Altitude control of a quadcopter using interval type-2 fuzzy controller with dynamic footprint of uncertainty

Footprint of uncertainty (FOU) characteristics of interval type-2 membership functions (IT2-MFs) play an important role in the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). In literature, fixed FOU structures are used in almost all IT2-FC designs. In this study, an IT2-FC with dynamic FOU is proposed to provide high performance and robustness in the altitude control of a quadcopter. A proportional-derivative (PD) type FC with Takagi-Sugeno rule structure is used in the design procedure of the proposed controller. Additionally, input variables (error and derivative of error) are defined by using triangular IT2-MFs. To provide a dynamic FOU structure, the height of the lower MF (LMF) of each interval type-2 fuzzy set is defined as a function of the system error. In this way, FOU levels of IT2-MFs are adjusted dynamically since the height value of the LMF directly determines the FOU level of the IT2-MF. To evaluate the effectiveness of the proposed controller, comparison studies are performed under different conditions, including unmodeled measurement noises, an external disturbance, and a system parameter uncertainty. A classical PD, a type-1 fuzzy PD, and an interval type-2 fuzzy PD with fixed FOU controllers are used in the comparisons. The comparison results demonstrate that the proposed interval type-2 fuzzy PD controller with dynamic FOU exhibits better performance and more robustness than the other controllers.