Kerala in 2008. He received the M.Tech. degree in signal processing from Guru Gobind Singh Indraprastha University, India in 2011. He is currently a Ph. D. degree candidate at Netaji Subhas Institute of technology, India.

His research interests include discretetime signal processing, statistical signal processing, image processing, microwave filter design and fractional control.

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Kumar, V., Rana, K.P.S., Kumar, J. et al. A robust fractional order fuzzy P + fuzzy I + fuzzy D controller for nonlinear and uncertain system. Int. J. Autom. Comput. 14, 474–488 (2017). https://doi.org/10.1007/s11633-016-0981-7

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  • DOI: https://doi.org/10.1007/s11633-016-0981-7

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