Influence of cross-point level of membership functions in fuzzy two-term control

In this paper, influence of cross-point level of membership functions in fuzzy two-term (PI or PD) control is studied. Important outcomes of this study are: (i) whenever membership functions are considered with cross-point level less than 0.5, control output generated by two-term controller is piecewise continuous and (ii) controller performance is inferior as long as cross-point level is less than 0.5. The first outcome of the study is proved analytically and the second outcome is discussed with intuitive reasoning and demonstrated numerically with examples as it is difficult to prove analytically.