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To avoid mathematical complexity, Interval T2FSs (IT2FSs) have been pertained in majority of the fields. Type-2 fuzzy sets (T2FSs) handle a greater modeling and uncertainties that exist in the real world applications especially in control systems. One of the important components that influence the fuzzy controller is the triangular norm, which is the aggregation operator. For getting the stability of a control system T-norm operator can be preferred. Gaussian Interval Type-2 Membership Function (GIT2MF) has been used in this research. Mathematical properties of aggregation operator also proved using Gaussian Interval Type-2 Weighted Arithmetic (GIT2WA) operator. The aim of this research is analyzing the stability of an inverted pendulum using Interval Type-2 Fuzzy Logic Controller (IT2FLC) and the results are compared with traditional Proportional Integrated Derivative (PID) controller. It is observed that IT2FL controller gives better stability under imprecise condition.

This paper presents the design and the experimental implementation of fast and periodic output feedback controllers to minimize structural vibration, using collocated piezoelectric actuators and sensors. A linear dynamic model of the smart cantilever beam is obtained using online recursive least squares parameter estimation. A digital control system that consists of simulink modeling software and a dSPACE1104 controller board has been used for identification and control. The effectiveness of the controllers is shown experimentally by exciting the structure at resonance.