The success in real applications of PID regulator has thought us that it is desirable a simple controller with clear and intuitive policy for tuning of feedback gains, as well as minimum or null dependency on the dynamics of the system. In this paper, theoretical and experimental results of PD-like structures for tracking of robots subject to friction and disturbances is presented. The salient feature of our proposal is a neuro-fuzzy schemes used to a single gain that multiplies the regressor-free PID structure. This bounded time-varying gain plays the role of enforcing a dissipative mapping to obtain exponential stability. Stability is obtained in the sense of Lyapunov and experimental study is presented and discussed, which highlights the viability and feasibility for real applications.

A simple, fast and robust Passive Velocity Field Control (PVFC) scheme for contour tracking in 2D and 3D is presented. A model-free and chattering-free second order sliding mode controller is proposed, which enforces an invariant manifold for all time such that the generalized velocity tracks the spatial velocity field. A constructive simple and intuitive method to design this velocity field is built upon a fuzzy aggregation of orthogonal vectors to guide the end-effector subject to a dissipative map. Stability properties in the sense of Lyapunov establish the fast and yet smooth tracking with typical robustness of sliding modes. In this way, the closed-loop system exhibits the mildness of PVFC but it evades the subtle complexities of the original approach PVFC. A simulation study is discussed, and experimental results highlight the characteristics of the proposed approach.