A novel global PID control scheme for nonlinear MIMO systems is proposed and implemented for a robot as study case, this scheme is called AWFPID from its adaptive wavelet fuzzy PID control structure. Basically, it identifies inverse error dynamics using a radial basis neural network with daughter RASP1 wavelets activation function; its output is in cascaded with an infinite impulse response (IIR) filter to prune irrelevant signals and nodes as well as to recover a canonical form. Then, online adaptive fuzzy tuning of a discrete PID regulator is proposed, whose closed-loop guarantees global regulation for nonlinear dynamical plants. The wavelet network includes a fuzzy inference system for online tuning of learning rates. A real-time experimental study on a three degrees of freedom haptic interface, the PHANToM Premium 1.0A, highlights the regulation with smooth control effort without using the mathematical model of the robot. 
Wavenet fuzzy PID controller for nonlinear MIMO systems: Experimental validation on a high-end haptic robotic interface