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Architecture, performance and stability analysis of a formula-based fuzzy I − fuzzy P − fuzzy D controller

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Abstract

In this paper, a formula-based fuzzy integral minus fuzzy proportional minus fuzzy derivative (FI − FP − FD) controller is proposed based on the modified conventional parallel PID controller, i.e. parallel integral minus proportional minus derivative (I − P − D) controller, in order to avoid some practical industrial process problems. It freezes the linear structure of conventional parallel I − P − D controller, with analytical formulas. The final shape of the controller is a discrete-time fuzzy version of conventional parallel I − P − D controller. Computer simulation is performed to evaluate the performance of FI − FP − FD controller for setpoint tracking and load-disturbance rejection for some complex processes, such as, first- and second-order process with delay, inverse response process with and without delay and higher order processes. The simulation is done using National Instrument™ software (LabVIEW™). The response of FI − FP − FD controller is compared with the conventional parallel I − P − D controller, tuned with the Ziegler–Nichols tuning technique. It is observed that the FI − FP − FD controller performed much better than conventional I − P/I − P − D controller. Simulation results demonstrate the effectiveness and usefulness of proposed formula-based FI − FP − FD controller. Also, the bounded-input bounded-output (BIBO) stability of the overall fuzzy control system is established with sufficient conditions, using the famous “Small Gain Theorem”.

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Acknowledgments

The authors would like to thank anonymous referees and the editor for their kind encouragement and valuable suggestions to improve the paper. Also, they would like to thank to Prof. B. C. Nakra for his valuable guidance and suggestions during the entire course of this work.

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Authors and Affiliations

  1. Division of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology (NSIT), Sector-3, Dwarka, New Delhi, 110075, India

    Vineet Kumar & A. P. Mittal

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  1. Vineet Kumar
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  2. A. P. Mittal
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Correspondence to Vineet Kumar.

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Kumar, V., Mittal, A.P. Architecture, performance and stability analysis of a formula-based fuzzy I − fuzzy P − fuzzy D controller. Soft Comput 15, 517–531 (2011). https://doi.org/10.1007/s00500-009-0536-8

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  • DOI: https://doi.org/10.1007/s00500-009-0536-8

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