We propose a simple but robust model independent self-tuning scheme for fuzzy logic controllers (FLC's). Here, the output scaling factor (SF) is adjusted on-line by fuzzy rules according to the current trend of the controlled process. The rulebase for tuning the output SF is defined on error (e) and change of error (1e) of the controlled variable using the most natural and unbiased membership functions (MF's). The proposed selftuning technique is applied to both PI-and PD-type FLC's to conduct simulation analysis for a wide range of different linear and nonlinear second-order processes including a marginally stable system where even the well known Ziegler-Nichols tuned conventional PI or PID controllers fail to provide an acceptable performance due to excessively large overshoot. Performances of the proposed self-tuning FLC's are compared with those of their corresponding conventional FLC's in terms of several performance measures such as peak overshoot, settling time, rise time, integral absolute error (IAE) and integral-of-timemultiplied absolute error (ITAE), in addition to the responses due to step set-point change and load disturbance and, in each case, the proposed scheme shows a remarkably improved performance over its conventional counterpart.

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An improved auto-tuning scheme is proposed for Ziegler-Nichols (ZN) tuned PID controllers (ZNPIDs), which usually provide excessively large overshoots, not tolerable in most of the situations, for high-order and nonlinear processes. To overcome this limitation ZNPIDs are upgraded by some easily interpretable heuristic rules through an online gain modifying factor defined on the instantaneous process states. This study is an extension of our earlier work [Mudi RK., Dey C. Lee TT. An improved auto-tuning scheme for PI controllers. ISA Trans 2008; 47: 45-52] to ZNPIDs, thereby making the scheme suitable for a wide range of processes and more generalized too. The proposed augmented ZNPID (AZNPID) is tested on various high-order linear and nonlinear dead-time processes with improved performance over ZNPID, refined ZNPID (RZNPID), and other schemes reported in the literature. Stability issues are addressed for linear processes. Robust performance of AZNPID is observed while changing its tunable parameters as well as the process dead-time. The proposed scheme is also implemented on a real time servo-based position control system.

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There are many important issues that need to be resolved for identification of a fuzzy rule-based system using clustering. We address three such important issues: 1) deciding on the proper domain(s) of clustering; 2) deciding on the number of rules; and 3) getting an initial estimate of parameters of the fuzzy systems. We justify that one should start with separate clustering of X (input) and Y (output). We propose a scheme to establish correspondence between the clusters obtained in X and Y. The correspondence dictates whether further splitting/merging of clusters is needed or not. If X and Y do not exhibit strong cluster substructures, then again clustering of X* (input data augmented by the output data) exploiting the results of separate clustering of X and Y, and of the correspondence scheme is recommended. We justify that usual cluster validity indices are not suitable for finding the number of rules, and the proposed scheme does not use any cluster validity index. Three methods are suggested to get the initial estimate of membership functions (MFs). The proposed scheme is used to identify the rule base needed to realize a self-tuning fuzzy PI-type controller and its performance is found to be quite satisfactory.