Modeling, simulation and experimental realization of a new nonlinear fuzzy PID controller using Center of Gravity defuzzification.

Though Center of Gravity (CoG) defuzzification is a well-known and long-standing method in the history of fuzzy systems, because of its computational complexity, its use in the field of modeling of fuzzy controllers is almost nil. From literature, it appears that modeling of fuzzy Proportional Integral Derivative (FPID) controllers is rarely attempted using CoG defuzzification. In fact, none of the FPID controller models are obtained using both two-dimensional input space and CoG defuzzification. The available mathematical models of fuzzy Proportional Integral (FPI) and fuzzy Proportional Derivative (FPD) controllers using two-dimensional input space and CoG defuzzification were due to Arun and Mohan (2017). In this paper, the authors make an attempt to model and design an FPID controller using two-dimensional input space and CoG defuzzification. The incremental control effort produced by the newly developed FPID controller is found by combining the individual control efforts produced by incremental FPI and incremental FPD controllers. The incremental FPI and incremental FPD controller structures are unveiled using two-dimensional input space, CoG defuzzification, Min t-norm, Max t-conorm, and Larsen Product (LP) inference. The applicability and usefulness of the newly obtained FPID controller are depicted with simulation and real-time experimentation.

Modeling, stability analysis, and computational aspects of some simplest nonlinear fuzzy two-term controllers derived via center of area/gravity defuzzification.

The mathematical models reported in the literature so far have been found using Center of Sums (CoS) defuzzification method only. It appears that no one has found models using Center of Area (CoA) or Center of Gravity (CoG) defuzzification method. Although there have been some works reported to deal with modeling of fuzzy controllers via Centroid method, all of them have in fact used CoS method only. In this paper, for the first time mathematical models of the simplest Mamdani type fuzzy Proportional Integral (PI)/Proportional Derivative (PD) controllers via CoG defuzzification are presented. L-type and Γ-type membership functions over different Universes of Discourse (UoDs) are considered for the input variables. L-type, Π-type and Γ-type membership functions are considered for the output variable. Three linear fuzzy control rules relating all four input fuzzy sets to three output fuzzy sets are chosen. Two triangular norms namely Algebraic Product (AP) and Minimum (Min), Maximum (Max) triangular co-norm, and two inference methods, Larsen Product (LP) and Mamdani Minimum (MM), are used. Properties of the models are studied. Stability analysis of closed-loop systems containing one of these controller models in the loop is done using the Small Gain theorem. Since digital controllers are implemented using digital processors, computational and memory requirements of these fuzzy controllers and conventional (nonfuzzy) controllers are compared. A rough estimate of the computational time taken by the digital computer while implementing any of these discrete-time fuzzy controllers is given. Two nonlinear plants are considered to show the superiority of the simplest fuzzy controller obtained using CoA or CoG defuzzification method over the simplest fuzzy controller obtained using CoS method and reported recently. Real-time implementation of one of the developed controller models is done on coupled tank experimental setup to show the feasibility of the developed model.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

Analytical structures and analysis of the simplest fuzzy PD controllers.

This paper deals with simplest fuzzy PD controllers which employ only two fuzzy sets on the universe of discourse of each input variable, and three fuzzy sets on the universe of discourse of output variable. First, analytical structures of the simplest fuzzy PD controllers are derived via triangular membership functions for fuzzification, intersection T-norm, Lukasiewicz OR and Zadeh (1965) OR T-conorms, Mamdani's minimum, Larsen's product and drastic product inference methods, and center of area method for defuzzification. Properties of such fuzzy PD controllers are investigated. Based on these properties a comparative study is made on fuzzy controllers derived, and also on the fuzzy controllers and their counterpart-conventional linear PD controller. Finally, sufficient conditions for bounded-input bounded-output stability of fuzzy PD control systems are established using the well known small gain theorem.

Serological and molecular analysis of serotype O foot-and-mouth disease virus isolated from disease outbreaks in India during 1987-91.

Foot-and-mouth disease virus (FMDV) type O outbreaks have been reported frequently in vaccinated cattle in India. Twenty-five field isolates, recovered from outbreaks in vaccinated and unvaccinated cattle between 1987 and 1991, were analyzed in relation to the vaccine strain (R2/75) by complement fixation, serum neutralization and partial nucleotide sequencing of the VP1 gene. These sequences were compared with the viral sequences in GenEMBL database. Although the Indian type O viruses were close to the European type O1 viruses, they constituted a separate group of type O FMDVs. One of the field viruses, isolated from an outbreak in vaccinated cattle and designated as BAK/90, showed significant serological and nucleotide sequence variations from the vaccine strain. Phylogenetic analysis showed that the BAK/90 and R2/75 viruses belong to separate subgroups. The other isolates were found to be serologically related to both the BAK/90 and the vaccine strain. The BAK/90 strain gave broader antigenic coverage, showed better immunogenicity, and yielded larger amounts of 146S particles in suspension cultures as compared with R2/75. Taken together, these results favour inclusion of the BAK/90 strain in the vaccine to provide adequate protection against the field variants of type O FMDV currently circulating in India.

N-substituted phenothiazines as redox indicators in titrations with chloramine-T and chloramine-B.

Profenamine hydrochloride, fluphenazine dihydrochloride, trifluopromazine hydrochloride, cyamepromazine maleate, perphenazine dihydrochloride and mepazine hydrochloride are proposed as redox indicators in the titration of hydroquinone, metol and ascorbic acid with chloramine-T and chloramine-B in sulphuric, hydrochloric and acetic acid media. They give a sharp reversible colour change at the equivalence point. A simple but accurate method for the determination of hydroquinone, metol and ascorbic acid is described. The conditional potentials and molar absorptivities of the indicators and redox potential of chloramine-B are reported.