Adaptive PID-type MIMO fuzzy controller for nonlinear dynamical systems: a relative rate observer-driven approach

This paper presents a novel adaptation mechanism employing a relative rate observer for the multiple-input/multiple-output (MIMO) fuzzy PID controller applied in nonlinear dynamical systems. Building upon the relative rate observer-based adaptation method originally introduced by Güzelkaya et al. (Eng Appl Artif Intell 16(3):227–236, 2003. https://doi.org/10.1016/S0952-1976(03)00050-2) for single-input/single-output (SISO) systems, we have extended and enhanced it specifically for use in nonlinear MIMO systems. The impacts of the proposed adaptation framework on control performance have been evaluated across a range of linear and nonlinear SISO and MIMO dynamic systems. To conduct a comprehensive analysis of the proposed adaptive structure’s impact on control performance, we compared the proposed adaptive MIMO architecture against a nonadaptive fuzzy PID controller and a fuzzy PID configuration in which two control parameters are adaptive. The results indicate a notable enhancement in control performance when all scaling coefficients of the fuzzy PID controller are adapted.