<![CDATA[This paper presents an adaptive functional-based Neuro-fuzzy-PID incremental (NFPID) controller structure that can be tuned either offline or online according to required controller performance. First, differential membership functions are used to represent the fuzzy membership functions of the input-output space of the three term controller. Second, controller rules are generated based on the discrete proportional, derivative, and integral function for the fuzzy space. Finally, a fully differentiable fuzzy neural network is constructed to represent the developed controller for either offline or online controller parameter adaptation. Two different adaptation methods are used for controller tuning, offline method based on controller transient performance cost function optimization using Bees Algorithm, and online method based on tracking error minimization using back-propagation with momentum algorithm. The proposed control system was tested to show the validity of the controller structure over a fixed PID controller gains to control SCARA type robot arm.]]>
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